TSTP Solution File: SWW473+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SWW473+1 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 21 00:50:23 EDT 2022
% Result : Theorem 156.64s 156.95s
% Output : CNFRefutation 161.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 698
% Syntax : Number of formulae : 4326 (2424 unt; 249 typ; 0 def)
% Number of atoms : 23134 (7532 equ; 0 cnn)
% Maximal formula atoms : 7 ( 5 avg)
% Number of connectives : 64277 (6194 ~;6947 |; 253 &;50448 @)
% ( 42 <=>; 393 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 348 ( 348 >; 0 *; 0 +; 0 <<)
% Number of symbols : 252 ( 249 usr; 58 con; 0-3 aty)
% Number of variables : 10108 ( 0 ^10102 !; 6 ?;10108 :)
% 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_sK10_AA,type,
sK10_AA: $i > $i > $i > $i ).
thf(tp_sK11_X_1,type,
sK11_X_1: $i > $i > $i > $i ).
thf(tp_sK12_X_1,type,
sK12_X_1: $i > $i > $i ).
thf(tp_sK13_N_2,type,
sK13_N_2: $i > $i > $i > $i ).
thf(tp_sK14_N_2,type,
sK14_N_2: $i > $i > $i > $i ).
thf(tp_sK15_N_2,type,
sK15_N_2: $i > $i > $i > $i ).
thf(tp_sK16_N_2,type,
sK16_N_2: $i > $i > $i > $i ).
thf(tp_sK17_C_2,type,
sK17_C_2: $i > $i > $i > $i ).
thf(tp_sK1_M,type,
sK1_M: $i > $i ).
thf(tp_sK2_X_1,type,
sK2_X_1: $i > $i > $i ).
thf(tp_sK3_X_1,type,
sK3_X_1: $i > $i > $i > $i ).
thf(tp_sK4_M,type,
sK4_M: $i > $i > $i ).
thf(tp_sK5_N_2,type,
sK5_N_2: $i > $i > $i > $i ).
thf(tp_sK6_X_1,type,
sK6_X_1: $i > $i > $i ).
thf(tp_sK7_X_1,type,
sK7_X_1: $i > $i > $i ).
thf(tp_sK8_X_1,type,
sK8_X_1: $i > $i > $i ).
thf(tp_sK9_X_1,type,
sK9_X_1: $i > $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(1,axiom,
! [P: $i,Q: $i,R: $i] :
( ( hAPP_f389811538l_bool @ ( hAPP_f1759205631l_bool @ ( cOMBC_336095980l_bool @ P ) @ Q ) @ R )
= ( hAPP_f389811538l_bool @ ( hAPP_f1759205631l_bool @ P @ R ) @ Q ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obo) ).
thf(2,axiom,
! [P: $i,Q: $i,R: $i] :
( ( hAPP_f937997336l_bool @ ( hAPP_f760187903l_bool @ ( cOMBC_1269652216l_bool @ P ) @ Q ) @ R )
= ( hAPP_f937997336l_bool @ ( hAPP_f760187903l_bool @ P @ R ) @ Q ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool) ).
thf(3,axiom,
! [P: $i,Q: $i,R: $i] :
( ( hAPP_f292226953l_bool @ ( hAPP_f1050622307l_bool @ ( cOMBC_636888218l_bool @ P ) @ Q ) @ R )
= ( hAPP_f292226953l_bool @ ( hAPP_f1050622307l_bool @ P @ R ) @ Q ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__H) ).
thf(4,axiom,
! [P: $i,Q: $i,R: $i] :
( ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ( cOMBC_7971162l_bool @ P ) @ Q ) @ R )
= ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ P @ R ) @ Q ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_) ).
thf(5,axiom,
! [P: $i,Q: $i,R: $i] :
( ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ( cOMBC_595898202l_bool @ P ) @ Q ) @ R )
= ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ P @ R ) @ Q ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__H) ).
thf(6,axiom,
! [P: $i,Q: $i,R: $i] :
( ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ( cOMBC_331553030l_bool @ P ) @ Q ) @ R )
= ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ P @ R ) @ Q ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool) ).
thf(7,axiom,
! [P: $i,Q: $i,R: $i] :
( ( hAPP_f1664156314l_bool @ ( hAPP_f559147733l_bool @ ( cOMBC_1988546018l_bool @ P ) @ Q ) @ R )
= ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ P @ R ) @ Q ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_012) ).
thf(8,axiom,
! [P: $i,Q: $i,R: $i] :
( ( hAPP_f54304608l_bool @ ( hAPP_f1246832597l_bool @ ( cOMBC_1245412066l_bool @ P ) @ Q ) @ R )
= ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ P @ R ) @ Q ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__011) ).
thf(9,axiom,
! [P: $i,Q: $i,R: $i] :
( ( hAPP_fun_a_bool_bool @ ( hAPP_f2117159681l_bool @ ( cOMBC_1880041174l_bool @ P ) @ Q ) @ R )
= ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_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_Itc__fun_It__) ).
thf(10,axiom,
! [P: $i,Q: $i,R: $i] :
( ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ P ) @ Q ) @ R )
= ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ P @ R ) @ Q ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It) ).
thf(11,axiom,
! [P: $i,Q: $i,R: $i] :
( ( hAPP_f1476298914l_bool @ ( cOMBB_2095475776e_bool @ P @ Q ) @ R )
= ( hAPP_b589554111l_bool @ P @ ( hAPP_f1664156314l_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_010) ).
thf(12,axiom,
! [P: $i,Q: $i,R: $i] :
( ( hAPP_f1748468828l_bool @ ( cOMBB_444170502t_bool @ P @ Q ) @ R )
= ( hAPP_b589554111l_bool @ P @ ( hAPP_f54304608l_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_009) ).
thf(13,axiom,
! [P: $i,Q: $i,R: $i] :
( ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ( cOMBC_1693257480l_bool @ P ) @ Q ) @ R )
= ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ P @ R ) @ Q ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc_) ).
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(16,axiom,
! [P: $i,Q: $i,R: $i] :
( ( hAPP_pname_bool @ ( hAPP_f759274231e_bool @ ( cOMBC_1058051404l_bool @ P ) @ Q ) @ R )
= ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ P @ R ) @ Q ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob) ).
thf(17,axiom,
! [P: $i,Q: $i,R: $i] :
( ( hAPP_f1664156314l_bool @ ( cOMBS_350070575l_bool @ P @ Q ) @ R )
= ( hAPP_bool_bool @ ( hAPP_f1476298914l_bool @ P @ R ) @ ( hAPP_f1664156314l_bool @ Q @ R ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__O) ).
thf(18,axiom,
! [P: $i,Q: $i,R: $i] :
( ( hAPP_p393069232l_bool @ ( cOMBB_675860798_pname @ P @ Q ) @ R )
= ( hAPP_b589554111l_bool @ P @ ( hAPP_pname_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_007) ).
thf(19,axiom,
! [P: $i,Q: $i,R: $i] :
( ( hAPP_f1664156314l_bool @ ( cOMBB_307249310e_bool @ P @ Q ) @ R )
= ( hAPP_bool_bool @ P @ ( hAPP_f1664156314l_bool @ Q @ R ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Op) ).
thf(20,axiom,
! [P: $i,Q: $i,R: $i] :
( ( hAPP_f54304608l_bool @ ( cOMBS_1187019125l_bool @ P @ Q ) @ R )
= ( hAPP_bool_bool @ ( hAPP_f1748468828l_bool @ P @ R ) @ ( hAPP_f54304608l_bool @ Q @ R ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obo) ).
thf(21,axiom,
! [P: $i,Q: $i,R: $i] :
( ( hAPP_n1006566506l_bool @ ( cOMBB_1015721476ol_nat @ P @ Q ) @ R )
= ( hAPP_b589554111l_bool @ P @ ( hAPP_nat_bool @ Q @ R ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_006) ).
thf(22,axiom,
! [P: $i,Q: $i,R: $i] :
( ( hAPP_f54304608l_bool @ ( cOMBB_238756964t_bool @ P @ Q ) @ R )
= ( hAPP_bool_bool @ P @ ( hAPP_f54304608l_bool @ Q @ R ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Nat__On) ).
thf(23,axiom,
! [P: $i,Q: $i,R: $i] :
( ( hAPP_nat_bool @ ( hAPP_f800510211t_bool @ ( cOMBC_226598744l_bool @ P ) @ Q ) @ R )
= ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ P @ R ) @ Q ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_) ).
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(25,axiom,
! [P: $i,Q: $i,R: $i] :
( ( hAPP_a_fun_bool_bool @ ( cOMBB_1972296269bool_a @ P @ Q ) @ R )
= ( hAPP_b589554111l_bool @ P @ ( hAPP_a_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) ).
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(28,axiom,
! [P: $i,Q: $i,R: $i] :
( ( hAPP_a_bool @ ( hAPP_f2050579477a_bool @ ( cOMBC_1355376034l_bool @ P ) @ Q ) @ R )
= ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ P @ R ) @ Q ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Oboo) ).
thf(29,axiom,
! [P: $i,Q: $i,R: $i] :
( ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ P ) @ Q ) @ R )
= ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ P @ R ) @ Q ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Com__Opname_000tc__HOL__Obool_U) ).
thf(30,axiom,
! [P: $i,Q: $i,R: $i] :
( ( hAPP_pname_bool @ ( cOMBS_568398431l_bool @ P @ Q ) @ R )
= ( hAPP_bool_bool @ ( hAPP_p393069232l_bool @ P @ R ) @ ( hAPP_pname_bool @ Q @ R ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool_U) ).
thf(31,axiom,
! [P: $i,Q: $i,R: $i] :
( ( hAPP_pname_bool @ ( cOMBB_647938656_pname @ P @ Q ) @ R )
= ( hAPP_bool_bool @ P @ ( hAPP_pname_bool @ Q @ R ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname_U) ).
thf(32,axiom,
! [P: $i,Q: $i,R: $i] :
( ( hAPP_nat_bool @ ( cOMBS_nat_bool_bool @ P @ Q ) @ R )
= ( hAPP_bool_bool @ ( hAPP_n1006566506l_bool @ P @ R ) @ ( hAPP_nat_bool @ Q @ R ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__HOL__Obool_000tc__HOL__Obool_U) ).
thf(33,axiom,
! [P: $i,Q: $i,R: $i] :
( ( hAPP_nat_bool @ ( cOMBB_bool_bool_nat @ P @ Q ) @ R )
= ( hAPP_bool_bool @ P @ ( hAPP_nat_bool @ Q @ R ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Nat__Onat_U) ).
thf(34,axiom,
! [P: $i,Q: $i,R: $i] :
( ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ P ) @ Q ) @ R )
= ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ P @ R ) @ Q ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__HOL__Obool_U) ).
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(36,axiom,
! [X: $i,Y: $i] :
( ( ( is_fun_pname_bool @ X )
& ( is_fun_pname_bool @ Y ) )
=> ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ X ) @ Y ) )
| ( X = Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_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(39,axiom,
! [P: $i,Q: $i,R: $i] :
( ( hAPP_pname_bool @ ( hAPP_a93125764e_bool @ ( cOMBC_pname_a_bool @ P ) @ Q ) @ R )
= ( hAPP_a_bool @ ( hAPP_p1534023578a_bool @ P @ R ) @ Q ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000t__a_000tc__HOL__Obool_U) ).
thf(40,axiom,
! [P: $i,Q: $i,R: $i] :
( ( hAPP_a_bool @ ( cOMBS_a_bool_bool @ P @ Q ) @ R )
= ( hAPP_bool_bool @ ( hAPP_a_fun_bool_bool @ P @ R ) @ ( hAPP_a_bool @ Q @ R ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000t__a_000tc__HOL__Obool_000tc__HOL__Obool_U) ).
thf(41,axiom,
! [P: $i,Q: $i,R: $i] :
( ( hAPP_a_bool @ ( cOMBB_bool_bool_a @ P @ Q ) @ R )
= ( hAPP_bool_bool @ P @ ( hAPP_a_bool @ Q @ R ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000t__a_U) ).
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(44,axiom,
! [P: $i,Q: $i,R: $i] :
( ( hAPP_a_bool @ ( hAPP_a_fun_a_bool @ ( cOMBC_a_a_bool @ P ) @ Q ) @ R )
= ( hAPP_a_bool @ ( hAPP_a_fun_a_bool @ P @ R ) @ Q ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000t__a_000t__a_000tc__HOL__Obool_U) ).
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(46,axiom,
! [X: $i,Y: $i] :
( ( ( is_pname @ X )
& ( is_pname @ Y ) )
=> ( ~ ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ fequal_pname @ X ) @ Y ) )
| ( X = Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_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(50,axiom,
! [X: $i,Y: $i] :
( ( ( is_a @ X )
& ( is_a @ Y ) )
=> ( ~ ( hBOOL @ ( hAPP_a_bool @ ( hAPP_a_fun_a_bool @ fequal_a @ X ) @ Y ) )
| ( X = Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_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(62,axiom,
! [N: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ N ) )
<=> ? [M: $i] :
! [X_1: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ X_1 ) @ N ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_1 ) @ M ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_299_finite__nat__set__iff__bounded__le) ).
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(67,axiom,
! [F: $i,B: $i,A: $i] :
( ! [X_1: $i] :
( ( is_pname @ X_1 )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_1 ) @ A ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( hAPP_pname_a @ F @ X_1 ) ) @ B ) ) ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_pname_a @ F @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_image__subsetI) ).
thf(68,axiom,
! [N_1: $i,M_1: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ N_1 ) ) @ M_1 ) )
=> ? [M: $i] :
( M_1
= ( hAPP_nat_nat @ suc @ M ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_Suc__le__D) ).
thf(69,axiom,
! [I: $i,Pa: $i,K: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ Pa @ K ) )
=> ( ! [N_2: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ Pa @ ( hAPP_nat_nat @ suc @ N_2 ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ Pa @ N_2 ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ Pa @ ( hAPP_nat_nat @ ( minus_minus_nat @ K ) @ I ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_292_zero__induct__lemma) ).
thf(70,axiom,
! [B: $i,A: $i] :
( ! [X_1: $i] :
( ( is_pname @ X_1 )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_1 ) @ A ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_1 ) @ B ) ) ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_subsetI) ).
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(72,axiom,
! [B: $i,A: $i] :
( ! [X_1: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ X_1 ) @ A ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ X_1 ) @ B ) ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_289_subsetI) ).
thf(73,axiom,
! [B_1: $i,F: $i,A: $i] :
( ( is_a @ B_1 )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B_1 ) @ ( image_pname_a @ F @ A ) ) )
=> ~ ! [X_1: $i] :
( ( is_pname @ X_1 )
=> ( ( B_1
= ( hAPP_pname_a @ F @ X_1 ) )
=> ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_1 ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_imageE) ).
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(75,axiom,
! [B: $i,F: $i,A: $i] :
( ( is_fun_a_bool @ B )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ ( image_pname_a @ F @ A ) ) )
<=> ? [AA: $i] :
( ( is_fun_pname_bool @ AA )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ AA ) @ A ) )
& ( B
= ( image_pname_a @ F @ AA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_subset__image__iff) ).
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(79,axiom,
! [A_1: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ D ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ A_1 @ C ) ) @ ( insert_pname @ A_1 @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_insert__mono) ).
thf(80,axiom,
! [A_1: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ D ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( insert_nat @ A_1 @ C ) ) @ ( insert_nat @ A_1 @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281_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(82,axiom,
! [B_1: $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 @ A ) @ ( insert_pname @ B_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_279_subset__insertI2) ).
thf(83,axiom,
! [B_1: $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 @ A ) @ ( insert_nat @ B_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_278_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(85,axiom,
! [B: $i,X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ A ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( insert_pname @ X_2 @ B ) ) )
<=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_276_subset__insert) ).
thf(86,axiom,
! [B: $i,X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ X_2 ) @ A ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ ( insert_nat @ X_2 @ B ) ) )
<=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_275_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(88,axiom,
! [X_2: $i,A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ X_2 @ A ) ) @ B ) )
<=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ B ) )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_insert__subset) ).
thf(89,axiom,
! [X_2: $i,A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( insert_nat @ X_2 @ A ) ) @ B ) )
<=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ X_2 ) @ B ) )
& ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_272_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(91,axiom,
! [B: $i,A_1: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ ( insert_pname @ A_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_subset__insertI) ).
thf(92,axiom,
! [B: $i,A_1: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ ( insert_nat @ A_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_subset__insertI) ).
thf(93,axiom,
! [X_1: $i,Xa: $i] :
( ( insert_fun_a_bool @ X_1 @ Xa )
= ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ fequal_fun_a_bool ) @ X_1 ) ) @ ( hAPP_f2117159681l_bool @ ( cOMBC_1880041174l_bool @ member_fun_a_bool ) @ Xa ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_insert__compr__raw) ).
thf(94,axiom,
! [X_1: $i,Xa: $i] :
( ( insert1325755072e_bool @ X_1 @ Xa )
= ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ X_1 ) ) @ ( hAPP_f559147733l_bool @ ( cOMBC_1988546018l_bool @ member799430823e_bool ) @ Xa ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_insert__compr__raw) ).
thf(95,axiom,
! [X_1: $i,Xa: $i] :
( ( insert_fun_nat_bool @ X_1 @ Xa )
= ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ ( hAPP_f103356543l_bool @ ( cOMBC_1693257480l_bool @ fequal_fun_nat_bool ) @ X_1 ) ) @ ( hAPP_f1246832597l_bool @ ( cOMBC_1245412066l_bool @ member_fun_nat_bool ) @ Xa ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_266_insert__compr__raw) ).
thf(96,axiom,
! [X_1: $i,Xa: $i] :
( ( insert_a @ X_1 @ Xa )
= ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ ( hAPP_a_fun_a_bool @ ( cOMBC_a_a_bool @ fequal_a ) @ X_1 ) ) @ ( hAPP_f2050579477a_bool @ ( cOMBC_1355376034l_bool @ member_a ) @ Xa ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_insert__compr__raw) ).
thf(97,axiom,
! [X_1: $i,Xa: $i] :
( ( insert_pname @ X_1 @ Xa )
= ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ fequal_pname ) @ X_1 ) ) @ ( hAPP_f759274231e_bool @ ( cOMBC_1058051404l_bool @ member_pname ) @ Xa ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_insert__compr__raw) ).
thf(98,axiom,
! [X_1: $i,Xa: $i] :
( ( insert_nat @ X_1 @ Xa )
= ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ fequal_nat ) @ X_1 ) ) @ ( hAPP_f800510211t_bool @ ( cOMBC_226598744l_bool @ member_nat ) @ Xa ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_insert__compr__raw) ).
thf(99,axiom,
! [B_1: $i,F: $i,X_2: $i,A: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ A ) )
=> ( ( B_1
= ( hAPP_pname_a @ F @ X_2 ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B_1 ) @ ( image_pname_a @ F @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_rev__image__eqI) ).
thf(100,axiom,
! [F: $i,X_2: $i,A: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ A ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( hAPP_pname_a @ F @ X_2 ) ) @ ( image_pname_a @ F @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_imageI) ).
thf(101,axiom,
! [Z: $i,F: $i,A: $i] :
( ( is_a @ Z )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ Z ) @ ( image_pname_a @ F @ A ) ) )
<=> ? [X_1: $i] :
( ( is_pname @ X_1 )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_1 ) @ A ) )
& ( Z
= ( hAPP_pname_a @ F @ X_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_image__iff) ).
thf(102,axiom,
! [Pa: $i] :
( ( collect_nat @ Pa )
= Pa ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_Collect__def) ).
thf(103,axiom,
! [Pa: $i] :
( ( is_fun949378684l_bool @ Pa )
=> ( ( collect_fun_a_bool @ Pa )
= Pa ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_Collect__def) ).
thf(104,axiom,
! [Pa: $i] :
( ( is_fun1661590463l_bool @ Pa )
=> ( ( collec1974731493e_bool @ Pa )
= Pa ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_Collect__def) ).
thf(105,axiom,
! [Pa: $i] :
( ( collect_fun_nat_bool @ Pa )
= Pa ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_Collect__def) ).
thf(106,axiom,
! [Pa: $i] :
( ( is_fun_pname_bool @ Pa )
=> ( ( collect_pname @ Pa )
= Pa ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_Collect__def) ).
thf(107,axiom,
! [X_2: $i,A: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ A ) )
<=> ( hBOOL @ ( hAPP_pname_bool @ A @ X_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_mem__def) ).
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(109,axiom,
! [X_2: $i,A: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ X_2 ) @ A ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ A @ X_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_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(116,axiom,
! [X_2: $i,A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ A ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_set__mp) ).
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(118,axiom,
! [X_2: $i,A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ X_2 ) @ A ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ X_2 ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_set__mp) ).
thf(119,axiom,
! [B: $i,X_2: $i,A: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ A ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_set__rev__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(121,axiom,
! [B: $i,X_2: $i,A: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ X_2 ) @ A ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ X_2 ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_set__rev__mp) ).
thf(122,axiom,
! [X_2: $i,A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ A ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_in__mono) ).
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(124,axiom,
! [X_2: $i,A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ X_2 ) @ A ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ X_2 ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_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(132,axiom,
! [A: $i,B: $i] :
( ( ( is_fun_pname_bool @ A )
& ( is_fun_pname_bool @ B ) )
=> ( ( 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_229_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(138,axiom,
! [A_1: $i,A: $i] :
( ( is_fun_pname_bool @ A )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A_1 ) @ A ) )
=> ( ( insert_pname @ A_1 @ A )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_insert__absorb) ).
thf(139,axiom,
! [A_1: $i,A: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A_1 ) @ A ) )
=> ( ( insert_nat @ A_1 @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_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(141,axiom,
! [B_1: $i,A_1: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A_1 ) @ B ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A_1 ) @ ( insert_pname @ B_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_insertI2) ).
thf(142,axiom,
! [B_1: $i,A_1: $i,B: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A_1 ) @ B ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A_1 ) @ ( insert_nat @ B_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_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(144,axiom,
! [B: $i,X_2: $i,A: $i] :
( ( ( is_fun_pname_bool @ B )
& ( is_fun_pname_bool @ A ) )
=> ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ A ) )
=> ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ B ) )
=> ( ( ( insert_pname @ X_2 @ A )
= ( insert_pname @ X_2 @ B ) )
<=> ( A = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_insert__ident) ).
thf(145,axiom,
! [B: $i,X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ X_2 ) @ A ) )
=> ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ X_2 ) @ B ) )
=> ( ( ( insert_nat @ X_2 @ A )
= ( insert_nat @ X_2 @ B ) )
<=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_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(150,axiom,
! [A_1: $i,B_1: $i,A: $i] :
( ( ( is_pname @ A_1 )
& ( is_pname @ B_1 ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A_1 ) @ ( insert_pname @ B_1 @ A ) ) )
<=> ( ( A_1 = B_1 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A_1 ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_insert__iff) ).
thf(151,axiom,
! [A_1: $i,B_1: $i,A: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A_1 ) @ ( insert_nat @ B_1 @ A ) ) )
<=> ( ( A_1 = B_1 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A_1 ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_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(153,axiom,
! [X_2: $i,Y_1: $i,A: $i] :
( ( insert_pname @ X_2 @ ( insert_pname @ Y_1 @ A ) )
= ( insert_pname @ Y_1 @ ( insert_pname @ X_2 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_insert__commute) ).
thf(154,axiom,
! [X_2: $i,Y_1: $i,A: $i] :
( ( insert_nat @ X_2 @ ( insert_nat @ Y_1 @ A ) )
= ( insert_nat @ Y_1 @ ( insert_nat @ X_2 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_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(156,axiom,
! [X_2: $i,A: $i] :
( ( insert_pname @ X_2 @ ( insert_pname @ X_2 @ A ) )
= ( insert_pname @ X_2 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_insert__absorb2) ).
thf(157,axiom,
! [X_2: $i,A: $i] :
( ( insert_nat @ X_2 @ ( insert_nat @ X_2 @ A ) )
= ( insert_nat @ X_2 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_insert__absorb2) ).
thf(158,axiom,
! [A_1: $i,Pa: $i] :
( ( insert_fun_a_bool @ A_1 @ ( collect_fun_a_bool @ Pa ) )
= ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fimplies @ ( cOMBB_2140588453a_bool @ fNot @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ fequal_fun_a_bool ) @ A_1 ) ) ) @ Pa ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_insert__Collect) ).
thf(159,axiom,
! [A_1: $i,Pa: $i] :
( ( insert1325755072e_bool @ A_1 @ ( collec1974731493e_bool @ Pa ) )
= ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fimplies @ ( cOMBB_307249310e_bool @ fNot @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ A_1 ) ) ) @ Pa ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_insert__Collect) ).
thf(160,axiom,
! [A_1: $i,Pa: $i] :
( ( insert_fun_nat_bool @ A_1 @ ( collect_fun_nat_bool @ Pa ) )
= ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fimplies @ ( cOMBB_238756964t_bool @ fNot @ ( hAPP_f103356543l_bool @ ( cOMBC_1693257480l_bool @ fequal_fun_nat_bool ) @ A_1 ) ) ) @ Pa ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_insert__Collect) ).
thf(161,axiom,
! [A_1: $i,Pa: $i] :
( ( insert_a @ A_1 @ ( collect_a @ Pa ) )
= ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fimplies @ ( cOMBB_bool_bool_a @ fNot @ ( hAPP_a_fun_a_bool @ ( cOMBC_a_a_bool @ fequal_a ) @ A_1 ) ) ) @ Pa ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_insert__Collect) ).
thf(162,axiom,
! [A_1: $i,Pa: $i] :
( ( insert_pname @ A_1 @ ( collect_pname @ Pa ) )
= ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fimplies @ ( cOMBB_647938656_pname @ fNot @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ fequal_pname ) @ A_1 ) ) ) @ Pa ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_insert__Collect) ).
thf(163,axiom,
! [A_1: $i,Pa: $i] :
( ( insert_nat @ A_1 @ ( collect_nat @ Pa ) )
= ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fimplies @ ( cOMBB_bool_bool_nat @ fNot @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ fequal_nat ) @ A_1 ) ) ) @ Pa ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_insert__Collect) ).
thf(164,axiom,
! [A_1: $i,B: $i] :
( ( insert_fun_a_bool @ A_1 @ B )
= ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ fequal_fun_a_bool ) @ A_1 ) ) @ ( hAPP_f2117159681l_bool @ ( cOMBC_1880041174l_bool @ member_fun_a_bool ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_insert__compr) ).
thf(165,axiom,
! [A_1: $i,B: $i] :
( ( insert1325755072e_bool @ A_1 @ B )
= ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ A_1 ) ) @ ( hAPP_f559147733l_bool @ ( cOMBC_1988546018l_bool @ member799430823e_bool ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_insert__compr) ).
thf(166,axiom,
! [A_1: $i,B: $i] :
( ( insert_fun_nat_bool @ A_1 @ B )
= ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ ( hAPP_f103356543l_bool @ ( cOMBC_1693257480l_bool @ fequal_fun_nat_bool ) @ A_1 ) ) @ ( hAPP_f1246832597l_bool @ ( cOMBC_1245412066l_bool @ member_fun_nat_bool ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_insert__compr) ).
thf(167,axiom,
! [A_1: $i,B: $i] :
( ( insert_a @ A_1 @ B )
= ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ ( hAPP_a_fun_a_bool @ ( cOMBC_a_a_bool @ fequal_a ) @ A_1 ) ) @ ( hAPP_f2050579477a_bool @ ( cOMBC_1355376034l_bool @ member_a ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_insert__compr) ).
thf(168,axiom,
! [A_1: $i,B: $i] :
( ( insert_pname @ A_1 @ B )
= ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ fequal_pname ) @ A_1 ) ) @ ( hAPP_f759274231e_bool @ ( cOMBC_1058051404l_bool @ member_pname ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_insert__compr) ).
thf(169,axiom,
! [A_1: $i,B: $i] :
( ( insert_nat @ A_1 @ B )
= ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ fequal_nat ) @ A_1 ) ) @ ( hAPP_f800510211t_bool @ ( cOMBC_226598744l_bool @ member_nat ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_insert__compr) ).
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(171,axiom,
! [A_1: $i,B: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A_1 ) @ ( insert_pname @ A_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_insertI1) ).
thf(172,axiom,
! [A_1: $i,B: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A_1 ) @ ( insert_nat @ A_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_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(174,axiom,
! [A_1: $i,B_1: $i,A: $i] :
( ( ( is_pname @ A_1 )
& ( is_pname @ B_1 ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A_1 ) @ ( insert_pname @ B_1 @ A ) ) )
=> ( ( A_1 != B_1 )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A_1 ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_insertE) ).
thf(175,axiom,
! [A_1: $i,B_1: $i,A: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A_1 ) @ ( insert_nat @ B_1 @ A ) ) )
=> ( ( A_1 != B_1 )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A_1 ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_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(177,axiom,
! [B_1: $i,A_1: $i,B: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A_1 ) @ B ) )
=> ( A_1 = B_1 ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A_1 ) @ ( insert_pname @ B_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_insertCI) ).
thf(178,axiom,
! [B_1: $i,A_1: $i,B: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A_1 ) @ B ) )
=> ( A_1 = B_1 ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A_1 ) @ ( insert_nat @ B_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_insertCI) ).
thf(179,axiom,
! [C_1: $i,A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C_1 ) @ A ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C_1 ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_subsetD) ).
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(181,axiom,
! [C_1: $i,A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C_1 ) @ A ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C_1 ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_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(183,axiom,
! [A: $i,B: $i] :
( ( ( is_fun_pname_bool @ A )
& ( is_fun_pname_bool @ 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 ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_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(185,axiom,
! [A: $i,B_1: $i,F: $i,X_2: $i] :
( ( B_1
= ( hAPP_pname_a @ F @ X_2 ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ A ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B_1 ) @ ( image_pname_a @ F @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_image__eqI) ).
thf(186,axiom,
! [F: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_pname_a @ F @ A ) ) )
=> ? [X_1: $i] :
( ( is_pname @ X_1 )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_1 ) @ A ) )
& ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ ( hAPP_f759274231e_bool @ ( cOMBC_1058051404l_bool @ member_pname ) @ A ) ) @ ( hAPP_a93125764e_bool @ ( cOMBC_pname_a_bool @ ( cOMBB_1897541054_pname @ fequal_a @ F ) ) @ ( hAPP_pname_a @ F @ X_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_pigeonhole__infinite) ).
thf(187,axiom,
! [Na: $i,N_3: $i,F: $i] :
( ! [N_2: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_nat_fun_a_bool @ F @ N_2 ) ) @ ( hAPP_nat_fun_a_bool @ F @ ( hAPP_nat_nat @ suc @ N_2 ) ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Na ) @ N_3 ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_nat_fun_a_bool @ F @ Na ) ) @ ( hAPP_nat_fun_a_bool @ F @ N_3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_lift__Suc__mono__le) ).
thf(188,axiom,
! [Na: $i,N_3: $i,F: $i] :
( ! [N_2: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ F @ N_2 ) ) @ ( hAPP_nat_nat @ F @ ( hAPP_nat_nat @ suc @ N_2 ) ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Na ) @ N_3 ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ F @ Na ) ) @ ( hAPP_nat_nat @ F @ N_3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_lift__Suc__mono__le) ).
thf(189,axiom,
! [Na: $i,N_3: $i,F: $i] :
( ! [N_2: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_n1025906991e_bool @ F @ N_2 ) ) @ ( hAPP_n1025906991e_bool @ F @ ( hAPP_nat_nat @ suc @ N_2 ) ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Na ) @ N_3 ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_n1025906991e_bool @ F @ Na ) ) @ ( hAPP_n1025906991e_bool @ F @ N_3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_lift__Suc__mono__le) ).
thf(190,axiom,
! [Na: $i,N_3: $i,F: $i] :
( ! [N_2: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( hAPP_n1699378549t_bool @ F @ N_2 ) ) @ ( hAPP_n1699378549t_bool @ F @ ( hAPP_nat_nat @ suc @ N_2 ) ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Na ) @ N_3 ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( hAPP_n1699378549t_bool @ F @ Na ) ) @ ( hAPP_n1699378549t_bool @ F @ N_3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_lift__Suc__mono__le) ).
thf(191,axiom,
! [F: $i,A: $i,B: $i] :
( ( is_fun_a_bool @ B )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ ( image_pname_a @ F @ A ) ) )
=> ? [C_2: $i] :
( ( is_fun_pname_bool @ C_2 )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C_2 ) @ A ) )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C_2 ) )
& ( B
= ( image_pname_a @ F @ C_2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_finite__subset__image) ).
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(193,axiom,
! [M_2: $i,N_1: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ M_2 ) @ N_1 ) ) @ M_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_diff__le__self) ).
thf(194,axiom,
! [L: $i,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 @ ( hAPP_nat_nat @ ( minus_minus_nat @ L ) @ N_1 ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ L ) @ M_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_diff__le__mono2) ).
thf(195,axiom,
! [L: $i,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 @ ( hAPP_nat_nat @ ( minus_minus_nat @ M_2 ) @ L ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ N_1 ) @ L ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_diff__le__mono) ).
thf(196,axiom,
! [I_1: $i,N_1: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ I_1 ) @ N_1 ) )
=> ( ( hAPP_nat_nat @ ( minus_minus_nat @ N_1 ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ N_1 ) @ I_1 ) )
= I_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_diff__diff__cancel) ).
thf(197,axiom,
! [Na: $i,K: $i,M_3: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ K ) @ M_3 ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ K ) @ Na ) )
=> ( ( ( hAPP_nat_nat @ ( minus_minus_nat @ M_3 ) @ K )
= ( hAPP_nat_nat @ ( minus_minus_nat @ Na ) @ K ) )
<=> ( M_3 = Na ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_eq__diff__iff) ).
thf(198,axiom,
! [N_1: $i,K_1: $i,M_2: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ K_1 ) @ M_2 ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ K_1 ) @ N_1 ) )
=> ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ M_2 ) @ K_1 ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ N_1 ) @ K_1 ) )
= ( hAPP_nat_nat @ ( minus_minus_nat @ M_2 ) @ N_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_Nat_Odiff__diff__eq) ).
thf(199,axiom,
! [Na: $i,K: $i,M_3: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ K ) @ M_3 ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ K ) @ Na ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ M_3 ) @ K ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ Na ) @ K ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ M_3 ) @ Na ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_le__diff__iff) ).
thf(200,axiom,
! [M_2: $i,N_1: $i] :
( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ suc @ M_2 ) ) @ ( hAPP_nat_nat @ suc @ N_1 ) )
= ( hAPP_nat_nat @ ( minus_minus_nat @ M_2 ) @ N_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_diff__Suc__Suc) ).
thf(201,axiom,
! [M_2: $i,N_1: $i,K_1: $i] :
( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ suc @ M_2 ) ) @ N_1 ) ) @ ( hAPP_nat_nat @ suc @ K_1 ) )
= ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ M_2 ) @ N_1 ) ) @ K_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_Suc__diff__diff) ).
thf(202,axiom,
! [N_1: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ N_1 ) ) @ N_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_Suc__n__not__le__n) ).
thf(203,axiom,
! [M_3: $i,Na: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ M_3 ) @ Na ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ Na ) ) @ M_3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_not__less__eq__eq) ).
thf(204,axiom,
! [M_3: $i,Na: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ M_3 ) @ ( hAPP_nat_nat @ suc @ Na ) ) )
<=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ M_3 ) @ Na ) )
| ( M_3
= ( hAPP_nat_nat @ suc @ Na ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_le__Suc__eq) ).
thf(205,axiom,
! [Na: $i,M_3: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ Na ) ) @ ( hAPP_nat_nat @ suc @ M_3 ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Na ) @ M_3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_Suc__le__mono) ).
thf(206,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 @ M_2 ) @ ( hAPP_nat_nat @ suc @ N_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_le__SucI) ).
thf(207,axiom,
! [M_2: $i,N_1: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ M_2 ) @ ( hAPP_nat_nat @ suc @ N_1 ) ) )
=> ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ M_2 ) @ N_1 ) )
=> ( M_2
= ( hAPP_nat_nat @ suc @ N_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_le__SucE) ).
thf(208,axiom,
! [M_2: $i,N_1: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ 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_153_Suc__leD) ).
thf(209,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_rev__finite__subset) ).
thf(210,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_rev__finite__subset) ).
thf(211,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_rev__finite__subset) ).
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(213,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_rev__finite__subset) ).
thf(214,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_rev__finite__subset) ).
thf(215,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_finite__subset) ).
thf(216,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_finite__subset) ).
thf(217,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
=> ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_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(219,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
=> ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_finite__subset) ).
thf(220,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
=> ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_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(227,axiom,
! [Pa: $i,Q_1: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ Pa ) @ Q_1 ) ) ) )
<=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ Pa ) ) )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ Q_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_finite__Collect__disjI) ).
thf(228,axiom,
! [Pa: $i,Q_1: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ Pa ) @ Q_1 ) ) ) )
<=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ Pa ) ) )
& ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ Q_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_finite__Collect__disjI) ).
thf(229,axiom,
! [Pa: $i,Q_1: $i] :
( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ Pa ) @ Q_1 ) ) ) )
<=> ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ Pa ) ) )
& ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ Q_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_finite__Collect__disjI) ).
thf(230,axiom,
! [Pa: $i,Q_1: $i] :
( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ Pa ) @ Q_1 ) ) ) )
<=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ Pa ) ) )
& ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ Q_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_finite__Collect__disjI) ).
thf(231,axiom,
! [Pa: $i,Q_1: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ Pa ) @ Q_1 ) ) ) )
<=> ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ Pa ) ) )
& ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ Q_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_finite__Collect__disjI) ).
thf(232,axiom,
! [Pa: $i,Q_1: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ Pa ) @ Q_1 ) ) ) )
<=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ Pa ) ) )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ Q_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_finite__Collect__disjI) ).
thf(233,axiom,
! [I_1: $i,J: $i,K_1: $i] :
( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ I_1 ) @ J ) ) @ K_1 )
= ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ I_1 ) @ K_1 ) ) @ J ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_diff__commute) ).
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(239,axiom,
! [N_1: $i] :
( N_1
!= ( hAPP_nat_nat @ suc @ N_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_n__not__Suc__n) ).
thf(240,axiom,
! [N_1: $i] :
( ( hAPP_nat_nat @ suc @ N_1 )
!= N_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_Suc__n__not__n) ).
thf(241,axiom,
! [Nat_1: $i,Nat: $i] :
( ( ( hAPP_nat_nat @ suc @ Nat_1 )
= ( hAPP_nat_nat @ suc @ Nat ) )
<=> ( Nat_1 = Nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_nat_Oinject) ).
thf(242,axiom,
! [X: $i,Y: $i] :
( ( ( hAPP_nat_nat @ suc @ X )
= ( hAPP_nat_nat @ suc @ Y ) )
=> ( X = Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_Suc__inject) ).
thf(243,axiom,
! [Na: $i] :
( ( hAPP_f22106695ol_nat @ finite_card_nat @ ( collect_nat @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ ord_less_eq_nat ) @ Na ) ) )
= ( hAPP_nat_nat @ suc @ Na ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_card__Collect__le__nat) ).
thf(244,axiom,
! [K: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ ord_less_eq_nat ) @ K ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_finite__Collect__le__nat) ).
thf(245,axiom,
! [N_1: $i,M_2: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ N_1 ) @ M_2 ) )
=> ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ suc @ M_2 ) ) @ N_1 )
= ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( minus_minus_nat @ M_2 ) @ N_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_Suc__diff__le) ).
thf(246,axiom,
! [Q_1: $i,Pa: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ Pa ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ Q_1 ) ) ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ Pa ) @ Q_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_finite__Collect__conjI) ).
thf(247,axiom,
! [Q_1: $i,Pa: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ Pa ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ Q_1 ) ) ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ Pa ) @ Q_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_finite__Collect__conjI) ).
thf(248,axiom,
! [Q_1: $i,Pa: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ Pa ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ Q_1 ) ) ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ Pa ) @ Q_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_finite__Collect__conjI) ).
thf(249,axiom,
! [Q_1: $i,Pa: $i] :
( ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ Pa ) ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ Q_1 ) ) ) )
=> ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fconj @ Pa ) @ Q_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_finite__Collect__conjI) ).
thf(250,axiom,
! [Q_1: $i,Pa: $i] :
( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ Pa ) ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ Q_1 ) ) ) )
=> ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fconj @ Pa ) @ Q_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_finite__Collect__conjI) ).
thf(251,axiom,
! [Q_1: $i,Pa: $i] :
( ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ Pa ) ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ Q_1 ) ) ) )
=> ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fconj @ Pa ) @ Q_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_finite__Collect__conjI) ).
thf(252,axiom,
! [X_2: $i,A: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) )
=> ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_2 ) @ A ) )
=> ( ( hAPP_fun_a_bool_nat @ finite_card_a @ ( insert_a @ X_2 @ A ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_fun_a_bool_nat @ finite_card_a @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_card__insert__disjoint) ).
thf(253,axiom,
! [X_2: $i,A: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
=> ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ A ) )
=> ( ( hAPP_f921600141ol_nat @ finite_card_pname @ ( insert_pname @ X_2 @ A ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f921600141ol_nat @ finite_card_pname @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_card__insert__disjoint) ).
thf(254,axiom,
! [X_2: $i,A: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) )
=> ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ X_2 ) @ A ) )
=> ( ( hAPP_f22106695ol_nat @ finite_card_nat @ ( insert_nat @ X_2 @ A ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f22106695ol_nat @ finite_card_nat @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_card__insert__disjoint) ).
thf(255,axiom,
! [X_2: $i,A: $i] :
( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A ) )
=> ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ X_2 ) @ A ) )
=> ( ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( insert_fun_a_bool @ X_2 @ A ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_card__insert__disjoint) ).
thf(256,axiom,
! [X_2: $i,A: $i] :
( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) )
=> ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ X_2 ) @ A ) )
=> ( ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( insert1325755072e_bool @ X_2 @ A ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_card__insert__disjoint) ).
thf(257,axiom,
! [X_2: $i,A: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A ) )
=> ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ X_2 ) @ A ) )
=> ( ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( insert_fun_nat_bool @ X_2 @ A ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_card__insert__disjoint) ).
thf(258,axiom,
! [X_2: $i,A: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) )
=> ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_2 ) @ A ) )
=> ( ( hAPP_fun_a_bool_nat @ finite_card_a @ ( insert_a @ X_2 @ A ) )
= ( hAPP_fun_a_bool_nat @ finite_card_a @ A ) ) )
& ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_2 ) @ A ) )
=> ( ( hAPP_fun_a_bool_nat @ finite_card_a @ ( insert_a @ X_2 @ A ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_fun_a_bool_nat @ finite_card_a @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_card__insert__if) ).
thf(259,axiom,
! [X_2: $i,A: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
=> ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ A ) )
=> ( ( hAPP_f921600141ol_nat @ finite_card_pname @ ( insert_pname @ X_2 @ A ) )
= ( hAPP_f921600141ol_nat @ finite_card_pname @ A ) ) )
& ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ A ) )
=> ( ( hAPP_f921600141ol_nat @ finite_card_pname @ ( insert_pname @ X_2 @ A ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f921600141ol_nat @ finite_card_pname @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_card__insert__if) ).
thf(260,axiom,
! [X_2: $i,A: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) )
=> ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ X_2 ) @ A ) )
=> ( ( hAPP_f22106695ol_nat @ finite_card_nat @ ( insert_nat @ X_2 @ A ) )
= ( hAPP_f22106695ol_nat @ finite_card_nat @ A ) ) )
& ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ X_2 ) @ A ) )
=> ( ( hAPP_f22106695ol_nat @ finite_card_nat @ ( insert_nat @ X_2 @ A ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f22106695ol_nat @ finite_card_nat @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_card__insert__if) ).
thf(261,axiom,
! [X_2: $i,A: $i] :
( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A ) )
=> ( ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ X_2 ) @ A ) )
=> ( ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( insert_fun_a_bool @ X_2 @ A ) )
= ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ A ) ) )
& ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ X_2 ) @ A ) )
=> ( ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( insert_fun_a_bool @ X_2 @ A ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_card__insert__if) ).
thf(262,axiom,
! [X_2: $i,A: $i] :
( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) )
=> ( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ X_2 ) @ A ) )
=> ( ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( insert1325755072e_bool @ X_2 @ A ) )
= ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ A ) ) )
& ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ X_2 ) @ A ) )
=> ( ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( insert1325755072e_bool @ X_2 @ A ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_card__insert__if) ).
thf(263,axiom,
! [X_2: $i,A: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A ) )
=> ( ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ X_2 ) @ A ) )
=> ( ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( insert_fun_nat_bool @ X_2 @ A ) )
= ( hAPP_f696928925ol_nat @ finite346522414t_bool @ A ) ) )
& ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ X_2 ) @ A ) )
=> ( ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( insert_fun_nat_bool @ X_2 @ A ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_card__insert__if) ).
thf(264,axiom,
! [X_2: $i,A: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ A ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( insert_a @ X_2 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_card__insert__le) ).
thf(265,axiom,
! [X_2: $i,A: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ A ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( insert_nat @ X_2 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_card__insert__le) ).
thf(266,axiom,
! [X_2: $i,A: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ A ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( insert_pname @ X_2 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_card__insert__le) ).
thf(267,axiom,
! [X_2: $i,A: $i] :
( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ A ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( insert_fun_a_bool @ X_2 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_card__insert__le) ).
thf(268,axiom,
! [X_2: $i,A: $i] :
( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ A ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( insert1325755072e_bool @ X_2 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_card__insert__le) ).
thf(269,axiom,
! [X_2: $i,A: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ A ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( insert_fun_nat_bool @ X_2 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_card__insert__le) ).
thf(270,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ B ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ A ) ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_card__seteq) ).
thf(271,axiom,
! [A: $i,B: $i] :
( ( ( is_fun_a_bool @ A )
& ( is_fun_a_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ B ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ A ) ) )
=> ( A = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_card__seteq) ).
thf(272,axiom,
! [A: $i,B: $i] :
( ( ( is_fun_pname_bool @ A )
& ( is_fun_pname_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ B ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ A ) ) )
=> ( A = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_card__seteq) ).
thf(273,axiom,
! [A: $i,B: $i] :
( ( ( is_fun949378684l_bool @ A )
& ( is_fun949378684l_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ B ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ A ) ) )
=> ( A = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_card__seteq) ).
thf(274,axiom,
! [A: $i,B: $i] :
( ( ( is_fun1661590463l_bool @ A )
& ( is_fun1661590463l_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ B ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ A ) ) )
=> ( A = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_card__seteq) ).
thf(275,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ B ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ A ) ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_card__seteq) ).
thf(276,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ A ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_card__mono) ).
thf(277,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_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ A ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_card__mono) ).
thf(278,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ A ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_card__mono) ).
thf(279,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ A ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_card__mono) ).
thf(280,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ A ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_card__mono) ).
thf(281,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ A ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_card__mono) ).
thf(282,axiom,
! [F: $i,A: $i] :
( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( image_1854862208_pname @ F @ A ) ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_card__image__le) ).
thf(283,axiom,
! [F: $i,A: $i] :
( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( image_1283814551_pname @ F @ A ) ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_card__image__le) ).
thf(284,axiom,
! [F: $i,A: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( image_1921560913_pname @ F @ A ) ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_card__image__le) ).
thf(285,axiom,
! [F: $i,A: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( image_nat_fun_a_bool @ F @ A ) ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_card__image__le) ).
thf(286,axiom,
! [F: $i,A: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( image_1655916159e_bool @ F @ A ) ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_card__image__le) ).
thf(287,axiom,
! [F: $i,A: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( image_26036933t_bool @ F @ A ) ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_card__image__le) ).
thf(288,axiom,
! [F: $i,A: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_nat_a @ F @ A ) ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_card__image__le) ).
thf(289,axiom,
! [F: $i,A: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( image_112932426a_bool @ F @ A ) ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_card__image__le) ).
thf(290,axiom,
! [F: $i,A: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( image_47868345e_bool @ F @ A ) ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_card__image__le) ).
thf(291,axiom,
! [F: $i,A: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( image_2129980159t_bool @ F @ A ) ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_card__image__le) ).
thf(292,axiom,
! [F: $i,A: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( image_pname_pname @ F @ A ) ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_card__image__le) ).
thf(293,axiom,
! [F: $i,A: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_a_a @ F @ A ) ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_card__image__le) ).
thf(294,axiom,
! [F: $i,A: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_fun_nat_bool_a @ F @ A ) ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_card__image__le) ).
thf(295,axiom,
! [F: $i,A: $i] :
( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_876012084bool_a @ F @ A ) ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_card__image__le) ).
thf(296,axiom,
! [F: $i,A: $i] :
( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_fun_a_bool_a @ F @ A ) ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_card__image__le) ).
thf(297,axiom,
! [F: $i,A: $i] :
( ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_573985017bool_a @ F @ A ) ) ) @ ( hAPP_f1253658590ol_nat @ finite1659325229l_bool @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_card__image__le) ).
thf(298,axiom,
! [F: $i,A: $i] :
( ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_349102846bool_a @ F @ A ) ) ) @ ( hAPP_f98387925ol_nat @ finite269641166l_bool @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_card__image__le) ).
thf(299,axiom,
! [F: $i,A: $i] :
( ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_526090948bool_a @ F @ A ) ) ) @ ( hAPP_f1690079119ol_nat @ finite1352710292l_bool @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_card__image__le) ).
thf(300,axiom,
! [F: $i,A: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_pname_a @ F @ A ) ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_card__image__le) ).
thf(301,axiom,
! [F: $i,A: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( image_nat_pname @ F @ A ) ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_card__image__le) ).
thf(302,axiom,
! [F: $i,A: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( image_a_pname @ F @ A ) ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_card__image__le) ).
thf(303,axiom,
! [F: $i,A: $i] :
( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( image_fun_a_bool_nat @ F @ A ) ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_card__image__le) ).
thf(304,axiom,
! [F: $i,A: $i] :
( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( image_1551609309ol_nat @ F @ A ) ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_card__image__le) ).
thf(305,axiom,
! [F: $i,A: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( image_496248727ol_nat @ F @ A ) ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_card__image__le) ).
thf(306,axiom,
! [F: $i,A: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( image_a_nat @ F @ A ) ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_card__image__le) ).
thf(307,axiom,
! [F: $i,A: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( image_pname_nat @ F @ A ) ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_card__image__le) ).
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(317,axiom,
! [H: $i,F_1: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ F_1 ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_nat_pname @ H @ F_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_finite__imageI) ).
thf(318,axiom,
! [H: $i,F_1: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ F_1 ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_pname_nat @ H @ F_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_finite__imageI) ).
thf(319,axiom,
! [H: $i,F_1: $i] :
( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ F_1 ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_fun_a_bool_a @ H @ F_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_finite__imageI) ).
thf(320,axiom,
! [H: $i,F_1: $i] :
( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ F_1 ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_876012084bool_a @ H @ F_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_finite__imageI) ).
thf(321,axiom,
! [H: $i,F_1: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ F_1 ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_fun_nat_bool_a @ H @ F_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_finite__imageI) ).
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(324,axiom,
! [H: $i,F_1: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ F_1 ) )
=> ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( image_2129980159t_bool @ H @ F_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_finite__imageI) ).
thf(325,axiom,
! [H: $i,F_1: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ F_1 ) )
=> ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( image_47868345e_bool @ H @ F_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_finite__imageI) ).
thf(326,axiom,
! [H: $i,F_1: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ F_1 ) )
=> ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( image_112932426a_bool @ H @ F_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_finite__imageI) ).
thf(327,axiom,
! [H: $i,F_1: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ F_1 ) )
=> ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ ( image_1420695166l_bool @ H @ F_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_finite__imageI) ).
thf(328,axiom,
! [H: $i,F_1: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ F_1 ) )
=> ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ ( image_1642285373l_bool @ H @ F_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_finite__imageI) ).
thf(329,axiom,
! [H: $i,F_1: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ F_1 ) )
=> ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ ( image_1154884483l_bool @ H @ F_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_finite__imageI) ).
thf(330,axiom,
! [H: $i,F_1: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ F_1 ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_nat_a @ H @ F_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_finite__imageI) ).
thf(331,axiom,
! [H: $i,F_1: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ F_1 ) )
=> ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( image_26036933t_bool @ H @ F_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_finite__imageI) ).
thf(332,axiom,
! [H: $i,F_1: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ F_1 ) )
=> ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( image_1655916159e_bool @ H @ F_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_finite__imageI) ).
thf(333,axiom,
! [H: $i,F_1: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ F_1 ) )
=> ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( image_nat_fun_a_bool @ H @ F_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_finite__imageI) ).
thf(334,axiom,
! [H: $i,F_1: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ F_1 ) )
=> ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ ( image_1208015684l_bool @ H @ F_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_finite__imageI) ).
thf(335,axiom,
! [H: $i,F_1: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ F_1 ) )
=> ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ ( image_1874789623l_bool @ H @ F_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_finite__imageI) ).
thf(336,axiom,
! [H: $i,F_1: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ F_1 ) )
=> ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ ( image_1607900221l_bool @ H @ F_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_finite__imageI) ).
thf(337,axiom,
! [H: $i,F_1: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ F_1 ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_a_pname @ H @ F_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_finite__imageI) ).
thf(338,axiom,
! [H: $i,F_1: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ F_1 ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1921560913_pname @ H @ F_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_finite__imageI) ).
thf(339,axiom,
! [H: $i,F_1: $i] :
( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ F_1 ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1283814551_pname @ H @ F_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_finite__imageI) ).
thf(340,axiom,
! [H: $i,F_1: $i] :
( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ F_1 ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1854862208_pname @ H @ F_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_finite__imageI) ).
thf(341,axiom,
! [H: $i,F_1: $i] :
( ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ F_1 ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_990671762_pname @ H @ F_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_finite__imageI) ).
thf(342,axiom,
! [H: $i,F_1: $i] :
( ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ F_1 ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1705983821_pname @ H @ F_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_finite__imageI) ).
thf(343,axiom,
! [H: $i,F_1: $i] :
( ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ F_1 ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1604018183_pname @ H @ F_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_finite__imageI) ).
thf(344,axiom,
! [H: $i,F_1: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ F_1 ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_a_nat @ H @ F_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_finite__imageI) ).
thf(345,axiom,
! [H: $i,F_1: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ F_1 ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_496248727ol_nat @ H @ F_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_finite__imageI) ).
thf(346,axiom,
! [H: $i,F_1: $i] :
( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ F_1 ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_1551609309ol_nat @ H @ F_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_finite__imageI) ).
thf(347,axiom,
! [H: $i,F_1: $i] :
( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ F_1 ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_fun_a_bool_nat @ H @ F_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_finite__imageI) ).
thf(348,axiom,
! [H: $i,F_1: $i] :
( ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ F_1 ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_1802975832ol_nat @ H @ F_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_finite__imageI) ).
thf(349,axiom,
! [H: $i,F_1: $i] :
( ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ F_1 ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_1079571347ol_nat @ H @ F_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_finite__imageI) ).
thf(350,axiom,
! [H: $i,F_1: $i] :
( ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ F_1 ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_2089570637ol_nat @ H @ F_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_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(352,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A ) )
=> ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ ( collec1015864663l_bool @ ( hAPP_f1772781669l_bool @ ( cOMBC_595898202l_bool @ ord_le1454342156l_bool ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_finite__Collect__subsets) ).
thf(353,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) )
=> ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ ( collec1613912337l_bool @ ( hAPP_f510955609l_bool @ ( cOMBC_7971162l_bool @ ord_le675606854l_bool ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_finite__Collect__subsets) ).
thf(354,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A ) )
=> ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ ( collec707592106l_bool @ ( hAPP_f1434722111l_bool @ ( cOMBC_331553030l_bool @ ord_le1375614389l_bool ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_finite__Collect__subsets) ).
thf(355,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ A ) )
=> ( hBOOL @ ( hAPP_f1363661463l_bool @ finite1343359508l_bool @ ( collec1635217238l_bool @ ( hAPP_f1050622307l_bool @ ( cOMBC_636888218l_bool @ ord_le967226251l_bool ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_finite__Collect__subsets) ).
thf(356,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ A ) )
=> ( hBOOL @ ( hAPP_f595608956l_bool @ finite1491191519l_bool @ ( collec792590109l_bool @ ( hAPP_f1759205631l_bool @ ( cOMBC_336095980l_bool @ ord_le1375671464l_bool ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_finite__Collect__subsets) ).
thf(357,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ A ) )
=> ( hBOOL @ ( hAPP_f1295398978l_bool @ finite719726885l_bool @ ( collec1874991203l_bool @ ( hAPP_f760187903l_bool @ ( cOMBC_1269652216l_bool @ ord_le65145710l_bool ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_finite__Collect__subsets) ).
thf(358,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) )
=> ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ ord_le1311769555a_bool ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_finite__Collect__subsets) ).
thf(359,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
=> ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ ord_le313189616e_bool ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_finite__Collect__subsets) ).
thf(360,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) )
=> ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( hAPP_f103356543l_bool @ ( cOMBC_1693257480l_bool @ ord_le1568362934t_bool ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_finite__Collect__subsets) ).
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(362,axiom,
! [B_1_1: $i] :
( ( is_fun_a_bool @ B_1_1 )
=> ( is_fun949378684l_bool @ ( p @ B_1_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_P) ).
thf(363,axiom,
! [B_1_1: $i,B_2: $i] : ( is_bool @ ( hAPP_f1295398978l_bool @ B_1_1 @ B_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_) ).
thf(364,axiom,
! [B_1_1: $i,B_2: $i] : ( is_bool @ ( hAPP_f595608956l_bool @ B_1_1 @ B_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Oboo) ).
thf(365,axiom,
! [B_1_1: $i,B_2: $i] : ( is_bool @ ( hAPP_f1363661463l_bool @ B_1_1 @ B_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HO) ).
thf(366,axiom,
! [B_1_1: $i,B_2: $i] : ( is_bool @ ( hAPP_f937997336l_bool @ B_1_1 @ B_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HO) ).
thf(367,axiom,
! [B_1_1: $i,B_2: $i] : ( is_bool @ ( hAPP_f389811538l_bool @ B_1_1 @ B_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__) ).
thf(368,axiom,
! [B_1_1: $i,B_2: $i] : ( is_bool @ ( hAPP_f292226953l_bool @ B_1_1 @ B_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_) ).
thf(369,axiom,
! [B_1_1: $i,B_2: $i] : ( is_bool @ ( hAPP_f1637334154l_bool @ B_1_1 @ B_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HOL__Obool_) ).
thf(370,axiom,
! [B_1_1: $i,B_2: $i] :
( ( is_fun1661590463l_bool @ B_2 )
=> ( is_fun1661590463l_bool @ ( hAPP_f559147733l_bool @ B_1_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo_005) ).
thf(371,axiom,
! [B_1_1: $i,B_2: $i] :
( ( is_fun1661590463l_bool @ B_2 )
=> ( is_bool @ ( hAPP_f1935102916l_bool @ B_1_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo) ).
thf(372,axiom,
! [B_1_1: $i,B_2: $i] :
( ( is_fun949378684l_bool @ B_2 )
=> ( is_fun949378684l_bool @ ( hAPP_f2117159681l_bool @ B_1_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J_000tc___004) ).
thf(373,axiom,
! [B_1_1: $i,B_2: $i] :
( ( is_fun949378684l_bool @ B_2 )
=> ( is_bool @ ( hAPP_f621171935l_bool @ B_1_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J_000tc__) ).
thf(374,axiom,
! [B_1_1: $i,B_2: $i] : ( is_bool @ ( hAPP_f54304608l_bool @ B_1_1 @ B_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obool) ).
thf(375,axiom,
! [B_1_1: $i,B_2: $i] :
( ( is_fun_pname_bool @ B_2 )
=> ( is_fun1661590463l_bool @ ( hAPP_f434788991l_bool @ B_1_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc) ).
thf(376,axiom,
! [B_1_1: $i,B_2: $i] :
( ( is_fun_pname_bool @ B_2 )
=> ( is_fun_pname_bool @ ( hAPP_f759274231e_bool @ B_1_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_Itc__Com__Op) ).
thf(377,axiom,
! [B_1_1: $i,B_2: $i] :
( ( is_fun_a_bool @ B_2 )
=> ( is_fun_a_bool @ ( hAPP_f2050579477a_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_It__a_Mtc__HOL__Obool_J) ).
thf(378,axiom,
! [B_1_1: $i,B_2: $i] : ( is_fun_pname_bool @ ( hAPP_n1025906991e_bool @ B_1_1 @ B_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).
thf(379,axiom,
! [B_1_1: $i,B_2: $i] : ( is_fun_a_bool @ ( hAPP_nat_fun_a_bool @ B_1_1 @ B_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
thf(380,axiom,
! [B_1_1: $i,B_2: $i] :
( ( is_bool @ B_2 )
=> ( is_bool @ ( hAPP_bool_bool @ B_1_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool) ).
thf(381,axiom,
! [B_1_1: $i,B_2: $i] :
( ( is_pname @ B_2 )
=> ( is_fun_pname_bool @ ( hAPP_p61793385e_bool @ B_1_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).
thf(382,axiom,
! [B_1_1: $i,B_2: $i] :
( ( is_pname @ B_2 )
=> ( is_fun_a_bool @ ( hAPP_p1534023578a_bool @ B_1_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Com__Opname_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
thf(383,axiom,
! [B_1_1: $i,B_2: $i] :
( ( ( is_fun_pname_bool @ B_1_1 )
& ( is_pname @ B_2 ) )
=> ( is_bool @ ( hAPP_pname_bool @ B_1_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Com__Opname_000tc__HOL__Obool) ).
thf(384,axiom,
! [B_1_1: $i,B_2: $i] :
( ( is_a @ B_2 )
=> ( is_fun_pname_bool @ ( hAPP_a93125764e_bool @ B_1_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000t__a_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).
thf(385,axiom,
! [B_1_1: $i,B_2: $i] :
( ( is_a @ B_2 )
=> ( is_fun_a_bool @ ( hAPP_a_fun_a_bool @ B_1_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
thf(386,axiom,
! [B_1_1: $i,B_2: $i] :
( ( ( is_fun_a_bool @ B_1_1 )
& ( is_a @ B_2 ) )
=> ( is_bool @ ( hAPP_a_bool @ B_1_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000t__a_000tc__HOL__Obool) ).
thf(387,axiom,
! [B_1_1: $i,B_2: $i] :
( ( ( is_fun_pname_bool @ B_1_1 )
& ( is_fun1661590463l_bool @ B_2 ) )
=> ( is_fun1661590463l_bool @ ( insert1325755072e_bool @ B_1_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oinsert_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).
thf(388,axiom,
! [B_1_1: $i,B_2: $i] :
( ( ( is_fun_a_bool @ B_1_1 )
& ( is_fun949378684l_bool @ B_2 ) )
=> ( is_fun949378684l_bool @ ( insert_fun_a_bool @ B_1_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oinsert_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
thf(389,axiom,
! [B_1_1: $i,B_2: $i] :
( ( ( is_pname @ B_1_1 )
& ( is_fun_pname_bool @ B_2 ) )
=> ( is_fun_pname_bool @ ( insert_pname @ B_1_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oinsert_000tc__Com__Opname) ).
thf(390,axiom,
! [B_1_1: $i,B_2: $i] : ( is_fun_pname_bool @ ( image_1604018183_pname @ B_1_1 @ B_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HOL___003) ).
thf(391,axiom,
! [B_1_1: $i,B_2: $i] : ( is_fun_a_bool @ ( image_526090948bool_a @ B_1_1 @ B_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HOL__) ).
thf(392,axiom,
! [B_1_1: $i,B_2: $i] : ( is_fun_pname_bool @ ( image_1705983821_pname @ B_1_1 @ B_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL_002) ).
thf(393,axiom,
! [B_1_1: $i,B_2: $i] : ( is_fun_a_bool @ ( image_349102846bool_a @ B_1_1 @ B_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL) ).
thf(394,axiom,
! [B_1_1: $i,B_2: $i] : ( is_fun_pname_bool @ ( image_990671762_pname @ B_1_1 @ B_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J_0_001) ).
thf(395,axiom,
! [B_1_1: $i,B_2: $i] : ( is_fun_a_bool @ ( image_573985017bool_a @ B_1_1 @ B_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J_0) ).
thf(396,axiom,
! [B_1_1: $i,B_2: $i] : ( is_fun_pname_bool @ ( image_1921560913_pname @ B_1_1 @ B_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Com__Opname) ).
thf(397,axiom,
! [B_1_1: $i,B_2: $i] : ( is_fun_a_bool @ ( image_fun_nat_bool_a @ B_1_1 @ B_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000t__a) ).
thf(398,axiom,
! [B_1_1: $i,B_2: $i] :
( ( is_fun1661590463l_bool @ B_2 )
=> ( is_fun_pname_bool @ ( image_1283814551_pname @ B_1_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__Opnam) ).
thf(399,axiom,
! [B_1_1: $i,B_2: $i] :
( ( is_fun1661590463l_bool @ B_2 )
=> ( is_fun_a_bool @ ( image_876012084bool_a @ B_1_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000t__a) ).
thf(400,axiom,
! [B_1_1: $i,B_2: $i] :
( ( is_fun949378684l_bool @ B_2 )
=> ( is_fun_pname_bool @ ( image_1854862208_pname @ B_1_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opname) ).
thf(401,axiom,
! [B_1_1: $i,B_2: $i] :
( ( is_fun949378684l_bool @ B_2 )
=> ( is_fun_a_bool @ ( image_fun_a_bool_a @ B_1_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_It__a_Mtc__HOL__Obool_J_000t__a) ).
thf(402,axiom,
! [B_1_1: $i,B_2: $i] : ( is_fun1661590463l_bool @ ( image_1655916159e_bool @ B_1_1 @ B_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).
thf(403,axiom,
! [B_1_1: $i,B_2: $i] : ( is_fun949378684l_bool @ ( image_nat_fun_a_bool @ B_1_1 @ B_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
thf(404,axiom,
! [B_1_1: $i,B_2: $i] : ( is_fun_pname_bool @ ( image_nat_pname @ B_1_1 @ B_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__Com__Opname) ).
thf(405,axiom,
! [B_1_1: $i,B_2: $i] : ( is_fun_a_bool @ ( image_nat_a @ B_1_1 @ B_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__Nat__Onat_000t__a) ).
thf(406,axiom,
! [B_1_1: $i,B_2: $i] :
( ( is_fun_pname_bool @ B_2 )
=> ( is_fun1661590463l_bool @ ( image_47868345e_bool @ B_1_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_) ).
thf(407,axiom,
! [B_1_1: $i,B_2: $i] :
( ( is_fun_pname_bool @ B_2 )
=> ( is_fun949378684l_bool @ ( image_112932426a_bool @ B_1_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__Com__Opname_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
thf(408,axiom,
! [B_1_1: $i,B_2: $i] :
( ( is_fun_pname_bool @ B_2 )
=> ( is_fun_pname_bool @ ( image_pname_pname @ B_1_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__Com__Opname_000tc__Com__Opname) ).
thf(409,axiom,
! [B_1_1: $i,B_2: $i] :
( ( is_fun_a_bool @ B_2 )
=> ( is_fun_pname_bool @ ( image_a_pname @ B_1_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000t__a_000tc__Com__Opname) ).
thf(410,axiom,
! [B_1_1: $i,B_2: $i] :
( ( is_fun_a_bool @ B_2 )
=> ( is_fun_a_bool @ ( image_a_a @ B_1_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000t__a_000t__a) ).
thf(411,axiom,
! [B_1_1: $i] :
( ( is_fun1661590463l_bool @ B_1_1 )
=> ( is_fun1661590463l_bool @ ( collec1974731493e_bool @ B_1_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_OCollect_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).
thf(412,axiom,
! [B_1_1: $i] :
( ( is_fun949378684l_bool @ B_1_1 )
=> ( is_fun949378684l_bool @ ( collect_fun_a_bool @ B_1_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_OCollect_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
thf(413,axiom,
! [B_1_1: $i] :
( ( is_fun_pname_bool @ B_1_1 )
=> ( is_fun_pname_bool @ ( collect_pname @ B_1_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_OCollect_000tc__Com__Opname) ).
thf(414,axiom,
! [B_1_1: $i] :
( ( is_fun_a_bool @ B_1_1 )
=> ( is_fun_a_bool @ ( collect_a @ B_1_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_OCollect_000t__a) ).
thf(415,axiom,
is_fun1661590463l_bool @ ( undefi64961550l_bool @ ( fun @ ( fun @ pname @ bool ) @ bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_HOL_Oundefined_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_) ).
thf(416,axiom,
is_fun949378684l_bool @ ( undefi1699038445l_bool @ ( fun @ ( fun @ x_a @ bool ) @ bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_HOL_Oundefined_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool) ).
thf(417,axiom,
is_fun_pname_bool @ ( undefi17486888e_bool @ ( fun @ pname @ bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_HOL_Oundefined_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).
thf(418,axiom,
is_fun_a_bool @ ( undefined_fun_a_bool @ ( fun @ x_a @ bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_HOL_Oundefined_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
thf(419,axiom,
is_pname @ ( undefined_pname @ pname ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_HOL_Oundefined_000tc__Com__Opname) ).
thf(420,axiom,
is_a @ ( undefined_a @ x_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_HOL_Oundefined_000t__a) ).
thf(421,axiom,
is_fun949378684l_bool @ finite_finite_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Finite__Set_Ofinite_000t__a) ).
thf(422,axiom,
! [B_1_1: $i,B_2: $i] :
( ( is_fun1661590463l_bool @ B_2 )
=> ( is_fun1661590463l_bool @ ( cOMBS_350070575l_bool @ B_1_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__Obool_000t) ).
thf(423,axiom,
! [B_1_1: $i,B_2: $i] :
( ( is_fun949378684l_bool @ B_2 )
=> ( is_fun949378684l_bool @ ( cOMBS_1035972772l_bool @ B_1_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_COMBS_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000tc__HOL__Obo) ).
thf(424,axiom,
! [B_1_1: $i,B_2: $i] :
( ( is_fun_pname_bool @ B_2 )
=> ( is_fun_pname_bool @ ( cOMBS_568398431l_bool @ B_1_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool) ).
thf(425,axiom,
! [B_1_1: $i,B_2: $i] :
( ( is_fun_a_bool @ B_2 )
=> ( is_fun_a_bool @ ( cOMBS_a_bool_bool @ B_1_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_COMBS_000t__a_000tc__HOL__Obool_000tc__HOL__Obool) ).
thf(426,axiom,
! [B_1_1: $i,B_2: $i] :
( ( is_fun1661590463l_bool @ B_2 )
=> ( is_fun1661590463l_bool @ ( cOMBB_307249310e_bool @ B_1_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc_) ).
thf(427,axiom,
! [B_1_1: $i,B_2: $i] :
( ( is_fun949378684l_bool @ B_2 )
=> ( is_fun949378684l_bool @ ( cOMBB_2140588453a_bool @ B_1_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_It__a_Mtc__HOL__Obool) ).
thf(428,axiom,
! [B_1_1: $i,B_2: $i] :
( ( is_fun_pname_bool @ B_2 )
=> ( is_fun_pname_bool @ ( cOMBB_647938656_pname @ B_1_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname) ).
thf(429,axiom,
! [B_1_1: $i,B_2: $i] :
( ( is_fun_a_bool @ B_2 )
=> ( is_fun_a_bool @ ( cOMBB_bool_bool_a @ B_1_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000t__a) ).
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(432,axiom,
( ( hAPP_fun_a_bool_nat @ finite_card_a @ g )
= ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_pname_a @ mgt_call @ u ) ) ) @ ( hAPP_nat_nat @ suc @ na ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_3) ).
thf(433,axiom,
hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ na ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_pname_a @ mgt_call @ u ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
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(439,axiom,
! [B_1_1: $i,B_2: $i] :
( ( ( is_fun1661590463l_bool @ B_1_1 )
& ( is_fun_pname_bool @ B_2 ) )
=> ( is_bool @ ( hAPP_f1664156314l_bool @ B_1_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__Obool) ).
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(442,axiom,
! [B_1_1: $i,B_2: $i] : ( is_bool @ ( hAPP_nat_bool @ B_1_1 @ B_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool) ).
thf(443,axiom,
! [B_1_1: $i,B_2: $i] :
( ( is_pname @ B_2 )
=> ( is_fun1661590463l_bool @ ( hAPP_p338031245l_bool @ B_1_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obo) ).
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(445,axiom,
! [B_1_1: $i,B_2: $i] :
( ( is_a @ B_2 )
=> ( is_fun949378684l_bool @ ( hAPP_a85458249l_bool @ B_1_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000t__a_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J) ).
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(448,axiom,
is_fun1661590463l_bool @ finite_finite_pname,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Finite__Set_Ofinite_000tc__Com__Opname) ).
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 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[450]) ).
thf(452,plain,
( ( ! [X: $i,Y: $i] :
( ( X != Y )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ X ) @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[35]) ).
thf(453,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( is_fun_pname_bool @ X )
| ~ ( is_fun_pname_bool @ Y )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ X ) @ Y ) )
| ( X = Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[36]) ).
thf(454,plain,
( ( ! [X: $i,Y: $i] :
( ( X != Y )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ X ) @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[37]) ).
thf(455,plain,
( ( ! [X: $i,Y: $i] :
( ( X != Y )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ X ) @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[42]) ).
thf(456,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(extcnf_combined,[status(esa)],[43]) ).
thf(457,plain,
( ( ! [X: $i,Y: $i] :
( ( X != Y )
| ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ fequal_pname @ X ) @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[45]) ).
thf(458,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( is_pname @ X )
| ~ ( is_pname @ Y )
| ~ ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ fequal_pname @ X ) @ Y ) )
| ( X = Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[46]) ).
thf(459,plain,
( ( ! [X: $i,Y: $i] :
( ( X != Y )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ X ) @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[47]) ).
thf(460,plain,
( ( ! [X: $i,Y: $i] :
( ( X != Y )
| ( hBOOL @ ( hAPP_a_bool @ ( hAPP_a_fun_a_bool @ fequal_a @ X ) @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[49]) ).
thf(461,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( is_a @ X )
| ~ ( is_a @ Y )
| ~ ( hBOOL @ ( hAPP_a_bool @ ( hAPP_a_fun_a_bool @ fequal_a @ X ) @ Y ) )
| ( X = Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[50]) ).
thf(462,plain,
( ( ! [P: $i,Q: $i] :
( ( hBOOL @ Q )
| ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ P ) @ Q ) )
| ~ ( hBOOL @ P ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[51]) ).
thf(463,plain,
( ( ! [P: $i,Q: $i] :
( ( hBOOL @ Q )
| ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ P ) @ Q ) )
| ( hBOOL @ P ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[54]) ).
thf(464,plain,
( ( ! [P: $i] :
( ! [Q: $i] :
~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ P ) @ Q ) )
| ( hBOOL @ P ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[58]) ).
thf(465,plain,
( ( ! [Q: $i,P: $i] :
( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ P ) @ Q ) )
| ~ ( hBOOL @ P )
| ~ ( hBOOL @ Q ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[59]) ).
thf(466,plain,
( ( ! [N: $i] :
( ! [M: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ ( sK2_X_1 @ M @ N ) ) @ N ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( sK2_X_1 @ M @ N ) ) @ M ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ N ) ) )
& ! [N: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ N ) )
| ! [SY425: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SY425 ) @ N ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY425 ) @ ( sK1_M @ N ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[62]) ).
thf(467,plain,
( ( ! [F: $i,B: $i,A: $i] :
( ( ( is_pname @ ( sK3_X_1 @ A @ B @ F ) )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK3_X_1 @ A @ B @ F ) ) @ A ) )
& ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( hAPP_pname_a @ F @ ( sK3_X_1 @ A @ B @ F ) ) ) @ B ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_pname_a @ F @ A ) ) @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[67]) ).
thf(468,plain,
( ( ! [N_1: $i,M_1: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ N_1 ) ) @ M_1 ) )
| ( M_1
= ( hAPP_nat_nat @ suc @ ( sK4_M @ M_1 @ N_1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[68]) ).
thf(469,plain,
( ( ! [I: $i,Pa: $i,K: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ Pa @ K ) )
| ( ( hBOOL @ ( hAPP_nat_bool @ Pa @ ( hAPP_nat_nat @ suc @ ( sK5_N_2 @ K @ Pa @ I ) ) ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ Pa @ ( sK5_N_2 @ K @ Pa @ I ) ) ) )
| ( hBOOL @ ( hAPP_nat_bool @ Pa @ ( hAPP_nat_nat @ ( minus_minus_nat @ K ) @ I ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[69]) ).
thf(470,plain,
( ( ! [B: $i,A: $i] :
( ( ( is_pname @ ( sK6_X_1 @ A @ B ) )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK6_X_1 @ A @ B ) ) @ A ) )
& ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK6_X_1 @ A @ B ) ) @ B ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[70]) ).
thf(471,plain,
( ( ! [B: $i,A: $i] :
( ( ( is_a @ ( sK7_X_1 @ A @ B ) )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( sK7_X_1 @ A @ B ) ) @ A ) )
& ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( sK7_X_1 @ A @ B ) ) @ B ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[71]) ).
thf(472,plain,
( ( ! [B: $i,A: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ ( sK8_X_1 @ A @ B ) ) @ A ) )
& ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ ( sK8_X_1 @ A @ B ) ) @ B ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[72]) ).
thf(473,plain,
( ( ! [B_1: $i] :
( ~ ( is_a @ B_1 )
| ! [F: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B_1 ) @ ( image_pname_a @ F @ A ) ) )
| ( ( is_pname @ ( sK9_X_1 @ A @ F @ B_1 ) )
& ( B_1
= ( hAPP_pname_a @ F @ ( sK9_X_1 @ A @ F @ B_1 ) ) )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK9_X_1 @ A @ F @ B_1 ) ) @ A ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[73]) ).
thf(474,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(extcnf_combined,[status(esa)],[74]) ).
thf(475,plain,
( ( ! [B: $i] :
( ( ~ ( is_fun_a_bool @ B )
| ! [F: $i,A: $i] :
( ! [AA: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ AA ) @ A ) )
| ~ ( is_fun_pname_bool @ AA )
| ( B
!= ( image_pname_a @ F @ AA ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ ( image_pname_a @ F @ A ) ) ) ) )
& ( ~ ( is_fun_a_bool @ B )
| ! [F: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ ( image_pname_a @ F @ A ) ) )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( sK10_AA @ A @ F @ B ) ) @ A ) )
& ( is_fun_pname_bool @ ( sK10_AA @ A @ F @ B ) )
& ( B
= ( image_pname_a @ F @ ( sK10_AA @ A @ F @ B ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[75]) ).
thf(476,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(extcnf_combined,[status(esa)],[76]) ).
thf(477,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(extcnf_combined,[status(esa)],[78]) ).
thf(478,plain,
( ( ! [A_1: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ D ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ A_1 @ C ) ) @ ( insert_pname @ A_1 @ D ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[79]) ).
thf(479,plain,
( ( ! [A_1: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ D ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( insert_nat @ A_1 @ C ) ) @ ( insert_nat @ A_1 @ D ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[80]) ).
thf(480,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(extcnf_combined,[status(esa)],[81]) ).
thf(481,plain,
( ( ! [B_1: $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 @ A ) @ ( insert_pname @ B_1 @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[82]) ).
thf(482,plain,
( ( ! [B_1: $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 @ A ) @ ( insert_nat @ B_1 @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[83]) ).
thf(483,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 ) ) )
& ! [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_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ ( insert_a @ X_2 @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[84]) ).
thf(484,plain,
( ( ! [B: $i] :
( ! [X_2: $i,A: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ A ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( insert_pname @ X_2 @ B ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) ) )
& ! [X_2: $i,A: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ A ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( insert_pname @ X_2 @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[85]) ).
thf(485,plain,
( ( ! [B: $i] :
( ! [X_2: $i,A: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ X_2 ) @ A ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ ( insert_nat @ X_2 @ B ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) ) )
& ! [X_2: $i,A: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ X_2 ) @ A ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ ( insert_nat @ X_2 @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[86]) ).
thf(486,plain,
( ( ! [X_2: $i] :
( ! [A: $i,B: $i] :
( ~ ( 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 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ X_2 @ A ) ) @ B ) ) )
& ! [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 ) ) )
& ! [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_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[87]) ).
thf(487,plain,
( ( ! [X_2: $i] :
( ! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ B ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ X_2 @ A ) ) @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ X_2 @ A ) ) @ B ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ X_2 @ A ) ) @ B ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[88]) ).
thf(488,plain,
( ( ! [X_2: $i] :
( ! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ X_2 ) @ B ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( insert_nat @ X_2 @ A ) ) @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( insert_nat @ X_2 @ A ) ) @ B ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ X_2 ) @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( insert_nat @ X_2 @ A ) ) @ B ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[89]) ).
thf(489,plain,
( ( ! [B_1: $i,F: $i,X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ A ) )
| ( B_1
!= ( hAPP_pname_a @ F @ X_2 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B_1 ) @ ( image_pname_a @ F @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[99]) ).
thf(490,plain,
( ( ! [F: $i,X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ A ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( hAPP_pname_a @ F @ X_2 ) ) @ ( image_pname_a @ F @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[100]) ).
thf(491,plain,
( ( ! [Z: $i] :
( ( ~ ( is_a @ Z )
| ! [F: $i,A: $i] :
( ! [X_1: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_1 ) @ A ) )
| ~ ( is_pname @ X_1 )
| ( Z
!= ( hAPP_pname_a @ F @ X_1 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ Z ) @ ( image_pname_a @ F @ A ) ) ) ) )
& ( ~ ( is_a @ Z )
| ! [F: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ Z ) @ ( image_pname_a @ F @ A ) ) )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK11_X_1 @ A @ F @ Z ) ) @ A ) )
& ( is_pname @ ( sK11_X_1 @ A @ F @ Z ) )
& ( Z
= ( hAPP_pname_a @ F @ ( sK11_X_1 @ A @ F @ Z ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[101]) ).
thf(492,plain,
( ( ! [Pa: $i] :
( ~ ( is_fun949378684l_bool @ Pa )
| ( ( collect_fun_a_bool @ Pa )
= Pa ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[103]) ).
thf(493,plain,
( ( ! [Pa: $i] :
( ~ ( is_fun1661590463l_bool @ Pa )
| ( ( collec1974731493e_bool @ Pa )
= Pa ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[104]) ).
thf(494,plain,
( ( ! [Pa: $i] :
( ~ ( is_fun_pname_bool @ Pa )
| ( ( collect_pname @ Pa )
= Pa ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[106]) ).
thf(495,plain,
( ( ! [X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ A ) )
| ( hBOOL @ ( hAPP_pname_bool @ A @ X_2 ) ) )
& ! [X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_pname_bool @ A @ X_2 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[107]) ).
thf(496,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 ) ) )
& ! [X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_a_bool @ A @ X_2 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_2 ) @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[108]) ).
thf(497,plain,
( ( ! [X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ X_2 ) @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ A @ X_2 ) ) )
& ! [X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ A @ X_2 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ X_2 ) @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[109]) ).
thf(498,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) ) )
& ! [A: $i,B: $i] :
( ( A != B )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[110]) ).
thf(499,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) ) )
& ! [A: $i,B: $i] :
( ( A != B )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[111]) ).
thf(500,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) ) )
& ! [A: $i,B: $i] :
( ( A != B )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[112]) ).
thf(501,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(extcnf_combined,[status(esa)],[113]) ).
thf(502,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(extcnf_combined,[status(esa)],[114]) ).
thf(503,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(extcnf_combined,[status(esa)],[115]) ).
thf(504,plain,
( ( ! [X_2: $i,A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ A ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[116]) ).
thf(505,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(extcnf_combined,[status(esa)],[117]) ).
thf(506,plain,
( ( ! [X_2: $i,A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ X_2 ) @ A ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ X_2 ) @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[118]) ).
thf(507,plain,
( ( ! [B: $i,X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ A ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[119]) ).
thf(508,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(extcnf_combined,[status(esa)],[120]) ).
thf(509,plain,
( ( ! [B: $i,X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ X_2 ) @ A ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ X_2 ) @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[121]) ).
thf(510,plain,
( ( ! [X_2: $i,A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ A ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[122]) ).
thf(511,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(extcnf_combined,[status(esa)],[123]) ).
thf(512,plain,
( ( ! [X_2: $i,A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ X_2 ) @ A ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ X_2 ) @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[124]) ).
thf(513,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[125]) ).
thf(514,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[126]) ).
thf(515,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[127]) ).
thf(516,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[128]) ).
thf(517,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[129]) ).
thf(518,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[130]) ).
thf(519,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 ) )
& ! [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 ) ) )
& ! [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 @ B ) @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[131]) ).
thf(520,plain,
( ( ! [A: $i,B: $i] :
( ~ ( is_fun_pname_bool @ A )
| ~ ( is_fun_pname_bool @ 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 ) )
| ( A = B ) )
& ! [A: $i,B: $i] :
( ~ ( is_fun_pname_bool @ A )
| ~ ( is_fun_pname_bool @ B )
| ( A != B )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( is_fun_pname_bool @ A )
| ~ ( is_fun_pname_bool @ B )
| ( A != B )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[132]) ).
thf(521,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 ) )
& ! [A: $i,B: $i] :
( ( A != B )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) ) )
& ! [A: $i,B: $i] :
( ( A != B )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[133]) ).
thf(522,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(extcnf_combined,[status(esa)],[137]) ).
thf(523,plain,
( ( ! [A_1: $i,A: $i] :
( ~ ( is_fun_pname_bool @ A )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A_1 ) @ A ) )
| ( ( insert_pname @ A_1 @ A )
= A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[138]) ).
thf(524,plain,
( ( ! [A_1: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A_1 ) @ A ) )
| ( ( insert_nat @ A_1 @ A )
= A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[139]) ).
thf(525,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(extcnf_combined,[status(esa)],[140]) ).
thf(526,plain,
( ( ! [B_1: $i,A_1: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A_1 ) @ B ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A_1 ) @ ( insert_pname @ B_1 @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[141]) ).
thf(527,plain,
( ( ! [B_1: $i,A_1: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A_1 ) @ B ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A_1 ) @ ( insert_nat @ B_1 @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[142]) ).
thf(528,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 ) )
& ! [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 ) )
| ( A != B )
| ( ( insert_a @ X_2 @ A )
= ( insert_a @ X_2 @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[143]) ).
thf(529,plain,
( ( ! [B: $i] :
( ! [X_2: $i,A: $i] :
( ~ ( is_fun_pname_bool @ B )
| ~ ( is_fun_pname_bool @ A )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ A ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ B ) )
| ( ( insert_pname @ X_2 @ A )
!= ( insert_pname @ X_2 @ B ) )
| ( A = B ) )
& ! [X_2: $i,A: $i] :
( ~ ( is_fun_pname_bool @ B )
| ~ ( is_fun_pname_bool @ A )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ A ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ B ) )
| ( A != B )
| ( ( insert_pname @ X_2 @ A )
= ( insert_pname @ X_2 @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[144]) ).
thf(530,plain,
( ( ! [B: $i] :
( ! [X_2: $i,A: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ X_2 ) @ A ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ X_2 ) @ B ) )
| ( ( insert_nat @ X_2 @ A )
!= ( insert_nat @ X_2 @ B ) )
| ( A = B ) )
& ! [X_2: $i,A: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ X_2 ) @ A ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ X_2 ) @ B ) )
| ( A != B )
| ( ( insert_nat @ X_2 @ A )
= ( insert_nat @ X_2 @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[145]) ).
thf(531,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 ) ) )
& ! [A: $i,X_2: $i] :
( ~ ( is_a @ Y_1 )
| ~ ( is_a @ X_2 )
| ( Y_1 != X_2 )
| ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ Y_1 @ A ) @ X_2 ) ) )
& ! [A: $i,X_2: $i] :
( ~ ( is_a @ Y_1 )
| ~ ( is_a @ X_2 )
| ~ ( hBOOL @ ( hAPP_a_bool @ A @ X_2 ) )
| ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ Y_1 @ A ) @ X_2 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[146]) ).
thf(532,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 ) ) )
& ! [A: $i,X_2: $i] :
( ~ ( is_pname @ Y_1 )
| ~ ( is_pname @ X_2 )
| ( Y_1 != X_2 )
| ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ Y_1 @ A ) @ X_2 ) ) )
& ! [A: $i,X_2: $i] :
( ~ ( is_pname @ Y_1 )
| ~ ( is_pname @ X_2 )
| ~ ( hBOOL @ ( hAPP_pname_bool @ A @ X_2 ) )
| ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ Y_1 @ A ) @ X_2 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[147]) ).
thf(533,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 ) ) )
& ! [A: $i,X_2: $i] :
( ( Y_1 != X_2 )
| ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ Y_1 @ A ) @ X_2 ) ) )
& ! [A: $i,X_2: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ A @ X_2 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ Y_1 @ A ) @ X_2 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[148]) ).
thf(534,plain,
( ( ! [A_1: $i] :
( ! [B_1: $i] :
( ~ ( is_a @ A_1 )
| ~ ( is_a @ B_1 )
| ! [A: $i] :
( ~ ( 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 ) ) ) )
& ! [B_1: $i] :
( ~ ( is_a @ A_1 )
| ~ ( is_a @ B_1 )
| ( A_1 != B_1 )
| ! [A: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_1 ) @ ( insert_a @ B_1 @ A ) ) ) )
& ! [B_1: $i] :
( ~ ( is_a @ A_1 )
| ~ ( is_a @ B_1 )
| ! [A: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_1 ) @ A ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_1 ) @ ( insert_a @ B_1 @ A ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[149]) ).
thf(535,plain,
( ( ! [A_1: $i] :
( ! [B_1: $i] :
( ~ ( is_pname @ A_1 )
| ~ ( is_pname @ B_1 )
| ! [A: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A_1 ) @ ( insert_pname @ B_1 @ A ) ) )
| ( A_1 = B_1 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A_1 ) @ A ) ) ) )
& ! [B_1: $i] :
( ~ ( is_pname @ A_1 )
| ~ ( is_pname @ B_1 )
| ( A_1 != B_1 )
| ! [A: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A_1 ) @ ( insert_pname @ B_1 @ A ) ) ) )
& ! [B_1: $i] :
( ~ ( is_pname @ A_1 )
| ~ ( is_pname @ B_1 )
| ! [A: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A_1 ) @ A ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A_1 ) @ ( insert_pname @ B_1 @ A ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[150]) ).
thf(536,plain,
( ( ! [A_1: $i] :
( ! [B_1: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A_1 ) @ ( insert_nat @ B_1 @ A ) ) )
| ( A_1 = B_1 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A_1 ) @ A ) ) )
& ! [B_1: $i] :
( ( A_1 != B_1 )
| ! [A: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A_1 ) @ ( insert_nat @ B_1 @ A ) ) ) )
& ! [B_1: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A_1 ) @ A ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A_1 ) @ ( insert_nat @ B_1 @ A ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[151]) ).
thf(537,plain,
( ( ! [A_1: $i,B_1: $i] :
( ~ ( is_a @ A_1 )
| ~ ( is_a @ B_1 )
| ! [A: $i] :
( ~ ( 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(extcnf_combined,[status(esa)],[173]) ).
thf(538,plain,
( ( ! [A_1: $i,B_1: $i] :
( ~ ( is_pname @ A_1 )
| ~ ( is_pname @ B_1 )
| ! [A: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A_1 ) @ ( insert_pname @ B_1 @ A ) ) )
| ( A_1 = B_1 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A_1 ) @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[174]) ).
thf(539,plain,
( ( ! [A_1: $i,B_1: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A_1 ) @ ( insert_nat @ B_1 @ A ) ) )
| ( A_1 = B_1 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A_1 ) @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[175]) ).
thf(540,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 ) ) ) )
& ! [A_1: $i] :
( ( A_1 != B_1 )
| ! [B: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_1 ) @ ( insert_a @ B_1 @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[176]) ).
thf(541,plain,
( ( ! [B_1: $i] :
( ! [A_1: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A_1 ) @ B ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A_1 ) @ ( insert_pname @ B_1 @ B ) ) ) )
& ! [A_1: $i] :
( ( A_1 != B_1 )
| ! [B: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A_1 ) @ ( insert_pname @ B_1 @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[177]) ).
thf(542,plain,
( ( ! [B_1: $i] :
( ! [A_1: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A_1 ) @ B ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A_1 ) @ ( insert_nat @ B_1 @ B ) ) ) )
& ! [A_1: $i] :
( ( A_1 != B_1 )
| ! [B: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A_1 ) @ ( insert_nat @ B_1 @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[178]) ).
thf(543,plain,
( ( ! [C_1: $i,A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C_1 ) @ A ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C_1 ) @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[179]) ).
thf(544,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(extcnf_combined,[status(esa)],[180]) ).
thf(545,plain,
( ( ! [C_1: $i,A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C_1 ) @ A ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C_1 ) @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[181]) ).
thf(546,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(extcnf_combined,[status(esa)],[182]) ).
thf(547,plain,
( ( ! [A: $i,B: $i] :
( ~ ( is_fun_pname_bool @ A )
| ~ ( is_fun_pname_bool @ 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 ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[183]) ).
thf(548,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(extcnf_combined,[status(esa)],[184]) ).
thf(549,plain,
( ( ! [A: $i,B_1: $i,F: $i,X_2: $i] :
( ( B_1
!= ( hAPP_pname_a @ F @ X_2 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ A ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B_1 ) @ ( image_pname_a @ F @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[185]) ).
thf(550,plain,
( ( ! [F: $i,A: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_pname_a @ F @ A ) ) )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK12_X_1 @ A @ F ) ) @ A ) )
& ( is_pname @ ( sK12_X_1 @ A @ F ) )
& ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ ( hAPP_f759274231e_bool @ ( cOMBC_1058051404l_bool @ member_pname ) @ A ) ) @ ( hAPP_a93125764e_bool @ ( cOMBC_pname_a_bool @ ( cOMBB_1897541054_pname @ fequal_a @ F ) ) @ ( hAPP_pname_a @ F @ ( sK12_X_1 @ A @ F ) ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[186]) ).
thf(551,plain,
( ( ! [Na: $i,N_3: $i,F: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_nat_fun_a_bool @ F @ ( sK13_N_2 @ F @ N_3 @ Na ) ) ) @ ( hAPP_nat_fun_a_bool @ F @ ( hAPP_nat_nat @ suc @ ( sK13_N_2 @ F @ N_3 @ Na ) ) ) ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Na ) @ N_3 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_nat_fun_a_bool @ F @ Na ) ) @ ( hAPP_nat_fun_a_bool @ F @ N_3 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[187]) ).
thf(552,plain,
( ( ! [Na: $i,N_3: $i,F: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ F @ ( sK14_N_2 @ F @ N_3 @ Na ) ) ) @ ( hAPP_nat_nat @ F @ ( hAPP_nat_nat @ suc @ ( sK14_N_2 @ F @ N_3 @ Na ) ) ) ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Na ) @ N_3 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ F @ Na ) ) @ ( hAPP_nat_nat @ F @ N_3 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[188]) ).
thf(553,plain,
( ( ! [Na: $i,N_3: $i,F: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_n1025906991e_bool @ F @ ( sK15_N_2 @ F @ N_3 @ Na ) ) ) @ ( hAPP_n1025906991e_bool @ F @ ( hAPP_nat_nat @ suc @ ( sK15_N_2 @ F @ N_3 @ Na ) ) ) ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Na ) @ N_3 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_n1025906991e_bool @ F @ Na ) ) @ ( hAPP_n1025906991e_bool @ F @ N_3 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[189]) ).
thf(554,plain,
( ( ! [Na: $i,N_3: $i,F: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( hAPP_n1699378549t_bool @ F @ ( sK16_N_2 @ F @ N_3 @ Na ) ) ) @ ( hAPP_n1699378549t_bool @ F @ ( hAPP_nat_nat @ suc @ ( sK16_N_2 @ F @ N_3 @ Na ) ) ) ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Na ) @ N_3 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( hAPP_n1699378549t_bool @ F @ Na ) ) @ ( hAPP_n1699378549t_bool @ F @ N_3 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[190]) ).
thf(555,plain,
( ( ! [F: $i,A: $i,B: $i] :
( ~ ( is_fun_a_bool @ B )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ ( image_pname_a @ F @ A ) ) )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( sK17_C_2 @ B @ A @ F ) ) @ A ) )
& ( is_fun_pname_bool @ ( sK17_C_2 @ B @ A @ F ) )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( sK17_C_2 @ B @ A @ F ) ) )
& ( B
= ( image_pname_a @ F @ ( sK17_C_2 @ B @ A @ F ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[191]) ).
thf(556,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(extcnf_combined,[status(esa)],[192]) ).
thf(557,plain,
( ( ! [L: $i,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 @ ( hAPP_nat_nat @ ( minus_minus_nat @ L ) @ N_1 ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ L ) @ M_2 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[194]) ).
thf(558,plain,
( ( ! [L: $i,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 @ ( hAPP_nat_nat @ ( minus_minus_nat @ M_2 ) @ L ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ N_1 ) @ L ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[195]) ).
thf(559,plain,
( ( ! [I_1: $i,N_1: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ I_1 ) @ N_1 ) )
| ( ( hAPP_nat_nat @ ( minus_minus_nat @ N_1 ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ N_1 ) @ I_1 ) )
= I_1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[196]) ).
thf(560,plain,
( ( ! [Na: $i] :
( ! [K: $i,M_3: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ K ) @ M_3 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ K ) @ Na ) )
| ( ( hAPP_nat_nat @ ( minus_minus_nat @ M_3 ) @ K )
!= ( hAPP_nat_nat @ ( minus_minus_nat @ Na ) @ K ) )
| ( M_3 = Na ) )
& ! [K: $i,M_3: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ K ) @ M_3 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ K ) @ Na ) )
| ( M_3 != Na )
| ( ( hAPP_nat_nat @ ( minus_minus_nat @ M_3 ) @ K )
= ( hAPP_nat_nat @ ( minus_minus_nat @ Na ) @ K ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[197]) ).
thf(561,plain,
( ( ! [N_1: $i,K_1: $i,M_2: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ K_1 ) @ M_2 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ K_1 ) @ N_1 ) )
| ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ M_2 ) @ K_1 ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ N_1 ) @ K_1 ) )
= ( hAPP_nat_nat @ ( minus_minus_nat @ M_2 ) @ N_1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[198]) ).
thf(562,plain,
( ( ! [Na: $i] :
( ! [K: $i,M_3: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ K ) @ M_3 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ K ) @ Na ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ M_3 ) @ K ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ Na ) @ K ) ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ M_3 ) @ Na ) ) )
& ! [K: $i,M_3: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ K ) @ M_3 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ K ) @ Na ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ M_3 ) @ Na ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ M_3 ) @ K ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ Na ) @ K ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[199]) ).
thf(563,plain,
( ( ! [M_3: $i,Na: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ Na ) ) @ M_3 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ M_3 ) @ Na ) ) )
& ! [M_3: $i,Na: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ M_3 ) @ Na ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ Na ) ) @ M_3 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[203]) ).
thf(564,plain,
( ( ! [M_3: $i,Na: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ M_3 ) @ ( hAPP_nat_nat @ suc @ Na ) ) )
| ( M_3
= ( hAPP_nat_nat @ suc @ Na ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ M_3 ) @ Na ) ) )
& ! [M_3: $i,Na: $i] :
( ( M_3
!= ( hAPP_nat_nat @ suc @ Na ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ M_3 ) @ ( hAPP_nat_nat @ suc @ Na ) ) ) )
& ! [M_3: $i,Na: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ M_3 ) @ Na ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ M_3 ) @ ( hAPP_nat_nat @ suc @ Na ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[204]) ).
thf(565,plain,
( ( ! [Na: $i,M_3: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ Na ) ) @ ( hAPP_nat_nat @ suc @ M_3 ) ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Na ) @ M_3 ) ) )
& ! [Na: $i,M_3: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Na ) @ M_3 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ Na ) ) @ ( hAPP_nat_nat @ suc @ M_3 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[205]) ).
thf(566,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 @ M_2 ) @ ( hAPP_nat_nat @ suc @ N_1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[206]) ).
thf(567,plain,
( ( ! [M_2: $i,N_1: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ M_2 ) @ ( hAPP_nat_nat @ suc @ N_1 ) ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ M_2 ) @ N_1 ) )
| ( M_2
= ( hAPP_nat_nat @ suc @ N_1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[207]) ).
thf(568,plain,
( ( ! [M_2: $i,N_1: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ M_2 ) ) @ N_1 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ M_2 ) @ N_1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[208]) ).
thf(569,plain,
( ( ! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[209]) ).
thf(570,plain,
( ( ! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[210]) ).
thf(571,plain,
( ( ! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
| ~ ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ A ) @ B ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[211]) ).
thf(572,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(extcnf_combined,[status(esa)],[212]) ).
thf(573,plain,
( ( ! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
| ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ A ) @ B ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[213]) ).
thf(574,plain,
( ( ! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
| ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ A ) @ B ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[214]) ).
thf(575,plain,
( ( ! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[215]) ).
thf(576,plain,
( ( ! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[216]) ).
thf(577,plain,
( ( ! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[217]) ).
thf(578,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(extcnf_combined,[status(esa)],[218]) ).
thf(579,plain,
( ( ! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[219]) ).
thf(580,plain,
( ( ! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[220]) ).
thf(581,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 ) ) )
& ! [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(extcnf_combined,[status(esa)],[221]) ).
thf(582,plain,
( ( ! [A_1: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ A_1 @ A ) ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) ) )
& ! [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(extcnf_combined,[status(esa)],[222]) ).
thf(583,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 ) ) )
& ! [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(extcnf_combined,[status(esa)],[223]) ).
thf(584,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 ) ) )
& ! [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(extcnf_combined,[status(esa)],[224]) ).
thf(585,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 ) ) )
& ! [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(extcnf_combined,[status(esa)],[225]) ).
thf(586,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 ) ) )
& ! [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(extcnf_combined,[status(esa)],[226]) ).
thf(587,plain,
( ( ! [Pa: $i,Q_1: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ Pa ) ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ Q_1 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ Pa ) @ Q_1 ) ) ) ) )
& ! [Pa: $i] :
( ! [Q_1: $i] :
~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ Pa ) @ Q_1 ) ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ Pa ) ) ) )
& ! [Pa: $i,Q_1: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ Pa ) @ Q_1 ) ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ Q_1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[227]) ).
thf(588,plain,
( ( ! [Pa: $i,Q_1: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ Pa ) ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ Q_1 ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ Pa ) @ Q_1 ) ) ) ) )
& ! [Pa: $i] :
( ! [Q_1: $i] :
~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ Pa ) @ Q_1 ) ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ Pa ) ) ) )
& ! [Pa: $i,Q_1: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ Pa ) @ Q_1 ) ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ Q_1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[228]) ).
thf(589,plain,
( ( ! [Pa: $i,Q_1: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ Pa ) ) )
| ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ Q_1 ) ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ Pa ) @ Q_1 ) ) ) ) )
& ! [Pa: $i] :
( ! [Q_1: $i] :
~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ Pa ) @ Q_1 ) ) ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ Pa ) ) ) )
& ! [Pa: $i,Q_1: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ Pa ) @ Q_1 ) ) ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ Q_1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[229]) ).
thf(590,plain,
( ( ! [Pa: $i,Q_1: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ Pa ) ) )
| ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ Q_1 ) ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ Pa ) @ Q_1 ) ) ) ) )
& ! [Pa: $i] :
( ! [Q_1: $i] :
~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ Pa ) @ Q_1 ) ) ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ Pa ) ) ) )
& ! [Pa: $i,Q_1: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ Pa ) @ Q_1 ) ) ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ Q_1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[230]) ).
thf(591,plain,
( ( ! [Pa: $i,Q_1: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ Pa ) ) )
| ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ Q_1 ) ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ Pa ) @ Q_1 ) ) ) ) )
& ! [Pa: $i] :
( ! [Q_1: $i] :
~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ Pa ) @ Q_1 ) ) ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ Pa ) ) ) )
& ! [Pa: $i,Q_1: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ Pa ) @ Q_1 ) ) ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ Q_1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[231]) ).
thf(592,plain,
( ( ! [Pa: $i,Q_1: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ Pa ) ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ Q_1 ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ Pa ) @ Q_1 ) ) ) ) )
& ! [Pa: $i] :
( ! [Q_1: $i] :
~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ Pa ) @ Q_1 ) ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ Pa ) ) ) )
& ! [Pa: $i,Q_1: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ Pa ) @ Q_1 ) ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ Q_1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[232]) ).
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(extcnf_combined,[status(esa)],[236]) ).
thf(594,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(extcnf_combined,[status(esa)],[237]) ).
thf(595,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(extcnf_combined,[status(esa)],[238]) ).
thf(596,plain,
( ( ! [N_1: $i] :
( N_1
!= ( hAPP_nat_nat @ suc @ N_1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[239]) ).
thf(597,plain,
( ( ! [N_1: $i] :
( ( hAPP_nat_nat @ suc @ N_1 )
!= N_1 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[240]) ).
thf(598,plain,
( ( ! [Nat_1: $i,Nat: $i] :
( ( ( hAPP_nat_nat @ suc @ Nat_1 )
!= ( hAPP_nat_nat @ suc @ Nat ) )
| ( Nat_1 = Nat ) )
& ! [Nat_1: $i,Nat: $i] :
( ( Nat_1 != Nat )
| ( ( hAPP_nat_nat @ suc @ Nat_1 )
= ( hAPP_nat_nat @ suc @ Nat ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[241]) ).
thf(599,plain,
( ( ! [X: $i,Y: $i] :
( ( ( hAPP_nat_nat @ suc @ X )
!= ( hAPP_nat_nat @ suc @ Y ) )
| ( X = Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[242]) ).
thf(600,plain,
( ( ! [N_1: $i,M_2: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ N_1 ) @ M_2 ) )
| ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ suc @ M_2 ) ) @ N_1 )
= ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( minus_minus_nat @ M_2 ) @ N_1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[245]) ).
thf(601,plain,
( ( ! [Q_1: $i,Pa: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ Pa ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ Pa ) @ Q_1 ) ) ) ) )
& ! [Q_1: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ Q_1 ) ) )
| ! [Pa: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ Pa ) @ Q_1 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[246]) ).
thf(602,plain,
( ( ! [Q_1: $i,Pa: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ Pa ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ Pa ) @ Q_1 ) ) ) ) )
& ! [Q_1: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ Q_1 ) ) )
| ! [Pa: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ Pa ) @ Q_1 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[247]) ).
thf(603,plain,
( ( ! [Q_1: $i,Pa: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ Pa ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ Pa ) @ Q_1 ) ) ) ) )
& ! [Q_1: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ Q_1 ) ) )
| ! [Pa: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ Pa ) @ Q_1 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[248]) ).
thf(604,plain,
( ( ! [Q_1: $i,Pa: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ Pa ) ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fconj @ Pa ) @ Q_1 ) ) ) ) )
& ! [Q_1: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ Q_1 ) ) )
| ! [Pa: $i] : ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fconj @ Pa ) @ Q_1 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[249]) ).
thf(605,plain,
( ( ! [Q_1: $i,Pa: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ Pa ) ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fconj @ Pa ) @ Q_1 ) ) ) ) )
& ! [Q_1: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ Q_1 ) ) )
| ! [Pa: $i] : ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fconj @ Pa ) @ Q_1 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[250]) ).
thf(606,plain,
( ( ! [Q_1: $i,Pa: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ Pa ) ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fconj @ Pa ) @ Q_1 ) ) ) ) )
& ! [Q_1: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ Q_1 ) ) )
| ! [Pa: $i] : ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fconj @ Pa ) @ Q_1 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[251]) ).
thf(607,plain,
( ( ! [X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_2 ) @ A ) )
| ( ( hAPP_fun_a_bool_nat @ finite_card_a @ ( insert_a @ X_2 @ A ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_fun_a_bool_nat @ finite_card_a @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[252]) ).
thf(608,plain,
( ( ! [X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ A ) )
| ( ( hAPP_f921600141ol_nat @ finite_card_pname @ ( insert_pname @ X_2 @ A ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f921600141ol_nat @ finite_card_pname @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[253]) ).
thf(609,plain,
( ( ! [X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ X_2 ) @ A ) )
| ( ( hAPP_f22106695ol_nat @ finite_card_nat @ ( insert_nat @ X_2 @ A ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f22106695ol_nat @ finite_card_nat @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[254]) ).
thf(610,plain,
( ( ! [X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ X_2 ) @ A ) )
| ( ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( insert_fun_a_bool @ X_2 @ A ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[255]) ).
thf(611,plain,
( ( ! [X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ X_2 ) @ A ) )
| ( ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( insert1325755072e_bool @ X_2 @ A ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[256]) ).
thf(612,plain,
( ( ! [X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ X_2 ) @ A ) )
| ( ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( insert_fun_nat_bool @ X_2 @ A ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[257]) ).
thf(613,plain,
( ( ! [X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_2 ) @ A ) )
| ( ( hAPP_fun_a_bool_nat @ finite_card_a @ ( insert_a @ X_2 @ A ) )
= ( hAPP_fun_a_bool_nat @ finite_card_a @ A ) ) )
& ! [X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_2 ) @ A ) )
| ( ( hAPP_fun_a_bool_nat @ finite_card_a @ ( insert_a @ X_2 @ A ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_fun_a_bool_nat @ finite_card_a @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[258]) ).
thf(614,plain,
( ( ! [X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ A ) )
| ( ( hAPP_f921600141ol_nat @ finite_card_pname @ ( insert_pname @ X_2 @ A ) )
= ( hAPP_f921600141ol_nat @ finite_card_pname @ A ) ) )
& ! [X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ A ) )
| ( ( hAPP_f921600141ol_nat @ finite_card_pname @ ( insert_pname @ X_2 @ A ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f921600141ol_nat @ finite_card_pname @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[259]) ).
thf(615,plain,
( ( ! [X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ X_2 ) @ A ) )
| ( ( hAPP_f22106695ol_nat @ finite_card_nat @ ( insert_nat @ X_2 @ A ) )
= ( hAPP_f22106695ol_nat @ finite_card_nat @ A ) ) )
& ! [X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ X_2 ) @ A ) )
| ( ( hAPP_f22106695ol_nat @ finite_card_nat @ ( insert_nat @ X_2 @ A ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f22106695ol_nat @ finite_card_nat @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[260]) ).
thf(616,plain,
( ( ! [X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A ) )
| ~ ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ X_2 ) @ A ) )
| ( ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( insert_fun_a_bool @ X_2 @ A ) )
= ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ A ) ) )
& ! [X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ X_2 ) @ A ) )
| ( ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( insert_fun_a_bool @ X_2 @ A ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[261]) ).
thf(617,plain,
( ( ! [X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) )
| ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ X_2 ) @ A ) )
| ( ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( insert1325755072e_bool @ X_2 @ A ) )
= ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ A ) ) )
& ! [X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ X_2 ) @ A ) )
| ( ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( insert1325755072e_bool @ X_2 @ A ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[262]) ).
thf(618,plain,
( ( ! [X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A ) )
| ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ X_2 ) @ A ) )
| ( ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( insert_fun_nat_bool @ X_2 @ A ) )
= ( hAPP_f696928925ol_nat @ finite346522414t_bool @ A ) ) )
& ! [X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ X_2 ) @ A ) )
| ( ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( insert_fun_nat_bool @ X_2 @ A ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[263]) ).
thf(619,plain,
( ( ! [X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ A ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( insert_a @ X_2 @ A ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[264]) ).
thf(620,plain,
( ( ! [X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ A ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( insert_nat @ X_2 @ A ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[265]) ).
thf(621,plain,
( ( ! [X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ A ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( insert_pname @ X_2 @ A ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[266]) ).
thf(622,plain,
( ( ! [X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ A ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( insert_fun_a_bool @ X_2 @ A ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[267]) ).
thf(623,plain,
( ( ! [X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ A ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( insert1325755072e_bool @ X_2 @ A ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[268]) ).
thf(624,plain,
( ( ! [X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ A ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( insert_fun_nat_bool @ X_2 @ A ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[269]) ).
thf(625,plain,
( ( ! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ B ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ A ) ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[270]) ).
thf(626,plain,
( ( ! [A: $i,B: $i] :
( ~ ( is_fun_a_bool @ A )
| ~ ( is_fun_a_bool @ B )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ B ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ A ) ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[271]) ).
thf(627,plain,
( ( ! [A: $i,B: $i] :
( ~ ( is_fun_pname_bool @ A )
| ~ ( is_fun_pname_bool @ B )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ B ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ A ) ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[272]) ).
thf(628,plain,
( ( ! [A: $i,B: $i] :
( ~ ( is_fun949378684l_bool @ A )
| ~ ( is_fun949378684l_bool @ B )
| ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
| ~ ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ B ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ A ) ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[273]) ).
thf(629,plain,
( ( ! [A: $i,B: $i] :
( ~ ( is_fun1661590463l_bool @ A )
| ~ ( is_fun1661590463l_bool @ B )
| ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
| ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ B ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ A ) ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[274]) ).
thf(630,plain,
( ( ! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
| ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ B ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ A ) ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[275]) ).
thf(631,plain,
( ( ! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ A ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[276]) ).
thf(632,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_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ A ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[277]) ).
thf(633,plain,
( ( ! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ A ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[278]) ).
thf(634,plain,
( ( ! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
| ~ ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ A ) @ B ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ A ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[279]) ).
thf(635,plain,
( ( ! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
| ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ A ) @ B ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ A ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[280]) ).
thf(636,plain,
( ( ! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
| ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ A ) @ B ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ A ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[281]) ).
thf(637,plain,
( ( ! [F: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( image_1854862208_pname @ F @ A ) ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[282]) ).
thf(638,plain,
( ( ! [F: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( image_1283814551_pname @ F @ A ) ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[283]) ).
thf(639,plain,
( ( ! [F: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( image_1921560913_pname @ F @ A ) ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[284]) ).
thf(640,plain,
( ( ! [F: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( image_nat_fun_a_bool @ F @ A ) ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[285]) ).
thf(641,plain,
( ( ! [F: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( image_1655916159e_bool @ F @ A ) ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[286]) ).
thf(642,plain,
( ( ! [F: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( image_26036933t_bool @ F @ A ) ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[287]) ).
thf(643,plain,
( ( ! [F: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_nat_a @ F @ A ) ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[288]) ).
thf(644,plain,
( ( ! [F: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( image_112932426a_bool @ F @ A ) ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[289]) ).
thf(645,plain,
( ( ! [F: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( image_47868345e_bool @ F @ A ) ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[290]) ).
thf(646,plain,
( ( ! [F: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( image_2129980159t_bool @ F @ A ) ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[291]) ).
thf(647,plain,
( ( ! [F: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( image_pname_pname @ F @ A ) ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[292]) ).
thf(648,plain,
( ( ! [F: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_a_a @ F @ A ) ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[293]) ).
thf(649,plain,
( ( ! [F: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_fun_nat_bool_a @ F @ A ) ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[294]) ).
thf(650,plain,
( ( ! [F: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_876012084bool_a @ F @ A ) ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[295]) ).
thf(651,plain,
( ( ! [F: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_fun_a_bool_a @ F @ A ) ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[296]) ).
thf(652,plain,
( ( ! [F: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_573985017bool_a @ F @ A ) ) ) @ ( hAPP_f1253658590ol_nat @ finite1659325229l_bool @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[297]) ).
thf(653,plain,
( ( ! [F: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_349102846bool_a @ F @ A ) ) ) @ ( hAPP_f98387925ol_nat @ finite269641166l_bool @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[298]) ).
thf(654,plain,
( ( ! [F: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_526090948bool_a @ F @ A ) ) ) @ ( hAPP_f1690079119ol_nat @ finite1352710292l_bool @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[299]) ).
thf(655,plain,
( ( ! [F: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_pname_a @ F @ A ) ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[300]) ).
thf(656,plain,
( ( ! [F: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( image_nat_pname @ F @ A ) ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[301]) ).
thf(657,plain,
( ( ! [F: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( image_a_pname @ F @ A ) ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[302]) ).
thf(658,plain,
( ( ! [F: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( image_fun_a_bool_nat @ F @ A ) ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[303]) ).
thf(659,plain,
( ( ! [F: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( image_1551609309ol_nat @ F @ A ) ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[304]) ).
thf(660,plain,
( ( ! [F: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( image_496248727ol_nat @ F @ A ) ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[305]) ).
thf(661,plain,
( ( ! [F: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( image_a_nat @ F @ A ) ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[306]) ).
thf(662,plain,
( ( ! [F: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( image_pname_nat @ F @ A ) ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[307]) ).
thf(663,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(extcnf_combined,[status(esa)],[308]) ).
thf(664,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(extcnf_combined,[status(esa)],[309]) ).
thf(665,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(extcnf_combined,[status(esa)],[310]) ).
thf(666,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(extcnf_combined,[status(esa)],[311]) ).
thf(667,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(extcnf_combined,[status(esa)],[312]) ).
thf(668,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(extcnf_combined,[status(esa)],[313]) ).
thf(669,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(extcnf_combined,[status(esa)],[314]) ).
thf(670,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(extcnf_combined,[status(esa)],[315]) ).
thf(671,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(extcnf_combined,[status(esa)],[316]) ).
thf(672,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ F_1 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_nat_pname @ H @ F_1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[317]) ).
thf(673,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ F_1 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_pname_nat @ H @ F_1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[318]) ).
thf(674,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ F_1 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_fun_a_bool_a @ H @ F_1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[319]) ).
thf(675,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ F_1 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_876012084bool_a @ H @ F_1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[320]) ).
thf(676,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ F_1 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_fun_nat_bool_a @ H @ F_1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[321]) ).
thf(677,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(extcnf_combined,[status(esa)],[322]) ).
thf(678,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(extcnf_combined,[status(esa)],[323]) ).
thf(679,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ F_1 ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( image_2129980159t_bool @ H @ F_1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[324]) ).
thf(680,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ F_1 ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( image_47868345e_bool @ H @ F_1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[325]) ).
thf(681,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ F_1 ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( image_112932426a_bool @ H @ F_1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[326]) ).
thf(682,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ F_1 ) )
| ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ ( image_1420695166l_bool @ H @ F_1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[327]) ).
thf(683,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ F_1 ) )
| ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ ( image_1642285373l_bool @ H @ F_1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[328]) ).
thf(684,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ F_1 ) )
| ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ ( image_1154884483l_bool @ H @ F_1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[329]) ).
thf(685,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ F_1 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_nat_a @ H @ F_1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[330]) ).
thf(686,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ F_1 ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( image_26036933t_bool @ H @ F_1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[331]) ).
thf(687,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ F_1 ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( image_1655916159e_bool @ H @ F_1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[332]) ).
thf(688,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ F_1 ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( image_nat_fun_a_bool @ H @ F_1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[333]) ).
thf(689,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ F_1 ) )
| ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ ( image_1208015684l_bool @ H @ F_1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[334]) ).
thf(690,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ F_1 ) )
| ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ ( image_1874789623l_bool @ H @ F_1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[335]) ).
thf(691,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ F_1 ) )
| ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ ( image_1607900221l_bool @ H @ F_1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[336]) ).
thf(692,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ F_1 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_a_pname @ H @ F_1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[337]) ).
thf(693,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ F_1 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1921560913_pname @ H @ F_1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[338]) ).
thf(694,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ F_1 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1283814551_pname @ H @ F_1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[339]) ).
thf(695,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ F_1 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1854862208_pname @ H @ F_1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[340]) ).
thf(696,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ F_1 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_990671762_pname @ H @ F_1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[341]) ).
thf(697,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ F_1 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1705983821_pname @ H @ F_1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[342]) ).
thf(698,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ F_1 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1604018183_pname @ H @ F_1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[343]) ).
thf(699,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ F_1 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_a_nat @ H @ F_1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[344]) ).
thf(700,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ F_1 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_496248727ol_nat @ H @ F_1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[345]) ).
thf(701,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ F_1 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_1551609309ol_nat @ H @ F_1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[346]) ).
thf(702,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ F_1 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_fun_a_bool_nat @ H @ F_1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[347]) ).
thf(703,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ F_1 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_1802975832ol_nat @ H @ F_1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[348]) ).
thf(704,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ F_1 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_1079571347ol_nat @ H @ F_1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[349]) ).
thf(705,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ F_1 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_2089570637ol_nat @ H @ F_1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[350]) ).
thf(706,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(extcnf_combined,[status(esa)],[351]) ).
thf(707,plain,
( ( ! [A: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A ) )
| ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ ( collec1015864663l_bool @ ( hAPP_f1772781669l_bool @ ( cOMBC_595898202l_bool @ ord_le1454342156l_bool ) @ A ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[352]) ).
thf(708,plain,
( ( ! [A: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) )
| ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ ( collec1613912337l_bool @ ( hAPP_f510955609l_bool @ ( cOMBC_7971162l_bool @ ord_le675606854l_bool ) @ A ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[353]) ).
thf(709,plain,
( ( ! [A: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A ) )
| ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ ( collec707592106l_bool @ ( hAPP_f1434722111l_bool @ ( cOMBC_331553030l_bool @ ord_le1375614389l_bool ) @ A ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[354]) ).
thf(710,plain,
( ( ! [A: $i] :
( ~ ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ A ) )
| ( hBOOL @ ( hAPP_f1363661463l_bool @ finite1343359508l_bool @ ( collec1635217238l_bool @ ( hAPP_f1050622307l_bool @ ( cOMBC_636888218l_bool @ ord_le967226251l_bool ) @ A ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[355]) ).
thf(711,plain,
( ( ! [A: $i] :
( ~ ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ A ) )
| ( hBOOL @ ( hAPP_f595608956l_bool @ finite1491191519l_bool @ ( collec792590109l_bool @ ( hAPP_f1759205631l_bool @ ( cOMBC_336095980l_bool @ ord_le1375671464l_bool ) @ A ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[356]) ).
thf(712,plain,
( ( ! [A: $i] :
( ~ ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ A ) )
| ( hBOOL @ ( hAPP_f1295398978l_bool @ finite719726885l_bool @ ( collec1874991203l_bool @ ( hAPP_f760187903l_bool @ ( cOMBC_1269652216l_bool @ ord_le65145710l_bool ) @ A ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[357]) ).
thf(713,plain,
( ( ! [A: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ ord_le1311769555a_bool ) @ A ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[358]) ).
thf(714,plain,
( ( ! [A: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ ord_le313189616e_bool ) @ A ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[359]) ).
thf(715,plain,
( ( ! [A: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( hAPP_f103356543l_bool @ ( cOMBC_1693257480l_bool @ ord_le1568362934t_bool ) @ A ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[360]) ).
thf(716,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(extcnf_combined,[status(esa)],[361]) ).
thf(717,plain,
( ( ! [B_1_1: $i] :
( ~ ( is_fun_a_bool @ B_1_1 )
| ( is_fun949378684l_bool @ ( p @ B_1_1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[362]) ).
thf(718,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_fun1661590463l_bool @ B_2 )
| ( is_fun1661590463l_bool @ ( hAPP_f559147733l_bool @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[370]) ).
thf(719,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_fun1661590463l_bool @ B_2 )
| ( is_bool @ ( hAPP_f1935102916l_bool @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[371]) ).
thf(720,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_fun949378684l_bool @ B_2 )
| ( is_fun949378684l_bool @ ( hAPP_f2117159681l_bool @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[372]) ).
thf(721,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_fun949378684l_bool @ B_2 )
| ( is_bool @ ( hAPP_f621171935l_bool @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[373]) ).
thf(722,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_fun_pname_bool @ B_2 )
| ( is_fun1661590463l_bool @ ( hAPP_f434788991l_bool @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[375]) ).
thf(723,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_fun_pname_bool @ B_2 )
| ( is_fun_pname_bool @ ( hAPP_f759274231e_bool @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[376]) ).
thf(724,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_fun_a_bool @ B_2 )
| ( is_fun_a_bool @ ( hAPP_f2050579477a_bool @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[377]) ).
thf(725,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_bool @ B_2 )
| ( is_bool @ ( hAPP_bool_bool @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[380]) ).
thf(726,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_pname @ B_2 )
| ( is_fun_pname_bool @ ( hAPP_p61793385e_bool @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[381]) ).
thf(727,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_pname @ B_2 )
| ( is_fun_a_bool @ ( hAPP_p1534023578a_bool @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[382]) ).
thf(728,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_fun_pname_bool @ B_1_1 )
| ~ ( is_pname @ B_2 )
| ( is_bool @ ( hAPP_pname_bool @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[383]) ).
thf(729,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_a @ B_2 )
| ( is_fun_pname_bool @ ( hAPP_a93125764e_bool @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[384]) ).
thf(730,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_a @ B_2 )
| ( is_fun_a_bool @ ( hAPP_a_fun_a_bool @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[385]) ).
thf(731,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_a @ B_2 )
| ~ ( is_fun_a_bool @ B_1_1 )
| ( is_bool @ ( hAPP_a_bool @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[386]) ).
thf(732,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_fun1661590463l_bool @ B_2 )
| ~ ( is_fun_pname_bool @ B_1_1 )
| ( is_fun1661590463l_bool @ ( insert1325755072e_bool @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[387]) ).
thf(733,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_fun949378684l_bool @ B_2 )
| ~ ( is_fun_a_bool @ B_1_1 )
| ( is_fun949378684l_bool @ ( insert_fun_a_bool @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[388]) ).
thf(734,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_fun_pname_bool @ B_2 )
| ~ ( is_pname @ B_1_1 )
| ( is_fun_pname_bool @ ( insert_pname @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[389]) ).
thf(735,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_fun1661590463l_bool @ B_2 )
| ( is_fun_pname_bool @ ( image_1283814551_pname @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[398]) ).
thf(736,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_fun1661590463l_bool @ B_2 )
| ( is_fun_a_bool @ ( image_876012084bool_a @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[399]) ).
thf(737,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_fun949378684l_bool @ B_2 )
| ( is_fun_pname_bool @ ( image_1854862208_pname @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[400]) ).
thf(738,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_fun949378684l_bool @ B_2 )
| ( is_fun_a_bool @ ( image_fun_a_bool_a @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[401]) ).
thf(739,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_fun_pname_bool @ B_2 )
| ( is_fun1661590463l_bool @ ( image_47868345e_bool @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[406]) ).
thf(740,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_fun_pname_bool @ B_2 )
| ( is_fun949378684l_bool @ ( image_112932426a_bool @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[407]) ).
thf(741,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_fun_pname_bool @ B_2 )
| ( is_fun_pname_bool @ ( image_pname_pname @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[408]) ).
thf(742,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_fun_a_bool @ B_2 )
| ( is_fun_pname_bool @ ( image_a_pname @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[409]) ).
thf(743,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_fun_a_bool @ B_2 )
| ( is_fun_a_bool @ ( image_a_a @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[410]) ).
thf(744,plain,
( ( ! [B_1_1: $i] :
( ~ ( is_fun1661590463l_bool @ B_1_1 )
| ( is_fun1661590463l_bool @ ( collec1974731493e_bool @ B_1_1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[411]) ).
thf(745,plain,
( ( ! [B_1_1: $i] :
( ~ ( is_fun949378684l_bool @ B_1_1 )
| ( is_fun949378684l_bool @ ( collect_fun_a_bool @ B_1_1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[412]) ).
thf(746,plain,
( ( ! [B_1_1: $i] :
( ~ ( is_fun_pname_bool @ B_1_1 )
| ( is_fun_pname_bool @ ( collect_pname @ B_1_1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[413]) ).
thf(747,plain,
( ( ! [B_1_1: $i] :
( ~ ( is_fun_a_bool @ B_1_1 )
| ( is_fun_a_bool @ ( collect_a @ B_1_1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[414]) ).
thf(748,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_fun1661590463l_bool @ B_2 )
| ( is_fun1661590463l_bool @ ( cOMBS_350070575l_bool @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[422]) ).
thf(749,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_fun949378684l_bool @ B_2 )
| ( is_fun949378684l_bool @ ( cOMBS_1035972772l_bool @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[423]) ).
thf(750,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_fun_pname_bool @ B_2 )
| ( is_fun_pname_bool @ ( cOMBS_568398431l_bool @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[424]) ).
thf(751,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_fun_a_bool @ B_2 )
| ( is_fun_a_bool @ ( cOMBS_a_bool_bool @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[425]) ).
thf(752,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_fun1661590463l_bool @ B_2 )
| ( is_fun1661590463l_bool @ ( cOMBB_307249310e_bool @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[426]) ).
thf(753,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_fun949378684l_bool @ B_2 )
| ( is_fun949378684l_bool @ ( cOMBB_2140588453a_bool @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[427]) ).
thf(754,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_fun_pname_bool @ B_2 )
| ( is_fun_pname_bool @ ( cOMBB_647938656_pname @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[428]) ).
thf(755,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_fun_a_bool @ B_2 )
| ( is_fun_a_bool @ ( cOMBB_bool_bool_a @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[429]) ).
thf(756,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_fun1661590463l_bool @ B_1_1 )
| ~ ( is_fun_pname_bool @ B_2 )
| ( is_bool @ ( hAPP_f1664156314l_bool @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[439]) ).
thf(757,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(extcnf_combined,[status(esa)],[440]) ).
thf(758,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(extcnf_combined,[status(esa)],[441]) ).
thf(759,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_pname @ B_2 )
| ( is_fun1661590463l_bool @ ( hAPP_p338031245l_bool @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[443]) ).
thf(760,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_pname @ B_2 )
| ( is_a @ ( hAPP_pname_a @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[444]) ).
thf(761,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_a @ B_2 )
| ( is_fun949378684l_bool @ ( hAPP_a85458249l_bool @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[445]) ).
thf(762,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(extcnf_combined,[status(esa)],[446]) ).
thf(763,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(extcnf_combined,[status(esa)],[447]) ).
thf(764,plain,
( ( is_fun1661590463l_bool @ finite_finite_pname )
= $true ),
inference(copy,[status(thm)],[448]) ).
thf(765,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)],[763]) ).
thf(766,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)],[762]) ).
thf(767,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_a @ B_2 )
| ( is_fun949378684l_bool @ ( hAPP_a85458249l_bool @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[761]) ).
thf(768,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)],[760]) ).
thf(769,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_pname @ B_2 )
| ( is_fun1661590463l_bool @ ( hAPP_p338031245l_bool @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[759]) ).
thf(770,plain,
( ( ! [B_1_1: $i,B_2: $i] : ( is_bool @ ( hAPP_nat_bool @ B_1_1 @ B_2 ) ) )
= $true ),
inference(copy,[status(thm)],[442]) ).
thf(771,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)],[758]) ).
thf(772,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)],[757]) ).
thf(773,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_fun1661590463l_bool @ B_1_1 )
| ~ ( is_fun_pname_bool @ B_2 )
| ( is_bool @ ( hAPP_f1664156314l_bool @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[756]) ).
thf(774,plain,
( ( is_fun_a_bool @ g )
= $true ),
inference(copy,[status(thm)],[438]) ).
thf(775,plain,
( ( is_fun_pname_bool @ u )
= $true ),
inference(copy,[status(thm)],[437]) ).
thf(776,plain,
( ( is_pname @ pn )
= $true ),
inference(copy,[status(thm)],[436]) ).
thf(777,plain,
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ u ) )
= $true ),
inference(copy,[status(thm)],[435]) ).
thf(778,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)],[434]) ).
thf(779,plain,
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ na ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_pname_a @ mgt_call @ u ) ) ) )
= $true ),
inference(copy,[status(thm)],[433]) ).
thf(780,plain,
( ( ( hAPP_fun_a_bool_nat @ finite_card_a @ g )
= ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_pname_a @ mgt_call @ u ) ) ) @ ( hAPP_nat_nat @ suc @ na ) ) )
= $true ),
inference(copy,[status(thm)],[432]) ).
thf(781,plain,
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ pn ) @ u ) )
= $true ),
inference(copy,[status(thm)],[431]) ).
thf(782,plain,
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( hAPP_pname_a @ mgt_call @ pn ) ) @ g ) ) )
= $true ),
inference(copy,[status(thm)],[430]) ).
thf(783,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_fun_a_bool @ B_2 )
| ( is_fun_a_bool @ ( cOMBB_bool_bool_a @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[755]) ).
thf(784,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_fun_pname_bool @ B_2 )
| ( is_fun_pname_bool @ ( cOMBB_647938656_pname @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[754]) ).
thf(785,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_fun949378684l_bool @ B_2 )
| ( is_fun949378684l_bool @ ( cOMBB_2140588453a_bool @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[753]) ).
thf(786,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_fun1661590463l_bool @ B_2 )
| ( is_fun1661590463l_bool @ ( cOMBB_307249310e_bool @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[752]) ).
thf(787,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_fun_a_bool @ B_2 )
| ( is_fun_a_bool @ ( cOMBS_a_bool_bool @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[751]) ).
thf(788,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_fun_pname_bool @ B_2 )
| ( is_fun_pname_bool @ ( cOMBS_568398431l_bool @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[750]) ).
thf(789,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_fun949378684l_bool @ B_2 )
| ( is_fun949378684l_bool @ ( cOMBS_1035972772l_bool @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[749]) ).
thf(790,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_fun1661590463l_bool @ B_2 )
| ( is_fun1661590463l_bool @ ( cOMBS_350070575l_bool @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[748]) ).
thf(791,plain,
( ( is_fun949378684l_bool @ finite_finite_a )
= $true ),
inference(copy,[status(thm)],[421]) ).
thf(792,plain,
( ( is_a @ ( undefined_a @ x_a ) )
= $true ),
inference(copy,[status(thm)],[420]) ).
thf(793,plain,
( ( is_pname @ ( undefined_pname @ pname ) )
= $true ),
inference(copy,[status(thm)],[419]) ).
thf(794,plain,
( ( is_fun_a_bool @ ( undefined_fun_a_bool @ ( fun @ x_a @ bool ) ) )
= $true ),
inference(copy,[status(thm)],[418]) ).
thf(795,plain,
( ( is_fun_pname_bool @ ( undefi17486888e_bool @ ( fun @ pname @ bool ) ) )
= $true ),
inference(copy,[status(thm)],[417]) ).
thf(796,plain,
( ( is_fun949378684l_bool @ ( undefi1699038445l_bool @ ( fun @ ( fun @ x_a @ bool ) @ bool ) ) )
= $true ),
inference(copy,[status(thm)],[416]) ).
thf(797,plain,
( ( is_fun1661590463l_bool @ ( undefi64961550l_bool @ ( fun @ ( fun @ pname @ bool ) @ bool ) ) )
= $true ),
inference(copy,[status(thm)],[415]) ).
thf(798,plain,
( ( ! [B_1_1: $i] :
( ~ ( is_fun_a_bool @ B_1_1 )
| ( is_fun_a_bool @ ( collect_a @ B_1_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[747]) ).
thf(799,plain,
( ( ! [B_1_1: $i] :
( ~ ( is_fun_pname_bool @ B_1_1 )
| ( is_fun_pname_bool @ ( collect_pname @ B_1_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[746]) ).
thf(800,plain,
( ( ! [B_1_1: $i] :
( ~ ( is_fun949378684l_bool @ B_1_1 )
| ( is_fun949378684l_bool @ ( collect_fun_a_bool @ B_1_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[745]) ).
thf(801,plain,
( ( ! [B_1_1: $i] :
( ~ ( is_fun1661590463l_bool @ B_1_1 )
| ( is_fun1661590463l_bool @ ( collec1974731493e_bool @ B_1_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[744]) ).
thf(802,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_fun_a_bool @ B_2 )
| ( is_fun_a_bool @ ( image_a_a @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[743]) ).
thf(803,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_fun_a_bool @ B_2 )
| ( is_fun_pname_bool @ ( image_a_pname @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[742]) ).
thf(804,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_fun_pname_bool @ B_2 )
| ( is_fun_pname_bool @ ( image_pname_pname @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[741]) ).
thf(805,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_fun_pname_bool @ B_2 )
| ( is_fun949378684l_bool @ ( image_112932426a_bool @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[740]) ).
thf(806,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_fun_pname_bool @ B_2 )
| ( is_fun1661590463l_bool @ ( image_47868345e_bool @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[739]) ).
thf(807,plain,
( ( ! [B_1_1: $i,B_2: $i] : ( is_fun_a_bool @ ( image_nat_a @ B_1_1 @ B_2 ) ) )
= $true ),
inference(copy,[status(thm)],[405]) ).
thf(808,plain,
( ( ! [B_1_1: $i,B_2: $i] : ( is_fun_pname_bool @ ( image_nat_pname @ B_1_1 @ B_2 ) ) )
= $true ),
inference(copy,[status(thm)],[404]) ).
thf(809,plain,
( ( ! [B_1_1: $i,B_2: $i] : ( is_fun949378684l_bool @ ( image_nat_fun_a_bool @ B_1_1 @ B_2 ) ) )
= $true ),
inference(copy,[status(thm)],[403]) ).
thf(810,plain,
( ( ! [B_1_1: $i,B_2: $i] : ( is_fun1661590463l_bool @ ( image_1655916159e_bool @ B_1_1 @ B_2 ) ) )
= $true ),
inference(copy,[status(thm)],[402]) ).
thf(811,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_fun949378684l_bool @ B_2 )
| ( is_fun_a_bool @ ( image_fun_a_bool_a @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[738]) ).
thf(812,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_fun949378684l_bool @ B_2 )
| ( is_fun_pname_bool @ ( image_1854862208_pname @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[737]) ).
thf(813,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_fun1661590463l_bool @ B_2 )
| ( is_fun_a_bool @ ( image_876012084bool_a @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[736]) ).
thf(814,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_fun1661590463l_bool @ B_2 )
| ( is_fun_pname_bool @ ( image_1283814551_pname @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[735]) ).
thf(815,plain,
( ( ! [B_1_1: $i,B_2: $i] : ( is_fun_a_bool @ ( image_fun_nat_bool_a @ B_1_1 @ B_2 ) ) )
= $true ),
inference(copy,[status(thm)],[397]) ).
thf(816,plain,
( ( ! [B_1_1: $i,B_2: $i] : ( is_fun_pname_bool @ ( image_1921560913_pname @ B_1_1 @ B_2 ) ) )
= $true ),
inference(copy,[status(thm)],[396]) ).
thf(817,plain,
( ( ! [B_1_1: $i,B_2: $i] : ( is_fun_a_bool @ ( image_573985017bool_a @ B_1_1 @ B_2 ) ) )
= $true ),
inference(copy,[status(thm)],[395]) ).
thf(818,plain,
( ( ! [B_1_1: $i,B_2: $i] : ( is_fun_pname_bool @ ( image_990671762_pname @ B_1_1 @ B_2 ) ) )
= $true ),
inference(copy,[status(thm)],[394]) ).
thf(819,plain,
( ( ! [B_1_1: $i,B_2: $i] : ( is_fun_a_bool @ ( image_349102846bool_a @ B_1_1 @ B_2 ) ) )
= $true ),
inference(copy,[status(thm)],[393]) ).
thf(820,plain,
( ( ! [B_1_1: $i,B_2: $i] : ( is_fun_pname_bool @ ( image_1705983821_pname @ B_1_1 @ B_2 ) ) )
= $true ),
inference(copy,[status(thm)],[392]) ).
thf(821,plain,
( ( ! [B_1_1: $i,B_2: $i] : ( is_fun_a_bool @ ( image_526090948bool_a @ B_1_1 @ B_2 ) ) )
= $true ),
inference(copy,[status(thm)],[391]) ).
thf(822,plain,
( ( ! [B_1_1: $i,B_2: $i] : ( is_fun_pname_bool @ ( image_1604018183_pname @ B_1_1 @ B_2 ) ) )
= $true ),
inference(copy,[status(thm)],[390]) ).
thf(823,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_fun_pname_bool @ B_2 )
| ~ ( is_pname @ B_1_1 )
| ( is_fun_pname_bool @ ( insert_pname @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[734]) ).
thf(824,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_fun949378684l_bool @ B_2 )
| ~ ( is_fun_a_bool @ B_1_1 )
| ( is_fun949378684l_bool @ ( insert_fun_a_bool @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[733]) ).
thf(825,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_fun1661590463l_bool @ B_2 )
| ~ ( is_fun_pname_bool @ B_1_1 )
| ( is_fun1661590463l_bool @ ( insert1325755072e_bool @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[732]) ).
thf(826,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_a @ B_2 )
| ~ ( is_fun_a_bool @ B_1_1 )
| ( is_bool @ ( hAPP_a_bool @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[731]) ).
thf(827,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_a @ B_2 )
| ( is_fun_a_bool @ ( hAPP_a_fun_a_bool @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[730]) ).
thf(828,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_a @ B_2 )
| ( is_fun_pname_bool @ ( hAPP_a93125764e_bool @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[729]) ).
thf(829,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_fun_pname_bool @ B_1_1 )
| ~ ( is_pname @ B_2 )
| ( is_bool @ ( hAPP_pname_bool @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[728]) ).
thf(830,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_pname @ B_2 )
| ( is_fun_a_bool @ ( hAPP_p1534023578a_bool @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[727]) ).
thf(831,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_pname @ B_2 )
| ( is_fun_pname_bool @ ( hAPP_p61793385e_bool @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[726]) ).
thf(832,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_bool @ B_2 )
| ( is_bool @ ( hAPP_bool_bool @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[725]) ).
thf(833,plain,
( ( ! [B_1_1: $i,B_2: $i] : ( is_fun_a_bool @ ( hAPP_nat_fun_a_bool @ B_1_1 @ B_2 ) ) )
= $true ),
inference(copy,[status(thm)],[379]) ).
thf(834,plain,
( ( ! [B_1_1: $i,B_2: $i] : ( is_fun_pname_bool @ ( hAPP_n1025906991e_bool @ B_1_1 @ B_2 ) ) )
= $true ),
inference(copy,[status(thm)],[378]) ).
thf(835,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_fun_a_bool @ B_2 )
| ( is_fun_a_bool @ ( hAPP_f2050579477a_bool @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[724]) ).
thf(836,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_fun_pname_bool @ B_2 )
| ( is_fun_pname_bool @ ( hAPP_f759274231e_bool @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[723]) ).
thf(837,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_fun_pname_bool @ B_2 )
| ( is_fun1661590463l_bool @ ( hAPP_f434788991l_bool @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[722]) ).
thf(838,plain,
( ( ! [B_1_1: $i,B_2: $i] : ( is_bool @ ( hAPP_f54304608l_bool @ B_1_1 @ B_2 ) ) )
= $true ),
inference(copy,[status(thm)],[374]) ).
thf(839,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_fun949378684l_bool @ B_2 )
| ( is_bool @ ( hAPP_f621171935l_bool @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[721]) ).
thf(840,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_fun949378684l_bool @ B_2 )
| ( is_fun949378684l_bool @ ( hAPP_f2117159681l_bool @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[720]) ).
thf(841,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_fun1661590463l_bool @ B_2 )
| ( is_bool @ ( hAPP_f1935102916l_bool @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[719]) ).
thf(842,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ~ ( is_fun1661590463l_bool @ B_2 )
| ( is_fun1661590463l_bool @ ( hAPP_f559147733l_bool @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[718]) ).
thf(843,plain,
( ( ! [B_1_1: $i,B_2: $i] : ( is_bool @ ( hAPP_f1637334154l_bool @ B_1_1 @ B_2 ) ) )
= $true ),
inference(copy,[status(thm)],[369]) ).
thf(844,plain,
( ( ! [B_1_1: $i,B_2: $i] : ( is_bool @ ( hAPP_f292226953l_bool @ B_1_1 @ B_2 ) ) )
= $true ),
inference(copy,[status(thm)],[368]) ).
thf(845,plain,
( ( ! [B_1_1: $i,B_2: $i] : ( is_bool @ ( hAPP_f389811538l_bool @ B_1_1 @ B_2 ) ) )
= $true ),
inference(copy,[status(thm)],[367]) ).
thf(846,plain,
( ( ! [B_1_1: $i,B_2: $i] : ( is_bool @ ( hAPP_f937997336l_bool @ B_1_1 @ B_2 ) ) )
= $true ),
inference(copy,[status(thm)],[366]) ).
thf(847,plain,
( ( ! [B_1_1: $i,B_2: $i] : ( is_bool @ ( hAPP_f1363661463l_bool @ B_1_1 @ B_2 ) ) )
= $true ),
inference(copy,[status(thm)],[365]) ).
thf(848,plain,
( ( ! [B_1_1: $i,B_2: $i] : ( is_bool @ ( hAPP_f595608956l_bool @ B_1_1 @ B_2 ) ) )
= $true ),
inference(copy,[status(thm)],[364]) ).
thf(849,plain,
( ( ! [B_1_1: $i,B_2: $i] : ( is_bool @ ( hAPP_f1295398978l_bool @ B_1_1 @ B_2 ) ) )
= $true ),
inference(copy,[status(thm)],[363]) ).
thf(850,plain,
( ( ! [B_1_1: $i] :
( ~ ( is_fun_a_bool @ B_1_1 )
| ( is_fun949378684l_bool @ ( p @ B_1_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[717]) ).
thf(851,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)],[716]) ).
thf(852,plain,
( ( ! [A: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( hAPP_f103356543l_bool @ ( cOMBC_1693257480l_bool @ ord_le1568362934t_bool ) @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[715]) ).
thf(853,plain,
( ( ! [A: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ ord_le313189616e_bool ) @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[714]) ).
thf(854,plain,
( ( ! [A: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ ord_le1311769555a_bool ) @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[713]) ).
thf(855,plain,
( ( ! [A: $i] :
( ~ ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ A ) )
| ( hBOOL @ ( hAPP_f1295398978l_bool @ finite719726885l_bool @ ( collec1874991203l_bool @ ( hAPP_f760187903l_bool @ ( cOMBC_1269652216l_bool @ ord_le65145710l_bool ) @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[712]) ).
thf(856,plain,
( ( ! [A: $i] :
( ~ ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ A ) )
| ( hBOOL @ ( hAPP_f595608956l_bool @ finite1491191519l_bool @ ( collec792590109l_bool @ ( hAPP_f1759205631l_bool @ ( cOMBC_336095980l_bool @ ord_le1375671464l_bool ) @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[711]) ).
thf(857,plain,
( ( ! [A: $i] :
( ~ ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ A ) )
| ( hBOOL @ ( hAPP_f1363661463l_bool @ finite1343359508l_bool @ ( collec1635217238l_bool @ ( hAPP_f1050622307l_bool @ ( cOMBC_636888218l_bool @ ord_le967226251l_bool ) @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[710]) ).
thf(858,plain,
( ( ! [A: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A ) )
| ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ ( collec707592106l_bool @ ( hAPP_f1434722111l_bool @ ( cOMBC_331553030l_bool @ ord_le1375614389l_bool ) @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[709]) ).
thf(859,plain,
( ( ! [A: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) )
| ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ ( collec1613912337l_bool @ ( hAPP_f510955609l_bool @ ( cOMBC_7971162l_bool @ ord_le675606854l_bool ) @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[708]) ).
thf(860,plain,
( ( ! [A: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A ) )
| ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ ( collec1015864663l_bool @ ( hAPP_f1772781669l_bool @ ( cOMBC_595898202l_bool @ ord_le1454342156l_bool ) @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[707]) ).
thf(861,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)],[706]) ).
thf(862,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ F_1 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_2089570637ol_nat @ H @ F_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[705]) ).
thf(863,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ F_1 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_1079571347ol_nat @ H @ F_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[704]) ).
thf(864,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ F_1 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_1802975832ol_nat @ H @ F_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[703]) ).
thf(865,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ F_1 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_fun_a_bool_nat @ H @ F_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[702]) ).
thf(866,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ F_1 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_1551609309ol_nat @ H @ F_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[701]) ).
thf(867,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ F_1 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_496248727ol_nat @ H @ F_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[700]) ).
thf(868,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ F_1 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_a_nat @ H @ F_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[699]) ).
thf(869,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ F_1 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1604018183_pname @ H @ F_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[698]) ).
thf(870,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ F_1 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1705983821_pname @ H @ F_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[697]) ).
thf(871,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ F_1 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_990671762_pname @ H @ F_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[696]) ).
thf(872,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ F_1 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1854862208_pname @ H @ F_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[695]) ).
thf(873,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ F_1 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1283814551_pname @ H @ F_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[694]) ).
thf(874,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ F_1 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1921560913_pname @ H @ F_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[693]) ).
thf(875,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ F_1 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_a_pname @ H @ F_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[692]) ).
thf(876,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ F_1 ) )
| ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ ( image_1607900221l_bool @ H @ F_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[691]) ).
thf(877,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ F_1 ) )
| ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ ( image_1874789623l_bool @ H @ F_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[690]) ).
thf(878,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ F_1 ) )
| ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ ( image_1208015684l_bool @ H @ F_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[689]) ).
thf(879,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ F_1 ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( image_nat_fun_a_bool @ H @ F_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[688]) ).
thf(880,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ F_1 ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( image_1655916159e_bool @ H @ F_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[687]) ).
thf(881,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ F_1 ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( image_26036933t_bool @ H @ F_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[686]) ).
thf(882,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ F_1 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_nat_a @ H @ F_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[685]) ).
thf(883,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ F_1 ) )
| ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ ( image_1154884483l_bool @ H @ F_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[684]) ).
thf(884,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ F_1 ) )
| ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ ( image_1642285373l_bool @ H @ F_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[683]) ).
thf(885,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ F_1 ) )
| ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ ( image_1420695166l_bool @ H @ F_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[682]) ).
thf(886,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ F_1 ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( image_112932426a_bool @ H @ F_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[681]) ).
thf(887,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ F_1 ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( image_47868345e_bool @ H @ F_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[680]) ).
thf(888,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ F_1 ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( image_2129980159t_bool @ H @ F_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[679]) ).
thf(889,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)],[678]) ).
thf(890,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)],[677]) ).
thf(891,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ F_1 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_fun_nat_bool_a @ H @ F_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[676]) ).
thf(892,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ F_1 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_876012084bool_a @ H @ F_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[675]) ).
thf(893,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ F_1 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_fun_a_bool_a @ H @ F_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[674]) ).
thf(894,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ F_1 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_pname_nat @ H @ F_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[673]) ).
thf(895,plain,
( ( ! [H: $i,F_1: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ F_1 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_nat_pname @ H @ F_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[672]) ).
thf(896,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)],[671]) ).
thf(897,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)],[670]) ).
thf(898,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)],[669]) ).
thf(899,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)],[668]) ).
thf(900,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)],[667]) ).
thf(901,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)],[666]) ).
thf(902,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)],[665]) ).
thf(903,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)],[664]) ).
thf(904,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)],[663]) ).
thf(905,plain,
( ( ! [F: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( image_pname_nat @ F @ A ) ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[662]) ).
thf(906,plain,
( ( ! [F: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( image_a_nat @ F @ A ) ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[661]) ).
thf(907,plain,
( ( ! [F: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( image_496248727ol_nat @ F @ A ) ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[660]) ).
thf(908,plain,
( ( ! [F: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( image_1551609309ol_nat @ F @ A ) ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[659]) ).
thf(909,plain,
( ( ! [F: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( image_fun_a_bool_nat @ F @ A ) ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[658]) ).
thf(910,plain,
( ( ! [F: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( image_a_pname @ F @ A ) ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[657]) ).
thf(911,plain,
( ( ! [F: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( image_nat_pname @ F @ A ) ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[656]) ).
thf(912,plain,
( ( ! [F: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_pname_a @ F @ A ) ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[655]) ).
thf(913,plain,
( ( ! [F: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_526090948bool_a @ F @ A ) ) ) @ ( hAPP_f1690079119ol_nat @ finite1352710292l_bool @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[654]) ).
thf(914,plain,
( ( ! [F: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_349102846bool_a @ F @ A ) ) ) @ ( hAPP_f98387925ol_nat @ finite269641166l_bool @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[653]) ).
thf(915,plain,
( ( ! [F: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_573985017bool_a @ F @ A ) ) ) @ ( hAPP_f1253658590ol_nat @ finite1659325229l_bool @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[652]) ).
thf(916,plain,
( ( ! [F: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_fun_a_bool_a @ F @ A ) ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[651]) ).
thf(917,plain,
( ( ! [F: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_876012084bool_a @ F @ A ) ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[650]) ).
thf(918,plain,
( ( ! [F: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_fun_nat_bool_a @ F @ A ) ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[649]) ).
thf(919,plain,
( ( ! [F: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_a_a @ F @ A ) ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[648]) ).
thf(920,plain,
( ( ! [F: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( image_pname_pname @ F @ A ) ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[647]) ).
thf(921,plain,
( ( ! [F: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( image_2129980159t_bool @ F @ A ) ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[646]) ).
thf(922,plain,
( ( ! [F: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( image_47868345e_bool @ F @ A ) ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[645]) ).
thf(923,plain,
( ( ! [F: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( image_112932426a_bool @ F @ A ) ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[644]) ).
thf(924,plain,
( ( ! [F: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_nat_a @ F @ A ) ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[643]) ).
thf(925,plain,
( ( ! [F: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( image_26036933t_bool @ F @ A ) ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[642]) ).
thf(926,plain,
( ( ! [F: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( image_1655916159e_bool @ F @ A ) ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[641]) ).
thf(927,plain,
( ( ! [F: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( image_nat_fun_a_bool @ F @ A ) ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[640]) ).
thf(928,plain,
( ( ! [F: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( image_1921560913_pname @ F @ A ) ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[639]) ).
thf(929,plain,
( ( ! [F: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( image_1283814551_pname @ F @ A ) ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[638]) ).
thf(930,plain,
( ( ! [F: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( image_1854862208_pname @ F @ A ) ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[637]) ).
thf(931,plain,
( ( ! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
| ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ A ) @ B ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ A ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[636]) ).
thf(932,plain,
( ( ! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
| ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ A ) @ B ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ A ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[635]) ).
thf(933,plain,
( ( ! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
| ~ ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ A ) @ B ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ A ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[634]) ).
thf(934,plain,
( ( ! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ A ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[633]) ).
thf(935,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_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ A ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[632]) ).
thf(936,plain,
( ( ! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ A ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[631]) ).
thf(937,plain,
( ( ! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
| ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ B ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ A ) ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[630]) ).
thf(938,plain,
( ( ! [A: $i,B: $i] :
( ~ ( is_fun1661590463l_bool @ A )
| ~ ( is_fun1661590463l_bool @ B )
| ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
| ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ B ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ A ) ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[629]) ).
thf(939,plain,
( ( ! [A: $i,B: $i] :
( ~ ( is_fun949378684l_bool @ A )
| ~ ( is_fun949378684l_bool @ B )
| ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
| ~ ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ B ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ A ) ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[628]) ).
thf(940,plain,
( ( ! [A: $i,B: $i] :
( ~ ( is_fun_pname_bool @ A )
| ~ ( is_fun_pname_bool @ B )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ B ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ A ) ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[627]) ).
thf(941,plain,
( ( ! [A: $i,B: $i] :
( ~ ( is_fun_a_bool @ A )
| ~ ( is_fun_a_bool @ B )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ B ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ A ) ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[626]) ).
thf(942,plain,
( ( ! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ B ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ A ) ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[625]) ).
thf(943,plain,
( ( ! [X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ A ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( insert_fun_nat_bool @ X_2 @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[624]) ).
thf(944,plain,
( ( ! [X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ A ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( insert1325755072e_bool @ X_2 @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[623]) ).
thf(945,plain,
( ( ! [X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ A ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( insert_fun_a_bool @ X_2 @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[622]) ).
thf(946,plain,
( ( ! [X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ A ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( insert_pname @ X_2 @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[621]) ).
thf(947,plain,
( ( ! [X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ A ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( insert_nat @ X_2 @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[620]) ).
thf(948,plain,
( ( ! [X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ A ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( insert_a @ X_2 @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[619]) ).
thf(949,plain,
( ( ! [X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A ) )
| ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ X_2 ) @ A ) )
| ( ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( insert_fun_nat_bool @ X_2 @ A ) )
= ( hAPP_f696928925ol_nat @ finite346522414t_bool @ A ) ) )
& ! [X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ X_2 ) @ A ) )
| ( ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( insert_fun_nat_bool @ X_2 @ A ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[618]) ).
thf(950,plain,
( ( ! [X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) )
| ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ X_2 ) @ A ) )
| ( ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( insert1325755072e_bool @ X_2 @ A ) )
= ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ A ) ) )
& ! [X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ X_2 ) @ A ) )
| ( ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( insert1325755072e_bool @ X_2 @ A ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[617]) ).
thf(951,plain,
( ( ! [X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A ) )
| ~ ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ X_2 ) @ A ) )
| ( ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( insert_fun_a_bool @ X_2 @ A ) )
= ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ A ) ) )
& ! [X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ X_2 ) @ A ) )
| ( ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( insert_fun_a_bool @ X_2 @ A ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[616]) ).
thf(952,plain,
( ( ! [X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ X_2 ) @ A ) )
| ( ( hAPP_f22106695ol_nat @ finite_card_nat @ ( insert_nat @ X_2 @ A ) )
= ( hAPP_f22106695ol_nat @ finite_card_nat @ A ) ) )
& ! [X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ X_2 ) @ A ) )
| ( ( hAPP_f22106695ol_nat @ finite_card_nat @ ( insert_nat @ X_2 @ A ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f22106695ol_nat @ finite_card_nat @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[615]) ).
thf(953,plain,
( ( ! [X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ A ) )
| ( ( hAPP_f921600141ol_nat @ finite_card_pname @ ( insert_pname @ X_2 @ A ) )
= ( hAPP_f921600141ol_nat @ finite_card_pname @ A ) ) )
& ! [X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ A ) )
| ( ( hAPP_f921600141ol_nat @ finite_card_pname @ ( insert_pname @ X_2 @ A ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f921600141ol_nat @ finite_card_pname @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[614]) ).
thf(954,plain,
( ( ! [X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_2 ) @ A ) )
| ( ( hAPP_fun_a_bool_nat @ finite_card_a @ ( insert_a @ X_2 @ A ) )
= ( hAPP_fun_a_bool_nat @ finite_card_a @ A ) ) )
& ! [X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_2 ) @ A ) )
| ( ( hAPP_fun_a_bool_nat @ finite_card_a @ ( insert_a @ X_2 @ A ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_fun_a_bool_nat @ finite_card_a @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[613]) ).
thf(955,plain,
( ( ! [X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ X_2 ) @ A ) )
| ( ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( insert_fun_nat_bool @ X_2 @ A ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[612]) ).
thf(956,plain,
( ( ! [X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ X_2 ) @ A ) )
| ( ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( insert1325755072e_bool @ X_2 @ A ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[611]) ).
thf(957,plain,
( ( ! [X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ X_2 ) @ A ) )
| ( ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( insert_fun_a_bool @ X_2 @ A ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[610]) ).
thf(958,plain,
( ( ! [X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ X_2 ) @ A ) )
| ( ( hAPP_f22106695ol_nat @ finite_card_nat @ ( insert_nat @ X_2 @ A ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f22106695ol_nat @ finite_card_nat @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[609]) ).
thf(959,plain,
( ( ! [X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ A ) )
| ( ( hAPP_f921600141ol_nat @ finite_card_pname @ ( insert_pname @ X_2 @ A ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f921600141ol_nat @ finite_card_pname @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[608]) ).
thf(960,plain,
( ( ! [X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_2 ) @ A ) )
| ( ( hAPP_fun_a_bool_nat @ finite_card_a @ ( insert_a @ X_2 @ A ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_fun_a_bool_nat @ finite_card_a @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[607]) ).
thf(961,plain,
( ( ! [Q_1: $i,Pa: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ Pa ) ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fconj @ Pa ) @ Q_1 ) ) ) ) )
& ! [Q_1: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ Q_1 ) ) )
| ! [Pa: $i] : ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fconj @ Pa ) @ Q_1 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[606]) ).
thf(962,plain,
( ( ! [Q_1: $i,Pa: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ Pa ) ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fconj @ Pa ) @ Q_1 ) ) ) ) )
& ! [Q_1: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ Q_1 ) ) )
| ! [Pa: $i] : ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fconj @ Pa ) @ Q_1 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[605]) ).
thf(963,plain,
( ( ! [Q_1: $i,Pa: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ Pa ) ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fconj @ Pa ) @ Q_1 ) ) ) ) )
& ! [Q_1: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ Q_1 ) ) )
| ! [Pa: $i] : ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fconj @ Pa ) @ Q_1 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[604]) ).
thf(964,plain,
( ( ! [Q_1: $i,Pa: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ Pa ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ Pa ) @ Q_1 ) ) ) ) )
& ! [Q_1: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ Q_1 ) ) )
| ! [Pa: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ Pa ) @ Q_1 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[603]) ).
thf(965,plain,
( ( ! [Q_1: $i,Pa: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ Pa ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ Pa ) @ Q_1 ) ) ) ) )
& ! [Q_1: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ Q_1 ) ) )
| ! [Pa: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ Pa ) @ Q_1 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[602]) ).
thf(966,plain,
( ( ! [Q_1: $i,Pa: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ Pa ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ Pa ) @ Q_1 ) ) ) ) )
& ! [Q_1: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ Q_1 ) ) )
| ! [Pa: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ Pa ) @ Q_1 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[601]) ).
thf(967,plain,
( ( ! [N_1: $i,M_2: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ N_1 ) @ M_2 ) )
| ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ suc @ M_2 ) ) @ N_1 )
= ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( minus_minus_nat @ M_2 ) @ N_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[600]) ).
thf(968,plain,
( ( ! [K: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ ord_less_eq_nat ) @ K ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[244]) ).
thf(969,plain,
( ( ! [Na: $i] :
( ( hAPP_f22106695ol_nat @ finite_card_nat @ ( collect_nat @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ ord_less_eq_nat ) @ Na ) ) )
= ( hAPP_nat_nat @ suc @ Na ) ) )
= $true ),
inference(copy,[status(thm)],[243]) ).
thf(970,plain,
( ( ! [X: $i,Y: $i] :
( ( ( hAPP_nat_nat @ suc @ X )
!= ( hAPP_nat_nat @ suc @ Y ) )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[599]) ).
thf(971,plain,
( ( ! [Nat_1: $i,Nat: $i] :
( ( ( hAPP_nat_nat @ suc @ Nat_1 )
!= ( hAPP_nat_nat @ suc @ Nat ) )
| ( Nat_1 = Nat ) )
& ! [Nat_1: $i,Nat: $i] :
( ( Nat_1 != Nat )
| ( ( hAPP_nat_nat @ suc @ Nat_1 )
= ( hAPP_nat_nat @ suc @ Nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[598]) ).
thf(972,plain,
( ( ! [N_1: $i] :
( ( hAPP_nat_nat @ suc @ N_1 )
!= N_1 ) )
= $true ),
inference(copy,[status(thm)],[597]) ).
thf(973,plain,
( ( ! [N_1: $i] :
( N_1
!= ( hAPP_nat_nat @ suc @ N_1 ) ) )
= $true ),
inference(copy,[status(thm)],[596]) ).
thf(974,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)],[595]) ).
thf(975,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)],[594]) ).
thf(976,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)],[593]) ).
thf(977,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)],[235]) ).
thf(978,plain,
( ( ! [N_1: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ N_1 ) @ N_1 ) ) )
= $true ),
inference(copy,[status(thm)],[234]) ).
thf(979,plain,
( ( ! [I_1: $i,J: $i,K_1: $i] :
( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ I_1 ) @ J ) ) @ K_1 )
= ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ I_1 ) @ K_1 ) ) @ J ) ) )
= $true ),
inference(copy,[status(thm)],[233]) ).
thf(980,plain,
( ( ! [Pa: $i,Q_1: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ Pa ) ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ Q_1 ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ Pa ) @ Q_1 ) ) ) ) )
& ! [Pa: $i] :
( ! [Q_1: $i] :
~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ Pa ) @ Q_1 ) ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ Pa ) ) ) )
& ! [Pa: $i,Q_1: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ Pa ) @ Q_1 ) ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ Q_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[592]) ).
thf(981,plain,
( ( ! [Pa: $i,Q_1: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ Pa ) ) )
| ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ Q_1 ) ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ Pa ) @ Q_1 ) ) ) ) )
& ! [Pa: $i] :
( ! [Q_1: $i] :
~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ Pa ) @ Q_1 ) ) ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ Pa ) ) ) )
& ! [Pa: $i,Q_1: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ Pa ) @ Q_1 ) ) ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ Q_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[591]) ).
thf(982,plain,
( ( ! [Pa: $i,Q_1: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ Pa ) ) )
| ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ Q_1 ) ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ Pa ) @ Q_1 ) ) ) ) )
& ! [Pa: $i] :
( ! [Q_1: $i] :
~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ Pa ) @ Q_1 ) ) ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ Pa ) ) ) )
& ! [Pa: $i,Q_1: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ Pa ) @ Q_1 ) ) ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ Q_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[590]) ).
thf(983,plain,
( ( ! [Pa: $i,Q_1: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ Pa ) ) )
| ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ Q_1 ) ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ Pa ) @ Q_1 ) ) ) ) )
& ! [Pa: $i] :
( ! [Q_1: $i] :
~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ Pa ) @ Q_1 ) ) ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ Pa ) ) ) )
& ! [Pa: $i,Q_1: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ Pa ) @ Q_1 ) ) ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ Q_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[589]) ).
thf(984,plain,
( ( ! [Pa: $i,Q_1: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ Pa ) ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ Q_1 ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ Pa ) @ Q_1 ) ) ) ) )
& ! [Pa: $i] :
( ! [Q_1: $i] :
~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ Pa ) @ Q_1 ) ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ Pa ) ) ) )
& ! [Pa: $i,Q_1: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ Pa ) @ Q_1 ) ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ Q_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[588]) ).
thf(985,plain,
( ( ! [Pa: $i,Q_1: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ Pa ) ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ Q_1 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ Pa ) @ Q_1 ) ) ) ) )
& ! [Pa: $i] :
( ! [Q_1: $i] :
~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ Pa ) @ Q_1 ) ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ Pa ) ) ) )
& ! [Pa: $i,Q_1: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ Pa ) @ Q_1 ) ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ Q_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[587]) ).
thf(986,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 ) ) )
& ! [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)],[586]) ).
thf(987,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 ) ) )
& ! [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)],[585]) ).
thf(988,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 ) ) )
& ! [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)],[584]) ).
thf(989,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 ) ) )
& ! [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)],[583]) ).
thf(990,plain,
( ( ! [A_1: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ A_1 @ A ) ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) ) )
& ! [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)],[582]) ).
thf(991,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 ) ) )
& ! [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)],[581]) ).
thf(992,plain,
( ( ! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[580]) ).
thf(993,plain,
( ( ! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[579]) ).
thf(994,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)],[578]) ).
thf(995,plain,
( ( ! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[577]) ).
thf(996,plain,
( ( ! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[576]) ).
thf(997,plain,
( ( ! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[575]) ).
thf(998,plain,
( ( ! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
| ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ A ) @ B ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[574]) ).
thf(999,plain,
( ( ! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
| ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ A ) @ B ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[573]) ).
thf(1000,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)],[572]) ).
thf(1001,plain,
( ( ! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
| ~ ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ A ) @ B ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[571]) ).
thf(1002,plain,
( ( ! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[570]) ).
thf(1003,plain,
( ( ! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[569]) ).
thf(1004,plain,
( ( ! [M_2: $i,N_1: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ M_2 ) ) @ N_1 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ M_2 ) @ N_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[568]) ).
thf(1005,plain,
( ( ! [M_2: $i,N_1: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ M_2 ) @ ( hAPP_nat_nat @ suc @ N_1 ) ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ M_2 ) @ N_1 ) )
| ( M_2
= ( hAPP_nat_nat @ suc @ N_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[567]) ).
thf(1006,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 @ M_2 ) @ ( hAPP_nat_nat @ suc @ N_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[566]) ).
thf(1007,plain,
( ( ! [Na: $i,M_3: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ Na ) ) @ ( hAPP_nat_nat @ suc @ M_3 ) ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Na ) @ M_3 ) ) )
& ! [Na: $i,M_3: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Na ) @ M_3 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ Na ) ) @ ( hAPP_nat_nat @ suc @ M_3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[565]) ).
thf(1008,plain,
( ( ! [M_3: $i,Na: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ M_3 ) @ ( hAPP_nat_nat @ suc @ Na ) ) )
| ( M_3
= ( hAPP_nat_nat @ suc @ Na ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ M_3 ) @ Na ) ) )
& ! [M_3: $i,Na: $i] :
( ( M_3
!= ( hAPP_nat_nat @ suc @ Na ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ M_3 ) @ ( hAPP_nat_nat @ suc @ Na ) ) ) )
& ! [M_3: $i,Na: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ M_3 ) @ Na ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ M_3 ) @ ( hAPP_nat_nat @ suc @ Na ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[564]) ).
thf(1009,plain,
( ( ! [M_3: $i,Na: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ Na ) ) @ M_3 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ M_3 ) @ Na ) ) )
& ! [M_3: $i,Na: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ M_3 ) @ Na ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ Na ) ) @ M_3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[563]) ).
thf(1010,plain,
( ( ! [N_1: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ N_1 ) ) @ N_1 ) ) )
= $true ),
inference(copy,[status(thm)],[202]) ).
thf(1011,plain,
( ( ! [M_2: $i,N_1: $i,K_1: $i] :
( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ suc @ M_2 ) ) @ N_1 ) ) @ ( hAPP_nat_nat @ suc @ K_1 ) )
= ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ M_2 ) @ N_1 ) ) @ K_1 ) ) )
= $true ),
inference(copy,[status(thm)],[201]) ).
thf(1012,plain,
( ( ! [M_2: $i,N_1: $i] :
( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ suc @ M_2 ) ) @ ( hAPP_nat_nat @ suc @ N_1 ) )
= ( hAPP_nat_nat @ ( minus_minus_nat @ M_2 ) @ N_1 ) ) )
= $true ),
inference(copy,[status(thm)],[200]) ).
thf(1013,plain,
( ( ! [Na: $i] :
( ! [K: $i,M_3: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ K ) @ M_3 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ K ) @ Na ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ M_3 ) @ K ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ Na ) @ K ) ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ M_3 ) @ Na ) ) )
& ! [K: $i,M_3: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ K ) @ M_3 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ K ) @ Na ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ M_3 ) @ Na ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ M_3 ) @ K ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ Na ) @ K ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[562]) ).
thf(1014,plain,
( ( ! [N_1: $i,K_1: $i,M_2: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ K_1 ) @ M_2 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ K_1 ) @ N_1 ) )
| ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ M_2 ) @ K_1 ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ N_1 ) @ K_1 ) )
= ( hAPP_nat_nat @ ( minus_minus_nat @ M_2 ) @ N_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[561]) ).
thf(1015,plain,
( ( ! [Na: $i] :
( ! [K: $i,M_3: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ K ) @ M_3 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ K ) @ Na ) )
| ( ( hAPP_nat_nat @ ( minus_minus_nat @ M_3 ) @ K )
!= ( hAPP_nat_nat @ ( minus_minus_nat @ Na ) @ K ) )
| ( M_3 = Na ) )
& ! [K: $i,M_3: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ K ) @ M_3 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ K ) @ Na ) )
| ( M_3 != Na )
| ( ( hAPP_nat_nat @ ( minus_minus_nat @ M_3 ) @ K )
= ( hAPP_nat_nat @ ( minus_minus_nat @ Na ) @ K ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[560]) ).
thf(1016,plain,
( ( ! [I_1: $i,N_1: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ I_1 ) @ N_1 ) )
| ( ( hAPP_nat_nat @ ( minus_minus_nat @ N_1 ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ N_1 ) @ I_1 ) )
= I_1 ) ) )
= $true ),
inference(copy,[status(thm)],[559]) ).
thf(1017,plain,
( ( ! [L: $i,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 @ ( hAPP_nat_nat @ ( minus_minus_nat @ M_2 ) @ L ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ N_1 ) @ L ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[558]) ).
thf(1018,plain,
( ( ! [L: $i,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 @ ( hAPP_nat_nat @ ( minus_minus_nat @ L ) @ N_1 ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ L ) @ M_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[557]) ).
thf(1019,plain,
( ( ! [M_2: $i,N_1: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ M_2 ) @ N_1 ) ) @ M_2 ) ) )
= $true ),
inference(copy,[status(thm)],[193]) ).
thf(1020,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)],[556]) ).
thf(1021,plain,
( ( ! [F: $i,A: $i,B: $i] :
( ~ ( is_fun_a_bool @ B )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ ( image_pname_a @ F @ A ) ) )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( sK17_C_2 @ B @ A @ F ) ) @ A ) )
& ( is_fun_pname_bool @ ( sK17_C_2 @ B @ A @ F ) )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( sK17_C_2 @ B @ A @ F ) ) )
& ( B
= ( image_pname_a @ F @ ( sK17_C_2 @ B @ A @ F ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[555]) ).
thf(1022,plain,
( ( ! [Na: $i,N_3: $i,F: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( hAPP_n1699378549t_bool @ F @ ( sK16_N_2 @ F @ N_3 @ Na ) ) ) @ ( hAPP_n1699378549t_bool @ F @ ( hAPP_nat_nat @ suc @ ( sK16_N_2 @ F @ N_3 @ Na ) ) ) ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Na ) @ N_3 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( hAPP_n1699378549t_bool @ F @ Na ) ) @ ( hAPP_n1699378549t_bool @ F @ N_3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[554]) ).
thf(1023,plain,
( ( ! [Na: $i,N_3: $i,F: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_n1025906991e_bool @ F @ ( sK15_N_2 @ F @ N_3 @ Na ) ) ) @ ( hAPP_n1025906991e_bool @ F @ ( hAPP_nat_nat @ suc @ ( sK15_N_2 @ F @ N_3 @ Na ) ) ) ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Na ) @ N_3 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_n1025906991e_bool @ F @ Na ) ) @ ( hAPP_n1025906991e_bool @ F @ N_3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[553]) ).
thf(1024,plain,
( ( ! [Na: $i,N_3: $i,F: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ F @ ( sK14_N_2 @ F @ N_3 @ Na ) ) ) @ ( hAPP_nat_nat @ F @ ( hAPP_nat_nat @ suc @ ( sK14_N_2 @ F @ N_3 @ Na ) ) ) ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Na ) @ N_3 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ F @ Na ) ) @ ( hAPP_nat_nat @ F @ N_3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[552]) ).
thf(1025,plain,
( ( ! [Na: $i,N_3: $i,F: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_nat_fun_a_bool @ F @ ( sK13_N_2 @ F @ N_3 @ Na ) ) ) @ ( hAPP_nat_fun_a_bool @ F @ ( hAPP_nat_nat @ suc @ ( sK13_N_2 @ F @ N_3 @ Na ) ) ) ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Na ) @ N_3 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_nat_fun_a_bool @ F @ Na ) ) @ ( hAPP_nat_fun_a_bool @ F @ N_3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[551]) ).
thf(1026,plain,
( ( ! [F: $i,A: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_pname_a @ F @ A ) ) )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK12_X_1 @ A @ F ) ) @ A ) )
& ( is_pname @ ( sK12_X_1 @ A @ F ) )
& ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ ( hAPP_f759274231e_bool @ ( cOMBC_1058051404l_bool @ member_pname ) @ A ) ) @ ( hAPP_a93125764e_bool @ ( cOMBC_pname_a_bool @ ( cOMBB_1897541054_pname @ fequal_a @ F ) ) @ ( hAPP_pname_a @ F @ ( sK12_X_1 @ A @ F ) ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[550]) ).
thf(1027,plain,
( ( ! [A: $i,B_1: $i,F: $i,X_2: $i] :
( ( B_1
!= ( hAPP_pname_a @ F @ X_2 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ A ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B_1 ) @ ( image_pname_a @ F @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[549]) ).
thf(1028,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)],[548]) ).
thf(1029,plain,
( ( ! [A: $i,B: $i] :
( ~ ( is_fun_pname_bool @ A )
| ~ ( is_fun_pname_bool @ 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 ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[547]) ).
thf(1030,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)],[546]) ).
thf(1031,plain,
( ( ! [C_1: $i,A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C_1 ) @ A ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C_1 ) @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[545]) ).
thf(1032,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)],[544]) ).
thf(1033,plain,
( ( ! [C_1: $i,A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C_1 ) @ A ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C_1 ) @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[543]) ).
thf(1034,plain,
( ( ! [B_1: $i] :
( ! [A_1: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A_1 ) @ B ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A_1 ) @ ( insert_nat @ B_1 @ B ) ) ) )
& ! [A_1: $i] :
( ( A_1 != B_1 )
| ! [B: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A_1 ) @ ( insert_nat @ B_1 @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[542]) ).
thf(1035,plain,
( ( ! [B_1: $i] :
( ! [A_1: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A_1 ) @ B ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A_1 ) @ ( insert_pname @ B_1 @ B ) ) ) )
& ! [A_1: $i] :
( ( A_1 != B_1 )
| ! [B: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A_1 ) @ ( insert_pname @ B_1 @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[541]) ).
thf(1036,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 ) ) ) )
& ! [A_1: $i] :
( ( A_1 != B_1 )
| ! [B: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_1 ) @ ( insert_a @ B_1 @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[540]) ).
thf(1037,plain,
( ( ! [A_1: $i,B_1: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A_1 ) @ ( insert_nat @ B_1 @ A ) ) )
| ( A_1 = B_1 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A_1 ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[539]) ).
thf(1038,plain,
( ( ! [A_1: $i,B_1: $i] :
( ~ ( is_pname @ A_1 )
| ~ ( is_pname @ B_1 )
| ! [A: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A_1 ) @ ( insert_pname @ B_1 @ A ) ) )
| ( A_1 = B_1 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A_1 ) @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[538]) ).
thf(1039,plain,
( ( ! [A_1: $i,B_1: $i] :
( ~ ( is_a @ A_1 )
| ~ ( is_a @ B_1 )
| ! [A: $i] :
( ~ ( 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)],[537]) ).
thf(1040,plain,
( ( ! [A_1: $i,B: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A_1 ) @ ( insert_nat @ A_1 @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[172]) ).
thf(1041,plain,
( ( ! [A_1: $i,B: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A_1 ) @ ( insert_pname @ A_1 @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[171]) ).
thf(1042,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)],[170]) ).
thf(1043,plain,
( ( ! [A_1: $i,B: $i] :
( ( insert_nat @ A_1 @ B )
= ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ fequal_nat ) @ A_1 ) ) @ ( hAPP_f800510211t_bool @ ( cOMBC_226598744l_bool @ member_nat ) @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[169]) ).
thf(1044,plain,
( ( ! [A_1: $i,B: $i] :
( ( insert_pname @ A_1 @ B )
= ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ fequal_pname ) @ A_1 ) ) @ ( hAPP_f759274231e_bool @ ( cOMBC_1058051404l_bool @ member_pname ) @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[168]) ).
thf(1045,plain,
( ( ! [A_1: $i,B: $i] :
( ( insert_a @ A_1 @ B )
= ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ ( hAPP_a_fun_a_bool @ ( cOMBC_a_a_bool @ fequal_a ) @ A_1 ) ) @ ( hAPP_f2050579477a_bool @ ( cOMBC_1355376034l_bool @ member_a ) @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[167]) ).
thf(1046,plain,
( ( ! [A_1: $i,B: $i] :
( ( insert_fun_nat_bool @ A_1 @ B )
= ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ ( hAPP_f103356543l_bool @ ( cOMBC_1693257480l_bool @ fequal_fun_nat_bool ) @ A_1 ) ) @ ( hAPP_f1246832597l_bool @ ( cOMBC_1245412066l_bool @ member_fun_nat_bool ) @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[166]) ).
thf(1047,plain,
( ( ! [A_1: $i,B: $i] :
( ( insert1325755072e_bool @ A_1 @ B )
= ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ A_1 ) ) @ ( hAPP_f559147733l_bool @ ( cOMBC_1988546018l_bool @ member799430823e_bool ) @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[165]) ).
thf(1048,plain,
( ( ! [A_1: $i,B: $i] :
( ( insert_fun_a_bool @ A_1 @ B )
= ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ fequal_fun_a_bool ) @ A_1 ) ) @ ( hAPP_f2117159681l_bool @ ( cOMBC_1880041174l_bool @ member_fun_a_bool ) @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[164]) ).
thf(1049,plain,
( ( ! [A_1: $i,Pa: $i] :
( ( insert_nat @ A_1 @ ( collect_nat @ Pa ) )
= ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fimplies @ ( cOMBB_bool_bool_nat @ fNot @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ fequal_nat ) @ A_1 ) ) ) @ Pa ) ) ) )
= $true ),
inference(copy,[status(thm)],[163]) ).
thf(1050,plain,
( ( ! [A_1: $i,Pa: $i] :
( ( insert_pname @ A_1 @ ( collect_pname @ Pa ) )
= ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fimplies @ ( cOMBB_647938656_pname @ fNot @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ fequal_pname ) @ A_1 ) ) ) @ Pa ) ) ) )
= $true ),
inference(copy,[status(thm)],[162]) ).
thf(1051,plain,
( ( ! [A_1: $i,Pa: $i] :
( ( insert_a @ A_1 @ ( collect_a @ Pa ) )
= ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fimplies @ ( cOMBB_bool_bool_a @ fNot @ ( hAPP_a_fun_a_bool @ ( cOMBC_a_a_bool @ fequal_a ) @ A_1 ) ) ) @ Pa ) ) ) )
= $true ),
inference(copy,[status(thm)],[161]) ).
thf(1052,plain,
( ( ! [A_1: $i,Pa: $i] :
( ( insert_fun_nat_bool @ A_1 @ ( collect_fun_nat_bool @ Pa ) )
= ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fimplies @ ( cOMBB_238756964t_bool @ fNot @ ( hAPP_f103356543l_bool @ ( cOMBC_1693257480l_bool @ fequal_fun_nat_bool ) @ A_1 ) ) ) @ Pa ) ) ) )
= $true ),
inference(copy,[status(thm)],[160]) ).
thf(1053,plain,
( ( ! [A_1: $i,Pa: $i] :
( ( insert1325755072e_bool @ A_1 @ ( collec1974731493e_bool @ Pa ) )
= ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fimplies @ ( cOMBB_307249310e_bool @ fNot @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ A_1 ) ) ) @ Pa ) ) ) )
= $true ),
inference(copy,[status(thm)],[159]) ).
thf(1054,plain,
( ( ! [A_1: $i,Pa: $i] :
( ( insert_fun_a_bool @ A_1 @ ( collect_fun_a_bool @ Pa ) )
= ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fimplies @ ( cOMBB_2140588453a_bool @ fNot @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ fequal_fun_a_bool ) @ A_1 ) ) ) @ Pa ) ) ) )
= $true ),
inference(copy,[status(thm)],[158]) ).
thf(1055,plain,
( ( ! [X_2: $i,A: $i] :
( ( insert_nat @ X_2 @ ( insert_nat @ X_2 @ A ) )
= ( insert_nat @ X_2 @ A ) ) )
= $true ),
inference(copy,[status(thm)],[157]) ).
thf(1056,plain,
( ( ! [X_2: $i,A: $i] :
( ( insert_pname @ X_2 @ ( insert_pname @ X_2 @ A ) )
= ( insert_pname @ X_2 @ A ) ) )
= $true ),
inference(copy,[status(thm)],[156]) ).
thf(1057,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)],[155]) ).
thf(1058,plain,
( ( ! [X_2: $i,Y_1: $i,A: $i] :
( ( insert_nat @ X_2 @ ( insert_nat @ Y_1 @ A ) )
= ( insert_nat @ Y_1 @ ( insert_nat @ X_2 @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[154]) ).
thf(1059,plain,
( ( ! [X_2: $i,Y_1: $i,A: $i] :
( ( insert_pname @ X_2 @ ( insert_pname @ Y_1 @ A ) )
= ( insert_pname @ Y_1 @ ( insert_pname @ X_2 @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[153]) ).
thf(1060,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)],[152]) ).
thf(1061,plain,
( ( ! [A_1: $i] :
( ! [B_1: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A_1 ) @ ( insert_nat @ B_1 @ A ) ) )
| ( A_1 = B_1 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A_1 ) @ A ) ) )
& ! [B_1: $i] :
( ( A_1 != B_1 )
| ! [A: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A_1 ) @ ( insert_nat @ B_1 @ A ) ) ) )
& ! [B_1: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A_1 ) @ A ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A_1 ) @ ( insert_nat @ B_1 @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[536]) ).
thf(1062,plain,
( ( ! [A_1: $i] :
( ! [B_1: $i] :
( ~ ( is_pname @ A_1 )
| ~ ( is_pname @ B_1 )
| ! [A: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A_1 ) @ ( insert_pname @ B_1 @ A ) ) )
| ( A_1 = B_1 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A_1 ) @ A ) ) ) )
& ! [B_1: $i] :
( ~ ( is_pname @ A_1 )
| ~ ( is_pname @ B_1 )
| ( A_1 != B_1 )
| ! [A: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A_1 ) @ ( insert_pname @ B_1 @ A ) ) ) )
& ! [B_1: $i] :
( ~ ( is_pname @ A_1 )
| ~ ( is_pname @ B_1 )
| ! [A: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A_1 ) @ A ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A_1 ) @ ( insert_pname @ B_1 @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[535]) ).
thf(1063,plain,
( ( ! [A_1: $i] :
( ! [B_1: $i] :
( ~ ( is_a @ A_1 )
| ~ ( is_a @ B_1 )
| ! [A: $i] :
( ~ ( 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 ) ) ) )
& ! [B_1: $i] :
( ~ ( is_a @ A_1 )
| ~ ( is_a @ B_1 )
| ( A_1 != B_1 )
| ! [A: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_1 ) @ ( insert_a @ B_1 @ A ) ) ) )
& ! [B_1: $i] :
( ~ ( is_a @ A_1 )
| ~ ( is_a @ B_1 )
| ! [A: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_1 ) @ A ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_1 ) @ ( insert_a @ B_1 @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[534]) ).
thf(1064,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 ) ) )
& ! [A: $i,X_2: $i] :
( ( Y_1 != X_2 )
| ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ Y_1 @ A ) @ X_2 ) ) )
& ! [A: $i,X_2: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ A @ X_2 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ Y_1 @ A ) @ X_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[533]) ).
thf(1065,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 ) ) )
& ! [A: $i,X_2: $i] :
( ~ ( is_pname @ Y_1 )
| ~ ( is_pname @ X_2 )
| ( Y_1 != X_2 )
| ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ Y_1 @ A ) @ X_2 ) ) )
& ! [A: $i,X_2: $i] :
( ~ ( is_pname @ Y_1 )
| ~ ( is_pname @ X_2 )
| ~ ( hBOOL @ ( hAPP_pname_bool @ A @ X_2 ) )
| ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ Y_1 @ A ) @ X_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[532]) ).
thf(1066,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 ) ) )
& ! [A: $i,X_2: $i] :
( ~ ( is_a @ Y_1 )
| ~ ( is_a @ X_2 )
| ( Y_1 != X_2 )
| ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ Y_1 @ A ) @ X_2 ) ) )
& ! [A: $i,X_2: $i] :
( ~ ( is_a @ Y_1 )
| ~ ( is_a @ X_2 )
| ~ ( hBOOL @ ( hAPP_a_bool @ A @ X_2 ) )
| ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ Y_1 @ A ) @ X_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[531]) ).
thf(1067,plain,
( ( ! [B: $i] :
( ! [X_2: $i,A: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ X_2 ) @ A ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ X_2 ) @ B ) )
| ( ( insert_nat @ X_2 @ A )
!= ( insert_nat @ X_2 @ B ) )
| ( A = B ) )
& ! [X_2: $i,A: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ X_2 ) @ A ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ X_2 ) @ B ) )
| ( A != B )
| ( ( insert_nat @ X_2 @ A )
= ( insert_nat @ X_2 @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[530]) ).
thf(1068,plain,
( ( ! [B: $i] :
( ! [X_2: $i,A: $i] :
( ~ ( is_fun_pname_bool @ B )
| ~ ( is_fun_pname_bool @ A )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ A ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ B ) )
| ( ( insert_pname @ X_2 @ A )
!= ( insert_pname @ X_2 @ B ) )
| ( A = B ) )
& ! [X_2: $i,A: $i] :
( ~ ( is_fun_pname_bool @ B )
| ~ ( is_fun_pname_bool @ A )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ A ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ B ) )
| ( A != B )
| ( ( insert_pname @ X_2 @ A )
= ( insert_pname @ X_2 @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[529]) ).
thf(1069,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 ) )
& ! [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 ) )
| ( A != B )
| ( ( insert_a @ X_2 @ A )
= ( insert_a @ X_2 @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[528]) ).
thf(1070,plain,
( ( ! [B_1: $i,A_1: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A_1 ) @ B ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A_1 ) @ ( insert_nat @ B_1 @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[527]) ).
thf(1071,plain,
( ( ! [B_1: $i,A_1: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A_1 ) @ B ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A_1 ) @ ( insert_pname @ B_1 @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[526]) ).
thf(1072,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)],[525]) ).
thf(1073,plain,
( ( ! [A_1: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A_1 ) @ A ) )
| ( ( insert_nat @ A_1 @ A )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[524]) ).
thf(1074,plain,
( ( ! [A_1: $i,A: $i] :
( ~ ( is_fun_pname_bool @ A )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A_1 ) @ A ) )
| ( ( insert_pname @ A_1 @ A )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[523]) ).
thf(1075,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)],[522]) ).
thf(1076,plain,
( ( ! [A: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[136]) ).
thf(1077,plain,
( ( ! [A: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[135]) ).
thf(1078,plain,
( ( ! [A: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[134]) ).
thf(1079,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 ) )
& ! [A: $i,B: $i] :
( ( A != B )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) ) )
& ! [A: $i,B: $i] :
( ( A != B )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[521]) ).
thf(1080,plain,
( ( ! [A: $i,B: $i] :
( ~ ( is_fun_pname_bool @ A )
| ~ ( is_fun_pname_bool @ 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 ) )
| ( A = B ) )
& ! [A: $i,B: $i] :
( ~ ( is_fun_pname_bool @ A )
| ~ ( is_fun_pname_bool @ B )
| ( A != B )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( is_fun_pname_bool @ A )
| ~ ( is_fun_pname_bool @ B )
| ( A != B )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[520]) ).
thf(1081,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 ) )
& ! [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 ) ) )
& ! [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 @ B ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[519]) ).
thf(1082,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[518]) ).
thf(1083,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[517]) ).
thf(1084,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)],[516]) ).
thf(1085,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[515]) ).
thf(1086,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[514]) ).
thf(1087,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)],[513]) ).
thf(1088,plain,
( ( ! [X_2: $i,A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ X_2 ) @ A ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ X_2 ) @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[512]) ).
thf(1089,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)],[511]) ).
thf(1090,plain,
( ( ! [X_2: $i,A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ A ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[510]) ).
thf(1091,plain,
( ( ! [B: $i,X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ X_2 ) @ A ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ X_2 ) @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[509]) ).
thf(1092,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)],[508]) ).
thf(1093,plain,
( ( ! [B: $i,X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ A ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[507]) ).
thf(1094,plain,
( ( ! [X_2: $i,A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ X_2 ) @ A ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ X_2 ) @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[506]) ).
thf(1095,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)],[505]) ).
thf(1096,plain,
( ( ! [X_2: $i,A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ A ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[504]) ).
thf(1097,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)],[503]) ).
thf(1098,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)],[502]) ).
thf(1099,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)],[501]) ).
thf(1100,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) ) )
& ! [A: $i,B: $i] :
( ( A != B )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[500]) ).
thf(1101,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) ) )
& ! [A: $i,B: $i] :
( ( A != B )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[499]) ).
thf(1102,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) ) )
& ! [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)],[498]) ).
thf(1103,plain,
( ( ! [X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ X_2 ) @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ A @ X_2 ) ) )
& ! [X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ A @ X_2 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ X_2 ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[497]) ).
thf(1104,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 ) ) )
& ! [X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_a_bool @ A @ X_2 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_2 ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[496]) ).
thf(1105,plain,
( ( ! [X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ A ) )
| ( hBOOL @ ( hAPP_pname_bool @ A @ X_2 ) ) )
& ! [X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_pname_bool @ A @ X_2 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[495]) ).
thf(1106,plain,
( ( ! [Pa: $i] :
( ~ ( is_fun_pname_bool @ Pa )
| ( ( collect_pname @ Pa )
= Pa ) ) )
= $true ),
inference(copy,[status(thm)],[494]) ).
thf(1107,plain,
( ( ! [Pa: $i] :
( ( collect_fun_nat_bool @ Pa )
= Pa ) )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(1108,plain,
( ( ! [Pa: $i] :
( ~ ( is_fun1661590463l_bool @ Pa )
| ( ( collec1974731493e_bool @ Pa )
= Pa ) ) )
= $true ),
inference(copy,[status(thm)],[493]) ).
thf(1109,plain,
( ( ! [Pa: $i] :
( ~ ( is_fun949378684l_bool @ Pa )
| ( ( collect_fun_a_bool @ Pa )
= Pa ) ) )
= $true ),
inference(copy,[status(thm)],[492]) ).
thf(1110,plain,
( ( ! [Pa: $i] :
( ( collect_nat @ Pa )
= Pa ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(1111,plain,
( ( ! [Z: $i] :
( ( ~ ( is_a @ Z )
| ! [F: $i,A: $i] :
( ! [X_1: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_1 ) @ A ) )
| ~ ( is_pname @ X_1 )
| ( Z
!= ( hAPP_pname_a @ F @ X_1 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ Z ) @ ( image_pname_a @ F @ A ) ) ) ) )
& ( ~ ( is_a @ Z )
| ! [F: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ Z ) @ ( image_pname_a @ F @ A ) ) )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK11_X_1 @ A @ F @ Z ) ) @ A ) )
& ( is_pname @ ( sK11_X_1 @ A @ F @ Z ) )
& ( Z
= ( hAPP_pname_a @ F @ ( sK11_X_1 @ A @ F @ Z ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[491]) ).
thf(1112,plain,
( ( ! [F: $i,X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ A ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( hAPP_pname_a @ F @ X_2 ) ) @ ( image_pname_a @ F @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[490]) ).
thf(1113,plain,
( ( ! [B_1: $i,F: $i,X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ A ) )
| ( B_1
!= ( hAPP_pname_a @ F @ X_2 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B_1 ) @ ( image_pname_a @ F @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[489]) ).
thf(1114,plain,
( ( ! [X_1: $i,Xa: $i] :
( ( insert_nat @ X_1 @ Xa )
= ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ fequal_nat ) @ X_1 ) ) @ ( hAPP_f800510211t_bool @ ( cOMBC_226598744l_bool @ member_nat ) @ Xa ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(1115,plain,
( ( ! [X_1: $i,Xa: $i] :
( ( insert_pname @ X_1 @ Xa )
= ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ fequal_pname ) @ X_1 ) ) @ ( hAPP_f759274231e_bool @ ( cOMBC_1058051404l_bool @ member_pname ) @ Xa ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(1116,plain,
( ( ! [X_1: $i,Xa: $i] :
( ( insert_a @ X_1 @ Xa )
= ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ ( hAPP_a_fun_a_bool @ ( cOMBC_a_a_bool @ fequal_a ) @ X_1 ) ) @ ( hAPP_f2050579477a_bool @ ( cOMBC_1355376034l_bool @ member_a ) @ Xa ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(1117,plain,
( ( ! [X_1: $i,Xa: $i] :
( ( insert_fun_nat_bool @ X_1 @ Xa )
= ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ ( hAPP_f103356543l_bool @ ( cOMBC_1693257480l_bool @ fequal_fun_nat_bool ) @ X_1 ) ) @ ( hAPP_f1246832597l_bool @ ( cOMBC_1245412066l_bool @ member_fun_nat_bool ) @ Xa ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(1118,plain,
( ( ! [X_1: $i,Xa: $i] :
( ( insert1325755072e_bool @ X_1 @ Xa )
= ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ X_1 ) ) @ ( hAPP_f559147733l_bool @ ( cOMBC_1988546018l_bool @ member799430823e_bool ) @ Xa ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(1119,plain,
( ( ! [X_1: $i,Xa: $i] :
( ( insert_fun_a_bool @ X_1 @ Xa )
= ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ fequal_fun_a_bool ) @ X_1 ) ) @ ( hAPP_f2117159681l_bool @ ( cOMBC_1880041174l_bool @ member_fun_a_bool ) @ Xa ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(1120,plain,
( ( ! [B: $i,A_1: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ ( insert_nat @ A_1 @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(1121,plain,
( ( ! [B: $i,A_1: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ ( insert_pname @ A_1 @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(1122,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)],[90]) ).
thf(1123,plain,
( ( ! [X_2: $i] :
( ! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ X_2 ) @ B ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( insert_nat @ X_2 @ A ) ) @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( insert_nat @ X_2 @ A ) ) @ B ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ X_2 ) @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( insert_nat @ X_2 @ A ) ) @ B ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[488]) ).
thf(1124,plain,
( ( ! [X_2: $i] :
( ! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ B ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ X_2 @ A ) ) @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ X_2 @ A ) ) @ B ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ X_2 @ A ) ) @ B ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[487]) ).
thf(1125,plain,
( ( ! [X_2: $i] :
( ! [A: $i,B: $i] :
( ~ ( 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 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ X_2 @ A ) ) @ B ) ) )
& ! [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 ) ) )
& ! [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_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[486]) ).
thf(1126,plain,
( ( ! [B: $i] :
( ! [X_2: $i,A: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ X_2 ) @ A ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ ( insert_nat @ X_2 @ B ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) ) )
& ! [X_2: $i,A: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ X_2 ) @ A ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ ( insert_nat @ X_2 @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[485]) ).
thf(1127,plain,
( ( ! [B: $i] :
( ! [X_2: $i,A: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ A ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( insert_pname @ X_2 @ B ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) ) )
& ! [X_2: $i,A: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ A ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( insert_pname @ X_2 @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[484]) ).
thf(1128,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 ) ) )
& ! [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_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ ( insert_a @ X_2 @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[483]) ).
thf(1129,plain,
( ( ! [B_1: $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 @ A ) @ ( insert_nat @ B_1 @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[482]) ).
thf(1130,plain,
( ( ! [B_1: $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 @ A ) @ ( insert_pname @ B_1 @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[481]) ).
thf(1131,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)],[480]) ).
thf(1132,plain,
( ( ! [A_1: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ D ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( insert_nat @ A_1 @ C ) ) @ ( insert_nat @ A_1 @ D ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[479]) ).
thf(1133,plain,
( ( ! [A_1: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ D ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ A_1 @ C ) ) @ ( insert_pname @ A_1 @ D ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[478]) ).
thf(1134,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)],[477]) ).
thf(1135,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)],[77]) ).
thf(1136,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)],[476]) ).
thf(1137,plain,
( ( ! [B: $i] :
( ( ~ ( is_fun_a_bool @ B )
| ! [F: $i,A: $i] :
( ! [AA: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ AA ) @ A ) )
| ~ ( is_fun_pname_bool @ AA )
| ( B
!= ( image_pname_a @ F @ AA ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ ( image_pname_a @ F @ A ) ) ) ) )
& ( ~ ( is_fun_a_bool @ B )
| ! [F: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ ( image_pname_a @ F @ A ) ) )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( sK10_AA @ A @ F @ B ) ) @ A ) )
& ( is_fun_pname_bool @ ( sK10_AA @ A @ F @ B ) )
& ( B
= ( image_pname_a @ F @ ( sK10_AA @ A @ F @ B ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[475]) ).
thf(1138,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)],[474]) ).
thf(1139,plain,
( ( ! [B_1: $i] :
( ~ ( is_a @ B_1 )
| ! [F: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B_1 ) @ ( image_pname_a @ F @ A ) ) )
| ( ( is_pname @ ( sK9_X_1 @ A @ F @ B_1 ) )
& ( B_1
= ( hAPP_pname_a @ F @ ( sK9_X_1 @ A @ F @ B_1 ) ) )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK9_X_1 @ A @ F @ B_1 ) ) @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[473]) ).
thf(1140,plain,
( ( ! [B: $i,A: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ ( sK8_X_1 @ A @ B ) ) @ A ) )
& ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ ( sK8_X_1 @ A @ B ) ) @ B ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[472]) ).
thf(1141,plain,
( ( ! [B: $i,A: $i] :
( ( ( is_a @ ( sK7_X_1 @ A @ B ) )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( sK7_X_1 @ A @ B ) ) @ A ) )
& ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( sK7_X_1 @ A @ B ) ) @ B ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[471]) ).
thf(1142,plain,
( ( ! [B: $i,A: $i] :
( ( ( is_pname @ ( sK6_X_1 @ A @ B ) )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK6_X_1 @ A @ B ) ) @ A ) )
& ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK6_X_1 @ A @ B ) ) @ B ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[470]) ).
thf(1143,plain,
( ( ! [I: $i,Pa: $i,K: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ Pa @ K ) )
| ( ( hBOOL @ ( hAPP_nat_bool @ Pa @ ( hAPP_nat_nat @ suc @ ( sK5_N_2 @ K @ Pa @ I ) ) ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ Pa @ ( sK5_N_2 @ K @ Pa @ I ) ) ) )
| ( hBOOL @ ( hAPP_nat_bool @ Pa @ ( hAPP_nat_nat @ ( minus_minus_nat @ K ) @ I ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[469]) ).
thf(1144,plain,
( ( ! [N_1: $i,M_1: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ N_1 ) ) @ M_1 ) )
| ( M_1
= ( hAPP_nat_nat @ suc @ ( sK4_M @ M_1 @ N_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[468]) ).
thf(1145,plain,
( ( ! [F: $i,B: $i,A: $i] :
( ( ( is_pname @ ( sK3_X_1 @ A @ B @ F ) )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK3_X_1 @ A @ B @ F ) ) @ A ) )
& ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( hAPP_pname_a @ F @ ( sK3_X_1 @ A @ B @ F ) ) ) @ B ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_pname_a @ F @ A ) ) @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[467]) ).
thf(1146,plain,
( ( ! [X_2: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ X_2 ) @ X_2 ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(1147,plain,
( ( ! [X_2: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ X_2 ) @ X_2 ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(1148,plain,
( ( ! [X_3: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_3 ) @ X_3 ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(1149,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)],[63]) ).
thf(1150,plain,
( ( ! [N: $i] :
( ! [M: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ ( sK2_X_1 @ M @ N ) ) @ N ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( sK2_X_1 @ M @ N ) ) @ M ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ N ) ) )
& ! [N: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ N ) )
| ! [SY425: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SY425 ) @ N ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY425 ) @ ( sK1_M @ N ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[466]) ).
thf(1151,plain,
( ( ! [P: $i] :
( ~ ( hBOOL @ ( hAPP_bool_bool @ fNot @ P ) )
| ~ ( hBOOL @ P ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(1152,plain,
( ( ! [P: $i] :
( ( hBOOL @ P )
| ( hBOOL @ ( hAPP_bool_bool @ fNot @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(1153,plain,
( ( ! [Q: $i,P: $i] :
( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ P ) @ Q ) )
| ~ ( hBOOL @ P )
| ~ ( hBOOL @ Q ) ) )
= $true ),
inference(copy,[status(thm)],[465]) ).
thf(1154,plain,
( ( ! [P: $i] :
( ! [Q: $i] :
~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ P ) @ Q ) )
| ( hBOOL @ P ) ) )
= $true ),
inference(copy,[status(thm)],[464]) ).
thf(1155,plain,
( ( ! [P: $i,Q: $i] :
( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ P ) @ Q ) )
| ( hBOOL @ Q ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(1156,plain,
( ( ! [Q: $i,P: $i] :
( ~ ( hBOOL @ P )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ P ) @ Q ) ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(1157,plain,
( ( ! [P: $i,Q: $i] :
( ~ ( hBOOL @ Q )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ P ) @ Q ) ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(1158,plain,
( ( ! [P: $i,Q: $i] :
( ( hBOOL @ Q )
| ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ P ) @ Q ) )
| ( hBOOL @ P ) ) )
= $true ),
inference(copy,[status(thm)],[463]) ).
thf(1159,plain,
( ( ! [Q: $i,P: $i] :
( ( hBOOL @ P )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ P ) @ Q ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(1160,plain,
( ( ! [P: $i,Q: $i] :
( ~ ( hBOOL @ Q )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ P ) @ Q ) ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(1161,plain,
( ( ! [P: $i,Q: $i] :
( ( hBOOL @ Q )
| ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ P ) @ Q ) )
| ~ ( hBOOL @ P ) ) )
= $true ),
inference(copy,[status(thm)],[462]) ).
thf(1162,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( is_a @ X )
| ~ ( is_a @ Y )
| ~ ( hBOOL @ ( hAPP_a_bool @ ( hAPP_a_fun_a_bool @ fequal_a @ X ) @ Y ) )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[461]) ).
thf(1163,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)],[460]) ).
thf(1164,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ X ) @ Y ) )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(1165,plain,
( ( ! [X: $i,Y: $i] :
( ( X != Y )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ X ) @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[459]) ).
thf(1166,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( is_pname @ X )
| ~ ( is_pname @ Y )
| ~ ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ fequal_pname @ X ) @ Y ) )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[458]) ).
thf(1167,plain,
( ( ! [X: $i,Y: $i] :
( ( X != Y )
| ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ fequal_pname @ X ) @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[457]) ).
thf(1168,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ( hAPP_a_bool @ ( hAPP_a_fun_a_bool @ ( cOMBC_a_a_bool @ P ) @ Q ) @ R )
= ( hAPP_a_bool @ ( hAPP_a_fun_a_bool @ P @ R ) @ Q ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(1169,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)],[456]) ).
thf(1170,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)],[455]) ).
thf(1171,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ( hAPP_a_bool @ ( cOMBB_bool_bool_a @ P @ Q ) @ R )
= ( hAPP_bool_bool @ P @ ( hAPP_a_bool @ Q @ R ) ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(1172,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ( hAPP_a_bool @ ( cOMBS_a_bool_bool @ P @ Q ) @ R )
= ( hAPP_bool_bool @ ( hAPP_a_fun_bool_bool @ P @ R ) @ ( hAPP_a_bool @ Q @ R ) ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(1173,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ( hAPP_pname_bool @ ( hAPP_a93125764e_bool @ ( cOMBC_pname_a_bool @ P ) @ Q ) @ R )
= ( hAPP_a_bool @ ( hAPP_p1534023578a_bool @ P @ R ) @ Q ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(1174,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)],[38]) ).
thf(1175,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)],[454]) ).
thf(1176,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( is_fun_pname_bool @ X )
| ~ ( is_fun_pname_bool @ Y )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ X ) @ Y ) )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[453]) ).
thf(1177,plain,
( ( ! [X: $i,Y: $i] :
( ( X != Y )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ X ) @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[452]) ).
thf(1178,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ P ) @ Q ) @ R )
= ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ P @ R ) @ Q ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(1179,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ( hAPP_nat_bool @ ( cOMBB_bool_bool_nat @ P @ Q ) @ R )
= ( hAPP_bool_bool @ P @ ( hAPP_nat_bool @ Q @ R ) ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(1180,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ( hAPP_nat_bool @ ( cOMBS_nat_bool_bool @ P @ Q ) @ R )
= ( hAPP_bool_bool @ ( hAPP_n1006566506l_bool @ P @ R ) @ ( hAPP_nat_bool @ Q @ R ) ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(1181,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ( hAPP_pname_bool @ ( cOMBB_647938656_pname @ P @ Q ) @ R )
= ( hAPP_bool_bool @ P @ ( hAPP_pname_bool @ Q @ R ) ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(1182,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ( hAPP_pname_bool @ ( cOMBS_568398431l_bool @ P @ Q ) @ R )
= ( hAPP_bool_bool @ ( hAPP_p393069232l_bool @ P @ R ) @ ( hAPP_pname_bool @ Q @ R ) ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(1183,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ P ) @ Q ) @ R )
= ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ P @ R ) @ Q ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(1184,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ( hAPP_a_bool @ ( hAPP_f2050579477a_bool @ ( cOMBC_1355376034l_bool @ P ) @ Q ) @ R )
= ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ P @ R ) @ Q ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(1185,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)],[27]) ).
thf(1186,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)],[26]) ).
thf(1187,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ( hAPP_a_fun_bool_bool @ ( cOMBB_1972296269bool_a @ P @ Q ) @ R )
= ( hAPP_b589554111l_bool @ P @ ( hAPP_a_bool @ Q @ R ) ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(1188,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)],[24]) ).
thf(1189,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ( hAPP_nat_bool @ ( hAPP_f800510211t_bool @ ( cOMBC_226598744l_bool @ P ) @ Q ) @ R )
= ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ P @ R ) @ Q ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(1190,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ( hAPP_f54304608l_bool @ ( cOMBB_238756964t_bool @ P @ Q ) @ R )
= ( hAPP_bool_bool @ P @ ( hAPP_f54304608l_bool @ Q @ R ) ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(1191,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ( hAPP_n1006566506l_bool @ ( cOMBB_1015721476ol_nat @ P @ Q ) @ R )
= ( hAPP_b589554111l_bool @ P @ ( hAPP_nat_bool @ Q @ R ) ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(1192,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ( hAPP_f54304608l_bool @ ( cOMBS_1187019125l_bool @ P @ Q ) @ R )
= ( hAPP_bool_bool @ ( hAPP_f1748468828l_bool @ P @ R ) @ ( hAPP_f54304608l_bool @ Q @ R ) ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(1193,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ( hAPP_f1664156314l_bool @ ( cOMBB_307249310e_bool @ P @ Q ) @ R )
= ( hAPP_bool_bool @ P @ ( hAPP_f1664156314l_bool @ Q @ R ) ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(1194,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ( hAPP_p393069232l_bool @ ( cOMBB_675860798_pname @ P @ Q ) @ R )
= ( hAPP_b589554111l_bool @ P @ ( hAPP_pname_bool @ Q @ R ) ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(1195,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ( hAPP_f1664156314l_bool @ ( cOMBS_350070575l_bool @ P @ Q ) @ R )
= ( hAPP_bool_bool @ ( hAPP_f1476298914l_bool @ P @ R ) @ ( hAPP_f1664156314l_bool @ Q @ R ) ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(1196,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ( hAPP_pname_bool @ ( hAPP_f759274231e_bool @ ( cOMBC_1058051404l_bool @ P ) @ Q ) @ R )
= ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ P @ R ) @ Q ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(1197,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)],[15]) ).
thf(1198,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)],[14]) ).
thf(1199,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ( cOMBC_1693257480l_bool @ P ) @ Q ) @ R )
= ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ P @ R ) @ Q ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(1200,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ( hAPP_f1748468828l_bool @ ( cOMBB_444170502t_bool @ P @ Q ) @ R )
= ( hAPP_b589554111l_bool @ P @ ( hAPP_f54304608l_bool @ Q @ R ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(1201,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ( hAPP_f1476298914l_bool @ ( cOMBB_2095475776e_bool @ P @ Q ) @ R )
= ( hAPP_b589554111l_bool @ P @ ( hAPP_f1664156314l_bool @ Q @ R ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(1202,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ P ) @ Q ) @ R )
= ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ P @ R ) @ Q ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(1203,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ( hAPP_fun_a_bool_bool @ ( hAPP_f2117159681l_bool @ ( cOMBC_1880041174l_bool @ P ) @ Q ) @ R )
= ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ P @ R ) @ Q ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(1204,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ( hAPP_f54304608l_bool @ ( hAPP_f1246832597l_bool @ ( cOMBC_1245412066l_bool @ P ) @ Q ) @ R )
= ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ P @ R ) @ Q ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(1205,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ( hAPP_f1664156314l_bool @ ( hAPP_f559147733l_bool @ ( cOMBC_1988546018l_bool @ P ) @ Q ) @ R )
= ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ P @ R ) @ Q ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(1206,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ( cOMBC_331553030l_bool @ P ) @ Q ) @ R )
= ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ P @ R ) @ Q ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(1207,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ( cOMBC_595898202l_bool @ P ) @ Q ) @ R )
= ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ P @ R ) @ Q ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(1208,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ( cOMBC_7971162l_bool @ P ) @ Q ) @ R )
= ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ P @ R ) @ Q ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(1209,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ( hAPP_f292226953l_bool @ ( hAPP_f1050622307l_bool @ ( cOMBC_636888218l_bool @ P ) @ Q ) @ R )
= ( hAPP_f292226953l_bool @ ( hAPP_f1050622307l_bool @ P @ R ) @ Q ) ) )
= $true ),
inference(copy,[status(thm)],[3]) ).
thf(1210,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ( hAPP_f937997336l_bool @ ( hAPP_f760187903l_bool @ ( cOMBC_1269652216l_bool @ P ) @ Q ) @ R )
= ( hAPP_f937997336l_bool @ ( hAPP_f760187903l_bool @ P @ R ) @ Q ) ) )
= $true ),
inference(copy,[status(thm)],[2]) ).
thf(1211,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ( hAPP_f389811538l_bool @ ( hAPP_f1759205631l_bool @ ( cOMBC_336095980l_bool @ P ) @ Q ) @ R )
= ( hAPP_f389811538l_bool @ ( hAPP_f1759205631l_bool @ P @ R ) @ Q ) ) )
= $true ),
inference(copy,[status(thm)],[1]) ).
thf(1212,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)],[451]) ).
thf(1213,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SX0 ) @ SX1 ) )
| ( hBOOL @ ( hAPP_nat_bool @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ SX1 @ SX0 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SX0 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1103]) ).
thf(1214,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SX0 ) @ SX1 ) )
| ( hBOOL @ ( hAPP_pname_bool @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_pname_bool @ SX1 @ SX0 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SX0 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1105]) ).
thf(1215,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fconj @ SX1 ) @ SX0 ) ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ SX0 ) ) )
| ! [SX1: $i] : ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fconj @ SX1 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[961]) ).
thf(1216,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX0 ) @ SX1 ) ) )
| ~ ! [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)],[1102]) ).
thf(1217,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( is_fun_a_bool @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ! [SX3: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SX3 ) @ SX2 ) )
| ~ ( is_fun_pname_bool @ SX3 )
| ( SX0
!= ( image_pname_a @ SX1 @ SX3 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX0 ) @ ( image_pname_a @ SX1 @ SX2 ) ) ) ) )
| ~ ( ~ ( is_fun_a_bool @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX0 ) @ ( image_pname_a @ SX1 @ SX2 ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( sK10_AA @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ( is_fun_pname_bool @ ( sK10_AA @ SX2 @ SX1 @ SX0 ) ) )
| ( SX0
!= ( image_pname_a @ SX1 @ ( sK10_AA @ SX2 @ SX1 @ SX0 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1137]) ).
thf(1218,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX0 ) @ ( hAPP_nat_nat @ suc @ SX1 ) ) )
| ( SX0
= ( hAPP_nat_nat @ suc @ SX1 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX0 ) @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( hAPP_nat_nat @ suc @ SX1 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX0 ) @ ( hAPP_nat_nat @ suc @ SX1 ) ) ) )
| ~ ! [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 @ SX0 ) @ ( hAPP_nat_nat @ suc @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1008]) ).
thf(1219,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 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX0 ) @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX1 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1079]) ).
thf(1220,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SX1 ) )
| ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ SX0 ) @ SX1 ) )
| ( ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( insert_fun_nat_bool @ SX0 @ SX1 ) )
= ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SX1 ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ SX0 ) @ SX1 ) )
| ( ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( insert_fun_nat_bool @ SX0 @ SX1 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[949]) ).
thf(1221,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( is_fun_pname_bool @ SX0 )
| ~ ( is_fun_pname_bool @ 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 ) )
| ( SX0 = SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( is_fun_pname_bool @ SX0 )
| ~ ( is_fun_pname_bool @ SX1 )
| ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SX0 ) @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( is_fun_pname_bool @ SX0 )
| ~ ( is_fun_pname_bool @ SX1 )
| ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SX1 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1080]) ).
thf(1222,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ SX1 ) @ SX0 ) ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ SX0 ) ) )
| ! [SX1: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ SX1 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[965]) ).
thf(1223,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_nat @ suc @ SX0 )
!= ( hAPP_nat_nat @ suc @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( hAPP_nat_nat @ suc @ SX0 )
= ( hAPP_nat_nat @ suc @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[971]) ).
thf(1224,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 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( is_pname @ SX0 )
| ~ ( is_pname @ SX2 )
| ( SX0 != SX2 )
| ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SX0 @ SX1 ) @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( is_pname @ SX0 )
| ~ ( is_pname @ SX2 )
| ~ ( hBOOL @ ( hAPP_pname_bool @ SX1 @ SX2 ) )
| ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SX0 @ SX1 ) @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1065]) ).
thf(1225,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SX0 ) @ ( insert_nat @ SX1 @ SX2 ) ) )
| ( SX0 = SX1 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SX0 ) @ SX2 ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ( SX0 != SX1 )
| ! [SX2: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SX0 ) @ ( insert_nat @ SX1 @ SX2 ) ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SX0 ) @ SX2 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SX0 ) @ ( insert_nat @ SX1 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1061]) ).
thf(1226,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ SX0 @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SX1 ) ) )
| ~ ! [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)],[986]) ).
thf(1227,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( is_a @ SX0 )
| ~ ( is_a @ SX1 )
| ! [SX2: $i] :
( ~ ( 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 ) ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( is_a @ SX0 )
| ~ ( is_a @ SX1 )
| ( SX0 != SX1 )
| ! [SX2: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX0 ) @ ( insert_a @ SX1 @ SX2 ) ) ) )
| ~ ! [SX1: $i] :
( ~ ( is_a @ SX0 )
| ~ ( is_a @ SX1 )
| ! [SX2: $i] :
( ~ ( 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)],[1063]) ).
thf(1228,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ SX1 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ SX1 ) @ SX0 ) ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ SX0 ) ) )
| ! [SX1: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ SX1 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[964]) ).
thf(1229,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 ) ) )
| ~ ! [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_f1631501043l_bool @ ord_le1311769555a_bool @ SX2 ) @ ( insert_a @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1128]) ).
thf(1230,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( is_a @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ! [SX3: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SX3 ) @ SX2 ) )
| ~ ( is_pname @ SX3 )
| ( SX0
!= ( hAPP_pname_a @ SX1 @ SX3 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX0 ) @ ( image_pname_a @ SX1 @ SX2 ) ) ) ) )
| ~ ( ~ ( is_a @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX0 ) @ ( image_pname_a @ SX1 @ SX2 ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK11_X_1 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ( is_pname @ ( sK11_X_1 @ SX2 @ SX1 @ SX0 ) ) )
| ( SX0
!= ( hAPP_pname_a @ SX1 @ ( sK11_X_1 @ SX2 @ SX1 @ SX0 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1111]) ).
thf(1231,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SX1 ) @ SX2 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX2 ) @ ( insert_nat @ SX1 @ SX0 ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX2 ) @ SX0 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SX1 ) @ SX2 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX2 ) @ SX0 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX2 ) @ ( insert_nat @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1126]) ).
thf(1232,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fconj @ SX1 ) @ SX0 ) ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ SX0 ) ) )
| ! [SX1: $i] : ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fconj @ SX1 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[963]) ).
thf(1233,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SX0 @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SX1 ) ) )
| ~ ! [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)],[990]) ).
thf(1234,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SX1 ) @ SX2 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SX1 ) @ ( insert_nat @ SX0 @ SX2 ) ) ) )
| ~ ! [SX1: $i] :
( ( SX1 != SX0 )
| ! [SX2: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SX1 ) @ ( insert_nat @ SX0 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1034]) ).
thf(1235,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 ) )
| ~ ~ ( ~ ! [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 ) ) )
| ~ ! [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 @ SX1 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1081]) ).
thf(1236,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( is_fun_a_bool @ SX2 )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SX2 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX2 ) @ ( image_pname_a @ SX0 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( sK17_C_2 @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( is_fun_pname_bool @ ( sK17_C_2 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( sK17_C_2 @ SX2 @ SX1 @ SX0 ) ) ) )
| ( SX2
!= ( image_pname_a @ SX0 @ ( sK17_C_2 @ SX2 @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1021]) ).
thf(1237,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ SX1 ) ) @ SX0 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX0 ) @ SX1 ) ) )
| ~ ! [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 @ ( hAPP_nat_nat @ suc @ SX1 ) ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1009]) ).
thf(1238,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SX1 ) @ SX2 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SX1 ) @ ( insert_pname @ SX0 @ SX2 ) ) ) )
| ~ ! [SX1: $i] :
( ( SX1 != SX0 )
| ! [SX2: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SX1 ) @ ( insert_pname @ SX0 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1035]) ).
thf(1239,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ SX0 ) ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ SX1 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ SX0 ) @ SX1 ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ SX0 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[985]) ).
thf(1240,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( 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 ) ) )
| ~ ~ ( ~ ! [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 ) ) )
| ~ ! [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_f1631501043l_bool @ ord_le1311769555a_bool @ SX1 ) @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1125]) ).
thf(1241,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ SX0 ) ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ SX0 ) @ SX1 ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ SX0 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[984]) ).
thf(1242,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 ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK12_X_1 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( is_pname @ ( sK12_X_1 @ SX1 @ SX0 ) ) )
| ~ ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ ( hAPP_f759274231e_bool @ ( cOMBC_1058051404l_bool @ member_pname ) @ SX1 ) ) @ ( hAPP_a93125764e_bool @ ( cOMBC_pname_a_bool @ ( cOMBB_1897541054_pname @ fequal_a @ SX0 ) ) @ ( hAPP_pname_a @ SX0 @ ( sK12_X_1 @ SX1 @ SX0 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1026]) ).
thf(1243,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SX0 ) @ SX2 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX1 ) @ SX2 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( insert_nat @ SX0 @ SX1 ) ) @ SX2 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( insert_nat @ SX0 @ SX1 ) ) @ SX2 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SX0 ) @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( insert_nat @ SX0 @ SX1 ) ) @ SX2 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX1 ) @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1123]) ).
thf(1244,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SX1 ) )
| ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ SX0 ) @ SX1 ) )
| ( ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( insert1325755072e_bool @ SX0 @ SX1 ) )
= ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SX1 ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ SX0 ) @ SX1 ) )
| ( ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( insert1325755072e_bool @ SX0 @ SX1 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[950]) ).
thf(1245,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ SX0 @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SX1 ) ) )
| ~ ! [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)],[987]) ).
thf(1246,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SX1 ) @ SX2 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SX1 ) @ SX0 ) )
| ( ( insert_nat @ SX1 @ SX2 )
!= ( insert_nat @ SX1 @ SX0 ) )
| ( SX2 = SX0 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SX1 ) @ SX2 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SX1 ) @ SX0 ) )
| ( SX2 != SX0 )
| ( ( insert_nat @ SX1 @ SX2 )
= ( insert_nat @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1067]) ).
thf(1247,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( is_a @ ( sK7_X_1 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( sK7_X_1 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( sK7_X_1 @ SX1 @ SX0 ) ) @ SX0 ) ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1141]) ).
thf(1248,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX0 ) @ SX1 ) )
| ( hBOOL @ ( hAPP_a_bool @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[1104]) ).
thf(1249,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 ) ) ) )
| ~ ! [SX1: $i] :
( ( SX1 != SX0 )
| ! [SX2: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX1 ) @ ( insert_a @ SX0 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1036]) ).
thf(1250,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SX1 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SX0 ) @ SX1 ) )
| ( ( hAPP_f22106695ol_nat @ finite_card_nat @ ( insert_nat @ SX0 @ SX1 ) )
= ( hAPP_f22106695ol_nat @ finite_card_nat @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SX1 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SX0 ) @ SX1 ) )
| ( ( hAPP_f22106695ol_nat @ finite_card_nat @ ( insert_nat @ SX0 @ SX1 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[952]) ).
thf(1251,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ SX0 @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SX1 ) ) )
| ~ ! [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)],[991]) ).
thf(1252,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SX1 ) )
| ~ ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ SX0 ) @ SX1 ) )
| ( ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( insert_fun_a_bool @ SX0 @ SX1 ) )
= ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SX1 ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ SX0 ) @ SX1 ) )
| ( ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( insert_fun_a_bool @ SX0 @ SX1 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[951]) ).
thf(1253,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SX0 ) @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1101]) ).
thf(1254,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( ~ ( is_pname @ ( sK3_X_1 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK3_X_1 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( hAPP_pname_a @ SX0 @ ( sK3_X_1 @ SX2 @ SX1 @ SX0 ) ) ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_pname_a @ SX0 @ SX2 ) ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1145]) ).
thf(1255,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 @ SX1 ) @ SX0 ) )
| ( ( hAPP_nat_nat @ ( minus_minus_nat @ SX2 ) @ SX1 )
!= ( hAPP_nat_nat @ ( minus_minus_nat @ SX0 ) @ SX1 ) )
| ( SX2 = SX0 ) )
| ~ ! [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 @ SX1 ) @ SX0 ) )
| ( SX2 != SX0 )
| ( ( hAPP_nat_nat @ ( minus_minus_nat @ SX2 ) @ SX1 )
= ( hAPP_nat_nat @ ( minus_minus_nat @ SX0 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1015]) ).
thf(1256,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ ( sK8_X_1 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ ( sK8_X_1 @ SX1 @ SX0 ) ) @ SX0 ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1140]) ).
thf(1257,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ SX0 ) ) )
| ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ SX0 ) @ SX1 ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ SX0 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[982]) ).
thf(1258,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fconj @ SX1 ) @ SX0 ) ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ SX0 ) ) )
| ! [SX1: $i] : ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fconj @ SX1 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[962]) ).
thf(1259,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SX1 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX0 ) @ SX1 ) )
| ( ( hAPP_fun_a_bool_nat @ finite_card_a @ ( insert_a @ SX0 @ SX1 ) )
= ( hAPP_fun_a_bool_nat @ finite_card_a @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SX1 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX0 ) @ SX1 ) )
| ( ( hAPP_fun_a_bool_nat @ finite_card_a @ ( insert_a @ SX0 @ SX1 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[954]) ).
thf(1260,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SX1 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SX0 ) @ SX1 ) )
| ( ( hAPP_f921600141ol_nat @ finite_card_pname @ ( insert_pname @ SX0 @ SX1 ) )
= ( hAPP_f921600141ol_nat @ finite_card_pname @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SX1 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SX0 ) @ SX1 ) )
| ( ( hAPP_f921600141ol_nat @ finite_card_pname @ ( insert_pname @ SX0 @ SX1 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[953]) ).
thf(1261,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( is_pname @ SX0 )
| ~ ( is_pname @ SX1 )
| ! [SX2: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SX0 ) @ ( insert_pname @ SX1 @ SX2 ) ) )
| ( SX0 = SX1 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SX0 ) @ SX2 ) ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( is_pname @ SX0 )
| ~ ( is_pname @ SX1 )
| ( SX0 != SX1 )
| ! [SX2: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SX0 ) @ ( insert_pname @ SX1 @ SX2 ) ) ) )
| ~ ! [SX1: $i] :
( ~ ( is_pname @ SX0 )
| ~ ( is_pname @ SX1 )
| ! [SX2: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SX0 ) @ SX2 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SX0 ) @ ( insert_pname @ SX1 @ SX2 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1062]) ).
thf(1262,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SX0 ) @ SX2 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SX1 ) @ SX2 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ SX0 @ SX1 ) ) @ SX2 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ SX0 @ SX1 ) ) @ SX2 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SX0 ) @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ SX0 @ SX1 ) ) @ SX2 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SX1 ) @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1124]) ).
thf(1263,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ SX0 ) ) )
| ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ SX0 ) @ SX1 ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ SX0 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[983]) ).
thf(1264,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 ) )
| ~ ! [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 ) )
| ( SX2 != SX0 )
| ( ( insert_a @ SX1 @ SX2 )
= ( insert_a @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1069]) ).
thf(1265,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX0 ) @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1100]) ).
thf(1266,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 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( is_a @ SX0 )
| ~ ( is_a @ SX2 )
| ( SX0 != SX2 )
| ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SX0 @ SX1 ) @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( is_a @ SX0 )
| ~ ( is_a @ SX2 )
| ~ ( hBOOL @ ( hAPP_a_bool @ SX1 @ SX2 ) )
| ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SX0 @ SX1 ) @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1066]) ).
thf(1267,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ SX1 ) @ SX0 ) ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ SX0 ) ) )
| ! [SX1: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ SX1 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[966]) ).
thf(1268,plain,
( ( ! [SX0: $i] :
( ~ ( is_a @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX0 ) @ ( image_pname_a @ SX1 @ SX2 ) ) )
| ~ ( ~ ( is_pname @ ( sK9_X_1 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( ( SX0
!= ( hAPP_pname_a @ SX1 @ ( sK9_X_1 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK9_X_1 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1139]) ).
thf(1269,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ SX0 @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SX1 ) ) )
| ~ ! [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)],[989]) ).
thf(1270,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ SX0 ) ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ SX0 ) @ SX1 ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ SX0 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[980]) ).
thf(1271,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ SX1 @ SX2 ) )
| ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ SX1 @ ( hAPP_nat_nat @ suc @ ( sK5_N_2 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ~ ( hBOOL @ ( hAPP_nat_bool @ SX1 @ ( sK5_N_2 @ SX2 @ SX1 @ SX0 ) ) ) )
| ( hBOOL @ ( hAPP_nat_bool @ SX1 @ ( hAPP_nat_nat @ ( minus_minus_nat @ SX2 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1143]) ).
thf(1272,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ SX0 ) ) )
| ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ SX0 ) @ SX1 ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ SX0 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[981]) ).
thf(1273,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( is_fun_pname_bool @ SX0 )
| ~ ( is_fun_pname_bool @ SX2 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SX1 ) @ SX2 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SX1 ) @ SX0 ) )
| ( ( insert_pname @ SX1 @ SX2 )
!= ( insert_pname @ SX1 @ SX0 ) )
| ( SX2 = SX0 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( is_fun_pname_bool @ SX0 )
| ~ ( is_fun_pname_bool @ SX2 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SX1 ) @ SX2 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SX1 ) @ SX0 ) )
| ( SX2 != SX0 )
| ( ( insert_pname @ SX1 @ SX2 )
= ( insert_pname @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1068]) ).
thf(1274,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ SX0 ) ) @ ( hAPP_nat_nat @ suc @ SX1 ) ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX0 ) @ SX1 ) ) )
| ~ ! [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 @ ( hAPP_nat_nat @ suc @ SX0 ) ) @ ( hAPP_nat_nat @ suc @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1007]) ).
thf(1275,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SX1 ) @ SX2 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SX2 ) @ ( insert_pname @ SX1 @ SX0 ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SX2 ) @ SX0 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SX1 ) @ SX2 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SX2 ) @ SX0 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SX2 ) @ ( insert_pname @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1127]) ).
thf(1276,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 @ SX1 ) @ SX0 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ SX2 ) @ SX1 ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ SX0 ) @ SX1 ) ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX2 ) @ SX0 ) ) )
| ~ ! [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 @ SX1 ) @ SX0 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX2 ) @ SX0 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ SX2 ) @ SX1 ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ SX0 ) @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1013]) ).
thf(1277,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( is_pname @ ( sK6_X_1 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK6_X_1 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK6_X_1 @ SX1 @ SX0 ) ) @ SX0 ) ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1142]) ).
thf(1278,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SX0 @ SX1 ) @ SX2 ) )
| ( SX0 = SX2 )
| ( hBOOL @ ( hAPP_nat_bool @ SX1 @ SX2 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( SX0 != SX2 )
| ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SX0 @ SX1 ) @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ SX1 @ SX2 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SX0 @ SX1 ) @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1064]) ).
thf(1279,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ ( sK2_X_1 @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( sK2_X_1 @ SX1 @ SX0 ) ) @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SX0 ) )
| ! [SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX1 ) @ ( sK1_M @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1150]) ).
thf(1280,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 ) ) )
| ~ ! [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)],[988]) ).
thf(1281,plain,
! [SV1: $i] :
( ( ! [SY426: $i] :
( ~ ( is_fun_pname_bool @ SY426 )
| ( is_fun_a_bool @ ( image_pname_a @ SV1 @ SY426 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[765]) ).
thf(1282,plain,
! [SV2: $i] :
( ( ! [SY427: $i] :
( ~ ( is_a @ SV2 )
| ~ ( is_fun_a_bool @ SY427 )
| ( is_fun_a_bool @ ( insert_a @ SV2 @ SY427 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[766]) ).
thf(1283,plain,
! [SV3: $i] :
( ( ! [SY428: $i] :
( ~ ( is_a @ SY428 )
| ( is_fun949378684l_bool @ ( hAPP_a85458249l_bool @ SV3 @ SY428 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[767]) ).
thf(1284,plain,
! [SV4: $i] :
( ( ! [SY429: $i] :
( ~ ( is_pname @ SY429 )
| ( is_a @ ( hAPP_pname_a @ SV4 @ SY429 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[768]) ).
thf(1285,plain,
! [SV5: $i] :
( ( ! [SY430: $i] :
( ~ ( is_pname @ SY430 )
| ( is_fun1661590463l_bool @ ( hAPP_p338031245l_bool @ SV5 @ SY430 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[769]) ).
thf(1286,plain,
! [SV6: $i] :
( ( ! [SY431: $i] : ( is_bool @ ( hAPP_nat_bool @ SV6 @ SY431 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[770]) ).
thf(1287,plain,
! [SV7: $i] :
( ( ! [SY432: $i] :
( ~ ( is_fun949378684l_bool @ SV7 )
| ~ ( is_fun_a_bool @ SY432 )
| ( is_bool @ ( hAPP_fun_a_bool_bool @ SV7 @ SY432 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[771]) ).
thf(1288,plain,
! [SV8: $i] :
( ( ! [SY433: $i] :
( ~ ( is_fun_a_bool @ SY433 )
| ( is_fun949378684l_bool @ ( hAPP_f1631501043l_bool @ SV8 @ SY433 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[772]) ).
thf(1289,plain,
! [SV9: $i] :
( ( ! [SY434: $i] :
( ~ ( is_fun1661590463l_bool @ SV9 )
| ~ ( is_fun_pname_bool @ SY434 )
| ( is_bool @ ( hAPP_f1664156314l_bool @ SV9 @ SY434 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[773]) ).
thf(1290,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)],[782]) ).
thf(1291,plain,
! [SV10: $i] :
( ( ! [SY435: $i] :
( ~ ( is_fun_a_bool @ SY435 )
| ( is_fun_a_bool @ ( cOMBB_bool_bool_a @ SV10 @ SY435 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[783]) ).
thf(1292,plain,
! [SV11: $i] :
( ( ! [SY436: $i] :
( ~ ( is_fun_pname_bool @ SY436 )
| ( is_fun_pname_bool @ ( cOMBB_647938656_pname @ SV11 @ SY436 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[784]) ).
thf(1293,plain,
! [SV12: $i] :
( ( ! [SY437: $i] :
( ~ ( is_fun949378684l_bool @ SY437 )
| ( is_fun949378684l_bool @ ( cOMBB_2140588453a_bool @ SV12 @ SY437 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[785]) ).
thf(1294,plain,
! [SV13: $i] :
( ( ! [SY438: $i] :
( ~ ( is_fun1661590463l_bool @ SY438 )
| ( is_fun1661590463l_bool @ ( cOMBB_307249310e_bool @ SV13 @ SY438 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[786]) ).
thf(1295,plain,
! [SV14: $i] :
( ( ! [SY439: $i] :
( ~ ( is_fun_a_bool @ SY439 )
| ( is_fun_a_bool @ ( cOMBS_a_bool_bool @ SV14 @ SY439 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[787]) ).
thf(1296,plain,
! [SV15: $i] :
( ( ! [SY440: $i] :
( ~ ( is_fun_pname_bool @ SY440 )
| ( is_fun_pname_bool @ ( cOMBS_568398431l_bool @ SV15 @ SY440 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[788]) ).
thf(1297,plain,
! [SV16: $i] :
( ( ! [SY441: $i] :
( ~ ( is_fun949378684l_bool @ SY441 )
| ( is_fun949378684l_bool @ ( cOMBS_1035972772l_bool @ SV16 @ SY441 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[789]) ).
thf(1298,plain,
! [SV17: $i] :
( ( ! [SY442: $i] :
( ~ ( is_fun1661590463l_bool @ SY442 )
| ( is_fun1661590463l_bool @ ( cOMBS_350070575l_bool @ SV17 @ SY442 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[790]) ).
thf(1299,plain,
! [SV18: $i] :
( ( ~ ( is_fun_a_bool @ SV18 )
| ( is_fun_a_bool @ ( collect_a @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[798]) ).
thf(1300,plain,
! [SV19: $i] :
( ( ~ ( is_fun_pname_bool @ SV19 )
| ( is_fun_pname_bool @ ( collect_pname @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[799]) ).
thf(1301,plain,
! [SV20: $i] :
( ( ~ ( is_fun949378684l_bool @ SV20 )
| ( is_fun949378684l_bool @ ( collect_fun_a_bool @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[800]) ).
thf(1302,plain,
! [SV21: $i] :
( ( ~ ( is_fun1661590463l_bool @ SV21 )
| ( is_fun1661590463l_bool @ ( collec1974731493e_bool @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[801]) ).
thf(1303,plain,
! [SV22: $i] :
( ( ! [SY443: $i] :
( ~ ( is_fun_a_bool @ SY443 )
| ( is_fun_a_bool @ ( image_a_a @ SV22 @ SY443 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[802]) ).
thf(1304,plain,
! [SV23: $i] :
( ( ! [SY444: $i] :
( ~ ( is_fun_a_bool @ SY444 )
| ( is_fun_pname_bool @ ( image_a_pname @ SV23 @ SY444 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[803]) ).
thf(1305,plain,
! [SV24: $i] :
( ( ! [SY445: $i] :
( ~ ( is_fun_pname_bool @ SY445 )
| ( is_fun_pname_bool @ ( image_pname_pname @ SV24 @ SY445 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[804]) ).
thf(1306,plain,
! [SV25: $i] :
( ( ! [SY446: $i] :
( ~ ( is_fun_pname_bool @ SY446 )
| ( is_fun949378684l_bool @ ( image_112932426a_bool @ SV25 @ SY446 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[805]) ).
thf(1307,plain,
! [SV26: $i] :
( ( ! [SY447: $i] :
( ~ ( is_fun_pname_bool @ SY447 )
| ( is_fun1661590463l_bool @ ( image_47868345e_bool @ SV26 @ SY447 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[806]) ).
thf(1308,plain,
! [SV27: $i] :
( ( ! [SY448: $i] : ( is_fun_a_bool @ ( image_nat_a @ SV27 @ SY448 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[807]) ).
thf(1309,plain,
! [SV28: $i] :
( ( ! [SY449: $i] : ( is_fun_pname_bool @ ( image_nat_pname @ SV28 @ SY449 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[808]) ).
thf(1310,plain,
! [SV29: $i] :
( ( ! [SY450: $i] : ( is_fun949378684l_bool @ ( image_nat_fun_a_bool @ SV29 @ SY450 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[809]) ).
thf(1311,plain,
! [SV30: $i] :
( ( ! [SY451: $i] : ( is_fun1661590463l_bool @ ( image_1655916159e_bool @ SV30 @ SY451 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[810]) ).
thf(1312,plain,
! [SV31: $i] :
( ( ! [SY452: $i] :
( ~ ( is_fun949378684l_bool @ SY452 )
| ( is_fun_a_bool @ ( image_fun_a_bool_a @ SV31 @ SY452 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[811]) ).
thf(1313,plain,
! [SV32: $i] :
( ( ! [SY453: $i] :
( ~ ( is_fun949378684l_bool @ SY453 )
| ( is_fun_pname_bool @ ( image_1854862208_pname @ SV32 @ SY453 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[812]) ).
thf(1314,plain,
! [SV33: $i] :
( ( ! [SY454: $i] :
( ~ ( is_fun1661590463l_bool @ SY454 )
| ( is_fun_a_bool @ ( image_876012084bool_a @ SV33 @ SY454 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[813]) ).
thf(1315,plain,
! [SV34: $i] :
( ( ! [SY455: $i] :
( ~ ( is_fun1661590463l_bool @ SY455 )
| ( is_fun_pname_bool @ ( image_1283814551_pname @ SV34 @ SY455 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[814]) ).
thf(1316,plain,
! [SV35: $i] :
( ( ! [SY456: $i] : ( is_fun_a_bool @ ( image_fun_nat_bool_a @ SV35 @ SY456 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[815]) ).
thf(1317,plain,
! [SV36: $i] :
( ( ! [SY457: $i] : ( is_fun_pname_bool @ ( image_1921560913_pname @ SV36 @ SY457 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[816]) ).
thf(1318,plain,
! [SV37: $i] :
( ( ! [SY458: $i] : ( is_fun_a_bool @ ( image_573985017bool_a @ SV37 @ SY458 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[817]) ).
thf(1319,plain,
! [SV38: $i] :
( ( ! [SY459: $i] : ( is_fun_pname_bool @ ( image_990671762_pname @ SV38 @ SY459 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[818]) ).
thf(1320,plain,
! [SV39: $i] :
( ( ! [SY460: $i] : ( is_fun_a_bool @ ( image_349102846bool_a @ SV39 @ SY460 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[819]) ).
thf(1321,plain,
! [SV40: $i] :
( ( ! [SY461: $i] : ( is_fun_pname_bool @ ( image_1705983821_pname @ SV40 @ SY461 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[820]) ).
thf(1322,plain,
! [SV41: $i] :
( ( ! [SY462: $i] : ( is_fun_a_bool @ ( image_526090948bool_a @ SV41 @ SY462 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[821]) ).
thf(1323,plain,
! [SV42: $i] :
( ( ! [SY463: $i] : ( is_fun_pname_bool @ ( image_1604018183_pname @ SV42 @ SY463 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[822]) ).
thf(1324,plain,
! [SV43: $i] :
( ( ! [SY464: $i] :
( ~ ( is_fun_pname_bool @ SY464 )
| ~ ( is_pname @ SV43 )
| ( is_fun_pname_bool @ ( insert_pname @ SV43 @ SY464 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[823]) ).
thf(1325,plain,
! [SV44: $i] :
( ( ! [SY465: $i] :
( ~ ( is_fun949378684l_bool @ SY465 )
| ~ ( is_fun_a_bool @ SV44 )
| ( is_fun949378684l_bool @ ( insert_fun_a_bool @ SV44 @ SY465 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[824]) ).
thf(1326,plain,
! [SV45: $i] :
( ( ! [SY466: $i] :
( ~ ( is_fun1661590463l_bool @ SY466 )
| ~ ( is_fun_pname_bool @ SV45 )
| ( is_fun1661590463l_bool @ ( insert1325755072e_bool @ SV45 @ SY466 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[825]) ).
thf(1327,plain,
! [SV46: $i] :
( ( ! [SY467: $i] :
( ~ ( is_a @ SY467 )
| ~ ( is_fun_a_bool @ SV46 )
| ( is_bool @ ( hAPP_a_bool @ SV46 @ SY467 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[826]) ).
thf(1328,plain,
! [SV47: $i] :
( ( ! [SY468: $i] :
( ~ ( is_a @ SY468 )
| ( is_fun_a_bool @ ( hAPP_a_fun_a_bool @ SV47 @ SY468 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[827]) ).
thf(1329,plain,
! [SV48: $i] :
( ( ! [SY469: $i] :
( ~ ( is_a @ SY469 )
| ( is_fun_pname_bool @ ( hAPP_a93125764e_bool @ SV48 @ SY469 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[828]) ).
thf(1330,plain,
! [SV49: $i] :
( ( ! [SY470: $i] :
( ~ ( is_fun_pname_bool @ SV49 )
| ~ ( is_pname @ SY470 )
| ( is_bool @ ( hAPP_pname_bool @ SV49 @ SY470 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[829]) ).
thf(1331,plain,
! [SV50: $i] :
( ( ! [SY471: $i] :
( ~ ( is_pname @ SY471 )
| ( is_fun_a_bool @ ( hAPP_p1534023578a_bool @ SV50 @ SY471 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[830]) ).
thf(1332,plain,
! [SV51: $i] :
( ( ! [SY472: $i] :
( ~ ( is_pname @ SY472 )
| ( is_fun_pname_bool @ ( hAPP_p61793385e_bool @ SV51 @ SY472 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[831]) ).
thf(1333,plain,
! [SV52: $i] :
( ( ! [SY473: $i] :
( ~ ( is_bool @ SY473 )
| ( is_bool @ ( hAPP_bool_bool @ SV52 @ SY473 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[832]) ).
thf(1334,plain,
! [SV53: $i] :
( ( ! [SY474: $i] : ( is_fun_a_bool @ ( hAPP_nat_fun_a_bool @ SV53 @ SY474 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[833]) ).
thf(1335,plain,
! [SV54: $i] :
( ( ! [SY475: $i] : ( is_fun_pname_bool @ ( hAPP_n1025906991e_bool @ SV54 @ SY475 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[834]) ).
thf(1336,plain,
! [SV55: $i] :
( ( ! [SY476: $i] :
( ~ ( is_fun_a_bool @ SY476 )
| ( is_fun_a_bool @ ( hAPP_f2050579477a_bool @ SV55 @ SY476 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[835]) ).
thf(1337,plain,
! [SV56: $i] :
( ( ! [SY477: $i] :
( ~ ( is_fun_pname_bool @ SY477 )
| ( is_fun_pname_bool @ ( hAPP_f759274231e_bool @ SV56 @ SY477 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[836]) ).
thf(1338,plain,
! [SV57: $i] :
( ( ! [SY478: $i] :
( ~ ( is_fun_pname_bool @ SY478 )
| ( is_fun1661590463l_bool @ ( hAPP_f434788991l_bool @ SV57 @ SY478 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[837]) ).
thf(1339,plain,
! [SV58: $i] :
( ( ! [SY479: $i] : ( is_bool @ ( hAPP_f54304608l_bool @ SV58 @ SY479 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[838]) ).
thf(1340,plain,
! [SV59: $i] :
( ( ! [SY480: $i] :
( ~ ( is_fun949378684l_bool @ SY480 )
| ( is_bool @ ( hAPP_f621171935l_bool @ SV59 @ SY480 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[839]) ).
thf(1341,plain,
! [SV60: $i] :
( ( ! [SY481: $i] :
( ~ ( is_fun949378684l_bool @ SY481 )
| ( is_fun949378684l_bool @ ( hAPP_f2117159681l_bool @ SV60 @ SY481 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[840]) ).
thf(1342,plain,
! [SV61: $i] :
( ( ! [SY482: $i] :
( ~ ( is_fun1661590463l_bool @ SY482 )
| ( is_bool @ ( hAPP_f1935102916l_bool @ SV61 @ SY482 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[841]) ).
thf(1343,plain,
! [SV62: $i] :
( ( ! [SY483: $i] :
( ~ ( is_fun1661590463l_bool @ SY483 )
| ( is_fun1661590463l_bool @ ( hAPP_f559147733l_bool @ SV62 @ SY483 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[842]) ).
thf(1344,plain,
! [SV63: $i] :
( ( ! [SY484: $i] : ( is_bool @ ( hAPP_f1637334154l_bool @ SV63 @ SY484 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[843]) ).
thf(1345,plain,
! [SV64: $i] :
( ( ! [SY485: $i] : ( is_bool @ ( hAPP_f292226953l_bool @ SV64 @ SY485 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[844]) ).
thf(1346,plain,
! [SV65: $i] :
( ( ! [SY486: $i] : ( is_bool @ ( hAPP_f389811538l_bool @ SV65 @ SY486 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[845]) ).
thf(1347,plain,
! [SV66: $i] :
( ( ! [SY487: $i] : ( is_bool @ ( hAPP_f937997336l_bool @ SV66 @ SY487 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[846]) ).
thf(1348,plain,
! [SV67: $i] :
( ( ! [SY488: $i] : ( is_bool @ ( hAPP_f1363661463l_bool @ SV67 @ SY488 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[847]) ).
thf(1349,plain,
! [SV68: $i] :
( ( ! [SY489: $i] : ( is_bool @ ( hAPP_f595608956l_bool @ SV68 @ SY489 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[848]) ).
thf(1350,plain,
! [SV69: $i] :
( ( ! [SY490: $i] : ( is_bool @ ( hAPP_f1295398978l_bool @ SV69 @ SY490 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[849]) ).
thf(1351,plain,
! [SV70: $i] :
( ( ~ ( is_fun_a_bool @ SV70 )
| ( is_fun949378684l_bool @ ( p @ SV70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[850]) ).
thf(1352,plain,
! [SV71: $i] :
( ( ! [SY491: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV71 ) @ SY491 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( p @ SY491 ) @ SV71 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[851]) ).
thf(1353,plain,
! [SV72: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV72 ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( hAPP_f103356543l_bool @ ( cOMBC_1693257480l_bool @ ord_le1568362934t_bool ) @ SV72 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[852]) ).
thf(1354,plain,
! [SV73: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV73 ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ ord_le313189616e_bool ) @ SV73 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[853]) ).
thf(1355,plain,
! [SV74: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV74 ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ ord_le1311769555a_bool ) @ SV74 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[854]) ).
thf(1356,plain,
! [SV75: $i] :
( ( ~ ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ SV75 ) )
| ( hBOOL @ ( hAPP_f1295398978l_bool @ finite719726885l_bool @ ( collec1874991203l_bool @ ( hAPP_f760187903l_bool @ ( cOMBC_1269652216l_bool @ ord_le65145710l_bool ) @ SV75 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[855]) ).
thf(1357,plain,
! [SV76: $i] :
( ( ~ ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ SV76 ) )
| ( hBOOL @ ( hAPP_f595608956l_bool @ finite1491191519l_bool @ ( collec792590109l_bool @ ( hAPP_f1759205631l_bool @ ( cOMBC_336095980l_bool @ ord_le1375671464l_bool ) @ SV76 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[856]) ).
thf(1358,plain,
! [SV77: $i] :
( ( ~ ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ SV77 ) )
| ( hBOOL @ ( hAPP_f1363661463l_bool @ finite1343359508l_bool @ ( collec1635217238l_bool @ ( hAPP_f1050622307l_bool @ ( cOMBC_636888218l_bool @ ord_le967226251l_bool ) @ SV77 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[857]) ).
thf(1359,plain,
! [SV78: $i] :
( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV78 ) )
| ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ ( collec707592106l_bool @ ( hAPP_f1434722111l_bool @ ( cOMBC_331553030l_bool @ ord_le1375614389l_bool ) @ SV78 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[858]) ).
thf(1360,plain,
! [SV79: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV79 ) )
| ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ ( collec1613912337l_bool @ ( hAPP_f510955609l_bool @ ( cOMBC_7971162l_bool @ ord_le675606854l_bool ) @ SV79 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[859]) ).
thf(1361,plain,
! [SV80: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV80 ) )
| ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ ( collec1015864663l_bool @ ( hAPP_f1772781669l_bool @ ( cOMBC_595898202l_bool @ ord_le1454342156l_bool ) @ SV80 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[860]) ).
thf(1362,plain,
! [SV81: $i] :
( ( ! [SY492: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SY492 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_pname_a @ SV81 @ SY492 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[861]) ).
thf(1363,plain,
! [SV82: $i] :
( ( ! [SY493: $i] :
( ~ ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ SY493 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_2089570637ol_nat @ SV82 @ SY493 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[862]) ).
thf(1364,plain,
! [SV83: $i] :
( ( ! [SY494: $i] :
( ~ ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ SY494 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_1079571347ol_nat @ SV83 @ SY494 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[863]) ).
thf(1365,plain,
! [SV84: $i] :
( ( ! [SY495: $i] :
( ~ ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ SY495 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_1802975832ol_nat @ SV84 @ SY495 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[864]) ).
thf(1366,plain,
! [SV85: $i] :
( ( ! [SY496: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SY496 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_fun_a_bool_nat @ SV85 @ SY496 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[865]) ).
thf(1367,plain,
! [SV86: $i] :
( ( ! [SY497: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SY497 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_1551609309ol_nat @ SV86 @ SY497 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[866]) ).
thf(1368,plain,
! [SV87: $i] :
( ( ! [SY498: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SY498 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_496248727ol_nat @ SV87 @ SY498 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[867]) ).
thf(1369,plain,
! [SV88: $i] :
( ( ! [SY499: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY499 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_a_nat @ SV88 @ SY499 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[868]) ).
thf(1370,plain,
! [SV89: $i] :
( ( ! [SY500: $i] :
( ~ ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ SY500 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1604018183_pname @ SV89 @ SY500 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[869]) ).
thf(1371,plain,
! [SV90: $i] :
( ( ! [SY501: $i] :
( ~ ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ SY501 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1705983821_pname @ SV90 @ SY501 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[870]) ).
thf(1372,plain,
! [SV91: $i] :
( ( ! [SY502: $i] :
( ~ ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ SY502 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_990671762_pname @ SV91 @ SY502 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[871]) ).
thf(1373,plain,
! [SV92: $i] :
( ( ! [SY503: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SY503 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1854862208_pname @ SV92 @ SY503 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[872]) ).
thf(1374,plain,
! [SV93: $i] :
( ( ! [SY504: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SY504 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1283814551_pname @ SV93 @ SY504 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[873]) ).
thf(1375,plain,
! [SV94: $i] :
( ( ! [SY505: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SY505 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1921560913_pname @ SV94 @ SY505 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[874]) ).
thf(1376,plain,
! [SV95: $i] :
( ( ! [SY506: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY506 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_a_pname @ SV95 @ SY506 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[875]) ).
thf(1377,plain,
! [SV96: $i] :
( ( ! [SY507: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SY507 ) )
| ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ ( image_1607900221l_bool @ SV96 @ SY507 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[876]) ).
thf(1378,plain,
! [SV97: $i] :
( ( ! [SY508: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SY508 ) )
| ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ ( image_1874789623l_bool @ SV97 @ SY508 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[877]) ).
thf(1379,plain,
! [SV98: $i] :
( ( ! [SY509: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SY509 ) )
| ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ ( image_1208015684l_bool @ SV98 @ SY509 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[878]) ).
thf(1380,plain,
! [SV99: $i] :
( ( ! [SY510: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SY510 ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( image_nat_fun_a_bool @ SV99 @ SY510 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[879]) ).
thf(1381,plain,
! [SV100: $i] :
( ( ! [SY511: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SY511 ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( image_1655916159e_bool @ SV100 @ SY511 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[880]) ).
thf(1382,plain,
! [SV101: $i] :
( ( ! [SY512: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SY512 ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( image_26036933t_bool @ SV101 @ SY512 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[881]) ).
thf(1383,plain,
! [SV102: $i] :
( ( ! [SY513: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SY513 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_nat_a @ SV102 @ SY513 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[882]) ).
thf(1384,plain,
! [SV103: $i] :
( ( ! [SY514: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SY514 ) )
| ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ ( image_1154884483l_bool @ SV103 @ SY514 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[883]) ).
thf(1385,plain,
! [SV104: $i] :
( ( ! [SY515: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SY515 ) )
| ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ ( image_1642285373l_bool @ SV104 @ SY515 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[884]) ).
thf(1386,plain,
! [SV105: $i] :
( ( ! [SY516: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SY516 ) )
| ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ ( image_1420695166l_bool @ SV105 @ SY516 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[885]) ).
thf(1387,plain,
! [SV106: $i] :
( ( ! [SY517: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SY517 ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( image_112932426a_bool @ SV106 @ SY517 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[886]) ).
thf(1388,plain,
! [SV107: $i] :
( ( ! [SY518: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SY518 ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( image_47868345e_bool @ SV107 @ SY518 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[887]) ).
thf(1389,plain,
! [SV108: $i] :
( ( ! [SY519: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SY519 ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( image_2129980159t_bool @ SV108 @ SY519 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[888]) ).
thf(1390,plain,
! [SV109: $i] :
( ( ! [SY520: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SY520 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_pname_pname @ SV109 @ SY520 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[889]) ).
thf(1391,plain,
! [SV110: $i] :
( ( ! [SY521: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY521 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_a_a @ SV110 @ SY521 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[890]) ).
thf(1392,plain,
! [SV111: $i] :
( ( ! [SY522: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SY522 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_fun_nat_bool_a @ SV111 @ SY522 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[891]) ).
thf(1393,plain,
! [SV112: $i] :
( ( ! [SY523: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SY523 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_876012084bool_a @ SV112 @ SY523 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[892]) ).
thf(1394,plain,
! [SV113: $i] :
( ( ! [SY524: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SY524 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_fun_a_bool_a @ SV113 @ SY524 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[893]) ).
thf(1395,plain,
! [SV114: $i] :
( ( ! [SY525: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SY525 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_pname_nat @ SV114 @ SY525 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[894]) ).
thf(1396,plain,
! [SV115: $i] :
( ( ! [SY526: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SY526 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_nat_pname @ SV115 @ SY526 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[895]) ).
thf(1397,plain,
! [SV116: $i] :
( ( ! [SY527: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY527 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ SV116 @ SY527 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[896]) ).
thf(1398,plain,
! [SV117: $i] :
( ( ! [SY528: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SY528 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ SV117 @ SY528 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[897]) ).
thf(1399,plain,
! [SV118: $i] :
( ( ! [SY529: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SY529 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ SV118 @ SY529 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[898]) ).
thf(1400,plain,
! [SV119: $i] :
( ( ! [SY530: $i] :
( ~ ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ SY530 ) )
| ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ ( insert2003652156l_bool @ SV119 @ SY530 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[899]) ).
thf(1401,plain,
! [SV120: $i] :
( ( ! [SY531: $i] :
( ~ ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ SY531 ) )
| ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ ( insert1117693814l_bool @ SV120 @ SY531 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[900]) ).
thf(1402,plain,
! [SV121: $i] :
( ( ! [SY532: $i] :
( ~ ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ SY532 ) )
| ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ ( insert1457093509l_bool @ SV121 @ SY532 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[901]) ).
thf(1403,plain,
! [SV122: $i] :
( ( ! [SY533: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SY533 ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ SV122 @ SY533 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[902]) ).
thf(1404,plain,
! [SV123: $i] :
( ( ! [SY534: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SY534 ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SV123 @ SY534 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[903]) ).
thf(1405,plain,
! [SV124: $i] :
( ( ! [SY535: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SY535 ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ SV124 @ SY535 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[904]) ).
thf(1406,plain,
! [SV125: $i] :
( ( ! [SY536: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SY536 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( image_pname_nat @ SV125 @ SY536 ) ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SY536 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[905]) ).
thf(1407,plain,
! [SV126: $i] :
( ( ! [SY537: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY537 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( image_a_nat @ SV126 @ SY537 ) ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SY537 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[906]) ).
thf(1408,plain,
! [SV127: $i] :
( ( ! [SY538: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SY538 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( image_496248727ol_nat @ SV127 @ SY538 ) ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SY538 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[907]) ).
thf(1409,plain,
! [SV128: $i] :
( ( ! [SY539: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SY539 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( image_1551609309ol_nat @ SV128 @ SY539 ) ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SY539 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[908]) ).
thf(1410,plain,
! [SV129: $i] :
( ( ! [SY540: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SY540 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( image_fun_a_bool_nat @ SV129 @ SY540 ) ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SY540 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[909]) ).
thf(1411,plain,
! [SV130: $i] :
( ( ! [SY541: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY541 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( image_a_pname @ SV130 @ SY541 ) ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SY541 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[910]) ).
thf(1412,plain,
! [SV131: $i] :
( ( ! [SY542: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SY542 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( image_nat_pname @ SV131 @ SY542 ) ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SY542 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[911]) ).
thf(1413,plain,
! [SV132: $i] :
( ( ! [SY543: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SY543 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_pname_a @ SV132 @ SY543 ) ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SY543 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[912]) ).
thf(1414,plain,
! [SV133: $i] :
( ( ! [SY544: $i] :
( ~ ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ SY544 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_526090948bool_a @ SV133 @ SY544 ) ) ) @ ( hAPP_f1690079119ol_nat @ finite1352710292l_bool @ SY544 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[913]) ).
thf(1415,plain,
! [SV134: $i] :
( ( ! [SY545: $i] :
( ~ ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ SY545 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_349102846bool_a @ SV134 @ SY545 ) ) ) @ ( hAPP_f98387925ol_nat @ finite269641166l_bool @ SY545 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[914]) ).
thf(1416,plain,
! [SV135: $i] :
( ( ! [SY546: $i] :
( ~ ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ SY546 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_573985017bool_a @ SV135 @ SY546 ) ) ) @ ( hAPP_f1253658590ol_nat @ finite1659325229l_bool @ SY546 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[915]) ).
thf(1417,plain,
! [SV136: $i] :
( ( ! [SY547: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SY547 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_fun_a_bool_a @ SV136 @ SY547 ) ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SY547 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[916]) ).
thf(1418,plain,
! [SV137: $i] :
( ( ! [SY548: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SY548 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_876012084bool_a @ SV137 @ SY548 ) ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SY548 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[917]) ).
thf(1419,plain,
! [SV138: $i] :
( ( ! [SY549: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SY549 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_fun_nat_bool_a @ SV138 @ SY549 ) ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SY549 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[918]) ).
thf(1420,plain,
! [SV139: $i] :
( ( ! [SY550: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY550 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_a_a @ SV139 @ SY550 ) ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SY550 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[919]) ).
thf(1421,plain,
! [SV140: $i] :
( ( ! [SY551: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SY551 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( image_pname_pname @ SV140 @ SY551 ) ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SY551 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[920]) ).
thf(1422,plain,
! [SV141: $i] :
( ( ! [SY552: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SY552 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( image_2129980159t_bool @ SV141 @ SY552 ) ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SY552 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[921]) ).
thf(1423,plain,
! [SV142: $i] :
( ( ! [SY553: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SY553 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( image_47868345e_bool @ SV142 @ SY553 ) ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SY553 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[922]) ).
thf(1424,plain,
! [SV143: $i] :
( ( ! [SY554: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SY554 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( image_112932426a_bool @ SV143 @ SY554 ) ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SY554 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[923]) ).
thf(1425,plain,
! [SV144: $i] :
( ( ! [SY555: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SY555 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_nat_a @ SV144 @ SY555 ) ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SY555 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[924]) ).
thf(1426,plain,
! [SV145: $i] :
( ( ! [SY556: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SY556 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( image_26036933t_bool @ SV145 @ SY556 ) ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SY556 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[925]) ).
thf(1427,plain,
! [SV146: $i] :
( ( ! [SY557: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SY557 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( image_1655916159e_bool @ SV146 @ SY557 ) ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SY557 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[926]) ).
thf(1428,plain,
! [SV147: $i] :
( ( ! [SY558: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SY558 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( image_nat_fun_a_bool @ SV147 @ SY558 ) ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SY558 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[927]) ).
thf(1429,plain,
! [SV148: $i] :
( ( ! [SY559: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SY559 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( image_1921560913_pname @ SV148 @ SY559 ) ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SY559 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[928]) ).
thf(1430,plain,
! [SV149: $i] :
( ( ! [SY560: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SY560 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( image_1283814551_pname @ SV149 @ SY560 ) ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SY560 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[929]) ).
thf(1431,plain,
! [SV150: $i] :
( ( ! [SY561: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SY561 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( image_1854862208_pname @ SV150 @ SY561 ) ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SY561 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[930]) ).
thf(1432,plain,
! [SV151: $i] :
( ( ! [SY562: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SY562 ) )
| ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ SV151 ) @ SY562 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SV151 ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SY562 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[931]) ).
thf(1433,plain,
! [SV152: $i] :
( ( ! [SY563: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SY563 ) )
| ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ SV152 ) @ SY563 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SV152 ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SY563 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[932]) ).
thf(1434,plain,
! [SV153: $i] :
( ( ! [SY564: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SY564 ) )
| ~ ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ SV153 ) @ SY564 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SV153 ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SY564 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[933]) ).
thf(1435,plain,
! [SV154: $i] :
( ( ! [SY565: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SY565 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV154 ) @ SY565 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV154 ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SY565 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[934]) ).
thf(1436,plain,
! [SV155: $i] :
( ( ! [SY566: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY566 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV155 ) @ SY566 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SV155 ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SY566 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[935]) ).
thf(1437,plain,
! [SV156: $i] :
( ( ! [SY567: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SY567 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV156 ) @ SY567 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SV156 ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SY567 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[936]) ).
thf(1438,plain,
! [SV157: $i] :
( ( ! [SY568: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SY568 ) )
| ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ SV157 ) @ SY568 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SY568 ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SV157 ) ) )
| ( SV157 = SY568 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[937]) ).
thf(1439,plain,
! [SV158: $i] :
( ( ! [SY569: $i] :
( ~ ( is_fun1661590463l_bool @ SV158 )
| ~ ( is_fun1661590463l_bool @ SY569 )
| ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SY569 ) )
| ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ SV158 ) @ SY569 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SY569 ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SV158 ) ) )
| ( SV158 = SY569 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[938]) ).
thf(1440,plain,
! [SV159: $i] :
( ( ! [SY570: $i] :
( ~ ( is_fun949378684l_bool @ SV159 )
| ~ ( is_fun949378684l_bool @ SY570 )
| ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SY570 ) )
| ~ ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ SV159 ) @ SY570 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SY570 ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SV159 ) ) )
| ( SV159 = SY570 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[939]) ).
thf(1441,plain,
! [SV160: $i] :
( ( ! [SY571: $i] :
( ~ ( is_fun_pname_bool @ SV160 )
| ~ ( is_fun_pname_bool @ SY571 )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SY571 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV160 ) @ SY571 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SY571 ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV160 ) ) )
| ( SV160 = SY571 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[940]) ).
thf(1442,plain,
! [SV161: $i] :
( ( ! [SY572: $i] :
( ~ ( is_fun_a_bool @ SV161 )
| ~ ( is_fun_a_bool @ SY572 )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY572 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV161 ) @ SY572 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SY572 ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SV161 ) ) )
| ( SV161 = SY572 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[941]) ).
thf(1443,plain,
! [SV162: $i] :
( ( ! [SY573: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SY573 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV162 ) @ SY573 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SY573 ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SV162 ) ) )
| ( SV162 = SY573 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[942]) ).
thf(1444,plain,
! [SV163: $i] :
( ( ! [SY574: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SY574 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SY574 ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( insert_fun_nat_bool @ SV163 @ SY574 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[943]) ).
thf(1445,plain,
! [SV164: $i] :
( ( ! [SY575: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SY575 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SY575 ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( insert1325755072e_bool @ SV164 @ SY575 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[944]) ).
thf(1446,plain,
! [SV165: $i] :
( ( ! [SY576: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SY576 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SY576 ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( insert_fun_a_bool @ SV165 @ SY576 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[945]) ).
thf(1447,plain,
! [SV166: $i] :
( ( ! [SY577: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SY577 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SY577 ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( insert_pname @ SV166 @ SY577 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[946]) ).
thf(1448,plain,
! [SV167: $i] :
( ( ! [SY578: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SY578 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SY578 ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( insert_nat @ SV167 @ SY578 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[947]) ).
thf(1449,plain,
! [SV168: $i] :
( ( ! [SY579: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY579 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SY579 ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( insert_a @ SV168 @ SY579 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[948]) ).
thf(1450,plain,
! [SV169: $i] :
( ( ! [SY580: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SY580 ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ SV169 ) @ SY580 ) )
| ( ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( insert_fun_nat_bool @ SV169 @ SY580 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SY580 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[955]) ).
thf(1451,plain,
! [SV170: $i] :
( ( ! [SY581: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SY581 ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ SV170 ) @ SY581 ) )
| ( ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( insert1325755072e_bool @ SV170 @ SY581 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SY581 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[956]) ).
thf(1452,plain,
! [SV171: $i] :
( ( ! [SY582: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SY582 ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ SV171 ) @ SY582 ) )
| ( ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( insert_fun_a_bool @ SV171 @ SY582 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SY582 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[957]) ).
thf(1453,plain,
! [SV172: $i] :
( ( ! [SY583: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SY583 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV172 ) @ SY583 ) )
| ( ( hAPP_f22106695ol_nat @ finite_card_nat @ ( insert_nat @ SV172 @ SY583 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SY583 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[958]) ).
thf(1454,plain,
! [SV173: $i] :
( ( ! [SY584: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SY584 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV173 ) @ SY584 ) )
| ( ( hAPP_f921600141ol_nat @ finite_card_pname @ ( insert_pname @ SV173 @ SY584 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SY584 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[959]) ).
thf(1455,plain,
! [SV174: $i] :
( ( ! [SY585: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY585 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV174 ) @ SY585 ) )
| ( ( hAPP_fun_a_bool_nat @ finite_card_a @ ( insert_a @ SV174 @ SY585 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SY585 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[960]) ).
thf(1456,plain,
! [SV175: $i] :
( ( ! [SY586: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV175 ) @ SY586 ) )
| ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ suc @ SY586 ) ) @ SV175 )
= ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( minus_minus_nat @ SY586 ) @ SV175 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[967]) ).
thf(1457,plain,
! [SV176: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ ord_less_eq_nat ) @ SV176 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[968]) ).
thf(1458,plain,
! [SV177: $i] :
( ( ( hAPP_f22106695ol_nat @ finite_card_nat @ ( collect_nat @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ ord_less_eq_nat ) @ SV177 ) ) )
= ( hAPP_nat_nat @ suc @ SV177 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[969]) ).
thf(1459,plain,
! [SV178: $i] :
( ( ! [SY587: $i] :
( ( ( hAPP_nat_nat @ suc @ SV178 )
!= ( hAPP_nat_nat @ suc @ SY587 ) )
| ( SV178 = SY587 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[970]) ).
thf(1460,plain,
! [SV179: $i] :
( ( ( ( hAPP_nat_nat @ suc @ SV179 )
!= SV179 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[972]) ).
thf(1461,plain,
! [SV180: $i] :
( ( ( SV180
!= ( hAPP_nat_nat @ suc @ SV180 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[973]) ).
thf(1462,plain,
! [SV181: $i] :
( ( ! [SY588: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV181 ) @ SY588 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY588 ) @ SV181 ) )
| ( SV181 = SY588 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[974]) ).
thf(1463,plain,
! [SV182: $i] :
( ( ! [SY589: $i,SY590: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY589 ) @ SY590 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY590 ) @ SV182 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY589 ) @ SV182 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[975]) ).
thf(1464,plain,
! [SV183: $i] :
( ( ! [SY591: $i] :
( ( SV183 != SY591 )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV183 ) @ SY591 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[976]) ).
thf(1465,plain,
! [SV184: $i] :
( ( ! [SY592: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV184 ) @ SY592 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY592 ) @ SV184 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[977]) ).
thf(1466,plain,
! [SV185: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV185 ) @ SV185 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[978]) ).
thf(1467,plain,
! [SV186: $i] :
( ( ! [SY593: $i,SY594: $i] :
( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV186 ) @ SY593 ) ) @ SY594 )
= ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV186 ) @ SY594 ) ) @ SY593 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[979]) ).
thf(1468,plain,
! [SV187: $i] :
( ( ! [SY595: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ SV187 ) @ SY595 ) )
| ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SY595 ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV187 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[992]) ).
thf(1469,plain,
! [SV188: $i] :
( ( ! [SY596: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ SV188 ) @ SY596 ) )
| ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SY596 ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV188 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[993]) ).
thf(1470,plain,
! [SV189: $i] :
( ( ! [SY597: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV189 ) @ SY597 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY597 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV189 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[994]) ).
thf(1471,plain,
! [SV190: $i] :
( ( ! [SY598: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ SV190 ) @ SY598 ) )
| ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SY598 ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV190 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[995]) ).
thf(1472,plain,
! [SV191: $i] :
( ( ! [SY599: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV191 ) @ SY599 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SY599 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV191 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[996]) ).
thf(1473,plain,
! [SV192: $i] :
( ( ! [SY600: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV192 ) @ SY600 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SY600 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV192 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[997]) ).
thf(1474,plain,
! [SV193: $i] :
( ( ! [SY601: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SY601 ) )
| ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ SV193 ) @ SY601 ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV193 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[998]) ).
thf(1475,plain,
! [SV194: $i] :
( ( ! [SY602: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SY602 ) )
| ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ SV194 ) @ SY602 ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV194 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[999]) ).
thf(1476,plain,
! [SV195: $i] :
( ( ! [SY603: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY603 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV195 ) @ SY603 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV195 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1000]) ).
thf(1477,plain,
! [SV196: $i] :
( ( ! [SY604: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SY604 ) )
| ~ ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ SV196 ) @ SY604 ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV196 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1001]) ).
thf(1478,plain,
! [SV197: $i] :
( ( ! [SY605: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SY605 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV197 ) @ SY605 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV197 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1002]) ).
thf(1479,plain,
! [SV198: $i] :
( ( ! [SY606: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SY606 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV198 ) @ SY606 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV198 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1003]) ).
thf(1480,plain,
! [SV199: $i] :
( ( ! [SY607: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ SV199 ) ) @ SY607 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV199 ) @ SY607 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1004]) ).
thf(1481,plain,
! [SV200: $i] :
( ( ! [SY608: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV200 ) @ ( hAPP_nat_nat @ suc @ SY608 ) ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV200 ) @ SY608 ) )
| ( SV200
= ( hAPP_nat_nat @ suc @ SY608 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1005]) ).
thf(1482,plain,
! [SV201: $i] :
( ( ! [SY609: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV201 ) @ SY609 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV201 ) @ ( hAPP_nat_nat @ suc @ SY609 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1006]) ).
thf(1483,plain,
! [SV202: $i] :
( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ SV202 ) ) @ SV202 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1010]) ).
thf(1484,plain,
! [SV203: $i] :
( ( ! [SY610: $i,SY611: $i] :
( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ suc @ SV203 ) ) @ SY610 ) ) @ ( hAPP_nat_nat @ suc @ SY611 ) )
= ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV203 ) @ SY610 ) ) @ SY611 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1011]) ).
thf(1485,plain,
! [SV204: $i] :
( ( ! [SY612: $i] :
( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ suc @ SV204 ) ) @ ( hAPP_nat_nat @ suc @ SY612 ) )
= ( hAPP_nat_nat @ ( minus_minus_nat @ SV204 ) @ SY612 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1012]) ).
thf(1486,plain,
! [SV205: $i] :
( ( ! [SY613: $i,SY614: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY613 ) @ SY614 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY613 ) @ SV205 ) )
| ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ SY614 ) @ SY613 ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV205 ) @ SY613 ) )
= ( hAPP_nat_nat @ ( minus_minus_nat @ SY614 ) @ SV205 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1014]) ).
thf(1487,plain,
! [SV206: $i] :
( ( ! [SY615: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV206 ) @ SY615 ) )
| ( ( hAPP_nat_nat @ ( minus_minus_nat @ SY615 ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ SY615 ) @ SV206 ) )
= SV206 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1016]) ).
thf(1488,plain,
! [SV207: $i] :
( ( ! [SY616: $i,SY617: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY616 ) @ SY617 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ SY616 ) @ SV207 ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ SY617 ) @ SV207 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1017]) ).
thf(1489,plain,
! [SV208: $i] :
( ( ! [SY618: $i,SY619: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY618 ) @ SY619 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV208 ) @ SY619 ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV208 ) @ SY618 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1018]) ).
thf(1490,plain,
! [SV209: $i] :
( ( ! [SY620: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV209 ) @ SY620 ) ) @ SV209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1019]) ).
thf(1491,plain,
! [SV210: $i] :
( ( ! [SY621: $i,SY622: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SY622 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV210 ) @ ( image_pname_a @ SY621 @ SY622 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV210 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1020]) ).
thf(1492,plain,
! [SV211: $i] :
( ( ! [SY623: $i,SY624: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( hAPP_n1699378549t_bool @ SY624 @ ( sK16_N_2 @ SY624 @ SY623 @ SV211 ) ) ) @ ( hAPP_n1699378549t_bool @ SY624 @ ( hAPP_nat_nat @ suc @ ( sK16_N_2 @ SY624 @ SY623 @ SV211 ) ) ) ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV211 ) @ SY623 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( hAPP_n1699378549t_bool @ SY624 @ SV211 ) ) @ ( hAPP_n1699378549t_bool @ SY624 @ SY623 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1022]) ).
thf(1493,plain,
! [SV212: $i] :
( ( ! [SY625: $i,SY626: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_n1025906991e_bool @ SY626 @ ( sK15_N_2 @ SY626 @ SY625 @ SV212 ) ) ) @ ( hAPP_n1025906991e_bool @ SY626 @ ( hAPP_nat_nat @ suc @ ( sK15_N_2 @ SY626 @ SY625 @ SV212 ) ) ) ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV212 ) @ SY625 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_n1025906991e_bool @ SY626 @ SV212 ) ) @ ( hAPP_n1025906991e_bool @ SY626 @ SY625 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1023]) ).
thf(1494,plain,
! [SV213: $i] :
( ( ! [SY627: $i,SY628: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ SY628 @ ( sK14_N_2 @ SY628 @ SY627 @ SV213 ) ) ) @ ( hAPP_nat_nat @ SY628 @ ( hAPP_nat_nat @ suc @ ( sK14_N_2 @ SY628 @ SY627 @ SV213 ) ) ) ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV213 ) @ SY627 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ SY628 @ SV213 ) ) @ ( hAPP_nat_nat @ SY628 @ SY627 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1024]) ).
thf(1495,plain,
! [SV214: $i] :
( ( ! [SY629: $i,SY630: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_nat_fun_a_bool @ SY630 @ ( sK13_N_2 @ SY630 @ SY629 @ SV214 ) ) ) @ ( hAPP_nat_fun_a_bool @ SY630 @ ( hAPP_nat_nat @ suc @ ( sK13_N_2 @ SY630 @ SY629 @ SV214 ) ) ) ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV214 ) @ SY629 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_nat_fun_a_bool @ SY630 @ SV214 ) ) @ ( hAPP_nat_fun_a_bool @ SY630 @ SY629 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1025]) ).
thf(1496,plain,
! [SV215: $i] :
( ( ! [SY631: $i,SY632: $i,SY633: $i] :
( ( SY631
!= ( hAPP_pname_a @ SY632 @ SY633 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SY633 ) @ SV215 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY631 ) @ ( image_pname_a @ SY632 @ SV215 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1027]) ).
thf(1497,plain,
! [SV216: $i] :
( ( ! [SY634: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV216 ) @ SY634 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY634 ) @ SV216 ) )
| ( SV216 = SY634 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1028]) ).
thf(1498,plain,
! [SV217: $i] :
( ( ! [SY635: $i] :
( ~ ( is_fun_pname_bool @ SV217 )
| ~ ( is_fun_pname_bool @ SY635 )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV217 ) @ SY635 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY635 ) @ SV217 ) )
| ( SV217 = SY635 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1029]) ).
thf(1499,plain,
! [SV218: $i] :
( ( ! [SY636: $i] :
( ~ ( is_fun_a_bool @ SV218 )
| ~ ( is_fun_a_bool @ SY636 )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV218 ) @ SY636 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY636 ) @ SV218 ) )
| ( SV218 = SY636 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1030]) ).
thf(1500,plain,
! [SV219: $i] :
( ( ! [SY637: $i,SY638: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY637 ) @ SY638 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV219 ) @ SY637 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV219 ) @ SY638 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1031]) ).
thf(1501,plain,
! [SV220: $i] :
( ( ! [SY639: $i,SY640: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY639 ) @ SY640 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV220 ) @ SY639 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV220 ) @ SY640 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1032]) ).
thf(1502,plain,
! [SV221: $i] :
( ( ! [SY641: $i,SY642: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY641 ) @ SY642 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV221 ) @ SY641 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV221 ) @ SY642 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1033]) ).
thf(1503,plain,
! [SV222: $i] :
( ( ! [SY643: $i,SY644: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV222 ) @ ( insert_nat @ SY643 @ SY644 ) ) )
| ( SV222 = SY643 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV222 ) @ SY644 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1037]) ).
thf(1504,plain,
! [SV223: $i] :
( ( ! [SY645: $i] :
( ~ ( is_pname @ SV223 )
| ~ ( is_pname @ SY645 )
| ! [SY646: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV223 ) @ ( insert_pname @ SY645 @ SY646 ) ) )
| ( SV223 = SY645 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV223 ) @ SY646 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1038]) ).
thf(1505,plain,
! [SV224: $i] :
( ( ! [SY647: $i] :
( ~ ( is_a @ SV224 )
| ~ ( is_a @ SY647 )
| ! [SY648: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV224 ) @ ( insert_a @ SY647 @ SY648 ) ) )
| ( SV224 = SY647 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV224 ) @ SY648 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1039]) ).
thf(1506,plain,
! [SV225: $i] :
( ( ! [SY649: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV225 ) @ ( insert_nat @ SV225 @ SY649 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1040]) ).
thf(1507,plain,
! [SV226: $i] :
( ( ! [SY650: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV226 ) @ ( insert_pname @ SV226 @ SY650 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1041]) ).
thf(1508,plain,
! [SV227: $i] :
( ( ! [SY651: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV227 ) @ ( insert_a @ SV227 @ SY651 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1042]) ).
thf(1509,plain,
! [SV228: $i] :
( ( ! [SY652: $i] :
( ( insert_nat @ SV228 @ SY652 )
= ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ fequal_nat ) @ SV228 ) ) @ ( hAPP_f800510211t_bool @ ( cOMBC_226598744l_bool @ member_nat ) @ SY652 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1043]) ).
thf(1510,plain,
! [SV229: $i] :
( ( ! [SY653: $i] :
( ( insert_pname @ SV229 @ SY653 )
= ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ fequal_pname ) @ SV229 ) ) @ ( hAPP_f759274231e_bool @ ( cOMBC_1058051404l_bool @ member_pname ) @ SY653 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1044]) ).
thf(1511,plain,
! [SV230: $i] :
( ( ! [SY654: $i] :
( ( insert_a @ SV230 @ SY654 )
= ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ ( hAPP_a_fun_a_bool @ ( cOMBC_a_a_bool @ fequal_a ) @ SV230 ) ) @ ( hAPP_f2050579477a_bool @ ( cOMBC_1355376034l_bool @ member_a ) @ SY654 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1045]) ).
thf(1512,plain,
! [SV231: $i] :
( ( ! [SY655: $i] :
( ( insert_fun_nat_bool @ SV231 @ SY655 )
= ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ ( hAPP_f103356543l_bool @ ( cOMBC_1693257480l_bool @ fequal_fun_nat_bool ) @ SV231 ) ) @ ( hAPP_f1246832597l_bool @ ( cOMBC_1245412066l_bool @ member_fun_nat_bool ) @ SY655 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1046]) ).
thf(1513,plain,
! [SV232: $i] :
( ( ! [SY656: $i] :
( ( insert1325755072e_bool @ SV232 @ SY656 )
= ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ SV232 ) ) @ ( hAPP_f559147733l_bool @ ( cOMBC_1988546018l_bool @ member799430823e_bool ) @ SY656 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1047]) ).
thf(1514,plain,
! [SV233: $i] :
( ( ! [SY657: $i] :
( ( insert_fun_a_bool @ SV233 @ SY657 )
= ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ fequal_fun_a_bool ) @ SV233 ) ) @ ( hAPP_f2117159681l_bool @ ( cOMBC_1880041174l_bool @ member_fun_a_bool ) @ SY657 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1048]) ).
thf(1515,plain,
! [SV234: $i] :
( ( ! [SY658: $i] :
( ( insert_nat @ SV234 @ ( collect_nat @ SY658 ) )
= ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fimplies @ ( cOMBB_bool_bool_nat @ fNot @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ fequal_nat ) @ SV234 ) ) ) @ SY658 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1049]) ).
thf(1516,plain,
! [SV235: $i] :
( ( ! [SY659: $i] :
( ( insert_pname @ SV235 @ ( collect_pname @ SY659 ) )
= ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fimplies @ ( cOMBB_647938656_pname @ fNot @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ fequal_pname ) @ SV235 ) ) ) @ SY659 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1050]) ).
thf(1517,plain,
! [SV236: $i] :
( ( ! [SY660: $i] :
( ( insert_a @ SV236 @ ( collect_a @ SY660 ) )
= ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fimplies @ ( cOMBB_bool_bool_a @ fNot @ ( hAPP_a_fun_a_bool @ ( cOMBC_a_a_bool @ fequal_a ) @ SV236 ) ) ) @ SY660 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1051]) ).
thf(1518,plain,
! [SV237: $i] :
( ( ! [SY661: $i] :
( ( insert_fun_nat_bool @ SV237 @ ( collect_fun_nat_bool @ SY661 ) )
= ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fimplies @ ( cOMBB_238756964t_bool @ fNot @ ( hAPP_f103356543l_bool @ ( cOMBC_1693257480l_bool @ fequal_fun_nat_bool ) @ SV237 ) ) ) @ SY661 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1052]) ).
thf(1519,plain,
! [SV238: $i] :
( ( ! [SY662: $i] :
( ( insert1325755072e_bool @ SV238 @ ( collec1974731493e_bool @ SY662 ) )
= ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fimplies @ ( cOMBB_307249310e_bool @ fNot @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ SV238 ) ) ) @ SY662 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1053]) ).
thf(1520,plain,
! [SV239: $i] :
( ( ! [SY663: $i] :
( ( insert_fun_a_bool @ SV239 @ ( collect_fun_a_bool @ SY663 ) )
= ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fimplies @ ( cOMBB_2140588453a_bool @ fNot @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ fequal_fun_a_bool ) @ SV239 ) ) ) @ SY663 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1054]) ).
thf(1521,plain,
! [SV240: $i] :
( ( ! [SY664: $i] :
( ( insert_nat @ SV240 @ ( insert_nat @ SV240 @ SY664 ) )
= ( insert_nat @ SV240 @ SY664 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1055]) ).
thf(1522,plain,
! [SV241: $i] :
( ( ! [SY665: $i] :
( ( insert_pname @ SV241 @ ( insert_pname @ SV241 @ SY665 ) )
= ( insert_pname @ SV241 @ SY665 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1056]) ).
thf(1523,plain,
! [SV242: $i] :
( ( ! [SY666: $i] :
( ( insert_a @ SV242 @ ( insert_a @ SV242 @ SY666 ) )
= ( insert_a @ SV242 @ SY666 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1057]) ).
thf(1524,plain,
! [SV243: $i] :
( ( ! [SY667: $i,SY668: $i] :
( ( insert_nat @ SV243 @ ( insert_nat @ SY667 @ SY668 ) )
= ( insert_nat @ SY667 @ ( insert_nat @ SV243 @ SY668 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1058]) ).
thf(1525,plain,
! [SV244: $i] :
( ( ! [SY669: $i,SY670: $i] :
( ( insert_pname @ SV244 @ ( insert_pname @ SY669 @ SY670 ) )
= ( insert_pname @ SY669 @ ( insert_pname @ SV244 @ SY670 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1059]) ).
thf(1526,plain,
! [SV245: $i] :
( ( ! [SY671: $i,SY672: $i] :
( ( insert_a @ SV245 @ ( insert_a @ SY671 @ SY672 ) )
= ( insert_a @ SY671 @ ( insert_a @ SV245 @ SY672 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1060]) ).
thf(1527,plain,
! [SV246: $i] :
( ( ! [SY673: $i,SY674: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SY673 ) @ SY674 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SY673 ) @ ( insert_nat @ SV246 @ SY674 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1070]) ).
thf(1528,plain,
! [SV247: $i] :
( ( ! [SY675: $i,SY676: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SY675 ) @ SY676 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SY675 ) @ ( insert_pname @ SV247 @ SY676 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1071]) ).
thf(1529,plain,
! [SV248: $i] :
( ( ! [SY677: $i,SY678: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY677 ) @ SY678 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY677 ) @ ( insert_a @ SV248 @ SY678 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1072]) ).
thf(1530,plain,
! [SV249: $i] :
( ( ! [SY679: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV249 ) @ SY679 ) )
| ( ( insert_nat @ SV249 @ SY679 )
= SY679 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1073]) ).
thf(1531,plain,
! [SV250: $i] :
( ( ! [SY680: $i] :
( ~ ( is_fun_pname_bool @ SY680 )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV250 ) @ SY680 ) )
| ( ( insert_pname @ SV250 @ SY680 )
= SY680 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1074]) ).
thf(1532,plain,
! [SV251: $i] :
( ( ! [SY681: $i] :
( ~ ( is_fun_a_bool @ SY681 )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV251 ) @ SY681 ) )
| ( ( insert_a @ SV251 @ SY681 )
= SY681 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1075]) ).
thf(1533,plain,
! [SV252: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV252 ) @ SV252 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1076]) ).
thf(1534,plain,
! [SV253: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV253 ) @ SV253 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1077]) ).
thf(1535,plain,
! [SV254: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV254 ) @ SV254 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1078]) ).
thf(1536,plain,
! [SV255: $i] :
( ( ! [SY682: $i] :
( ( SV255 != SY682 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV255 ) @ SY682 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1082]) ).
thf(1537,plain,
! [SV256: $i] :
( ( ! [SY683: $i] :
( ( SV256 != SY683 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV256 ) @ SY683 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1083]) ).
thf(1538,plain,
! [SV257: $i] :
( ( ! [SY684: $i] :
( ( SV257 != SY684 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV257 ) @ SY684 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1084]) ).
thf(1539,plain,
! [SV258: $i] :
( ( ! [SY685: $i] :
( ( SV258 != SY685 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY685 ) @ SV258 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1085]) ).
thf(1540,plain,
! [SV259: $i] :
( ( ! [SY686: $i] :
( ( SV259 != SY686 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY686 ) @ SV259 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1086]) ).
thf(1541,plain,
! [SV260: $i] :
( ( ! [SY687: $i] :
( ( SV260 != SY687 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY687 ) @ SV260 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1087]) ).
thf(1542,plain,
! [SV261: $i] :
( ( ! [SY688: $i,SY689: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY688 ) @ SY689 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV261 ) @ SY688 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV261 ) @ SY689 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1088]) ).
thf(1543,plain,
! [SV262: $i] :
( ( ! [SY690: $i,SY691: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY690 ) @ SY691 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV262 ) @ SY690 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV262 ) @ SY691 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1089]) ).
thf(1544,plain,
! [SV263: $i] :
( ( ! [SY692: $i,SY693: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY692 ) @ SY693 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV263 ) @ SY692 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV263 ) @ SY693 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1090]) ).
thf(1545,plain,
! [SV264: $i] :
( ( ! [SY694: $i,SY695: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SY694 ) @ SY695 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY695 ) @ SV264 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SY694 ) @ SV264 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1091]) ).
thf(1546,plain,
! [SV265: $i] :
( ( ! [SY696: $i,SY697: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY696 ) @ SY697 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY697 ) @ SV265 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY696 ) @ SV265 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1092]) ).
thf(1547,plain,
! [SV266: $i] :
( ( ! [SY698: $i,SY699: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SY698 ) @ SY699 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY699 ) @ SV266 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SY698 ) @ SV266 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1093]) ).
thf(1548,plain,
! [SV267: $i] :
( ( ! [SY700: $i,SY701: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY700 ) @ SY701 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV267 ) @ SY700 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV267 ) @ SY701 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1094]) ).
thf(1549,plain,
! [SV268: $i] :
( ( ! [SY702: $i,SY703: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY702 ) @ SY703 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV268 ) @ SY702 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV268 ) @ SY703 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1095]) ).
thf(1550,plain,
! [SV269: $i] :
( ( ! [SY704: $i,SY705: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY704 ) @ SY705 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV269 ) @ SY704 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV269 ) @ SY705 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1096]) ).
thf(1551,plain,
! [SV270: $i] :
( ( ! [SY706: $i,SY707: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY706 ) @ SY707 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY707 ) @ SV270 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY706 ) @ SV270 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1097]) ).
thf(1552,plain,
! [SV271: $i] :
( ( ! [SY708: $i,SY709: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY708 ) @ SY709 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY709 ) @ SV271 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY708 ) @ SV271 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1098]) ).
thf(1553,plain,
! [SV272: $i] :
( ( ! [SY710: $i,SY711: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY710 ) @ SY711 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY711 ) @ SV272 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY710 ) @ SV272 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1099]) ).
thf(1554,plain,
! [SV273: $i] :
( ( ~ ( is_fun_pname_bool @ SV273 )
| ( ( collect_pname @ SV273 )
= SV273 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1106]) ).
thf(1555,plain,
! [SV274: $i] :
( ( ( collect_fun_nat_bool @ SV274 )
= SV274 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1107]) ).
thf(1556,plain,
! [SV275: $i] :
( ( ~ ( is_fun1661590463l_bool @ SV275 )
| ( ( collec1974731493e_bool @ SV275 )
= SV275 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1108]) ).
thf(1557,plain,
! [SV276: $i] :
( ( ~ ( is_fun949378684l_bool @ SV276 )
| ( ( collect_fun_a_bool @ SV276 )
= SV276 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1109]) ).
thf(1558,plain,
! [SV277: $i] :
( ( ( collect_nat @ SV277 )
= SV277 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1110]) ).
thf(1559,plain,
! [SV278: $i] :
( ( ! [SY712: $i,SY713: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SY712 ) @ SY713 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( hAPP_pname_a @ SV278 @ SY712 ) ) @ ( image_pname_a @ SV278 @ SY713 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1112]) ).
thf(1560,plain,
! [SV279: $i] :
( ( ! [SY714: $i,SY715: $i,SY716: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SY715 ) @ SY716 ) )
| ( SV279
!= ( hAPP_pname_a @ SY714 @ SY715 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV279 ) @ ( image_pname_a @ SY714 @ SY716 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1113]) ).
thf(1561,plain,
! [SV280: $i] :
( ( ! [SY717: $i] :
( ( insert_nat @ SV280 @ SY717 )
= ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ fequal_nat ) @ SV280 ) ) @ ( hAPP_f800510211t_bool @ ( cOMBC_226598744l_bool @ member_nat ) @ SY717 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1114]) ).
thf(1562,plain,
! [SV281: $i] :
( ( ! [SY718: $i] :
( ( insert_pname @ SV281 @ SY718 )
= ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ fequal_pname ) @ SV281 ) ) @ ( hAPP_f759274231e_bool @ ( cOMBC_1058051404l_bool @ member_pname ) @ SY718 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1115]) ).
thf(1563,plain,
! [SV282: $i] :
( ( ! [SY719: $i] :
( ( insert_a @ SV282 @ SY719 )
= ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ ( hAPP_a_fun_a_bool @ ( cOMBC_a_a_bool @ fequal_a ) @ SV282 ) ) @ ( hAPP_f2050579477a_bool @ ( cOMBC_1355376034l_bool @ member_a ) @ SY719 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1116]) ).
thf(1564,plain,
! [SV283: $i] :
( ( ! [SY720: $i] :
( ( insert_fun_nat_bool @ SV283 @ SY720 )
= ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ ( hAPP_f103356543l_bool @ ( cOMBC_1693257480l_bool @ fequal_fun_nat_bool ) @ SV283 ) ) @ ( hAPP_f1246832597l_bool @ ( cOMBC_1245412066l_bool @ member_fun_nat_bool ) @ SY720 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1117]) ).
thf(1565,plain,
! [SV284: $i] :
( ( ! [SY721: $i] :
( ( insert1325755072e_bool @ SV284 @ SY721 )
= ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ SV284 ) ) @ ( hAPP_f559147733l_bool @ ( cOMBC_1988546018l_bool @ member799430823e_bool ) @ SY721 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1118]) ).
thf(1566,plain,
! [SV285: $i] :
( ( ! [SY722: $i] :
( ( insert_fun_a_bool @ SV285 @ SY722 )
= ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ fequal_fun_a_bool ) @ SV285 ) ) @ ( hAPP_f2117159681l_bool @ ( cOMBC_1880041174l_bool @ member_fun_a_bool ) @ SY722 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1119]) ).
thf(1567,plain,
! [SV286: $i] :
( ( ! [SY723: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV286 ) @ ( insert_nat @ SY723 @ SV286 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1120]) ).
thf(1568,plain,
! [SV287: $i] :
( ( ! [SY724: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV287 ) @ ( insert_pname @ SY724 @ SV287 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1121]) ).
thf(1569,plain,
! [SV288: $i] :
( ( ! [SY725: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV288 ) @ ( insert_a @ SY725 @ SV288 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1122]) ).
thf(1570,plain,
! [SV289: $i] :
( ( ! [SY726: $i,SY727: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY726 ) @ SY727 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY726 ) @ ( insert_nat @ SV289 @ SY727 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1129]) ).
thf(1571,plain,
! [SV290: $i] :
( ( ! [SY728: $i,SY729: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY728 ) @ SY729 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY728 ) @ ( insert_pname @ SV290 @ SY729 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1130]) ).
thf(1572,plain,
! [SV291: $i] :
( ( ! [SY730: $i,SY731: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY730 ) @ SY731 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY730 ) @ ( insert_a @ SV291 @ SY731 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1131]) ).
thf(1573,plain,
! [SV292: $i] :
( ( ! [SY732: $i,SY733: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY732 ) @ SY733 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( insert_nat @ SV292 @ SY732 ) ) @ ( insert_nat @ SV292 @ SY733 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1132]) ).
thf(1574,plain,
! [SV293: $i] :
( ( ! [SY734: $i,SY735: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY734 ) @ SY735 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ SV293 @ SY734 ) ) @ ( insert_pname @ SV293 @ SY735 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1133]) ).
thf(1575,plain,
! [SV294: $i] :
( ( ! [SY736: $i,SY737: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY736 ) @ SY737 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV294 @ SY736 ) ) @ ( insert_a @ SV294 @ SY737 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1134]) ).
thf(1576,plain,
! [SV295: $i] :
( ( ! [SY738: $i,SY739: $i] :
( ( image_pname_a @ SV295 @ ( insert_pname @ SY738 @ SY739 ) )
= ( insert_a @ ( hAPP_pname_a @ SV295 @ SY738 ) @ ( image_pname_a @ SV295 @ SY739 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1135]) ).
thf(1577,plain,
! [SV296: $i] :
( ( ! [SY740: $i,SY741: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SY740 ) @ SY741 ) )
| ( ( insert_a @ ( hAPP_pname_a @ SV296 @ SY740 ) @ ( image_pname_a @ SV296 @ SY741 ) )
= ( image_pname_a @ SV296 @ SY741 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1136]) ).
thf(1578,plain,
! [SV297: $i] :
( ( ! [SY742: $i,SY743: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY742 ) @ SY743 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_pname_a @ SV297 @ SY742 ) ) @ ( image_pname_a @ SV297 @ SY743 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1138]) ).
thf(1579,plain,
! [SV298: $i] :
( ( ! [SY744: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ SV298 ) ) @ SY744 ) )
| ( SY744
= ( hAPP_nat_nat @ suc @ ( sK4_M @ SY744 @ SV298 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1144]) ).
thf(1580,plain,
! [SV299: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV299 ) @ SV299 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1146]) ).
thf(1581,plain,
! [SV300: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV300 ) @ SV300 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1147]) ).
thf(1582,plain,
! [SV301: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV301 ) @ SV301 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1148]) ).
thf(1583,plain,
! [SV302: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV302 ) @ SV302 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1149]) ).
thf(1584,plain,
! [SV303: $i] :
( ( ~ ( hBOOL @ ( hAPP_bool_bool @ fNot @ SV303 ) )
| ~ ( hBOOL @ SV303 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1151]) ).
thf(1585,plain,
! [SV304: $i] :
( ( ( hBOOL @ SV304 )
| ( hBOOL @ ( hAPP_bool_bool @ fNot @ SV304 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1152]) ).
thf(1586,plain,
! [SV305: $i] :
( ( ! [SY745: $i] :
( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ SY745 ) @ SV305 ) )
| ~ ( hBOOL @ SY745 )
| ~ ( hBOOL @ SV305 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1153]) ).
thf(1587,plain,
! [SV306: $i] :
( ( ! [SY746: $i] :
~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ SV306 ) @ SY746 ) )
| ( hBOOL @ SV306 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1154]) ).
thf(1588,plain,
! [SV307: $i] :
( ( ! [SY747: $i] :
( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ SV307 ) @ SY747 ) )
| ( hBOOL @ SY747 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1155]) ).
thf(1589,plain,
! [SV308: $i] :
( ( ! [SY748: $i] :
( ~ ( hBOOL @ SY748 )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ SY748 ) @ SV308 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1156]) ).
thf(1590,plain,
! [SV309: $i] :
( ( ! [SY749: $i] :
( ~ ( hBOOL @ SY749 )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ SV309 ) @ SY749 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1157]) ).
thf(1591,plain,
! [SV310: $i] :
( ( ! [SY750: $i] :
( ( hBOOL @ SY750 )
| ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ SV310 ) @ SY750 ) )
| ( hBOOL @ SV310 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1158]) ).
thf(1592,plain,
! [SV311: $i] :
( ( ! [SY751: $i] :
( ( hBOOL @ SY751 )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ SY751 ) @ SV311 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1159]) ).
thf(1593,plain,
! [SV312: $i] :
( ( ! [SY752: $i] :
( ~ ( hBOOL @ SY752 )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ SV312 ) @ SY752 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1160]) ).
thf(1594,plain,
! [SV313: $i] :
( ( ! [SY753: $i] :
( ( hBOOL @ SY753 )
| ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ SV313 ) @ SY753 ) )
| ~ ( hBOOL @ SV313 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1161]) ).
thf(1595,plain,
! [SV314: $i] :
( ( ! [SY754: $i] :
( ~ ( is_a @ SV314 )
| ~ ( is_a @ SY754 )
| ~ ( hBOOL @ ( hAPP_a_bool @ ( hAPP_a_fun_a_bool @ fequal_a @ SV314 ) @ SY754 ) )
| ( SV314 = SY754 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1162]) ).
thf(1596,plain,
! [SV315: $i] :
( ( ! [SY755: $i] :
( ( SV315 != SY755 )
| ( hBOOL @ ( hAPP_a_bool @ ( hAPP_a_fun_a_bool @ fequal_a @ SV315 ) @ SY755 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1163]) ).
thf(1597,plain,
! [SV316: $i] :
( ( ! [SY756: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ SV316 ) @ SY756 ) )
| ( SV316 = SY756 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1164]) ).
thf(1598,plain,
! [SV317: $i] :
( ( ! [SY757: $i] :
( ( SV317 != SY757 )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ SV317 ) @ SY757 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1165]) ).
thf(1599,plain,
! [SV318: $i] :
( ( ! [SY758: $i] :
( ~ ( is_pname @ SV318 )
| ~ ( is_pname @ SY758 )
| ~ ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ fequal_pname @ SV318 ) @ SY758 ) )
| ( SV318 = SY758 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1166]) ).
thf(1600,plain,
! [SV319: $i] :
( ( ! [SY759: $i] :
( ( SV319 != SY759 )
| ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ fequal_pname @ SV319 ) @ SY759 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1167]) ).
thf(1601,plain,
! [SV320: $i] :
( ( ! [SY760: $i,SY761: $i] :
( ( hAPP_a_bool @ ( hAPP_a_fun_a_bool @ ( cOMBC_a_a_bool @ SV320 ) @ SY760 ) @ SY761 )
= ( hAPP_a_bool @ ( hAPP_a_fun_a_bool @ SV320 @ SY761 ) @ SY760 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1168]) ).
thf(1602,plain,
! [SV321: $i] :
( ( ! [SY762: $i] :
( ~ ( is_fun_a_bool @ SV321 )
| ~ ( is_fun_a_bool @ SY762 )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ SV321 ) @ SY762 ) )
| ( SV321 = SY762 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1169]) ).
thf(1603,plain,
! [SV322: $i] :
( ( ! [SY763: $i] :
( ( SV322 != SY763 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ SV322 ) @ SY763 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1170]) ).
thf(1604,plain,
! [SV323: $i] :
( ( ! [SY764: $i,SY765: $i] :
( ( hAPP_a_bool @ ( cOMBB_bool_bool_a @ SV323 @ SY764 ) @ SY765 )
= ( hAPP_bool_bool @ SV323 @ ( hAPP_a_bool @ SY764 @ SY765 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1171]) ).
thf(1605,plain,
! [SV324: $i] :
( ( ! [SY766: $i,SY767: $i] :
( ( hAPP_a_bool @ ( cOMBS_a_bool_bool @ SV324 @ SY766 ) @ SY767 )
= ( hAPP_bool_bool @ ( hAPP_a_fun_bool_bool @ SV324 @ SY767 ) @ ( hAPP_a_bool @ SY766 @ SY767 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1172]) ).
thf(1606,plain,
! [SV325: $i] :
( ( ! [SY768: $i,SY769: $i] :
( ( hAPP_pname_bool @ ( hAPP_a93125764e_bool @ ( cOMBC_pname_a_bool @ SV325 ) @ SY768 ) @ SY769 )
= ( hAPP_a_bool @ ( hAPP_p1534023578a_bool @ SV325 @ SY769 ) @ SY768 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1173]) ).
thf(1607,plain,
! [SV326: $i] :
( ( ! [SY770: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ SV326 ) @ SY770 ) )
| ( SV326 = SY770 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1174]) ).
thf(1608,plain,
! [SV327: $i] :
( ( ! [SY771: $i] :
( ( SV327 != SY771 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ SV327 ) @ SY771 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1175]) ).
thf(1609,plain,
! [SV328: $i] :
( ( ! [SY772: $i] :
( ~ ( is_fun_pname_bool @ SV328 )
| ~ ( is_fun_pname_bool @ SY772 )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ SV328 ) @ SY772 ) )
| ( SV328 = SY772 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1176]) ).
thf(1610,plain,
! [SV329: $i] :
( ( ! [SY773: $i] :
( ( SV329 != SY773 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ SV329 ) @ SY773 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1177]) ).
thf(1611,plain,
! [SV330: $i] :
( ( ! [SY774: $i,SY775: $i] :
( ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ SV330 ) @ SY774 ) @ SY775 )
= ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV330 @ SY775 ) @ SY774 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1178]) ).
thf(1612,plain,
! [SV331: $i] :
( ( ! [SY776: $i,SY777: $i] :
( ( hAPP_nat_bool @ ( cOMBB_bool_bool_nat @ SV331 @ SY776 ) @ SY777 )
= ( hAPP_bool_bool @ SV331 @ ( hAPP_nat_bool @ SY776 @ SY777 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1179]) ).
thf(1613,plain,
! [SV332: $i] :
( ( ! [SY778: $i,SY779: $i] :
( ( hAPP_nat_bool @ ( cOMBS_nat_bool_bool @ SV332 @ SY778 ) @ SY779 )
= ( hAPP_bool_bool @ ( hAPP_n1006566506l_bool @ SV332 @ SY779 ) @ ( hAPP_nat_bool @ SY778 @ SY779 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1180]) ).
thf(1614,plain,
! [SV333: $i] :
( ( ! [SY780: $i,SY781: $i] :
( ( hAPP_pname_bool @ ( cOMBB_647938656_pname @ SV333 @ SY780 ) @ SY781 )
= ( hAPP_bool_bool @ SV333 @ ( hAPP_pname_bool @ SY780 @ SY781 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1181]) ).
thf(1615,plain,
! [SV334: $i] :
( ( ! [SY782: $i,SY783: $i] :
( ( hAPP_pname_bool @ ( cOMBS_568398431l_bool @ SV334 @ SY782 ) @ SY783 )
= ( hAPP_bool_bool @ ( hAPP_p393069232l_bool @ SV334 @ SY783 ) @ ( hAPP_pname_bool @ SY782 @ SY783 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1182]) ).
thf(1616,plain,
! [SV335: $i] :
( ( ! [SY784: $i,SY785: $i] :
( ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ SV335 ) @ SY784 ) @ SY785 )
= ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ SV335 @ SY785 ) @ SY784 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1183]) ).
thf(1617,plain,
! [SV336: $i] :
( ( ! [SY786: $i,SY787: $i] :
( ( hAPP_a_bool @ ( hAPP_f2050579477a_bool @ ( cOMBC_1355376034l_bool @ SV336 ) @ SY786 ) @ SY787 )
= ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ SV336 @ SY787 ) @ SY786 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1184]) ).
thf(1618,plain,
! [SV337: $i] :
( ( ! [SY788: $i,SY789: $i] :
( ( hAPP_p1534023578a_bool @ ( cOMBB_1897541054_pname @ SV337 @ SY788 ) @ SY789 )
= ( hAPP_a_fun_a_bool @ SV337 @ ( hAPP_pname_a @ SY788 @ SY789 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1185]) ).
thf(1619,plain,
! [SV338: $i] :
( ( ! [SY790: $i,SY791: $i] :
( ( hAPP_fun_a_bool_bool @ ( cOMBB_2140588453a_bool @ SV338 @ SY790 ) @ SY791 )
= ( hAPP_bool_bool @ SV338 @ ( hAPP_fun_a_bool_bool @ SY790 @ SY791 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1186]) ).
thf(1620,plain,
! [SV339: $i] :
( ( ! [SY792: $i,SY793: $i] :
( ( hAPP_a_fun_bool_bool @ ( cOMBB_1972296269bool_a @ SV339 @ SY792 ) @ SY793 )
= ( hAPP_b589554111l_bool @ SV339 @ ( hAPP_a_bool @ SY792 @ SY793 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1187]) ).
thf(1621,plain,
! [SV340: $i] :
( ( ! [SY794: $i,SY795: $i] :
( ( hAPP_fun_a_bool_bool @ ( cOMBS_1035972772l_bool @ SV340 @ SY794 ) @ SY795 )
= ( hAPP_bool_bool @ ( hAPP_f198738859l_bool @ SV340 @ SY795 ) @ ( hAPP_fun_a_bool_bool @ SY794 @ SY795 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1188]) ).
thf(1622,plain,
! [SV341: $i] :
( ( ! [SY796: $i,SY797: $i] :
( ( hAPP_nat_bool @ ( hAPP_f800510211t_bool @ ( cOMBC_226598744l_bool @ SV341 ) @ SY796 ) @ SY797 )
= ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ SV341 @ SY797 ) @ SY796 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1189]) ).
thf(1623,plain,
! [SV342: $i] :
( ( ! [SY798: $i,SY799: $i] :
( ( hAPP_f54304608l_bool @ ( cOMBB_238756964t_bool @ SV342 @ SY798 ) @ SY799 )
= ( hAPP_bool_bool @ SV342 @ ( hAPP_f54304608l_bool @ SY798 @ SY799 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1190]) ).
thf(1624,plain,
! [SV343: $i] :
( ( ! [SY800: $i,SY801: $i] :
( ( hAPP_n1006566506l_bool @ ( cOMBB_1015721476ol_nat @ SV343 @ SY800 ) @ SY801 )
= ( hAPP_b589554111l_bool @ SV343 @ ( hAPP_nat_bool @ SY800 @ SY801 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1191]) ).
thf(1625,plain,
! [SV344: $i] :
( ( ! [SY802: $i,SY803: $i] :
( ( hAPP_f54304608l_bool @ ( cOMBS_1187019125l_bool @ SV344 @ SY802 ) @ SY803 )
= ( hAPP_bool_bool @ ( hAPP_f1748468828l_bool @ SV344 @ SY803 ) @ ( hAPP_f54304608l_bool @ SY802 @ SY803 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1192]) ).
thf(1626,plain,
! [SV345: $i] :
( ( ! [SY804: $i,SY805: $i] :
( ( hAPP_f1664156314l_bool @ ( cOMBB_307249310e_bool @ SV345 @ SY804 ) @ SY805 )
= ( hAPP_bool_bool @ SV345 @ ( hAPP_f1664156314l_bool @ SY804 @ SY805 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1193]) ).
thf(1627,plain,
! [SV346: $i] :
( ( ! [SY806: $i,SY807: $i] :
( ( hAPP_p393069232l_bool @ ( cOMBB_675860798_pname @ SV346 @ SY806 ) @ SY807 )
= ( hAPP_b589554111l_bool @ SV346 @ ( hAPP_pname_bool @ SY806 @ SY807 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1194]) ).
thf(1628,plain,
! [SV347: $i] :
( ( ! [SY808: $i,SY809: $i] :
( ( hAPP_f1664156314l_bool @ ( cOMBS_350070575l_bool @ SV347 @ SY808 ) @ SY809 )
= ( hAPP_bool_bool @ ( hAPP_f1476298914l_bool @ SV347 @ SY809 ) @ ( hAPP_f1664156314l_bool @ SY808 @ SY809 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1195]) ).
thf(1629,plain,
! [SV348: $i] :
( ( ! [SY810: $i,SY811: $i] :
( ( hAPP_pname_bool @ ( hAPP_f759274231e_bool @ ( cOMBC_1058051404l_bool @ SV348 ) @ SY810 ) @ SY811 )
= ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ SV348 @ SY811 ) @ SY810 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1196]) ).
thf(1630,plain,
! [SV349: $i] :
( ( ! [SY812: $i,SY813: $i] :
( ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ SV349 ) @ SY812 ) @ SY813 )
= ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ SV349 @ SY813 ) @ SY812 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1197]) ).
thf(1631,plain,
! [SV350: $i] :
( ( ! [SY814: $i,SY815: $i] :
( ( hAPP_f198738859l_bool @ ( cOMBB_338059395a_bool @ SV350 @ SY814 ) @ SY815 )
= ( hAPP_b589554111l_bool @ SV350 @ ( hAPP_fun_a_bool_bool @ SY814 @ SY815 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1198]) ).
thf(1632,plain,
! [SV351: $i] :
( ( ! [SY816: $i,SY817: $i] :
( ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ( cOMBC_1693257480l_bool @ SV351 ) @ SY816 ) @ SY817 )
= ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ SV351 @ SY817 ) @ SY816 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1199]) ).
thf(1633,plain,
! [SV352: $i] :
( ( ! [SY818: $i,SY819: $i] :
( ( hAPP_f1748468828l_bool @ ( cOMBB_444170502t_bool @ SV352 @ SY818 ) @ SY819 )
= ( hAPP_b589554111l_bool @ SV352 @ ( hAPP_f54304608l_bool @ SY818 @ SY819 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1200]) ).
thf(1634,plain,
! [SV353: $i] :
( ( ! [SY820: $i,SY821: $i] :
( ( hAPP_f1476298914l_bool @ ( cOMBB_2095475776e_bool @ SV353 @ SY820 ) @ SY821 )
= ( hAPP_b589554111l_bool @ SV353 @ ( hAPP_f1664156314l_bool @ SY820 @ SY821 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1201]) ).
thf(1635,plain,
! [SV354: $i] :
( ( ! [SY822: $i,SY823: $i] :
( ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ SV354 ) @ SY822 ) @ SY823 )
= ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ SV354 @ SY823 ) @ SY822 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1202]) ).
thf(1636,plain,
! [SV355: $i] :
( ( ! [SY824: $i,SY825: $i] :
( ( hAPP_fun_a_bool_bool @ ( hAPP_f2117159681l_bool @ ( cOMBC_1880041174l_bool @ SV355 ) @ SY824 ) @ SY825 )
= ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ SV355 @ SY825 ) @ SY824 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1203]) ).
thf(1637,plain,
! [SV356: $i] :
( ( ! [SY826: $i,SY827: $i] :
( ( hAPP_f54304608l_bool @ ( hAPP_f1246832597l_bool @ ( cOMBC_1245412066l_bool @ SV356 ) @ SY826 ) @ SY827 )
= ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ SV356 @ SY827 ) @ SY826 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1204]) ).
thf(1638,plain,
! [SV357: $i] :
( ( ! [SY828: $i,SY829: $i] :
( ( hAPP_f1664156314l_bool @ ( hAPP_f559147733l_bool @ ( cOMBC_1988546018l_bool @ SV357 ) @ SY828 ) @ SY829 )
= ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ SV357 @ SY829 ) @ SY828 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1205]) ).
thf(1639,plain,
! [SV358: $i] :
( ( ! [SY830: $i,SY831: $i] :
( ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ( cOMBC_331553030l_bool @ SV358 ) @ SY830 ) @ SY831 )
= ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ SV358 @ SY831 ) @ SY830 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1206]) ).
thf(1640,plain,
! [SV359: $i] :
( ( ! [SY832: $i,SY833: $i] :
( ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ( cOMBC_595898202l_bool @ SV359 ) @ SY832 ) @ SY833 )
= ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ SV359 @ SY833 ) @ SY832 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1207]) ).
thf(1641,plain,
! [SV360: $i] :
( ( ! [SY834: $i,SY835: $i] :
( ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ( cOMBC_7971162l_bool @ SV360 ) @ SY834 ) @ SY835 )
= ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ SV360 @ SY835 ) @ SY834 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1208]) ).
thf(1642,plain,
! [SV361: $i] :
( ( ! [SY836: $i,SY837: $i] :
( ( hAPP_f292226953l_bool @ ( hAPP_f1050622307l_bool @ ( cOMBC_636888218l_bool @ SV361 ) @ SY836 ) @ SY837 )
= ( hAPP_f292226953l_bool @ ( hAPP_f1050622307l_bool @ SV361 @ SY837 ) @ SY836 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1209]) ).
thf(1643,plain,
! [SV362: $i] :
( ( ! [SY838: $i,SY839: $i] :
( ( hAPP_f937997336l_bool @ ( hAPP_f760187903l_bool @ ( cOMBC_1269652216l_bool @ SV362 ) @ SY838 ) @ SY839 )
= ( hAPP_f937997336l_bool @ ( hAPP_f760187903l_bool @ SV362 @ SY839 ) @ SY838 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1210]) ).
thf(1644,plain,
! [SV363: $i] :
( ( ! [SY840: $i,SY841: $i] :
( ( hAPP_f389811538l_bool @ ( hAPP_f1759205631l_bool @ ( cOMBC_336095980l_bool @ SV363 ) @ SY840 ) @ SY841 )
= ( hAPP_f389811538l_bool @ ( hAPP_f1759205631l_bool @ SV363 @ SY841 ) @ SY840 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1211]) ).
thf(1645,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)],[1212]) ).
thf(1646,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SX0 ) @ SX1 ) )
| ( hBOOL @ ( hAPP_nat_bool @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ SX1 @ SX0 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SX0 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1213]) ).
thf(1647,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SX0 ) @ SX1 ) )
| ( hBOOL @ ( hAPP_pname_bool @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_pname_bool @ SX1 @ SX0 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SX0 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1214]) ).
thf(1648,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fconj @ SX1 ) @ SX0 ) ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ SX0 ) ) )
| ! [SX1: $i] : ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fconj @ SX1 ) @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1215]) ).
thf(1649,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX0 ) @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX1 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1216]) ).
thf(1650,plain,
! [SV364: $i] :
( ( ~ ( ~ ( ~ ( is_fun_a_bool @ SV364 )
| ! [SY842: $i,SY843: $i] :
( ! [SY844: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY844 ) @ SY843 ) )
| ~ ( is_fun_pname_bool @ SY844 )
| ( SV364
!= ( image_pname_a @ SY842 @ SY844 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV364 ) @ ( image_pname_a @ SY842 @ SY843 ) ) ) ) )
| ~ ( ~ ( is_fun_a_bool @ SV364 )
| ! [SY845: $i,SY846: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV364 ) @ ( image_pname_a @ SY845 @ SY846 ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( sK10_AA @ SY846 @ SY845 @ SV364 ) ) @ SY846 ) )
| ~ ( is_fun_pname_bool @ ( sK10_AA @ SY846 @ SY845 @ SV364 ) ) )
| ( SV364
!= ( image_pname_a @ SY845 @ ( sK10_AA @ SY846 @ SY845 @ SV364 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1217]) ).
thf(1651,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX0 ) @ ( hAPP_nat_nat @ suc @ SX1 ) ) )
| ( SX0
= ( hAPP_nat_nat @ suc @ SX1 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX0 ) @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( hAPP_nat_nat @ suc @ SX1 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX0 ) @ ( hAPP_nat_nat @ suc @ SX1 ) ) ) )
| ~ ! [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 @ SX0 ) @ ( hAPP_nat_nat @ suc @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1218]) ).
thf(1652,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 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX0 ) @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX1 ) @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1219]) ).
thf(1653,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SX1 ) )
| ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ SX0 ) @ SX1 ) )
| ( ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( insert_fun_nat_bool @ SX0 @ SX1 ) )
= ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SX1 ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ SX0 ) @ SX1 ) )
| ( ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( insert_fun_nat_bool @ SX0 @ SX1 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1220]) ).
thf(1654,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( is_fun_pname_bool @ SX0 )
| ~ ( is_fun_pname_bool @ 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 ) )
| ( SX0 = SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( is_fun_pname_bool @ SX0 )
| ~ ( is_fun_pname_bool @ SX1 )
| ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SX0 ) @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( is_fun_pname_bool @ SX0 )
| ~ ( is_fun_pname_bool @ SX1 )
| ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SX1 ) @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1221]) ).
thf(1655,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ SX1 ) @ SX0 ) ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ SX0 ) ) )
| ! [SX1: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ SX1 ) @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1222]) ).
thf(1656,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_nat @ suc @ SX0 )
!= ( hAPP_nat_nat @ suc @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( hAPP_nat_nat @ suc @ SX0 )
= ( hAPP_nat_nat @ suc @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1223]) ).
thf(1657,plain,
! [SV365: $i] :
( ( ~ ( ~ ! [SY847: $i,SY848: $i] :
( ~ ( is_pname @ SV365 )
| ~ ( is_pname @ SY848 )
| ~ ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV365 @ SY847 ) @ SY848 ) )
| ( SV365 = SY848 )
| ( hBOOL @ ( hAPP_pname_bool @ SY847 @ SY848 ) ) )
| ~ ~ ( ~ ! [SY849: $i,SY850: $i] :
( ~ ( is_pname @ SV365 )
| ~ ( is_pname @ SY850 )
| ( SV365 != SY850 )
| ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV365 @ SY849 ) @ SY850 ) ) )
| ~ ! [SY851: $i,SY852: $i] :
( ~ ( is_pname @ SV365 )
| ~ ( is_pname @ SY852 )
| ~ ( hBOOL @ ( hAPP_pname_bool @ SY851 @ SY852 ) )
| ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV365 @ SY851 ) @ SY852 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1224]) ).
thf(1658,plain,
! [SV366: $i] :
( ( ~ ( ~ ! [SY853: $i,SY854: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV366 ) @ ( insert_nat @ SY853 @ SY854 ) ) )
| ( SV366 = SY853 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV366 ) @ SY854 ) ) )
| ~ ~ ( ~ ! [SY855: $i] :
( ( SV366 != SY855 )
| ! [SY856: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV366 ) @ ( insert_nat @ SY855 @ SY856 ) ) ) )
| ~ ! [SY857: $i,SY858: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV366 ) @ SY858 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV366 ) @ ( insert_nat @ SY857 @ SY858 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1225]) ).
thf(1659,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ SX0 @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SX1 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ SX0 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1226]) ).
thf(1660,plain,
! [SV367: $i] :
( ( ~ ( ~ ! [SY859: $i] :
( ~ ( is_a @ SV367 )
| ~ ( is_a @ SY859 )
| ! [SY860: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ ( insert_a @ SY859 @ SY860 ) ) )
| ( SV367 = SY859 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ SY860 ) ) ) )
| ~ ~ ( ~ ! [SY861: $i] :
( ~ ( is_a @ SV367 )
| ~ ( is_a @ SY861 )
| ( SV367 != SY861 )
| ! [SY862: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ ( insert_a @ SY861 @ SY862 ) ) ) )
| ~ ! [SY863: $i] :
( ~ ( is_a @ SV367 )
| ~ ( is_a @ SY863 )
| ! [SY864: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ SY864 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ ( insert_a @ SY863 @ SY864 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1227]) ).
thf(1661,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ SX1 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ SX1 ) @ SX0 ) ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ SX0 ) ) )
| ! [SX1: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ SX1 ) @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1228]) ).
thf(1662,plain,
! [SV368: $i] :
( ( ~ ( ~ ! [SY865: $i,SY866: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY865 ) @ SY866 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY866 ) @ ( insert_a @ SY865 @ SV368 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY866 ) @ SV368 ) ) )
| ~ ! [SY867: $i,SY868: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY867 ) @ SY868 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY868 ) @ SV368 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY868 ) @ ( insert_a @ SY867 @ SV368 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1229]) ).
thf(1663,plain,
! [SV369: $i] :
( ( ~ ( ~ ( ~ ( is_a @ SV369 )
| ! [SY869: $i,SY870: $i] :
( ! [SY871: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SY871 ) @ SY870 ) )
| ~ ( is_pname @ SY871 )
| ( SV369
!= ( hAPP_pname_a @ SY869 @ SY871 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV369 ) @ ( image_pname_a @ SY869 @ SY870 ) ) ) ) )
| ~ ( ~ ( is_a @ SV369 )
| ! [SY872: $i,SY873: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV369 ) @ ( image_pname_a @ SY872 @ SY873 ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK11_X_1 @ SY873 @ SY872 @ SV369 ) ) @ SY873 ) )
| ~ ( is_pname @ ( sK11_X_1 @ SY873 @ SY872 @ SV369 ) ) )
| ( SV369
!= ( hAPP_pname_a @ SY872 @ ( sK11_X_1 @ SY873 @ SY872 @ SV369 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1230]) ).
thf(1664,plain,
! [SV370: $i] :
( ( ~ ( ~ ! [SY874: $i,SY875: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SY874 ) @ SY875 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY875 ) @ ( insert_nat @ SY874 @ SV370 ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY875 ) @ SV370 ) ) )
| ~ ! [SY876: $i,SY877: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SY876 ) @ SY877 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY877 ) @ SV370 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY877 ) @ ( insert_nat @ SY876 @ SV370 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1231]) ).
thf(1665,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fconj @ SX1 ) @ SX0 ) ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ SX0 ) ) )
| ! [SX1: $i] : ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fconj @ SX1 ) @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1232]) ).
thf(1666,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SX0 @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SX1 ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SX0 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1233]) ).
thf(1667,plain,
! [SV371: $i] :
( ( ~ ( ~ ! [SY878: $i,SY879: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SY878 ) @ SY879 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SY878 ) @ ( insert_nat @ SV371 @ SY879 ) ) ) )
| ~ ! [SY880: $i] :
( ( SY880 != SV371 )
| ! [SY881: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SY880 ) @ ( insert_nat @ SV371 @ SY881 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1234]) ).
thf(1668,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 ) )
| ~ ~ ( ~ ! [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 ) ) )
| ~ ! [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 @ SX1 ) @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1235]) ).
thf(1669,plain,
! [SV372: $i] :
( ( ! [SY882: $i,SY883: $i] :
( ~ ( is_fun_a_bool @ SY883 )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY883 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY883 ) @ ( image_pname_a @ SV372 @ SY882 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( sK17_C_2 @ SY883 @ SY882 @ SV372 ) ) @ SY882 ) )
| ~ ( is_fun_pname_bool @ ( sK17_C_2 @ SY883 @ SY882 @ SV372 ) ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( sK17_C_2 @ SY883 @ SY882 @ SV372 ) ) ) )
| ( SY883
!= ( image_pname_a @ SV372 @ ( sK17_C_2 @ SY883 @ SY882 @ SV372 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1236]) ).
thf(1670,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ SX1 ) ) @ SX0 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX0 ) @ SX1 ) ) )
| ~ ! [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 @ ( hAPP_nat_nat @ suc @ SX1 ) ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1237]) ).
thf(1671,plain,
! [SV373: $i] :
( ( ~ ( ~ ! [SY884: $i,SY885: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SY884 ) @ SY885 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SY884 ) @ ( insert_pname @ SV373 @ SY885 ) ) ) )
| ~ ! [SY886: $i] :
( ( SY886 != SV373 )
| ! [SY887: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SY886 ) @ ( insert_pname @ SV373 @ SY887 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1238]) ).
thf(1672,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ SX0 ) ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ SX1 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ SX0 ) @ SX1 ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ SX0 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1239]) ).
thf(1673,plain,
! [SV374: $i] :
( ( ~ ( ~ ! [SY888: $i,SY889: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV374 ) @ SY889 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY888 ) @ SY889 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV374 @ SY888 ) ) @ SY889 ) ) )
| ~ ~ ( ~ ! [SY890: $i,SY891: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV374 @ SY890 ) ) @ SY891 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV374 ) @ SY891 ) ) )
| ~ ! [SY892: $i,SY893: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV374 @ SY892 ) ) @ SY893 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY892 ) @ SY893 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1240]) ).
thf(1674,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ SX0 ) ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ SX0 ) @ SX1 ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ SX0 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1241]) ).
thf(1675,plain,
! [SV375: $i] :
( ( ! [SY894: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SY894 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_pname_a @ SV375 @ SY894 ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK12_X_1 @ SY894 @ SV375 ) ) @ SY894 ) )
| ~ ( is_pname @ ( sK12_X_1 @ SY894 @ SV375 ) ) )
| ~ ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ ( hAPP_f759274231e_bool @ ( cOMBC_1058051404l_bool @ member_pname ) @ SY894 ) ) @ ( hAPP_a93125764e_bool @ ( cOMBC_pname_a_bool @ ( cOMBB_1897541054_pname @ fequal_a @ SV375 ) ) @ ( hAPP_pname_a @ SV375 @ ( sK12_X_1 @ SY894 @ SV375 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1242]) ).
thf(1676,plain,
! [SV376: $i] :
( ( ~ ( ~ ! [SY895: $i,SY896: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV376 ) @ SY896 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY895 ) @ SY896 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( insert_nat @ SV376 @ SY895 ) ) @ SY896 ) ) )
| ~ ~ ( ~ ! [SY897: $i,SY898: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( insert_nat @ SV376 @ SY897 ) ) @ SY898 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV376 ) @ SY898 ) ) )
| ~ ! [SY899: $i,SY900: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( insert_nat @ SV376 @ SY899 ) ) @ SY900 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY899 ) @ SY900 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1243]) ).
thf(1677,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SX1 ) )
| ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ SX0 ) @ SX1 ) )
| ( ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( insert1325755072e_bool @ SX0 @ SX1 ) )
= ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SX1 ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ SX0 ) @ SX1 ) )
| ( ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( insert1325755072e_bool @ SX0 @ SX1 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1244]) ).
thf(1678,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ SX0 @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SX1 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ SX0 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1245]) ).
thf(1679,plain,
! [SV377: $i] :
( ( ~ ( ~ ! [SY901: $i,SY902: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SY901 ) @ SY902 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SY901 ) @ SV377 ) )
| ( ( insert_nat @ SY901 @ SY902 )
!= ( insert_nat @ SY901 @ SV377 ) )
| ( SY902 = SV377 ) )
| ~ ! [SY903: $i,SY904: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SY903 ) @ SY904 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SY903 ) @ SV377 ) )
| ( SY904 != SV377 )
| ( ( insert_nat @ SY903 @ SY904 )
= ( insert_nat @ SY903 @ SV377 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1246]) ).
thf(1680,plain,
! [SV378: $i] :
( ( ! [SY905: $i] :
( ~ ( ~ ( is_a @ ( sK7_X_1 @ SY905 @ SV378 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( sK7_X_1 @ SY905 @ SV378 ) ) @ SY905 ) )
| ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( sK7_X_1 @ SY905 @ SV378 ) ) @ SV378 ) ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY905 ) @ SV378 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1247]) ).
thf(1681,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX0 ) @ SX1 ) )
| ( hBOOL @ ( hAPP_a_bool @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_a_bool @ SX1 @ SX0 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX0 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1248]) ).
thf(1682,plain,
! [SV379: $i] :
( ( ~ ( ~ ! [SY906: $i,SY907: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY906 ) @ SY907 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY906 ) @ ( insert_a @ SV379 @ SY907 ) ) ) )
| ~ ! [SY908: $i] :
( ( SY908 != SV379 )
| ! [SY909: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY908 ) @ ( insert_a @ SV379 @ SY909 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1249]) ).
thf(1683,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SX1 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SX0 ) @ SX1 ) )
| ( ( hAPP_f22106695ol_nat @ finite_card_nat @ ( insert_nat @ SX0 @ SX1 ) )
= ( hAPP_f22106695ol_nat @ finite_card_nat @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SX1 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SX0 ) @ SX1 ) )
| ( ( hAPP_f22106695ol_nat @ finite_card_nat @ ( insert_nat @ SX0 @ SX1 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1250]) ).
thf(1684,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ SX0 @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SX1 ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ SX0 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1251]) ).
thf(1685,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SX1 ) )
| ~ ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ SX0 ) @ SX1 ) )
| ( ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( insert_fun_a_bool @ SX0 @ SX1 ) )
= ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SX1 ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ SX0 ) @ SX1 ) )
| ( ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( insert_fun_a_bool @ SX0 @ SX1 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1252]) ).
thf(1686,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SX0 ) @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SX1 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1253]) ).
thf(1687,plain,
! [SV380: $i] :
( ( ! [SY910: $i,SY911: $i] :
( ~ ( ~ ( is_pname @ ( sK3_X_1 @ SY911 @ SY910 @ SV380 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK3_X_1 @ SY911 @ SY910 @ SV380 ) ) @ SY911 ) )
| ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( hAPP_pname_a @ SV380 @ ( sK3_X_1 @ SY911 @ SY910 @ SV380 ) ) ) @ SY910 ) ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_pname_a @ SV380 @ SY911 ) ) @ SY910 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1254]) ).
thf(1688,plain,
! [SV381: $i] :
( ( ~ ( ~ ! [SY912: $i,SY913: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY912 ) @ SY913 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY912 ) @ SV381 ) )
| ( ( hAPP_nat_nat @ ( minus_minus_nat @ SY913 ) @ SY912 )
!= ( hAPP_nat_nat @ ( minus_minus_nat @ SV381 ) @ SY912 ) )
| ( SY913 = SV381 ) )
| ~ ! [SY914: $i,SY915: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY914 ) @ SY915 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY914 ) @ SV381 ) )
| ( SY915 != SV381 )
| ( ( hAPP_nat_nat @ ( minus_minus_nat @ SY915 ) @ SY914 )
= ( hAPP_nat_nat @ ( minus_minus_nat @ SV381 ) @ SY914 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1255]) ).
thf(1689,plain,
! [SV382: $i] :
( ( ! [SY916: $i] :
( ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ ( sK8_X_1 @ SY916 @ SV382 ) ) @ SY916 ) )
| ~ ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ ( sK8_X_1 @ SY916 @ SV382 ) ) @ SV382 ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY916 ) @ SV382 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1256]) ).
thf(1690,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ SX0 ) ) )
| ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ SX0 ) @ SX1 ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ SX0 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1257]) ).
thf(1691,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fconj @ SX1 ) @ SX0 ) ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ SX0 ) ) )
| ! [SX1: $i] : ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fconj @ SX1 ) @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1258]) ).
thf(1692,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SX1 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX0 ) @ SX1 ) )
| ( ( hAPP_fun_a_bool_nat @ finite_card_a @ ( insert_a @ SX0 @ SX1 ) )
= ( hAPP_fun_a_bool_nat @ finite_card_a @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SX1 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX0 ) @ SX1 ) )
| ( ( hAPP_fun_a_bool_nat @ finite_card_a @ ( insert_a @ SX0 @ SX1 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1259]) ).
thf(1693,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SX1 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SX0 ) @ SX1 ) )
| ( ( hAPP_f921600141ol_nat @ finite_card_pname @ ( insert_pname @ SX0 @ SX1 ) )
= ( hAPP_f921600141ol_nat @ finite_card_pname @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SX1 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SX0 ) @ SX1 ) )
| ( ( hAPP_f921600141ol_nat @ finite_card_pname @ ( insert_pname @ SX0 @ SX1 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1260]) ).
thf(1694,plain,
! [SV383: $i] :
( ( ~ ( ~ ! [SY917: $i] :
( ~ ( is_pname @ SV383 )
| ~ ( is_pname @ SY917 )
| ! [SY918: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ ( insert_pname @ SY917 @ SY918 ) ) )
| ( SV383 = SY917 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ SY918 ) ) ) )
| ~ ~ ( ~ ! [SY919: $i] :
( ~ ( is_pname @ SV383 )
| ~ ( is_pname @ SY919 )
| ( SV383 != SY919 )
| ! [SY920: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ ( insert_pname @ SY919 @ SY920 ) ) ) )
| ~ ! [SY921: $i] :
( ~ ( is_pname @ SV383 )
| ~ ( is_pname @ SY921 )
| ! [SY922: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ SY922 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ ( insert_pname @ SY921 @ SY922 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1261]) ).
thf(1695,plain,
! [SV384: $i] :
( ( ~ ( ~ ! [SY923: $i,SY924: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV384 ) @ SY924 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY923 ) @ SY924 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ SV384 @ SY923 ) ) @ SY924 ) ) )
| ~ ~ ( ~ ! [SY925: $i,SY926: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ SV384 @ SY925 ) ) @ SY926 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV384 ) @ SY926 ) ) )
| ~ ! [SY927: $i,SY928: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ SV384 @ SY927 ) ) @ SY928 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY927 ) @ SY928 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1262]) ).
thf(1696,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ SX0 ) ) )
| ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ SX0 ) @ SX1 ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ SX0 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1263]) ).
thf(1697,plain,
! [SV385: $i] :
( ( ~ ( ~ ! [SY929: $i,SY930: $i] :
( ~ ( is_fun_a_bool @ SV385 )
| ~ ( is_fun_a_bool @ SY930 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY929 ) @ SY930 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY929 ) @ SV385 ) )
| ( ( insert_a @ SY929 @ SY930 )
!= ( insert_a @ SY929 @ SV385 ) )
| ( SY930 = SV385 ) )
| ~ ! [SY931: $i,SY932: $i] :
( ~ ( is_fun_a_bool @ SV385 )
| ~ ( is_fun_a_bool @ SY932 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY931 ) @ SY932 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY931 ) @ SV385 ) )
| ( SY932 != SV385 )
| ( ( insert_a @ SY931 @ SY932 )
= ( insert_a @ SY931 @ SV385 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1264]) ).
thf(1698,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX0 ) @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX1 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1265]) ).
thf(1699,plain,
! [SV386: $i] :
( ( ~ ( ~ ! [SY933: $i,SY934: $i] :
( ~ ( is_a @ SV386 )
| ~ ( is_a @ SY934 )
| ~ ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV386 @ SY933 ) @ SY934 ) )
| ( SV386 = SY934 )
| ( hBOOL @ ( hAPP_a_bool @ SY933 @ SY934 ) ) )
| ~ ~ ( ~ ! [SY935: $i,SY936: $i] :
( ~ ( is_a @ SV386 )
| ~ ( is_a @ SY936 )
| ( SV386 != SY936 )
| ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV386 @ SY935 ) @ SY936 ) ) )
| ~ ! [SY937: $i,SY938: $i] :
( ~ ( is_a @ SV386 )
| ~ ( is_a @ SY938 )
| ~ ( hBOOL @ ( hAPP_a_bool @ SY937 @ SY938 ) )
| ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV386 @ SY937 ) @ SY938 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1266]) ).
thf(1700,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ SX1 ) @ SX0 ) ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ SX0 ) ) )
| ! [SX1: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ SX1 ) @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1267]) ).
thf(1701,plain,
! [SV387: $i] :
( ( ~ ( is_a @ SV387 )
| ! [SY939: $i,SY940: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV387 ) @ ( image_pname_a @ SY939 @ SY940 ) ) )
| ~ ( ~ ( is_pname @ ( sK9_X_1 @ SY940 @ SY939 @ SV387 ) )
| ~ ~ ( ( SV387
!= ( hAPP_pname_a @ SY939 @ ( sK9_X_1 @ SY940 @ SY939 @ SV387 ) ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK9_X_1 @ SY940 @ SY939 @ SV387 ) ) @ SY940 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1268]) ).
thf(1702,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ SX0 @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SX1 ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ SX0 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1269]) ).
thf(1703,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ SX0 ) ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ SX0 ) @ SX1 ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ SX0 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1270]) ).
thf(1704,plain,
! [SV388: $i] :
( ( ! [SY941: $i,SY942: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ SY941 @ SY942 ) )
| ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ SY941 @ ( hAPP_nat_nat @ suc @ ( sK5_N_2 @ SY942 @ SY941 @ SV388 ) ) ) )
| ~ ~ ( hBOOL @ ( hAPP_nat_bool @ SY941 @ ( sK5_N_2 @ SY942 @ SY941 @ SV388 ) ) ) )
| ( hBOOL @ ( hAPP_nat_bool @ SY941 @ ( hAPP_nat_nat @ ( minus_minus_nat @ SY942 ) @ SV388 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1271]) ).
thf(1705,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ SX0 ) ) )
| ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ SX0 ) @ SX1 ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ SX0 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1272]) ).
thf(1706,plain,
! [SV389: $i] :
( ( ~ ( ~ ! [SY943: $i,SY944: $i] :
( ~ ( is_fun_pname_bool @ SV389 )
| ~ ( is_fun_pname_bool @ SY944 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SY943 ) @ SY944 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SY943 ) @ SV389 ) )
| ( ( insert_pname @ SY943 @ SY944 )
!= ( insert_pname @ SY943 @ SV389 ) )
| ( SY944 = SV389 ) )
| ~ ! [SY945: $i,SY946: $i] :
( ~ ( is_fun_pname_bool @ SV389 )
| ~ ( is_fun_pname_bool @ SY946 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SY945 ) @ SY946 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SY945 ) @ SV389 ) )
| ( SY946 != SV389 )
| ( ( insert_pname @ SY945 @ SY946 )
= ( insert_pname @ SY945 @ SV389 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1273]) ).
thf(1707,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ SX0 ) ) @ ( hAPP_nat_nat @ suc @ SX1 ) ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX0 ) @ SX1 ) ) )
| ~ ! [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 @ ( hAPP_nat_nat @ suc @ SX0 ) ) @ ( hAPP_nat_nat @ suc @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1274]) ).
thf(1708,plain,
! [SV390: $i] :
( ( ~ ( ~ ! [SY947: $i,SY948: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SY947 ) @ SY948 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY948 ) @ ( insert_pname @ SY947 @ SV390 ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY948 ) @ SV390 ) ) )
| ~ ! [SY949: $i,SY950: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SY949 ) @ SY950 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY950 ) @ SV390 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY950 ) @ ( insert_pname @ SY949 @ SV390 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1275]) ).
thf(1709,plain,
! [SV391: $i] :
( ( ~ ( ~ ! [SY951: $i,SY952: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY951 ) @ SY952 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY951 ) @ SV391 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ SY952 ) @ SY951 ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV391 ) @ SY951 ) ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY952 ) @ SV391 ) ) )
| ~ ! [SY953: $i,SY954: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY953 ) @ SY954 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY953 ) @ SV391 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY954 ) @ SV391 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ SY954 ) @ SY953 ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV391 ) @ SY953 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1276]) ).
thf(1710,plain,
! [SV392: $i] :
( ( ! [SY955: $i] :
( ~ ( ~ ( is_pname @ ( sK6_X_1 @ SY955 @ SV392 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK6_X_1 @ SY955 @ SV392 ) ) @ SY955 ) )
| ~ ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK6_X_1 @ SY955 @ SV392 ) ) @ SV392 ) ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY955 ) @ SV392 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1277]) ).
thf(1711,plain,
! [SV393: $i] :
( ( ~ ( ~ ! [SY956: $i,SY957: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV393 @ SY956 ) @ SY957 ) )
| ( SV393 = SY957 )
| ( hBOOL @ ( hAPP_nat_bool @ SY956 @ SY957 ) ) )
| ~ ~ ( ~ ! [SY958: $i,SY959: $i] :
( ( SV393 != SY959 )
| ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV393 @ SY958 ) @ SY959 ) ) )
| ~ ! [SY960: $i,SY961: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ SY960 @ SY961 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV393 @ SY960 ) @ SY961 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1278]) ).
thf(1712,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ ( sK2_X_1 @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( sK2_X_1 @ SX1 @ SX0 ) ) @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SX0 ) )
| ! [SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX1 ) @ ( sK1_M @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1279]) ).
thf(1713,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 ) ) )
| ~ ! [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 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1280]) ).
thf(1714,plain,
! [SV1: $i,SV394: $i] :
( ( ~ ( is_fun_pname_bool @ SV394 )
| ( is_fun_a_bool @ ( image_pname_a @ SV1 @ SV394 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1281]) ).
thf(1715,plain,
! [SV395: $i,SV2: $i] :
( ( ~ ( is_a @ SV2 )
| ~ ( is_fun_a_bool @ SV395 )
| ( is_fun_a_bool @ ( insert_a @ SV2 @ SV395 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1282]) ).
thf(1716,plain,
! [SV3: $i,SV396: $i] :
( ( ~ ( is_a @ SV396 )
| ( is_fun949378684l_bool @ ( hAPP_a85458249l_bool @ SV3 @ SV396 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1283]) ).
thf(1717,plain,
! [SV4: $i,SV397: $i] :
( ( ~ ( is_pname @ SV397 )
| ( is_a @ ( hAPP_pname_a @ SV4 @ SV397 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1284]) ).
thf(1718,plain,
! [SV5: $i,SV398: $i] :
( ( ~ ( is_pname @ SV398 )
| ( is_fun1661590463l_bool @ ( hAPP_p338031245l_bool @ SV5 @ SV398 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1285]) ).
thf(1719,plain,
! [SV399: $i,SV6: $i] :
( ( is_bool @ ( hAPP_nat_bool @ SV6 @ SV399 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1286]) ).
thf(1720,plain,
! [SV400: $i,SV7: $i] :
( ( ~ ( is_fun949378684l_bool @ SV7 )
| ~ ( is_fun_a_bool @ SV400 )
| ( is_bool @ ( hAPP_fun_a_bool_bool @ SV7 @ SV400 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1287]) ).
thf(1721,plain,
! [SV8: $i,SV401: $i] :
( ( ~ ( is_fun_a_bool @ SV401 )
| ( is_fun949378684l_bool @ ( hAPP_f1631501043l_bool @ SV8 @ SV401 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1288]) ).
thf(1722,plain,
! [SV402: $i,SV9: $i] :
( ( ~ ( is_fun1661590463l_bool @ SV9 )
| ~ ( is_fun_pname_bool @ SV402 )
| ( is_bool @ ( hAPP_f1664156314l_bool @ SV9 @ SV402 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1289]) ).
thf(1723,plain,
! [SV10: $i,SV403: $i] :
( ( ~ ( is_fun_a_bool @ SV403 )
| ( is_fun_a_bool @ ( cOMBB_bool_bool_a @ SV10 @ SV403 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1291]) ).
thf(1724,plain,
! [SV11: $i,SV404: $i] :
( ( ~ ( is_fun_pname_bool @ SV404 )
| ( is_fun_pname_bool @ ( cOMBB_647938656_pname @ SV11 @ SV404 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1292]) ).
thf(1725,plain,
! [SV12: $i,SV405: $i] :
( ( ~ ( is_fun949378684l_bool @ SV405 )
| ( is_fun949378684l_bool @ ( cOMBB_2140588453a_bool @ SV12 @ SV405 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1293]) ).
thf(1726,plain,
! [SV13: $i,SV406: $i] :
( ( ~ ( is_fun1661590463l_bool @ SV406 )
| ( is_fun1661590463l_bool @ ( cOMBB_307249310e_bool @ SV13 @ SV406 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1294]) ).
thf(1727,plain,
! [SV14: $i,SV407: $i] :
( ( ~ ( is_fun_a_bool @ SV407 )
| ( is_fun_a_bool @ ( cOMBS_a_bool_bool @ SV14 @ SV407 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1295]) ).
thf(1728,plain,
! [SV15: $i,SV408: $i] :
( ( ~ ( is_fun_pname_bool @ SV408 )
| ( is_fun_pname_bool @ ( cOMBS_568398431l_bool @ SV15 @ SV408 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1296]) ).
thf(1729,plain,
! [SV16: $i,SV409: $i] :
( ( ~ ( is_fun949378684l_bool @ SV409 )
| ( is_fun949378684l_bool @ ( cOMBS_1035972772l_bool @ SV16 @ SV409 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1297]) ).
thf(1730,plain,
! [SV17: $i,SV410: $i] :
( ( ~ ( is_fun1661590463l_bool @ SV410 )
| ( is_fun1661590463l_bool @ ( cOMBS_350070575l_bool @ SV17 @ SV410 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1298]) ).
thf(1731,plain,
! [SV18: $i] :
( ( ( ~ ( is_fun_a_bool @ SV18 ) )
= $true )
| ( ( is_fun_a_bool @ ( collect_a @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1299]) ).
thf(1732,plain,
! [SV19: $i] :
( ( ( ~ ( is_fun_pname_bool @ SV19 ) )
= $true )
| ( ( is_fun_pname_bool @ ( collect_pname @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1300]) ).
thf(1733,plain,
! [SV20: $i] :
( ( ( ~ ( is_fun949378684l_bool @ SV20 ) )
= $true )
| ( ( is_fun949378684l_bool @ ( collect_fun_a_bool @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1301]) ).
thf(1734,plain,
! [SV21: $i] :
( ( ( ~ ( is_fun1661590463l_bool @ SV21 ) )
= $true )
| ( ( is_fun1661590463l_bool @ ( collec1974731493e_bool @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1302]) ).
thf(1735,plain,
! [SV22: $i,SV411: $i] :
( ( ~ ( is_fun_a_bool @ SV411 )
| ( is_fun_a_bool @ ( image_a_a @ SV22 @ SV411 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1303]) ).
thf(1736,plain,
! [SV23: $i,SV412: $i] :
( ( ~ ( is_fun_a_bool @ SV412 )
| ( is_fun_pname_bool @ ( image_a_pname @ SV23 @ SV412 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1304]) ).
thf(1737,plain,
! [SV24: $i,SV413: $i] :
( ( ~ ( is_fun_pname_bool @ SV413 )
| ( is_fun_pname_bool @ ( image_pname_pname @ SV24 @ SV413 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1305]) ).
thf(1738,plain,
! [SV25: $i,SV414: $i] :
( ( ~ ( is_fun_pname_bool @ SV414 )
| ( is_fun949378684l_bool @ ( image_112932426a_bool @ SV25 @ SV414 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1306]) ).
thf(1739,plain,
! [SV26: $i,SV415: $i] :
( ( ~ ( is_fun_pname_bool @ SV415 )
| ( is_fun1661590463l_bool @ ( image_47868345e_bool @ SV26 @ SV415 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1307]) ).
thf(1740,plain,
! [SV416: $i,SV27: $i] :
( ( is_fun_a_bool @ ( image_nat_a @ SV27 @ SV416 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1308]) ).
thf(1741,plain,
! [SV417: $i,SV28: $i] :
( ( is_fun_pname_bool @ ( image_nat_pname @ SV28 @ SV417 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1309]) ).
thf(1742,plain,
! [SV418: $i,SV29: $i] :
( ( is_fun949378684l_bool @ ( image_nat_fun_a_bool @ SV29 @ SV418 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1310]) ).
thf(1743,plain,
! [SV419: $i,SV30: $i] :
( ( is_fun1661590463l_bool @ ( image_1655916159e_bool @ SV30 @ SV419 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1311]) ).
thf(1744,plain,
! [SV31: $i,SV420: $i] :
( ( ~ ( is_fun949378684l_bool @ SV420 )
| ( is_fun_a_bool @ ( image_fun_a_bool_a @ SV31 @ SV420 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1312]) ).
thf(1745,plain,
! [SV32: $i,SV421: $i] :
( ( ~ ( is_fun949378684l_bool @ SV421 )
| ( is_fun_pname_bool @ ( image_1854862208_pname @ SV32 @ SV421 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1313]) ).
thf(1746,plain,
! [SV33: $i,SV422: $i] :
( ( ~ ( is_fun1661590463l_bool @ SV422 )
| ( is_fun_a_bool @ ( image_876012084bool_a @ SV33 @ SV422 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1314]) ).
thf(1747,plain,
! [SV34: $i,SV423: $i] :
( ( ~ ( is_fun1661590463l_bool @ SV423 )
| ( is_fun_pname_bool @ ( image_1283814551_pname @ SV34 @ SV423 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1315]) ).
thf(1748,plain,
! [SV424: $i,SV35: $i] :
( ( is_fun_a_bool @ ( image_fun_nat_bool_a @ SV35 @ SV424 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1316]) ).
thf(1749,plain,
! [SV425: $i,SV36: $i] :
( ( is_fun_pname_bool @ ( image_1921560913_pname @ SV36 @ SV425 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1317]) ).
thf(1750,plain,
! [SV426: $i,SV37: $i] :
( ( is_fun_a_bool @ ( image_573985017bool_a @ SV37 @ SV426 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1318]) ).
thf(1751,plain,
! [SV427: $i,SV38: $i] :
( ( is_fun_pname_bool @ ( image_990671762_pname @ SV38 @ SV427 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1319]) ).
thf(1752,plain,
! [SV428: $i,SV39: $i] :
( ( is_fun_a_bool @ ( image_349102846bool_a @ SV39 @ SV428 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1320]) ).
thf(1753,plain,
! [SV429: $i,SV40: $i] :
( ( is_fun_pname_bool @ ( image_1705983821_pname @ SV40 @ SV429 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1321]) ).
thf(1754,plain,
! [SV430: $i,SV41: $i] :
( ( is_fun_a_bool @ ( image_526090948bool_a @ SV41 @ SV430 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1322]) ).
thf(1755,plain,
! [SV431: $i,SV42: $i] :
( ( is_fun_pname_bool @ ( image_1604018183_pname @ SV42 @ SV431 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1323]) ).
thf(1756,plain,
! [SV43: $i,SV432: $i] :
( ( ~ ( is_fun_pname_bool @ SV432 )
| ~ ( is_pname @ SV43 )
| ( is_fun_pname_bool @ ( insert_pname @ SV43 @ SV432 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1324]) ).
thf(1757,plain,
! [SV44: $i,SV433: $i] :
( ( ~ ( is_fun949378684l_bool @ SV433 )
| ~ ( is_fun_a_bool @ SV44 )
| ( is_fun949378684l_bool @ ( insert_fun_a_bool @ SV44 @ SV433 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1325]) ).
thf(1758,plain,
! [SV45: $i,SV434: $i] :
( ( ~ ( is_fun1661590463l_bool @ SV434 )
| ~ ( is_fun_pname_bool @ SV45 )
| ( is_fun1661590463l_bool @ ( insert1325755072e_bool @ SV45 @ SV434 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1326]) ).
thf(1759,plain,
! [SV46: $i,SV435: $i] :
( ( ~ ( is_a @ SV435 )
| ~ ( is_fun_a_bool @ SV46 )
| ( is_bool @ ( hAPP_a_bool @ SV46 @ SV435 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1327]) ).
thf(1760,plain,
! [SV47: $i,SV436: $i] :
( ( ~ ( is_a @ SV436 )
| ( is_fun_a_bool @ ( hAPP_a_fun_a_bool @ SV47 @ SV436 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1328]) ).
thf(1761,plain,
! [SV48: $i,SV437: $i] :
( ( ~ ( is_a @ SV437 )
| ( is_fun_pname_bool @ ( hAPP_a93125764e_bool @ SV48 @ SV437 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1329]) ).
thf(1762,plain,
! [SV438: $i,SV49: $i] :
( ( ~ ( is_fun_pname_bool @ SV49 )
| ~ ( is_pname @ SV438 )
| ( is_bool @ ( hAPP_pname_bool @ SV49 @ SV438 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1330]) ).
thf(1763,plain,
! [SV50: $i,SV439: $i] :
( ( ~ ( is_pname @ SV439 )
| ( is_fun_a_bool @ ( hAPP_p1534023578a_bool @ SV50 @ SV439 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1331]) ).
thf(1764,plain,
! [SV51: $i,SV440: $i] :
( ( ~ ( is_pname @ SV440 )
| ( is_fun_pname_bool @ ( hAPP_p61793385e_bool @ SV51 @ SV440 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1332]) ).
thf(1765,plain,
! [SV52: $i,SV441: $i] :
( ( ~ ( is_bool @ SV441 )
| ( is_bool @ ( hAPP_bool_bool @ SV52 @ SV441 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1333]) ).
thf(1766,plain,
! [SV442: $i,SV53: $i] :
( ( is_fun_a_bool @ ( hAPP_nat_fun_a_bool @ SV53 @ SV442 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1334]) ).
thf(1767,plain,
! [SV443: $i,SV54: $i] :
( ( is_fun_pname_bool @ ( hAPP_n1025906991e_bool @ SV54 @ SV443 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1335]) ).
thf(1768,plain,
! [SV55: $i,SV444: $i] :
( ( ~ ( is_fun_a_bool @ SV444 )
| ( is_fun_a_bool @ ( hAPP_f2050579477a_bool @ SV55 @ SV444 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1336]) ).
thf(1769,plain,
! [SV56: $i,SV445: $i] :
( ( ~ ( is_fun_pname_bool @ SV445 )
| ( is_fun_pname_bool @ ( hAPP_f759274231e_bool @ SV56 @ SV445 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1337]) ).
thf(1770,plain,
! [SV57: $i,SV446: $i] :
( ( ~ ( is_fun_pname_bool @ SV446 )
| ( is_fun1661590463l_bool @ ( hAPP_f434788991l_bool @ SV57 @ SV446 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1338]) ).
thf(1771,plain,
! [SV447: $i,SV58: $i] :
( ( is_bool @ ( hAPP_f54304608l_bool @ SV58 @ SV447 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1339]) ).
thf(1772,plain,
! [SV59: $i,SV448: $i] :
( ( ~ ( is_fun949378684l_bool @ SV448 )
| ( is_bool @ ( hAPP_f621171935l_bool @ SV59 @ SV448 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1340]) ).
thf(1773,plain,
! [SV60: $i,SV449: $i] :
( ( ~ ( is_fun949378684l_bool @ SV449 )
| ( is_fun949378684l_bool @ ( hAPP_f2117159681l_bool @ SV60 @ SV449 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1341]) ).
thf(1774,plain,
! [SV61: $i,SV450: $i] :
( ( ~ ( is_fun1661590463l_bool @ SV450 )
| ( is_bool @ ( hAPP_f1935102916l_bool @ SV61 @ SV450 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1342]) ).
thf(1775,plain,
! [SV62: $i,SV451: $i] :
( ( ~ ( is_fun1661590463l_bool @ SV451 )
| ( is_fun1661590463l_bool @ ( hAPP_f559147733l_bool @ SV62 @ SV451 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1343]) ).
thf(1776,plain,
! [SV452: $i,SV63: $i] :
( ( is_bool @ ( hAPP_f1637334154l_bool @ SV63 @ SV452 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1344]) ).
thf(1777,plain,
! [SV453: $i,SV64: $i] :
( ( is_bool @ ( hAPP_f292226953l_bool @ SV64 @ SV453 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1345]) ).
thf(1778,plain,
! [SV454: $i,SV65: $i] :
( ( is_bool @ ( hAPP_f389811538l_bool @ SV65 @ SV454 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1346]) ).
thf(1779,plain,
! [SV455: $i,SV66: $i] :
( ( is_bool @ ( hAPP_f937997336l_bool @ SV66 @ SV455 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1347]) ).
thf(1780,plain,
! [SV456: $i,SV67: $i] :
( ( is_bool @ ( hAPP_f1363661463l_bool @ SV67 @ SV456 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1348]) ).
thf(1781,plain,
! [SV457: $i,SV68: $i] :
( ( is_bool @ ( hAPP_f595608956l_bool @ SV68 @ SV457 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1349]) ).
thf(1782,plain,
! [SV458: $i,SV69: $i] :
( ( is_bool @ ( hAPP_f1295398978l_bool @ SV69 @ SV458 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1350]) ).
thf(1783,plain,
! [SV70: $i] :
( ( ( ~ ( is_fun_a_bool @ SV70 ) )
= $true )
| ( ( is_fun949378684l_bool @ ( p @ SV70 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1351]) ).
thf(1784,plain,
! [SV459: $i,SV71: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV71 ) @ SV459 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( p @ SV459 ) @ SV71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1352]) ).
thf(1785,plain,
! [SV72: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV72 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( hAPP_f103356543l_bool @ ( cOMBC_1693257480l_bool @ ord_le1568362934t_bool ) @ SV72 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1353]) ).
thf(1786,plain,
! [SV73: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV73 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ ord_le313189616e_bool ) @ SV73 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1354]) ).
thf(1787,plain,
! [SV74: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV74 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ ord_le1311769555a_bool ) @ SV74 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1355]) ).
thf(1788,plain,
! [SV75: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ SV75 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1295398978l_bool @ finite719726885l_bool @ ( collec1874991203l_bool @ ( hAPP_f760187903l_bool @ ( cOMBC_1269652216l_bool @ ord_le65145710l_bool ) @ SV75 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1356]) ).
thf(1789,plain,
! [SV76: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ SV76 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f595608956l_bool @ finite1491191519l_bool @ ( collec792590109l_bool @ ( hAPP_f1759205631l_bool @ ( cOMBC_336095980l_bool @ ord_le1375671464l_bool ) @ SV76 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1357]) ).
thf(1790,plain,
! [SV77: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ SV77 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1363661463l_bool @ finite1343359508l_bool @ ( collec1635217238l_bool @ ( hAPP_f1050622307l_bool @ ( cOMBC_636888218l_bool @ ord_le967226251l_bool ) @ SV77 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1358]) ).
thf(1791,plain,
! [SV78: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV78 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ ( collec707592106l_bool @ ( hAPP_f1434722111l_bool @ ( cOMBC_331553030l_bool @ ord_le1375614389l_bool ) @ SV78 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1359]) ).
thf(1792,plain,
! [SV79: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV79 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ ( collec1613912337l_bool @ ( hAPP_f510955609l_bool @ ( cOMBC_7971162l_bool @ ord_le675606854l_bool ) @ SV79 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1360]) ).
thf(1793,plain,
! [SV80: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV80 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ ( collec1015864663l_bool @ ( hAPP_f1772781669l_bool @ ( cOMBC_595898202l_bool @ ord_le1454342156l_bool ) @ SV80 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1361]) ).
thf(1794,plain,
! [SV81: $i,SV460: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV460 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_pname_a @ SV81 @ SV460 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1362]) ).
thf(1795,plain,
! [SV82: $i,SV461: $i] :
( ( ~ ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ SV461 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_2089570637ol_nat @ SV82 @ SV461 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1363]) ).
thf(1796,plain,
! [SV83: $i,SV462: $i] :
( ( ~ ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ SV462 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_1079571347ol_nat @ SV83 @ SV462 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1364]) ).
thf(1797,plain,
! [SV84: $i,SV463: $i] :
( ( ~ ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ SV463 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_1802975832ol_nat @ SV84 @ SV463 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1365]) ).
thf(1798,plain,
! [SV85: $i,SV464: $i] :
( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV464 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_fun_a_bool_nat @ SV85 @ SV464 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1366]) ).
thf(1799,plain,
! [SV86: $i,SV465: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV465 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_1551609309ol_nat @ SV86 @ SV465 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1367]) ).
thf(1800,plain,
! [SV87: $i,SV466: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV466 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_496248727ol_nat @ SV87 @ SV466 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1368]) ).
thf(1801,plain,
! [SV88: $i,SV467: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV467 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_a_nat @ SV88 @ SV467 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1369]) ).
thf(1802,plain,
! [SV89: $i,SV468: $i] :
( ( ~ ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ SV468 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1604018183_pname @ SV89 @ SV468 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1370]) ).
thf(1803,plain,
! [SV90: $i,SV469: $i] :
( ( ~ ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ SV469 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1705983821_pname @ SV90 @ SV469 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1371]) ).
thf(1804,plain,
! [SV91: $i,SV470: $i] :
( ( ~ ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ SV470 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_990671762_pname @ SV91 @ SV470 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1372]) ).
thf(1805,plain,
! [SV92: $i,SV471: $i] :
( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV471 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1854862208_pname @ SV92 @ SV471 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1373]) ).
thf(1806,plain,
! [SV93: $i,SV472: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV472 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1283814551_pname @ SV93 @ SV472 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1374]) ).
thf(1807,plain,
! [SV94: $i,SV473: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV473 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1921560913_pname @ SV94 @ SV473 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1375]) ).
thf(1808,plain,
! [SV95: $i,SV474: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV474 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_a_pname @ SV95 @ SV474 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1376]) ).
thf(1809,plain,
! [SV96: $i,SV475: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV475 ) )
| ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ ( image_1607900221l_bool @ SV96 @ SV475 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1377]) ).
thf(1810,plain,
! [SV97: $i,SV476: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV476 ) )
| ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ ( image_1874789623l_bool @ SV97 @ SV476 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1378]) ).
thf(1811,plain,
! [SV98: $i,SV477: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV477 ) )
| ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ ( image_1208015684l_bool @ SV98 @ SV477 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1379]) ).
thf(1812,plain,
! [SV99: $i,SV478: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV478 ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( image_nat_fun_a_bool @ SV99 @ SV478 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1380]) ).
thf(1813,plain,
! [SV100: $i,SV479: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV479 ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( image_1655916159e_bool @ SV100 @ SV479 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1381]) ).
thf(1814,plain,
! [SV101: $i,SV480: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV480 ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( image_26036933t_bool @ SV101 @ SV480 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1382]) ).
thf(1815,plain,
! [SV102: $i,SV481: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV481 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_nat_a @ SV102 @ SV481 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1383]) ).
thf(1816,plain,
! [SV103: $i,SV482: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV482 ) )
| ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ ( image_1154884483l_bool @ SV103 @ SV482 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1384]) ).
thf(1817,plain,
! [SV104: $i,SV483: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV483 ) )
| ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ ( image_1642285373l_bool @ SV104 @ SV483 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1385]) ).
thf(1818,plain,
! [SV105: $i,SV484: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV484 ) )
| ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ ( image_1420695166l_bool @ SV105 @ SV484 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1386]) ).
thf(1819,plain,
! [SV106: $i,SV485: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV485 ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( image_112932426a_bool @ SV106 @ SV485 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1387]) ).
thf(1820,plain,
! [SV107: $i,SV486: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV486 ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( image_47868345e_bool @ SV107 @ SV486 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1388]) ).
thf(1821,plain,
! [SV108: $i,SV487: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV487 ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( image_2129980159t_bool @ SV108 @ SV487 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1389]) ).
thf(1822,plain,
! [SV109: $i,SV488: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV488 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_pname_pname @ SV109 @ SV488 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1390]) ).
thf(1823,plain,
! [SV110: $i,SV489: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV489 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_a_a @ SV110 @ SV489 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1391]) ).
thf(1824,plain,
! [SV111: $i,SV490: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV490 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_fun_nat_bool_a @ SV111 @ SV490 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1392]) ).
thf(1825,plain,
! [SV112: $i,SV491: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV491 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_876012084bool_a @ SV112 @ SV491 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1393]) ).
thf(1826,plain,
! [SV113: $i,SV492: $i] :
( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV492 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_fun_a_bool_a @ SV113 @ SV492 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1394]) ).
thf(1827,plain,
! [SV114: $i,SV493: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV493 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_pname_nat @ SV114 @ SV493 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1395]) ).
thf(1828,plain,
! [SV115: $i,SV494: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV494 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_nat_pname @ SV115 @ SV494 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1396]) ).
thf(1829,plain,
! [SV116: $i,SV495: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV495 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ SV116 @ SV495 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1397]) ).
thf(1830,plain,
! [SV117: $i,SV496: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV496 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ SV117 @ SV496 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1398]) ).
thf(1831,plain,
! [SV118: $i,SV497: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV497 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ SV118 @ SV497 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1399]) ).
thf(1832,plain,
! [SV119: $i,SV498: $i] :
( ( ~ ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ SV498 ) )
| ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ ( insert2003652156l_bool @ SV119 @ SV498 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1400]) ).
thf(1833,plain,
! [SV120: $i,SV499: $i] :
( ( ~ ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ SV499 ) )
| ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ ( insert1117693814l_bool @ SV120 @ SV499 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1401]) ).
thf(1834,plain,
! [SV121: $i,SV500: $i] :
( ( ~ ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ SV500 ) )
| ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ ( insert1457093509l_bool @ SV121 @ SV500 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1402]) ).
thf(1835,plain,
! [SV122: $i,SV501: $i] :
( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV501 ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ SV122 @ SV501 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1403]) ).
thf(1836,plain,
! [SV123: $i,SV502: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV502 ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SV123 @ SV502 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1404]) ).
thf(1837,plain,
! [SV124: $i,SV503: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV503 ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ SV124 @ SV503 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1405]) ).
thf(1838,plain,
! [SV125: $i,SV504: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV504 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( image_pname_nat @ SV125 @ SV504 ) ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV504 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1406]) ).
thf(1839,plain,
! [SV126: $i,SV505: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV505 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( image_a_nat @ SV126 @ SV505 ) ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SV505 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1407]) ).
thf(1840,plain,
! [SV127: $i,SV506: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV506 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( image_496248727ol_nat @ SV127 @ SV506 ) ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SV506 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1408]) ).
thf(1841,plain,
! [SV128: $i,SV507: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV507 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( image_1551609309ol_nat @ SV128 @ SV507 ) ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SV507 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1409]) ).
thf(1842,plain,
! [SV129: $i,SV508: $i] :
( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV508 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( image_fun_a_bool_nat @ SV129 @ SV508 ) ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SV508 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1410]) ).
thf(1843,plain,
! [SV130: $i,SV509: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV509 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( image_a_pname @ SV130 @ SV509 ) ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SV509 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1411]) ).
thf(1844,plain,
! [SV131: $i,SV510: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV510 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( image_nat_pname @ SV131 @ SV510 ) ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SV510 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1412]) ).
thf(1845,plain,
! [SV132: $i,SV511: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV511 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_pname_a @ SV132 @ SV511 ) ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV511 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1413]) ).
thf(1846,plain,
! [SV133: $i,SV512: $i] :
( ( ~ ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ SV512 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_526090948bool_a @ SV133 @ SV512 ) ) ) @ ( hAPP_f1690079119ol_nat @ finite1352710292l_bool @ SV512 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1414]) ).
thf(1847,plain,
! [SV134: $i,SV513: $i] :
( ( ~ ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ SV513 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_349102846bool_a @ SV134 @ SV513 ) ) ) @ ( hAPP_f98387925ol_nat @ finite269641166l_bool @ SV513 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1415]) ).
thf(1848,plain,
! [SV135: $i,SV514: $i] :
( ( ~ ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ SV514 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_573985017bool_a @ SV135 @ SV514 ) ) ) @ ( hAPP_f1253658590ol_nat @ finite1659325229l_bool @ SV514 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1416]) ).
thf(1849,plain,
! [SV136: $i,SV515: $i] :
( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV515 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_fun_a_bool_a @ SV136 @ SV515 ) ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SV515 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1417]) ).
thf(1850,plain,
! [SV137: $i,SV516: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV516 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_876012084bool_a @ SV137 @ SV516 ) ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SV516 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1418]) ).
thf(1851,plain,
! [SV138: $i,SV517: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV517 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_fun_nat_bool_a @ SV138 @ SV517 ) ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SV517 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1419]) ).
thf(1852,plain,
! [SV139: $i,SV518: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV518 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_a_a @ SV139 @ SV518 ) ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SV518 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1420]) ).
thf(1853,plain,
! [SV140: $i,SV519: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV519 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( image_pname_pname @ SV140 @ SV519 ) ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV519 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1421]) ).
thf(1854,plain,
! [SV141: $i,SV520: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV520 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( image_2129980159t_bool @ SV141 @ SV520 ) ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV520 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1422]) ).
thf(1855,plain,
! [SV142: $i,SV521: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV521 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( image_47868345e_bool @ SV142 @ SV521 ) ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV521 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1423]) ).
thf(1856,plain,
! [SV143: $i,SV522: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV522 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( image_112932426a_bool @ SV143 @ SV522 ) ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV522 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1424]) ).
thf(1857,plain,
! [SV144: $i,SV523: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV523 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_nat_a @ SV144 @ SV523 ) ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SV523 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1425]) ).
thf(1858,plain,
! [SV145: $i,SV524: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV524 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( image_26036933t_bool @ SV145 @ SV524 ) ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SV524 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1426]) ).
thf(1859,plain,
! [SV146: $i,SV525: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV525 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( image_1655916159e_bool @ SV146 @ SV525 ) ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SV525 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1427]) ).
thf(1860,plain,
! [SV147: $i,SV526: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV526 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( image_nat_fun_a_bool @ SV147 @ SV526 ) ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SV526 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1428]) ).
thf(1861,plain,
! [SV148: $i,SV527: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV527 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( image_1921560913_pname @ SV148 @ SV527 ) ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SV527 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1429]) ).
thf(1862,plain,
! [SV149: $i,SV528: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV528 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( image_1283814551_pname @ SV149 @ SV528 ) ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SV528 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1430]) ).
thf(1863,plain,
! [SV150: $i,SV529: $i] :
( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV529 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( image_1854862208_pname @ SV150 @ SV529 ) ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SV529 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1431]) ).
thf(1864,plain,
! [SV151: $i,SV530: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV530 ) )
| ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ SV151 ) @ SV530 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SV151 ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SV530 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1432]) ).
thf(1865,plain,
! [SV152: $i,SV531: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV531 ) )
| ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ SV152 ) @ SV531 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SV152 ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SV531 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1433]) ).
thf(1866,plain,
! [SV153: $i,SV532: $i] :
( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV532 ) )
| ~ ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ SV153 ) @ SV532 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SV153 ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SV532 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1434]) ).
thf(1867,plain,
! [SV154: $i,SV533: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV533 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV154 ) @ SV533 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV154 ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV533 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1435]) ).
thf(1868,plain,
! [SV155: $i,SV534: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV534 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV155 ) @ SV534 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SV155 ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SV534 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1436]) ).
thf(1869,plain,
! [SV156: $i,SV535: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV535 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV156 ) @ SV535 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SV156 ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SV535 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1437]) ).
thf(1870,plain,
! [SV157: $i,SV536: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV536 ) )
| ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ SV157 ) @ SV536 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SV536 ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SV157 ) ) )
| ( SV157 = SV536 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1438]) ).
thf(1871,plain,
! [SV537: $i,SV158: $i] :
( ( ~ ( is_fun1661590463l_bool @ SV158 )
| ~ ( is_fun1661590463l_bool @ SV537 )
| ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV537 ) )
| ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ SV158 ) @ SV537 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SV537 ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SV158 ) ) )
| ( SV158 = SV537 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1439]) ).
thf(1872,plain,
! [SV538: $i,SV159: $i] :
( ( ~ ( is_fun949378684l_bool @ SV159 )
| ~ ( is_fun949378684l_bool @ SV538 )
| ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV538 ) )
| ~ ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ SV159 ) @ SV538 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SV538 ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SV159 ) ) )
| ( SV159 = SV538 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1440]) ).
thf(1873,plain,
! [SV539: $i,SV160: $i] :
( ( ~ ( is_fun_pname_bool @ SV160 )
| ~ ( is_fun_pname_bool @ SV539 )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV539 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV160 ) @ SV539 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV539 ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV160 ) ) )
| ( SV160 = SV539 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1441]) ).
thf(1874,plain,
! [SV540: $i,SV161: $i] :
( ( ~ ( is_fun_a_bool @ SV161 )
| ~ ( is_fun_a_bool @ SV540 )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV540 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV161 ) @ SV540 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SV540 ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SV161 ) ) )
| ( SV161 = SV540 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1442]) ).
thf(1875,plain,
! [SV162: $i,SV541: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV541 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV162 ) @ SV541 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SV541 ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SV162 ) ) )
| ( SV162 = SV541 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1443]) ).
thf(1876,plain,
! [SV163: $i,SV542: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV542 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SV542 ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( insert_fun_nat_bool @ SV163 @ SV542 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1444]) ).
thf(1877,plain,
! [SV164: $i,SV543: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV543 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SV543 ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( insert1325755072e_bool @ SV164 @ SV543 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1445]) ).
thf(1878,plain,
! [SV165: $i,SV544: $i] :
( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV544 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SV544 ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( insert_fun_a_bool @ SV165 @ SV544 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1446]) ).
thf(1879,plain,
! [SV166: $i,SV545: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV545 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV545 ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( insert_pname @ SV166 @ SV545 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1447]) ).
thf(1880,plain,
! [SV167: $i,SV546: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV546 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SV546 ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( insert_nat @ SV167 @ SV546 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1448]) ).
thf(1881,plain,
! [SV168: $i,SV547: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV547 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SV547 ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( insert_a @ SV168 @ SV547 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1449]) ).
thf(1882,plain,
! [SV169: $i,SV548: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV548 ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ SV169 ) @ SV548 ) )
| ( ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( insert_fun_nat_bool @ SV169 @ SV548 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SV548 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1450]) ).
thf(1883,plain,
! [SV170: $i,SV549: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV549 ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ SV170 ) @ SV549 ) )
| ( ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( insert1325755072e_bool @ SV170 @ SV549 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SV549 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1451]) ).
thf(1884,plain,
! [SV171: $i,SV550: $i] :
( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV550 ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ SV171 ) @ SV550 ) )
| ( ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( insert_fun_a_bool @ SV171 @ SV550 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SV550 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1452]) ).
thf(1885,plain,
! [SV172: $i,SV551: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV551 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV172 ) @ SV551 ) )
| ( ( hAPP_f22106695ol_nat @ finite_card_nat @ ( insert_nat @ SV172 @ SV551 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SV551 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1453]) ).
thf(1886,plain,
! [SV173: $i,SV552: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV552 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV173 ) @ SV552 ) )
| ( ( hAPP_f921600141ol_nat @ finite_card_pname @ ( insert_pname @ SV173 @ SV552 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV552 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1454]) ).
thf(1887,plain,
! [SV174: $i,SV553: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV553 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV174 ) @ SV553 ) )
| ( ( hAPP_fun_a_bool_nat @ finite_card_a @ ( insert_a @ SV174 @ SV553 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SV553 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1455]) ).
thf(1888,plain,
! [SV554: $i,SV175: $i] :
( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV175 ) @ SV554 ) )
| ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ suc @ SV554 ) ) @ SV175 )
= ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV554 ) @ SV175 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1456]) ).
thf(1889,plain,
! [SV555: $i,SV178: $i] :
( ( ( ( hAPP_nat_nat @ suc @ SV178 )
!= ( hAPP_nat_nat @ suc @ SV555 ) )
| ( SV178 = SV555 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1459]) ).
thf(1890,plain,
! [SV179: $i] :
( ( ( hAPP_nat_nat @ suc @ SV179 )
= SV179 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1460]) ).
thf(1891,plain,
! [SV180: $i] :
( ( SV180
= ( hAPP_nat_nat @ suc @ SV180 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1461]) ).
thf(1892,plain,
! [SV556: $i,SV181: $i] :
( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV181 ) @ SV556 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV556 ) @ SV181 ) )
| ( SV181 = SV556 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1462]) ).
thf(1893,plain,
! [SV182: $i,SV557: $i] :
( ( ! [SY962: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV557 ) @ SY962 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY962 ) @ SV182 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV557 ) @ SV182 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1463]) ).
thf(1894,plain,
! [SV558: $i,SV183: $i] :
( ( ( SV183 != SV558 )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV183 ) @ SV558 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1464]) ).
thf(1895,plain,
! [SV559: $i,SV184: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV184 ) @ SV559 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV559 ) @ SV184 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1465]) ).
thf(1896,plain,
! [SV560: $i,SV186: $i] :
( ( ! [SY963: $i] :
( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV186 ) @ SV560 ) ) @ SY963 )
= ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV186 ) @ SY963 ) ) @ SV560 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1467]) ).
thf(1897,plain,
! [SV561: $i,SV187: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ SV187 ) @ SV561 ) )
| ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV561 ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV187 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1468]) ).
thf(1898,plain,
! [SV562: $i,SV188: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ SV188 ) @ SV562 ) )
| ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV562 ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV188 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1469]) ).
thf(1899,plain,
! [SV563: $i,SV189: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV189 ) @ SV563 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV563 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV189 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1470]) ).
thf(1900,plain,
! [SV564: $i,SV190: $i] :
( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ SV190 ) @ SV564 ) )
| ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV564 ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV190 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1471]) ).
thf(1901,plain,
! [SV565: $i,SV191: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV191 ) @ SV565 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV565 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV191 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1472]) ).
thf(1902,plain,
! [SV566: $i,SV192: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV192 ) @ SV566 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV566 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV192 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1473]) ).
thf(1903,plain,
! [SV193: $i,SV567: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV567 ) )
| ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ SV193 ) @ SV567 ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV193 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1474]) ).
thf(1904,plain,
! [SV194: $i,SV568: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV568 ) )
| ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ SV194 ) @ SV568 ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV194 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1475]) ).
thf(1905,plain,
! [SV195: $i,SV569: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV569 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV195 ) @ SV569 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV195 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1476]) ).
thf(1906,plain,
! [SV196: $i,SV570: $i] :
( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV570 ) )
| ~ ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ SV196 ) @ SV570 ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1477]) ).
thf(1907,plain,
! [SV197: $i,SV571: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV571 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV197 ) @ SV571 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV197 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1478]) ).
thf(1908,plain,
! [SV198: $i,SV572: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV572 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV198 ) @ SV572 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV198 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1479]) ).
thf(1909,plain,
! [SV573: $i,SV199: $i] :
( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ SV199 ) ) @ SV573 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV199 ) @ SV573 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1480]) ).
thf(1910,plain,
! [SV574: $i,SV200: $i] :
( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV200 ) @ ( hAPP_nat_nat @ suc @ SV574 ) ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV200 ) @ SV574 ) )
| ( SV200
= ( hAPP_nat_nat @ suc @ SV574 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1481]) ).
thf(1911,plain,
! [SV575: $i,SV201: $i] :
( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV201 ) @ SV575 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV201 ) @ ( hAPP_nat_nat @ suc @ SV575 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1482]) ).
thf(1912,plain,
! [SV202: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ SV202 ) ) @ SV202 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1483]) ).
thf(1913,plain,
! [SV576: $i,SV203: $i] :
( ( ! [SY964: $i] :
( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ suc @ SV203 ) ) @ SV576 ) ) @ ( hAPP_nat_nat @ suc @ SY964 ) )
= ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV203 ) @ SV576 ) ) @ SY964 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1484]) ).
thf(1914,plain,
! [SV577: $i,SV204: $i] :
( ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ suc @ SV204 ) ) @ ( hAPP_nat_nat @ suc @ SV577 ) )
= ( hAPP_nat_nat @ ( minus_minus_nat @ SV204 ) @ SV577 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1485]) ).
thf(1915,plain,
! [SV205: $i,SV578: $i] :
( ( ! [SY965: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV578 ) @ SY965 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV578 ) @ SV205 ) )
| ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ SY965 ) @ SV578 ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV205 ) @ SV578 ) )
= ( hAPP_nat_nat @ ( minus_minus_nat @ SY965 ) @ SV205 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1486]) ).
thf(1916,plain,
! [SV579: $i,SV206: $i] :
( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV206 ) @ SV579 ) )
| ( ( hAPP_nat_nat @ ( minus_minus_nat @ SV579 ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV579 ) @ SV206 ) )
= SV206 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1487]) ).
thf(1917,plain,
! [SV207: $i,SV580: $i] :
( ( ! [SY966: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV580 ) @ SY966 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV580 ) @ SV207 ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ SY966 ) @ SV207 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1488]) ).
thf(1918,plain,
! [SV208: $i,SV581: $i] :
( ( ! [SY967: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV581 ) @ SY967 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV208 ) @ SY967 ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV208 ) @ SV581 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1489]) ).
thf(1919,plain,
! [SV582: $i,SV209: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV209 ) @ SV582 ) ) @ SV209 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1490]) ).
thf(1920,plain,
! [SV583: $i,SV210: $i] :
( ( ! [SY968: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SY968 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV210 ) @ ( image_pname_a @ SV583 @ SY968 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV210 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1491]) ).
thf(1921,plain,
! [SV211: $i,SV584: $i] :
( ( ! [SY969: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( hAPP_n1699378549t_bool @ SY969 @ ( sK16_N_2 @ SY969 @ SV584 @ SV211 ) ) ) @ ( hAPP_n1699378549t_bool @ SY969 @ ( hAPP_nat_nat @ suc @ ( sK16_N_2 @ SY969 @ SV584 @ SV211 ) ) ) ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV211 ) @ SV584 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( hAPP_n1699378549t_bool @ SY969 @ SV211 ) ) @ ( hAPP_n1699378549t_bool @ SY969 @ SV584 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1492]) ).
thf(1922,plain,
! [SV212: $i,SV585: $i] :
( ( ! [SY970: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_n1025906991e_bool @ SY970 @ ( sK15_N_2 @ SY970 @ SV585 @ SV212 ) ) ) @ ( hAPP_n1025906991e_bool @ SY970 @ ( hAPP_nat_nat @ suc @ ( sK15_N_2 @ SY970 @ SV585 @ SV212 ) ) ) ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV212 ) @ SV585 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_n1025906991e_bool @ SY970 @ SV212 ) ) @ ( hAPP_n1025906991e_bool @ SY970 @ SV585 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1493]) ).
thf(1923,plain,
! [SV213: $i,SV586: $i] :
( ( ! [SY971: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ SY971 @ ( sK14_N_2 @ SY971 @ SV586 @ SV213 ) ) ) @ ( hAPP_nat_nat @ SY971 @ ( hAPP_nat_nat @ suc @ ( sK14_N_2 @ SY971 @ SV586 @ SV213 ) ) ) ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV213 ) @ SV586 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ SY971 @ SV213 ) ) @ ( hAPP_nat_nat @ SY971 @ SV586 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1494]) ).
thf(1924,plain,
! [SV214: $i,SV587: $i] :
( ( ! [SY972: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_nat_fun_a_bool @ SY972 @ ( sK13_N_2 @ SY972 @ SV587 @ SV214 ) ) ) @ ( hAPP_nat_fun_a_bool @ SY972 @ ( hAPP_nat_nat @ suc @ ( sK13_N_2 @ SY972 @ SV587 @ SV214 ) ) ) ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV214 ) @ SV587 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_nat_fun_a_bool @ SY972 @ SV214 ) ) @ ( hAPP_nat_fun_a_bool @ SY972 @ SV587 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1495]) ).
thf(1925,plain,
! [SV215: $i,SV588: $i] :
( ( ! [SY973: $i,SY974: $i] :
( ( SV588
!= ( hAPP_pname_a @ SY973 @ SY974 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SY974 ) @ SV215 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV588 ) @ ( image_pname_a @ SY973 @ SV215 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1496]) ).
thf(1926,plain,
! [SV589: $i,SV216: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV216 ) @ SV589 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV589 ) @ SV216 ) )
| ( SV216 = SV589 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1497]) ).
thf(1927,plain,
! [SV590: $i,SV217: $i] :
( ( ~ ( is_fun_pname_bool @ SV217 )
| ~ ( is_fun_pname_bool @ SV590 )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV217 ) @ SV590 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV590 ) @ SV217 ) )
| ( SV217 = SV590 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1498]) ).
thf(1928,plain,
! [SV591: $i,SV218: $i] :
( ( ~ ( is_fun_a_bool @ SV218 )
| ~ ( is_fun_a_bool @ SV591 )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV218 ) @ SV591 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV591 ) @ SV218 ) )
| ( SV218 = SV591 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1499]) ).
thf(1929,plain,
! [SV219: $i,SV592: $i] :
( ( ! [SY975: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV592 ) @ SY975 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV219 ) @ SV592 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV219 ) @ SY975 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1500]) ).
thf(1930,plain,
! [SV220: $i,SV593: $i] :
( ( ! [SY976: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV593 ) @ SY976 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV220 ) @ SV593 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV220 ) @ SY976 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1501]) ).
thf(1931,plain,
! [SV221: $i,SV594: $i] :
( ( ! [SY977: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV594 ) @ SY977 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV221 ) @ SV594 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV221 ) @ SY977 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1502]) ).
thf(1932,plain,
! [SV595: $i,SV222: $i] :
( ( ! [SY978: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV222 ) @ ( insert_nat @ SV595 @ SY978 ) ) )
| ( SV222 = SV595 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV222 ) @ SY978 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1503]) ).
thf(1933,plain,
! [SV596: $i,SV223: $i] :
( ( ~ ( is_pname @ SV223 )
| ~ ( is_pname @ SV596 )
| ! [SY979: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV223 ) @ ( insert_pname @ SV596 @ SY979 ) ) )
| ( SV223 = SV596 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV223 ) @ SY979 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1504]) ).
thf(1934,plain,
! [SV597: $i,SV224: $i] :
( ( ~ ( is_a @ SV224 )
| ~ ( is_a @ SV597 )
| ! [SY980: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV224 ) @ ( insert_a @ SV597 @ SY980 ) ) )
| ( SV224 = SV597 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV224 ) @ SY980 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1505]) ).
thf(1935,plain,
! [SV598: $i,SV225: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV225 ) @ ( insert_nat @ SV225 @ SV598 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1506]) ).
thf(1936,plain,
! [SV599: $i,SV226: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV226 ) @ ( insert_pname @ SV226 @ SV599 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1507]) ).
thf(1937,plain,
! [SV600: $i,SV227: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV227 ) @ ( insert_a @ SV227 @ SV600 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1508]) ).
thf(1938,plain,
! [SV601: $i,SV228: $i] :
( ( ( insert_nat @ SV228 @ SV601 )
= ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ fequal_nat ) @ SV228 ) ) @ ( hAPP_f800510211t_bool @ ( cOMBC_226598744l_bool @ member_nat ) @ SV601 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1509]) ).
thf(1939,plain,
! [SV602: $i,SV229: $i] :
( ( ( insert_pname @ SV229 @ SV602 )
= ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ fequal_pname ) @ SV229 ) ) @ ( hAPP_f759274231e_bool @ ( cOMBC_1058051404l_bool @ member_pname ) @ SV602 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1510]) ).
thf(1940,plain,
! [SV603: $i,SV230: $i] :
( ( ( insert_a @ SV230 @ SV603 )
= ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ ( hAPP_a_fun_a_bool @ ( cOMBC_a_a_bool @ fequal_a ) @ SV230 ) ) @ ( hAPP_f2050579477a_bool @ ( cOMBC_1355376034l_bool @ member_a ) @ SV603 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1511]) ).
thf(1941,plain,
! [SV604: $i,SV231: $i] :
( ( ( insert_fun_nat_bool @ SV231 @ SV604 )
= ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ ( hAPP_f103356543l_bool @ ( cOMBC_1693257480l_bool @ fequal_fun_nat_bool ) @ SV231 ) ) @ ( hAPP_f1246832597l_bool @ ( cOMBC_1245412066l_bool @ member_fun_nat_bool ) @ SV604 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1512]) ).
thf(1942,plain,
! [SV605: $i,SV232: $i] :
( ( ( insert1325755072e_bool @ SV232 @ SV605 )
= ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ SV232 ) ) @ ( hAPP_f559147733l_bool @ ( cOMBC_1988546018l_bool @ member799430823e_bool ) @ SV605 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1513]) ).
thf(1943,plain,
! [SV606: $i,SV233: $i] :
( ( ( insert_fun_a_bool @ SV233 @ SV606 )
= ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ fequal_fun_a_bool ) @ SV233 ) ) @ ( hAPP_f2117159681l_bool @ ( cOMBC_1880041174l_bool @ member_fun_a_bool ) @ SV606 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1514]) ).
thf(1944,plain,
! [SV607: $i,SV234: $i] :
( ( ( insert_nat @ SV234 @ ( collect_nat @ SV607 ) )
= ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fimplies @ ( cOMBB_bool_bool_nat @ fNot @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ fequal_nat ) @ SV234 ) ) ) @ SV607 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1515]) ).
thf(1945,plain,
! [SV608: $i,SV235: $i] :
( ( ( insert_pname @ SV235 @ ( collect_pname @ SV608 ) )
= ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fimplies @ ( cOMBB_647938656_pname @ fNot @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ fequal_pname ) @ SV235 ) ) ) @ SV608 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1516]) ).
thf(1946,plain,
! [SV609: $i,SV236: $i] :
( ( ( insert_a @ SV236 @ ( collect_a @ SV609 ) )
= ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fimplies @ ( cOMBB_bool_bool_a @ fNot @ ( hAPP_a_fun_a_bool @ ( cOMBC_a_a_bool @ fequal_a ) @ SV236 ) ) ) @ SV609 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1517]) ).
thf(1947,plain,
! [SV610: $i,SV237: $i] :
( ( ( insert_fun_nat_bool @ SV237 @ ( collect_fun_nat_bool @ SV610 ) )
= ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fimplies @ ( cOMBB_238756964t_bool @ fNot @ ( hAPP_f103356543l_bool @ ( cOMBC_1693257480l_bool @ fequal_fun_nat_bool ) @ SV237 ) ) ) @ SV610 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1518]) ).
thf(1948,plain,
! [SV611: $i,SV238: $i] :
( ( ( insert1325755072e_bool @ SV238 @ ( collec1974731493e_bool @ SV611 ) )
= ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fimplies @ ( cOMBB_307249310e_bool @ fNot @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ SV238 ) ) ) @ SV611 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1519]) ).
thf(1949,plain,
! [SV612: $i,SV239: $i] :
( ( ( insert_fun_a_bool @ SV239 @ ( collect_fun_a_bool @ SV612 ) )
= ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fimplies @ ( cOMBB_2140588453a_bool @ fNot @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ fequal_fun_a_bool ) @ SV239 ) ) ) @ SV612 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1520]) ).
thf(1950,plain,
! [SV613: $i,SV240: $i] :
( ( ( insert_nat @ SV240 @ ( insert_nat @ SV240 @ SV613 ) )
= ( insert_nat @ SV240 @ SV613 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1521]) ).
thf(1951,plain,
! [SV614: $i,SV241: $i] :
( ( ( insert_pname @ SV241 @ ( insert_pname @ SV241 @ SV614 ) )
= ( insert_pname @ SV241 @ SV614 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1522]) ).
thf(1952,plain,
! [SV615: $i,SV242: $i] :
( ( ( insert_a @ SV242 @ ( insert_a @ SV242 @ SV615 ) )
= ( insert_a @ SV242 @ SV615 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1523]) ).
thf(1953,plain,
! [SV616: $i,SV243: $i] :
( ( ! [SY981: $i] :
( ( insert_nat @ SV243 @ ( insert_nat @ SV616 @ SY981 ) )
= ( insert_nat @ SV616 @ ( insert_nat @ SV243 @ SY981 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1524]) ).
thf(1954,plain,
! [SV617: $i,SV244: $i] :
( ( ! [SY982: $i] :
( ( insert_pname @ SV244 @ ( insert_pname @ SV617 @ SY982 ) )
= ( insert_pname @ SV617 @ ( insert_pname @ SV244 @ SY982 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1525]) ).
thf(1955,plain,
! [SV618: $i,SV245: $i] :
( ( ! [SY983: $i] :
( ( insert_a @ SV245 @ ( insert_a @ SV618 @ SY983 ) )
= ( insert_a @ SV618 @ ( insert_a @ SV245 @ SY983 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1526]) ).
thf(1956,plain,
! [SV246: $i,SV619: $i] :
( ( ! [SY984: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV619 ) @ SY984 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV619 ) @ ( insert_nat @ SV246 @ SY984 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1527]) ).
thf(1957,plain,
! [SV247: $i,SV620: $i] :
( ( ! [SY985: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV620 ) @ SY985 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV620 ) @ ( insert_pname @ SV247 @ SY985 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1528]) ).
thf(1958,plain,
! [SV248: $i,SV621: $i] :
( ( ! [SY986: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV621 ) @ SY986 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV621 ) @ ( insert_a @ SV248 @ SY986 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1529]) ).
thf(1959,plain,
! [SV622: $i,SV249: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV249 ) @ SV622 ) )
| ( ( insert_nat @ SV249 @ SV622 )
= SV622 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1530]) ).
thf(1960,plain,
! [SV250: $i,SV623: $i] :
( ( ~ ( is_fun_pname_bool @ SV623 )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV250 ) @ SV623 ) )
| ( ( insert_pname @ SV250 @ SV623 )
= SV623 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1531]) ).
thf(1961,plain,
! [SV251: $i,SV624: $i] :
( ( ~ ( is_fun_a_bool @ SV624 )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV251 ) @ SV624 ) )
| ( ( insert_a @ SV251 @ SV624 )
= SV624 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1532]) ).
thf(1962,plain,
! [SV625: $i,SV255: $i] :
( ( ( SV255 != SV625 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV255 ) @ SV625 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1536]) ).
thf(1963,plain,
! [SV626: $i,SV256: $i] :
( ( ( SV256 != SV626 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV256 ) @ SV626 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1537]) ).
thf(1964,plain,
! [SV627: $i,SV257: $i] :
( ( ( SV257 != SV627 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV257 ) @ SV627 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1538]) ).
thf(1965,plain,
! [SV628: $i,SV258: $i] :
( ( ( SV258 != SV628 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV628 ) @ SV258 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1539]) ).
thf(1966,plain,
! [SV629: $i,SV259: $i] :
( ( ( SV259 != SV629 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV629 ) @ SV259 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1540]) ).
thf(1967,plain,
! [SV630: $i,SV260: $i] :
( ( ( SV260 != SV630 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV630 ) @ SV260 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1541]) ).
thf(1968,plain,
! [SV261: $i,SV631: $i] :
( ( ! [SY987: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV631 ) @ SY987 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV261 ) @ SV631 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV261 ) @ SY987 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1542]) ).
thf(1969,plain,
! [SV262: $i,SV632: $i] :
( ( ! [SY988: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV632 ) @ SY988 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV262 ) @ SV632 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV262 ) @ SY988 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1543]) ).
thf(1970,plain,
! [SV263: $i,SV633: $i] :
( ( ! [SY989: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV633 ) @ SY989 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV263 ) @ SV633 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV263 ) @ SY989 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1544]) ).
thf(1971,plain,
! [SV264: $i,SV634: $i] :
( ( ! [SY990: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV634 ) @ SY990 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY990 ) @ SV264 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV634 ) @ SV264 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1545]) ).
thf(1972,plain,
! [SV265: $i,SV635: $i] :
( ( ! [SY991: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV635 ) @ SY991 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY991 ) @ SV265 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV635 ) @ SV265 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1546]) ).
thf(1973,plain,
! [SV266: $i,SV636: $i] :
( ( ! [SY992: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV636 ) @ SY992 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY992 ) @ SV266 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV636 ) @ SV266 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1547]) ).
thf(1974,plain,
! [SV267: $i,SV637: $i] :
( ( ! [SY993: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV637 ) @ SY993 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV267 ) @ SV637 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV267 ) @ SY993 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1548]) ).
thf(1975,plain,
! [SV268: $i,SV638: $i] :
( ( ! [SY994: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV638 ) @ SY994 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV268 ) @ SV638 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV268 ) @ SY994 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1549]) ).
thf(1976,plain,
! [SV269: $i,SV639: $i] :
( ( ! [SY995: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV639 ) @ SY995 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV269 ) @ SV639 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV269 ) @ SY995 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1550]) ).
thf(1977,plain,
! [SV270: $i,SV640: $i] :
( ( ! [SY996: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV640 ) @ SY996 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY996 ) @ SV270 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV640 ) @ SV270 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1551]) ).
thf(1978,plain,
! [SV271: $i,SV641: $i] :
( ( ! [SY997: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV641 ) @ SY997 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY997 ) @ SV271 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV641 ) @ SV271 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1552]) ).
thf(1979,plain,
! [SV272: $i,SV642: $i] :
( ( ! [SY998: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV642 ) @ SY998 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY998 ) @ SV272 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV642 ) @ SV272 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1553]) ).
thf(1980,plain,
! [SV273: $i] :
( ( ( ~ ( is_fun_pname_bool @ SV273 ) )
= $true )
| ( ( ( collect_pname @ SV273 )
= SV273 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1554]) ).
thf(1981,plain,
! [SV275: $i] :
( ( ( ~ ( is_fun1661590463l_bool @ SV275 ) )
= $true )
| ( ( ( collec1974731493e_bool @ SV275 )
= SV275 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1556]) ).
thf(1982,plain,
! [SV276: $i] :
( ( ( ~ ( is_fun949378684l_bool @ SV276 ) )
= $true )
| ( ( ( collect_fun_a_bool @ SV276 )
= SV276 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1557]) ).
thf(1983,plain,
! [SV278: $i,SV643: $i] :
( ( ! [SY999: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV643 ) @ SY999 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( hAPP_pname_a @ SV278 @ SV643 ) ) @ ( image_pname_a @ SV278 @ SY999 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1559]) ).
thf(1984,plain,
! [SV644: $i,SV279: $i] :
( ( ! [SY1000: $i,SY1001: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SY1000 ) @ SY1001 ) )
| ( SV279
!= ( hAPP_pname_a @ SV644 @ SY1000 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV279 ) @ ( image_pname_a @ SV644 @ SY1001 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1560]) ).
thf(1985,plain,
! [SV645: $i,SV280: $i] :
( ( ( insert_nat @ SV280 @ SV645 )
= ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ fequal_nat ) @ SV280 ) ) @ ( hAPP_f800510211t_bool @ ( cOMBC_226598744l_bool @ member_nat ) @ SV645 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1561]) ).
thf(1986,plain,
! [SV646: $i,SV281: $i] :
( ( ( insert_pname @ SV281 @ SV646 )
= ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ fequal_pname ) @ SV281 ) ) @ ( hAPP_f759274231e_bool @ ( cOMBC_1058051404l_bool @ member_pname ) @ SV646 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1562]) ).
thf(1987,plain,
! [SV647: $i,SV282: $i] :
( ( ( insert_a @ SV282 @ SV647 )
= ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ ( hAPP_a_fun_a_bool @ ( cOMBC_a_a_bool @ fequal_a ) @ SV282 ) ) @ ( hAPP_f2050579477a_bool @ ( cOMBC_1355376034l_bool @ member_a ) @ SV647 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1563]) ).
thf(1988,plain,
! [SV648: $i,SV283: $i] :
( ( ( insert_fun_nat_bool @ SV283 @ SV648 )
= ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ ( hAPP_f103356543l_bool @ ( cOMBC_1693257480l_bool @ fequal_fun_nat_bool ) @ SV283 ) ) @ ( hAPP_f1246832597l_bool @ ( cOMBC_1245412066l_bool @ member_fun_nat_bool ) @ SV648 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1564]) ).
thf(1989,plain,
! [SV649: $i,SV284: $i] :
( ( ( insert1325755072e_bool @ SV284 @ SV649 )
= ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ SV284 ) ) @ ( hAPP_f559147733l_bool @ ( cOMBC_1988546018l_bool @ member799430823e_bool ) @ SV649 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1565]) ).
thf(1990,plain,
! [SV650: $i,SV285: $i] :
( ( ( insert_fun_a_bool @ SV285 @ SV650 )
= ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ fequal_fun_a_bool ) @ SV285 ) ) @ ( hAPP_f2117159681l_bool @ ( cOMBC_1880041174l_bool @ member_fun_a_bool ) @ SV650 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1566]) ).
thf(1991,plain,
! [SV651: $i,SV286: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV286 ) @ ( insert_nat @ SV651 @ SV286 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1567]) ).
thf(1992,plain,
! [SV652: $i,SV287: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV287 ) @ ( insert_pname @ SV652 @ SV287 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1568]) ).
thf(1993,plain,
! [SV653: $i,SV288: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV288 ) @ ( insert_a @ SV653 @ SV288 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1569]) ).
thf(1994,plain,
! [SV289: $i,SV654: $i] :
( ( ! [SY1002: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV654 ) @ SY1002 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV654 ) @ ( insert_nat @ SV289 @ SY1002 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1570]) ).
thf(1995,plain,
! [SV290: $i,SV655: $i] :
( ( ! [SY1003: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV655 ) @ SY1003 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV655 ) @ ( insert_pname @ SV290 @ SY1003 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1571]) ).
thf(1996,plain,
! [SV291: $i,SV656: $i] :
( ( ! [SY1004: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV656 ) @ SY1004 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV656 ) @ ( insert_a @ SV291 @ SY1004 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1572]) ).
thf(1997,plain,
! [SV292: $i,SV657: $i] :
( ( ! [SY1005: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV657 ) @ SY1005 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( insert_nat @ SV292 @ SV657 ) ) @ ( insert_nat @ SV292 @ SY1005 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1573]) ).
thf(1998,plain,
! [SV293: $i,SV658: $i] :
( ( ! [SY1006: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV658 ) @ SY1006 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ SV293 @ SV658 ) ) @ ( insert_pname @ SV293 @ SY1006 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1574]) ).
thf(1999,plain,
! [SV294: $i,SV659: $i] :
( ( ! [SY1007: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV659 ) @ SY1007 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV294 @ SV659 ) ) @ ( insert_a @ SV294 @ SY1007 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1575]) ).
thf(2000,plain,
! [SV660: $i,SV295: $i] :
( ( ! [SY1008: $i] :
( ( image_pname_a @ SV295 @ ( insert_pname @ SV660 @ SY1008 ) )
= ( insert_a @ ( hAPP_pname_a @ SV295 @ SV660 ) @ ( image_pname_a @ SV295 @ SY1008 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1576]) ).
thf(2001,plain,
! [SV296: $i,SV661: $i] :
( ( ! [SY1009: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV661 ) @ SY1009 ) )
| ( ( insert_a @ ( hAPP_pname_a @ SV296 @ SV661 ) @ ( image_pname_a @ SV296 @ SY1009 ) )
= ( image_pname_a @ SV296 @ SY1009 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1577]) ).
thf(2002,plain,
! [SV297: $i,SV662: $i] :
( ( ! [SY1010: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV662 ) @ SY1010 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_pname_a @ SV297 @ SV662 ) ) @ ( image_pname_a @ SV297 @ SY1010 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1578]) ).
thf(2003,plain,
! [SV663: $i,SV298: $i] :
( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ SV298 ) ) @ SV663 ) )
| ( SV663
= ( hAPP_nat_nat @ suc @ ( sK4_M @ SV663 @ SV298 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1579]) ).
thf(2004,plain,
! [SV303: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ fNot @ SV303 ) ) )
= $true )
| ( ( ~ ( hBOOL @ SV303 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1584]) ).
thf(2005,plain,
! [SV304: $i] :
( ( ( hBOOL @ SV304 )
= $true )
| ( ( hBOOL @ ( hAPP_bool_bool @ fNot @ SV304 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1585]) ).
thf(2006,plain,
! [SV305: $i,SV664: $i] :
( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ SV664 ) @ SV305 ) )
| ~ ( hBOOL @ SV664 )
| ~ ( hBOOL @ SV305 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1586]) ).
thf(2007,plain,
! [SV306: $i] :
( ( ( ! [SY746: $i] :
~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ SV306 ) @ SY746 ) ) )
= $true )
| ( ( hBOOL @ SV306 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1587]) ).
thf(2008,plain,
! [SV665: $i,SV307: $i] :
( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ SV307 ) @ SV665 ) )
| ( hBOOL @ SV665 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1588]) ).
thf(2009,plain,
! [SV308: $i,SV666: $i] :
( ( ~ ( hBOOL @ SV666 )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ SV666 ) @ SV308 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1589]) ).
thf(2010,plain,
! [SV309: $i,SV667: $i] :
( ( ~ ( hBOOL @ SV667 )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ SV309 ) @ SV667 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1590]) ).
thf(2011,plain,
! [SV310: $i,SV668: $i] :
( ( ( hBOOL @ SV668 )
| ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ SV310 ) @ SV668 ) )
| ( hBOOL @ SV310 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1591]) ).
thf(2012,plain,
! [SV311: $i,SV669: $i] :
( ( ( hBOOL @ SV669 )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ SV669 ) @ SV311 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1592]) ).
thf(2013,plain,
! [SV312: $i,SV670: $i] :
( ( ~ ( hBOOL @ SV670 )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ SV312 ) @ SV670 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1593]) ).
thf(2014,plain,
! [SV313: $i,SV671: $i] :
( ( ( hBOOL @ SV671 )
| ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ SV313 ) @ SV671 ) )
| ~ ( hBOOL @ SV313 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1594]) ).
thf(2015,plain,
! [SV672: $i,SV314: $i] :
( ( ~ ( is_a @ SV314 )
| ~ ( is_a @ SV672 )
| ~ ( hBOOL @ ( hAPP_a_bool @ ( hAPP_a_fun_a_bool @ fequal_a @ SV314 ) @ SV672 ) )
| ( SV314 = SV672 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1595]) ).
thf(2016,plain,
! [SV673: $i,SV315: $i] :
( ( ( SV315 != SV673 )
| ( hBOOL @ ( hAPP_a_bool @ ( hAPP_a_fun_a_bool @ fequal_a @ SV315 ) @ SV673 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1596]) ).
thf(2017,plain,
! [SV674: $i,SV316: $i] :
( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ SV316 ) @ SV674 ) )
| ( SV316 = SV674 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1597]) ).
thf(2018,plain,
! [SV675: $i,SV317: $i] :
( ( ( SV317 != SV675 )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ SV317 ) @ SV675 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1598]) ).
thf(2019,plain,
! [SV676: $i,SV318: $i] :
( ( ~ ( is_pname @ SV318 )
| ~ ( is_pname @ SV676 )
| ~ ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ fequal_pname @ SV318 ) @ SV676 ) )
| ( SV318 = SV676 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1599]) ).
thf(2020,plain,
! [SV677: $i,SV319: $i] :
( ( ( SV319 != SV677 )
| ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ fequal_pname @ SV319 ) @ SV677 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1600]) ).
thf(2021,plain,
! [SV678: $i,SV320: $i] :
( ( ! [SY1011: $i] :
( ( hAPP_a_bool @ ( hAPP_a_fun_a_bool @ ( cOMBC_a_a_bool @ SV320 ) @ SV678 ) @ SY1011 )
= ( hAPP_a_bool @ ( hAPP_a_fun_a_bool @ SV320 @ SY1011 ) @ SV678 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1601]) ).
thf(2022,plain,
! [SV679: $i,SV321: $i] :
( ( ~ ( is_fun_a_bool @ SV321 )
| ~ ( is_fun_a_bool @ SV679 )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ SV321 ) @ SV679 ) )
| ( SV321 = SV679 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1602]) ).
thf(2023,plain,
! [SV680: $i,SV322: $i] :
( ( ( SV322 != SV680 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ SV322 ) @ SV680 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1603]) ).
thf(2024,plain,
! [SV681: $i,SV323: $i] :
( ( ! [SY1012: $i] :
( ( hAPP_a_bool @ ( cOMBB_bool_bool_a @ SV323 @ SV681 ) @ SY1012 )
= ( hAPP_bool_bool @ SV323 @ ( hAPP_a_bool @ SV681 @ SY1012 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1604]) ).
thf(2025,plain,
! [SV682: $i,SV324: $i] :
( ( ! [SY1013: $i] :
( ( hAPP_a_bool @ ( cOMBS_a_bool_bool @ SV324 @ SV682 ) @ SY1013 )
= ( hAPP_bool_bool @ ( hAPP_a_fun_bool_bool @ SV324 @ SY1013 ) @ ( hAPP_a_bool @ SV682 @ SY1013 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1605]) ).
thf(2026,plain,
! [SV683: $i,SV325: $i] :
( ( ! [SY1014: $i] :
( ( hAPP_pname_bool @ ( hAPP_a93125764e_bool @ ( cOMBC_pname_a_bool @ SV325 ) @ SV683 ) @ SY1014 )
= ( hAPP_a_bool @ ( hAPP_p1534023578a_bool @ SV325 @ SY1014 ) @ SV683 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1606]) ).
thf(2027,plain,
! [SV684: $i,SV326: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ SV326 ) @ SV684 ) )
| ( SV326 = SV684 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1607]) ).
thf(2028,plain,
! [SV685: $i,SV327: $i] :
( ( ( SV327 != SV685 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ SV327 ) @ SV685 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1608]) ).
thf(2029,plain,
! [SV686: $i,SV328: $i] :
( ( ~ ( is_fun_pname_bool @ SV328 )
| ~ ( is_fun_pname_bool @ SV686 )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ SV328 ) @ SV686 ) )
| ( SV328 = SV686 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1609]) ).
thf(2030,plain,
! [SV687: $i,SV329: $i] :
( ( ( SV329 != SV687 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ SV329 ) @ SV687 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1610]) ).
thf(2031,plain,
! [SV688: $i,SV330: $i] :
( ( ! [SY1015: $i] :
( ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ SV330 ) @ SV688 ) @ SY1015 )
= ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV330 @ SY1015 ) @ SV688 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1611]) ).
thf(2032,plain,
! [SV689: $i,SV331: $i] :
( ( ! [SY1016: $i] :
( ( hAPP_nat_bool @ ( cOMBB_bool_bool_nat @ SV331 @ SV689 ) @ SY1016 )
= ( hAPP_bool_bool @ SV331 @ ( hAPP_nat_bool @ SV689 @ SY1016 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1612]) ).
thf(2033,plain,
! [SV690: $i,SV332: $i] :
( ( ! [SY1017: $i] :
( ( hAPP_nat_bool @ ( cOMBS_nat_bool_bool @ SV332 @ SV690 ) @ SY1017 )
= ( hAPP_bool_bool @ ( hAPP_n1006566506l_bool @ SV332 @ SY1017 ) @ ( hAPP_nat_bool @ SV690 @ SY1017 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1613]) ).
thf(2034,plain,
! [SV691: $i,SV333: $i] :
( ( ! [SY1018: $i] :
( ( hAPP_pname_bool @ ( cOMBB_647938656_pname @ SV333 @ SV691 ) @ SY1018 )
= ( hAPP_bool_bool @ SV333 @ ( hAPP_pname_bool @ SV691 @ SY1018 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1614]) ).
thf(2035,plain,
! [SV692: $i,SV334: $i] :
( ( ! [SY1019: $i] :
( ( hAPP_pname_bool @ ( cOMBS_568398431l_bool @ SV334 @ SV692 ) @ SY1019 )
= ( hAPP_bool_bool @ ( hAPP_p393069232l_bool @ SV334 @ SY1019 ) @ ( hAPP_pname_bool @ SV692 @ SY1019 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1615]) ).
thf(2036,plain,
! [SV693: $i,SV335: $i] :
( ( ! [SY1020: $i] :
( ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ SV335 ) @ SV693 ) @ SY1020 )
= ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ SV335 @ SY1020 ) @ SV693 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1616]) ).
thf(2037,plain,
! [SV694: $i,SV336: $i] :
( ( ! [SY1021: $i] :
( ( hAPP_a_bool @ ( hAPP_f2050579477a_bool @ ( cOMBC_1355376034l_bool @ SV336 ) @ SV694 ) @ SY1021 )
= ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ SV336 @ SY1021 ) @ SV694 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1617]) ).
thf(2038,plain,
! [SV695: $i,SV337: $i] :
( ( ! [SY1022: $i] :
( ( hAPP_p1534023578a_bool @ ( cOMBB_1897541054_pname @ SV337 @ SV695 ) @ SY1022 )
= ( hAPP_a_fun_a_bool @ SV337 @ ( hAPP_pname_a @ SV695 @ SY1022 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1618]) ).
thf(2039,plain,
! [SV696: $i,SV338: $i] :
( ( ! [SY1023: $i] :
( ( hAPP_fun_a_bool_bool @ ( cOMBB_2140588453a_bool @ SV338 @ SV696 ) @ SY1023 )
= ( hAPP_bool_bool @ SV338 @ ( hAPP_fun_a_bool_bool @ SV696 @ SY1023 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1619]) ).
thf(2040,plain,
! [SV697: $i,SV339: $i] :
( ( ! [SY1024: $i] :
( ( hAPP_a_fun_bool_bool @ ( cOMBB_1972296269bool_a @ SV339 @ SV697 ) @ SY1024 )
= ( hAPP_b589554111l_bool @ SV339 @ ( hAPP_a_bool @ SV697 @ SY1024 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1620]) ).
thf(2041,plain,
! [SV698: $i,SV340: $i] :
( ( ! [SY1025: $i] :
( ( hAPP_fun_a_bool_bool @ ( cOMBS_1035972772l_bool @ SV340 @ SV698 ) @ SY1025 )
= ( hAPP_bool_bool @ ( hAPP_f198738859l_bool @ SV340 @ SY1025 ) @ ( hAPP_fun_a_bool_bool @ SV698 @ SY1025 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1621]) ).
thf(2042,plain,
! [SV699: $i,SV341: $i] :
( ( ! [SY1026: $i] :
( ( hAPP_nat_bool @ ( hAPP_f800510211t_bool @ ( cOMBC_226598744l_bool @ SV341 ) @ SV699 ) @ SY1026 )
= ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ SV341 @ SY1026 ) @ SV699 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1622]) ).
thf(2043,plain,
! [SV700: $i,SV342: $i] :
( ( ! [SY1027: $i] :
( ( hAPP_f54304608l_bool @ ( cOMBB_238756964t_bool @ SV342 @ SV700 ) @ SY1027 )
= ( hAPP_bool_bool @ SV342 @ ( hAPP_f54304608l_bool @ SV700 @ SY1027 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1623]) ).
thf(2044,plain,
! [SV701: $i,SV343: $i] :
( ( ! [SY1028: $i] :
( ( hAPP_n1006566506l_bool @ ( cOMBB_1015721476ol_nat @ SV343 @ SV701 ) @ SY1028 )
= ( hAPP_b589554111l_bool @ SV343 @ ( hAPP_nat_bool @ SV701 @ SY1028 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1624]) ).
thf(2045,plain,
! [SV702: $i,SV344: $i] :
( ( ! [SY1029: $i] :
( ( hAPP_f54304608l_bool @ ( cOMBS_1187019125l_bool @ SV344 @ SV702 ) @ SY1029 )
= ( hAPP_bool_bool @ ( hAPP_f1748468828l_bool @ SV344 @ SY1029 ) @ ( hAPP_f54304608l_bool @ SV702 @ SY1029 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1625]) ).
thf(2046,plain,
! [SV703: $i,SV345: $i] :
( ( ! [SY1030: $i] :
( ( hAPP_f1664156314l_bool @ ( cOMBB_307249310e_bool @ SV345 @ SV703 ) @ SY1030 )
= ( hAPP_bool_bool @ SV345 @ ( hAPP_f1664156314l_bool @ SV703 @ SY1030 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1626]) ).
thf(2047,plain,
! [SV704: $i,SV346: $i] :
( ( ! [SY1031: $i] :
( ( hAPP_p393069232l_bool @ ( cOMBB_675860798_pname @ SV346 @ SV704 ) @ SY1031 )
= ( hAPP_b589554111l_bool @ SV346 @ ( hAPP_pname_bool @ SV704 @ SY1031 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1627]) ).
thf(2048,plain,
! [SV705: $i,SV347: $i] :
( ( ! [SY1032: $i] :
( ( hAPP_f1664156314l_bool @ ( cOMBS_350070575l_bool @ SV347 @ SV705 ) @ SY1032 )
= ( hAPP_bool_bool @ ( hAPP_f1476298914l_bool @ SV347 @ SY1032 ) @ ( hAPP_f1664156314l_bool @ SV705 @ SY1032 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1628]) ).
thf(2049,plain,
! [SV706: $i,SV348: $i] :
( ( ! [SY1033: $i] :
( ( hAPP_pname_bool @ ( hAPP_f759274231e_bool @ ( cOMBC_1058051404l_bool @ SV348 ) @ SV706 ) @ SY1033 )
= ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ SV348 @ SY1033 ) @ SV706 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1629]) ).
thf(2050,plain,
! [SV707: $i,SV349: $i] :
( ( ! [SY1034: $i] :
( ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ SV349 ) @ SV707 ) @ SY1034 )
= ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ SV349 @ SY1034 ) @ SV707 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1630]) ).
thf(2051,plain,
! [SV708: $i,SV350: $i] :
( ( ! [SY1035: $i] :
( ( hAPP_f198738859l_bool @ ( cOMBB_338059395a_bool @ SV350 @ SV708 ) @ SY1035 )
= ( hAPP_b589554111l_bool @ SV350 @ ( hAPP_fun_a_bool_bool @ SV708 @ SY1035 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1631]) ).
thf(2052,plain,
! [SV709: $i,SV351: $i] :
( ( ! [SY1036: $i] :
( ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ( cOMBC_1693257480l_bool @ SV351 ) @ SV709 ) @ SY1036 )
= ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ SV351 @ SY1036 ) @ SV709 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1632]) ).
thf(2053,plain,
! [SV710: $i,SV352: $i] :
( ( ! [SY1037: $i] :
( ( hAPP_f1748468828l_bool @ ( cOMBB_444170502t_bool @ SV352 @ SV710 ) @ SY1037 )
= ( hAPP_b589554111l_bool @ SV352 @ ( hAPP_f54304608l_bool @ SV710 @ SY1037 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1633]) ).
thf(2054,plain,
! [SV711: $i,SV353: $i] :
( ( ! [SY1038: $i] :
( ( hAPP_f1476298914l_bool @ ( cOMBB_2095475776e_bool @ SV353 @ SV711 ) @ SY1038 )
= ( hAPP_b589554111l_bool @ SV353 @ ( hAPP_f1664156314l_bool @ SV711 @ SY1038 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1634]) ).
thf(2055,plain,
! [SV712: $i,SV354: $i] :
( ( ! [SY1039: $i] :
( ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ SV354 ) @ SV712 ) @ SY1039 )
= ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ SV354 @ SY1039 ) @ SV712 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1635]) ).
thf(2056,plain,
! [SV713: $i,SV355: $i] :
( ( ! [SY1040: $i] :
( ( hAPP_fun_a_bool_bool @ ( hAPP_f2117159681l_bool @ ( cOMBC_1880041174l_bool @ SV355 ) @ SV713 ) @ SY1040 )
= ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ SV355 @ SY1040 ) @ SV713 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1636]) ).
thf(2057,plain,
! [SV714: $i,SV356: $i] :
( ( ! [SY1041: $i] :
( ( hAPP_f54304608l_bool @ ( hAPP_f1246832597l_bool @ ( cOMBC_1245412066l_bool @ SV356 ) @ SV714 ) @ SY1041 )
= ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ SV356 @ SY1041 ) @ SV714 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1637]) ).
thf(2058,plain,
! [SV715: $i,SV357: $i] :
( ( ! [SY1042: $i] :
( ( hAPP_f1664156314l_bool @ ( hAPP_f559147733l_bool @ ( cOMBC_1988546018l_bool @ SV357 ) @ SV715 ) @ SY1042 )
= ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ SV357 @ SY1042 ) @ SV715 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1638]) ).
thf(2059,plain,
! [SV716: $i,SV358: $i] :
( ( ! [SY1043: $i] :
( ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ( cOMBC_331553030l_bool @ SV358 ) @ SV716 ) @ SY1043 )
= ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ SV358 @ SY1043 ) @ SV716 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1639]) ).
thf(2060,plain,
! [SV717: $i,SV359: $i] :
( ( ! [SY1044: $i] :
( ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ( cOMBC_595898202l_bool @ SV359 ) @ SV717 ) @ SY1044 )
= ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ SV359 @ SY1044 ) @ SV717 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1640]) ).
thf(2061,plain,
! [SV718: $i,SV360: $i] :
( ( ! [SY1045: $i] :
( ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ( cOMBC_7971162l_bool @ SV360 ) @ SV718 ) @ SY1045 )
= ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ SV360 @ SY1045 ) @ SV718 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1641]) ).
thf(2062,plain,
! [SV719: $i,SV361: $i] :
( ( ! [SY1046: $i] :
( ( hAPP_f292226953l_bool @ ( hAPP_f1050622307l_bool @ ( cOMBC_636888218l_bool @ SV361 ) @ SV719 ) @ SY1046 )
= ( hAPP_f292226953l_bool @ ( hAPP_f1050622307l_bool @ SV361 @ SY1046 ) @ SV719 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1642]) ).
thf(2063,plain,
! [SV720: $i,SV362: $i] :
( ( ! [SY1047: $i] :
( ( hAPP_f937997336l_bool @ ( hAPP_f760187903l_bool @ ( cOMBC_1269652216l_bool @ SV362 ) @ SV720 ) @ SY1047 )
= ( hAPP_f937997336l_bool @ ( hAPP_f760187903l_bool @ SV362 @ SY1047 ) @ SV720 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1643]) ).
thf(2064,plain,
! [SV721: $i,SV363: $i] :
( ( ! [SY1048: $i] :
( ( hAPP_f389811538l_bool @ ( hAPP_f1759205631l_bool @ ( cOMBC_336095980l_bool @ SV363 ) @ SV721 ) @ SY1048 )
= ( hAPP_f389811538l_bool @ ( hAPP_f1759205631l_bool @ SV363 @ SY1048 ) @ SV721 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1644]) ).
thf(2065,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SX0 ) @ SX1 ) )
| ( hBOOL @ ( hAPP_nat_bool @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1646]) ).
thf(2066,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ SX1 @ SX0 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SX0 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1646]) ).
thf(2067,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SX0 ) @ SX1 ) )
| ( hBOOL @ ( hAPP_pname_bool @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1647]) ).
thf(2068,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_pname_bool @ SX1 @ SX0 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SX0 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1647]) ).
thf(2069,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fconj @ SX1 ) @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1648]) ).
thf(2070,plain,
( ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ SX0 ) ) )
| ! [SX1: $i] : ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fconj @ SX1 ) @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1648]) ).
thf(2071,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX0 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1649]) ).
thf(2072,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX1 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1649]) ).
thf(2073,plain,
! [SV364: $i] :
( ( ~ ( ~ ( is_fun_a_bool @ SV364 )
| ! [SY842: $i,SY843: $i] :
( ! [SY844: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY844 ) @ SY843 ) )
| ~ ( is_fun_pname_bool @ SY844 )
| ( SV364
!= ( image_pname_a @ SY842 @ SY844 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV364 ) @ ( image_pname_a @ SY842 @ SY843 ) ) ) ) )
| ~ ( ~ ( is_fun_a_bool @ SV364 )
| ! [SY845: $i,SY846: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV364 ) @ ( image_pname_a @ SY845 @ SY846 ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( sK10_AA @ SY846 @ SY845 @ SV364 ) ) @ SY846 ) )
| ~ ( is_fun_pname_bool @ ( sK10_AA @ SY846 @ SY845 @ SV364 ) ) )
| ( SV364
!= ( image_pname_a @ SY845 @ ( sK10_AA @ SY846 @ SY845 @ SV364 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1650]) ).
thf(2074,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX0 ) @ ( hAPP_nat_nat @ suc @ SX1 ) ) )
| ( SX0
= ( hAPP_nat_nat @ suc @ SX1 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX0 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1651]) ).
thf(2075,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( hAPP_nat_nat @ suc @ SX1 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX0 ) @ ( hAPP_nat_nat @ suc @ SX1 ) ) ) )
| ~ ! [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 @ SX0 ) @ ( hAPP_nat_nat @ suc @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1651]) ).
thf(2076,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 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1652]) ).
thf(2077,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX0 ) @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX1 ) @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1652]) ).
thf(2078,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SX1 ) )
| ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ SX0 ) @ SX1 ) )
| ( ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( insert_fun_nat_bool @ SX0 @ SX1 ) )
= ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1653]) ).
thf(2079,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SX1 ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ SX0 ) @ SX1 ) )
| ( ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( insert_fun_nat_bool @ SX0 @ SX1 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1653]) ).
thf(2080,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( is_fun_pname_bool @ SX0 )
| ~ ( is_fun_pname_bool @ 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 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1654]) ).
thf(2081,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( is_fun_pname_bool @ SX0 )
| ~ ( is_fun_pname_bool @ SX1 )
| ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SX0 ) @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( is_fun_pname_bool @ SX0 )
| ~ ( is_fun_pname_bool @ SX1 )
| ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SX1 ) @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1654]) ).
thf(2082,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ SX1 ) @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1655]) ).
thf(2083,plain,
( ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ SX0 ) ) )
| ! [SX1: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ SX1 ) @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1655]) ).
thf(2084,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_nat @ suc @ SX0 )
!= ( hAPP_nat_nat @ suc @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1656]) ).
thf(2085,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( hAPP_nat_nat @ suc @ SX0 )
= ( hAPP_nat_nat @ suc @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1656]) ).
thf(2086,plain,
! [SV365: $i] :
( ( ~ ! [SY847: $i,SY848: $i] :
( ~ ( is_pname @ SV365 )
| ~ ( is_pname @ SY848 )
| ~ ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV365 @ SY847 ) @ SY848 ) )
| ( SV365 = SY848 )
| ( hBOOL @ ( hAPP_pname_bool @ SY847 @ SY848 ) ) )
| ~ ~ ( ~ ! [SY849: $i,SY850: $i] :
( ~ ( is_pname @ SV365 )
| ~ ( is_pname @ SY850 )
| ( SV365 != SY850 )
| ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV365 @ SY849 ) @ SY850 ) ) )
| ~ ! [SY851: $i,SY852: $i] :
( ~ ( is_pname @ SV365 )
| ~ ( is_pname @ SY852 )
| ~ ( hBOOL @ ( hAPP_pname_bool @ SY851 @ SY852 ) )
| ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV365 @ SY851 ) @ SY852 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1657]) ).
thf(2087,plain,
! [SV366: $i] :
( ( ~ ! [SY853: $i,SY854: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV366 ) @ ( insert_nat @ SY853 @ SY854 ) ) )
| ( SV366 = SY853 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV366 ) @ SY854 ) ) )
| ~ ~ ( ~ ! [SY855: $i] :
( ( SV366 != SY855 )
| ! [SY856: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV366 ) @ ( insert_nat @ SY855 @ SY856 ) ) ) )
| ~ ! [SY857: $i,SY858: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV366 ) @ SY858 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV366 ) @ ( insert_nat @ SY857 @ SY858 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1658]) ).
thf(2088,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ SX0 @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1659]) ).
thf(2089,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SX1 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ SX0 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1659]) ).
thf(2090,plain,
! [SV367: $i] :
( ( ~ ! [SY859: $i] :
( ~ ( is_a @ SV367 )
| ~ ( is_a @ SY859 )
| ! [SY860: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ ( insert_a @ SY859 @ SY860 ) ) )
| ( SV367 = SY859 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ SY860 ) ) ) )
| ~ ~ ( ~ ! [SY861: $i] :
( ~ ( is_a @ SV367 )
| ~ ( is_a @ SY861 )
| ( SV367 != SY861 )
| ! [SY862: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ ( insert_a @ SY861 @ SY862 ) ) ) )
| ~ ! [SY863: $i] :
( ~ ( is_a @ SV367 )
| ~ ( is_a @ SY863 )
| ! [SY864: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ SY864 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ ( insert_a @ SY863 @ SY864 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1660]) ).
thf(2091,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ SX1 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ SX1 ) @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1661]) ).
thf(2092,plain,
( ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ SX0 ) ) )
| ! [SX1: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ SX1 ) @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1661]) ).
thf(2093,plain,
! [SV368: $i] :
( ( ~ ! [SY865: $i,SY866: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY865 ) @ SY866 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY866 ) @ ( insert_a @ SY865 @ SV368 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY866 ) @ SV368 ) ) )
| ~ ! [SY867: $i,SY868: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY867 ) @ SY868 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY868 ) @ SV368 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY868 ) @ ( insert_a @ SY867 @ SV368 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1662]) ).
thf(2094,plain,
! [SV369: $i] :
( ( ~ ( ~ ( is_a @ SV369 )
| ! [SY869: $i,SY870: $i] :
( ! [SY871: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SY871 ) @ SY870 ) )
| ~ ( is_pname @ SY871 )
| ( SV369
!= ( hAPP_pname_a @ SY869 @ SY871 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV369 ) @ ( image_pname_a @ SY869 @ SY870 ) ) ) ) )
| ~ ( ~ ( is_a @ SV369 )
| ! [SY872: $i,SY873: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV369 ) @ ( image_pname_a @ SY872 @ SY873 ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK11_X_1 @ SY873 @ SY872 @ SV369 ) ) @ SY873 ) )
| ~ ( is_pname @ ( sK11_X_1 @ SY873 @ SY872 @ SV369 ) ) )
| ( SV369
!= ( hAPP_pname_a @ SY872 @ ( sK11_X_1 @ SY873 @ SY872 @ SV369 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1663]) ).
thf(2095,plain,
! [SV370: $i] :
( ( ~ ! [SY874: $i,SY875: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SY874 ) @ SY875 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY875 ) @ ( insert_nat @ SY874 @ SV370 ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY875 ) @ SV370 ) ) )
| ~ ! [SY876: $i,SY877: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SY876 ) @ SY877 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY877 ) @ SV370 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY877 ) @ ( insert_nat @ SY876 @ SV370 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1664]) ).
thf(2096,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fconj @ SX1 ) @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1665]) ).
thf(2097,plain,
( ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ SX0 ) ) )
| ! [SX1: $i] : ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fconj @ SX1 ) @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1665]) ).
thf(2098,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SX0 @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1666]) ).
thf(2099,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SX1 ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SX0 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1666]) ).
thf(2100,plain,
! [SV371: $i] :
( ( ~ ! [SY878: $i,SY879: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SY878 ) @ SY879 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SY878 ) @ ( insert_nat @ SV371 @ SY879 ) ) ) )
| ~ ! [SY880: $i] :
( ( SY880 != SV371 )
| ! [SY881: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SY880 ) @ ( insert_nat @ SV371 @ SY881 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1667]) ).
thf(2101,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 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1668]) ).
thf(2102,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 ) ) )
| ~ ! [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 @ SX1 ) @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1668]) ).
thf(2103,plain,
! [SV722: $i,SV372: $i] :
( ( ! [SY1049: $i] :
( ~ ( is_fun_a_bool @ SY1049 )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY1049 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY1049 ) @ ( image_pname_a @ SV372 @ SV722 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( sK17_C_2 @ SY1049 @ SV722 @ SV372 ) ) @ SV722 ) )
| ~ ( is_fun_pname_bool @ ( sK17_C_2 @ SY1049 @ SV722 @ SV372 ) ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( sK17_C_2 @ SY1049 @ SV722 @ SV372 ) ) ) )
| ( SY1049
!= ( image_pname_a @ SV372 @ ( sK17_C_2 @ SY1049 @ SV722 @ SV372 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1669]) ).
thf(2104,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ SX1 ) ) @ SX0 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX0 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1670]) ).
thf(2105,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 @ ( hAPP_nat_nat @ suc @ SX1 ) ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1670]) ).
thf(2106,plain,
! [SV373: $i] :
( ( ~ ! [SY884: $i,SY885: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SY884 ) @ SY885 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SY884 ) @ ( insert_pname @ SV373 @ SY885 ) ) ) )
| ~ ! [SY886: $i] :
( ( SY886 != SV373 )
| ! [SY887: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SY886 ) @ ( insert_pname @ SV373 @ SY887 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1671]) ).
thf(2107,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ SX0 ) ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ SX1 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ SX0 ) @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1672]) ).
thf(2108,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ SX0 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1672]) ).
thf(2109,plain,
! [SV374: $i] :
( ( ~ ! [SY888: $i,SY889: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV374 ) @ SY889 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY888 ) @ SY889 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV374 @ SY888 ) ) @ SY889 ) ) )
| ~ ~ ( ~ ! [SY890: $i,SY891: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV374 @ SY890 ) ) @ SY891 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV374 ) @ SY891 ) ) )
| ~ ! [SY892: $i,SY893: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV374 @ SY892 ) ) @ SY893 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY892 ) @ SY893 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1673]) ).
thf(2110,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ SX0 ) ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ SX0 ) @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1674]) ).
thf(2111,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ SX0 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1674]) ).
thf(2112,plain,
! [SV375: $i,SV723: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV723 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_pname_a @ SV375 @ SV723 ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK12_X_1 @ SV723 @ SV375 ) ) @ SV723 ) )
| ~ ( is_pname @ ( sK12_X_1 @ SV723 @ SV375 ) ) )
| ~ ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ ( hAPP_f759274231e_bool @ ( cOMBC_1058051404l_bool @ member_pname ) @ SV723 ) ) @ ( hAPP_a93125764e_bool @ ( cOMBC_pname_a_bool @ ( cOMBB_1897541054_pname @ fequal_a @ SV375 ) ) @ ( hAPP_pname_a @ SV375 @ ( sK12_X_1 @ SV723 @ SV375 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1675]) ).
thf(2113,plain,
! [SV376: $i] :
( ( ~ ! [SY895: $i,SY896: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV376 ) @ SY896 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY895 ) @ SY896 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( insert_nat @ SV376 @ SY895 ) ) @ SY896 ) ) )
| ~ ~ ( ~ ! [SY897: $i,SY898: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( insert_nat @ SV376 @ SY897 ) ) @ SY898 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV376 ) @ SY898 ) ) )
| ~ ! [SY899: $i,SY900: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( insert_nat @ SV376 @ SY899 ) ) @ SY900 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY899 ) @ SY900 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1676]) ).
thf(2114,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SX1 ) )
| ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ SX0 ) @ SX1 ) )
| ( ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( insert1325755072e_bool @ SX0 @ SX1 ) )
= ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1677]) ).
thf(2115,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SX1 ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ SX0 ) @ SX1 ) )
| ( ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( insert1325755072e_bool @ SX0 @ SX1 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1677]) ).
thf(2116,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ SX0 @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1678]) ).
thf(2117,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SX1 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ SX0 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1678]) ).
thf(2118,plain,
! [SV377: $i] :
( ( ~ ! [SY901: $i,SY902: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SY901 ) @ SY902 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SY901 ) @ SV377 ) )
| ( ( insert_nat @ SY901 @ SY902 )
!= ( insert_nat @ SY901 @ SV377 ) )
| ( SY902 = SV377 ) )
| ~ ! [SY903: $i,SY904: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SY903 ) @ SY904 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SY903 ) @ SV377 ) )
| ( SY904 != SV377 )
| ( ( insert_nat @ SY903 @ SY904 )
= ( insert_nat @ SY903 @ SV377 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1679]) ).
thf(2119,plain,
! [SV378: $i,SV724: $i] :
( ( ~ ( ~ ( is_a @ ( sK7_X_1 @ SV724 @ SV378 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( sK7_X_1 @ SV724 @ SV378 ) ) @ SV724 ) )
| ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( sK7_X_1 @ SV724 @ SV378 ) ) @ SV378 ) ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV724 ) @ SV378 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1680]) ).
thf(2120,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX0 ) @ SX1 ) )
| ( hBOOL @ ( hAPP_a_bool @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1681]) ).
thf(2121,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_a_bool @ SX1 @ SX0 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX0 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1681]) ).
thf(2122,plain,
! [SV379: $i] :
( ( ~ ! [SY906: $i,SY907: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY906 ) @ SY907 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY906 ) @ ( insert_a @ SV379 @ SY907 ) ) ) )
| ~ ! [SY908: $i] :
( ( SY908 != SV379 )
| ! [SY909: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY908 ) @ ( insert_a @ SV379 @ SY909 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1682]) ).
thf(2123,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SX1 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SX0 ) @ SX1 ) )
| ( ( hAPP_f22106695ol_nat @ finite_card_nat @ ( insert_nat @ SX0 @ SX1 ) )
= ( hAPP_f22106695ol_nat @ finite_card_nat @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1683]) ).
thf(2124,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SX1 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SX0 ) @ SX1 ) )
| ( ( hAPP_f22106695ol_nat @ finite_card_nat @ ( insert_nat @ SX0 @ SX1 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1683]) ).
thf(2125,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ SX0 @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1684]) ).
thf(2126,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SX1 ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ SX0 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1684]) ).
thf(2127,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SX1 ) )
| ~ ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ SX0 ) @ SX1 ) )
| ( ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( insert_fun_a_bool @ SX0 @ SX1 ) )
= ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1685]) ).
thf(2128,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SX1 ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ SX0 ) @ SX1 ) )
| ( ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( insert_fun_a_bool @ SX0 @ SX1 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1685]) ).
thf(2129,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SX0 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1686]) ).
thf(2130,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SX1 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1686]) ).
thf(2131,plain,
! [SV380: $i,SV725: $i] :
( ( ! [SY1050: $i] :
( ~ ( ~ ( is_pname @ ( sK3_X_1 @ SY1050 @ SV725 @ SV380 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK3_X_1 @ SY1050 @ SV725 @ SV380 ) ) @ SY1050 ) )
| ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( hAPP_pname_a @ SV380 @ ( sK3_X_1 @ SY1050 @ SV725 @ SV380 ) ) ) @ SV725 ) ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_pname_a @ SV380 @ SY1050 ) ) @ SV725 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1687]) ).
thf(2132,plain,
! [SV381: $i] :
( ( ~ ! [SY912: $i,SY913: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY912 ) @ SY913 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY912 ) @ SV381 ) )
| ( ( hAPP_nat_nat @ ( minus_minus_nat @ SY913 ) @ SY912 )
!= ( hAPP_nat_nat @ ( minus_minus_nat @ SV381 ) @ SY912 ) )
| ( SY913 = SV381 ) )
| ~ ! [SY914: $i,SY915: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY914 ) @ SY915 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY914 ) @ SV381 ) )
| ( SY915 != SV381 )
| ( ( hAPP_nat_nat @ ( minus_minus_nat @ SY915 ) @ SY914 )
= ( hAPP_nat_nat @ ( minus_minus_nat @ SV381 ) @ SY914 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1688]) ).
thf(2133,plain,
! [SV382: $i,SV726: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ ( sK8_X_1 @ SV726 @ SV382 ) ) @ SV726 ) )
| ~ ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ ( sK8_X_1 @ SV726 @ SV382 ) ) @ SV382 ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV726 ) @ SV382 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1689]) ).
thf(2134,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ SX0 ) ) )
| ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ SX0 ) @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1690]) ).
thf(2135,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ SX0 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1690]) ).
thf(2136,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fconj @ SX1 ) @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1691]) ).
thf(2137,plain,
( ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ SX0 ) ) )
| ! [SX1: $i] : ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fconj @ SX1 ) @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1691]) ).
thf(2138,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SX1 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX0 ) @ SX1 ) )
| ( ( hAPP_fun_a_bool_nat @ finite_card_a @ ( insert_a @ SX0 @ SX1 ) )
= ( hAPP_fun_a_bool_nat @ finite_card_a @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1692]) ).
thf(2139,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SX1 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX0 ) @ SX1 ) )
| ( ( hAPP_fun_a_bool_nat @ finite_card_a @ ( insert_a @ SX0 @ SX1 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1692]) ).
thf(2140,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SX1 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SX0 ) @ SX1 ) )
| ( ( hAPP_f921600141ol_nat @ finite_card_pname @ ( insert_pname @ SX0 @ SX1 ) )
= ( hAPP_f921600141ol_nat @ finite_card_pname @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1693]) ).
thf(2141,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SX1 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SX0 ) @ SX1 ) )
| ( ( hAPP_f921600141ol_nat @ finite_card_pname @ ( insert_pname @ SX0 @ SX1 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1693]) ).
thf(2142,plain,
! [SV383: $i] :
( ( ~ ! [SY917: $i] :
( ~ ( is_pname @ SV383 )
| ~ ( is_pname @ SY917 )
| ! [SY918: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ ( insert_pname @ SY917 @ SY918 ) ) )
| ( SV383 = SY917 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ SY918 ) ) ) )
| ~ ~ ( ~ ! [SY919: $i] :
( ~ ( is_pname @ SV383 )
| ~ ( is_pname @ SY919 )
| ( SV383 != SY919 )
| ! [SY920: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ ( insert_pname @ SY919 @ SY920 ) ) ) )
| ~ ! [SY921: $i] :
( ~ ( is_pname @ SV383 )
| ~ ( is_pname @ SY921 )
| ! [SY922: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ SY922 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ ( insert_pname @ SY921 @ SY922 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1694]) ).
thf(2143,plain,
! [SV384: $i] :
( ( ~ ! [SY923: $i,SY924: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV384 ) @ SY924 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY923 ) @ SY924 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ SV384 @ SY923 ) ) @ SY924 ) ) )
| ~ ~ ( ~ ! [SY925: $i,SY926: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ SV384 @ SY925 ) ) @ SY926 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV384 ) @ SY926 ) ) )
| ~ ! [SY927: $i,SY928: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ SV384 @ SY927 ) ) @ SY928 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY927 ) @ SY928 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1695]) ).
thf(2144,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ SX0 ) ) )
| ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ SX0 ) @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1696]) ).
thf(2145,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ SX0 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1696]) ).
thf(2146,plain,
! [SV385: $i] :
( ( ~ ! [SY929: $i,SY930: $i] :
( ~ ( is_fun_a_bool @ SV385 )
| ~ ( is_fun_a_bool @ SY930 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY929 ) @ SY930 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY929 ) @ SV385 ) )
| ( ( insert_a @ SY929 @ SY930 )
!= ( insert_a @ SY929 @ SV385 ) )
| ( SY930 = SV385 ) )
| ~ ! [SY931: $i,SY932: $i] :
( ~ ( is_fun_a_bool @ SV385 )
| ~ ( is_fun_a_bool @ SY932 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY931 ) @ SY932 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY931 ) @ SV385 ) )
| ( SY932 != SV385 )
| ( ( insert_a @ SY931 @ SY932 )
= ( insert_a @ SY931 @ SV385 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1697]) ).
thf(2147,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX0 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1698]) ).
thf(2148,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX1 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1698]) ).
thf(2149,plain,
! [SV386: $i] :
( ( ~ ! [SY933: $i,SY934: $i] :
( ~ ( is_a @ SV386 )
| ~ ( is_a @ SY934 )
| ~ ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV386 @ SY933 ) @ SY934 ) )
| ( SV386 = SY934 )
| ( hBOOL @ ( hAPP_a_bool @ SY933 @ SY934 ) ) )
| ~ ~ ( ~ ! [SY935: $i,SY936: $i] :
( ~ ( is_a @ SV386 )
| ~ ( is_a @ SY936 )
| ( SV386 != SY936 )
| ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV386 @ SY935 ) @ SY936 ) ) )
| ~ ! [SY937: $i,SY938: $i] :
( ~ ( is_a @ SV386 )
| ~ ( is_a @ SY938 )
| ~ ( hBOOL @ ( hAPP_a_bool @ SY937 @ SY938 ) )
| ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV386 @ SY937 ) @ SY938 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1699]) ).
thf(2150,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ SX1 ) @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1700]) ).
thf(2151,plain,
( ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ SX0 ) ) )
| ! [SX1: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ SX1 ) @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1700]) ).
thf(2152,plain,
! [SV387: $i] :
( ( ( ~ ( is_a @ SV387 ) )
= $true )
| ( ( ! [SY939: $i,SY940: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV387 ) @ ( image_pname_a @ SY939 @ SY940 ) ) )
| ~ ( ~ ( is_pname @ ( sK9_X_1 @ SY940 @ SY939 @ SV387 ) )
| ~ ~ ( ( SV387
!= ( hAPP_pname_a @ SY939 @ ( sK9_X_1 @ SY940 @ SY939 @ SV387 ) ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK9_X_1 @ SY940 @ SY939 @ SV387 ) ) @ SY940 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1701]) ).
thf(2153,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ SX0 @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1702]) ).
thf(2154,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SX1 ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ SX0 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1702]) ).
thf(2155,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ SX0 ) ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ SX0 ) @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1703]) ).
thf(2156,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ SX0 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1703]) ).
thf(2157,plain,
! [SV388: $i,SV727: $i] :
( ( ! [SY1051: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ SV727 @ SY1051 ) )
| ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ SV727 @ ( hAPP_nat_nat @ suc @ ( sK5_N_2 @ SY1051 @ SV727 @ SV388 ) ) ) )
| ~ ~ ( hBOOL @ ( hAPP_nat_bool @ SV727 @ ( sK5_N_2 @ SY1051 @ SV727 @ SV388 ) ) ) )
| ( hBOOL @ ( hAPP_nat_bool @ SV727 @ ( hAPP_nat_nat @ ( minus_minus_nat @ SY1051 ) @ SV388 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1704]) ).
thf(2158,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ SX0 ) ) )
| ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ SX0 ) @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1705]) ).
thf(2159,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ SX0 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1705]) ).
thf(2160,plain,
! [SV389: $i] :
( ( ~ ! [SY943: $i,SY944: $i] :
( ~ ( is_fun_pname_bool @ SV389 )
| ~ ( is_fun_pname_bool @ SY944 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SY943 ) @ SY944 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SY943 ) @ SV389 ) )
| ( ( insert_pname @ SY943 @ SY944 )
!= ( insert_pname @ SY943 @ SV389 ) )
| ( SY944 = SV389 ) )
| ~ ! [SY945: $i,SY946: $i] :
( ~ ( is_fun_pname_bool @ SV389 )
| ~ ( is_fun_pname_bool @ SY946 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SY945 ) @ SY946 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SY945 ) @ SV389 ) )
| ( SY946 != SV389 )
| ( ( insert_pname @ SY945 @ SY946 )
= ( insert_pname @ SY945 @ SV389 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1706]) ).
thf(2161,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ SX0 ) ) @ ( hAPP_nat_nat @ suc @ SX1 ) ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX0 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1707]) ).
thf(2162,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 @ ( hAPP_nat_nat @ suc @ SX0 ) ) @ ( hAPP_nat_nat @ suc @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1707]) ).
thf(2163,plain,
! [SV390: $i] :
( ( ~ ! [SY947: $i,SY948: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SY947 ) @ SY948 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY948 ) @ ( insert_pname @ SY947 @ SV390 ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY948 ) @ SV390 ) ) )
| ~ ! [SY949: $i,SY950: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SY949 ) @ SY950 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY950 ) @ SV390 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY950 ) @ ( insert_pname @ SY949 @ SV390 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1708]) ).
thf(2164,plain,
! [SV391: $i] :
( ( ~ ! [SY951: $i,SY952: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY951 ) @ SY952 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY951 ) @ SV391 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ SY952 ) @ SY951 ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV391 ) @ SY951 ) ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY952 ) @ SV391 ) ) )
| ~ ! [SY953: $i,SY954: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY953 ) @ SY954 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY953 ) @ SV391 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY954 ) @ SV391 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ SY954 ) @ SY953 ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV391 ) @ SY953 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1709]) ).
thf(2165,plain,
! [SV392: $i,SV728: $i] :
( ( ~ ( ~ ( is_pname @ ( sK6_X_1 @ SV728 @ SV392 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK6_X_1 @ SV728 @ SV392 ) ) @ SV728 ) )
| ~ ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK6_X_1 @ SV728 @ SV392 ) ) @ SV392 ) ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV728 ) @ SV392 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1710]) ).
thf(2166,plain,
! [SV393: $i] :
( ( ~ ! [SY956: $i,SY957: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV393 @ SY956 ) @ SY957 ) )
| ( SV393 = SY957 )
| ( hBOOL @ ( hAPP_nat_bool @ SY956 @ SY957 ) ) )
| ~ ~ ( ~ ! [SY958: $i,SY959: $i] :
( ( SV393 != SY959 )
| ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV393 @ SY958 ) @ SY959 ) ) )
| ~ ! [SY960: $i,SY961: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ SY960 @ SY961 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV393 @ SY960 ) @ SY961 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1711]) ).
thf(2167,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ ( sK2_X_1 @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( sK2_X_1 @ SX1 @ SX0 ) ) @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1712]) ).
thf(2168,plain,
( ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SX0 ) )
| ! [SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX1 ) @ ( sK1_M @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1712]) ).
thf(2169,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 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1713]) ).
thf(2170,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 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1713]) ).
thf(2171,plain,
! [SV1: $i,SV394: $i] :
( ( ( ~ ( is_fun_pname_bool @ SV394 ) )
= $true )
| ( ( is_fun_a_bool @ ( image_pname_a @ SV1 @ SV394 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1714]) ).
thf(2172,plain,
! [SV395: $i,SV2: $i] :
( ( ( ~ ( is_a @ SV2 )
| ~ ( is_fun_a_bool @ SV395 ) )
= $true )
| ( ( is_fun_a_bool @ ( insert_a @ SV2 @ SV395 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1715]) ).
thf(2173,plain,
! [SV3: $i,SV396: $i] :
( ( ( ~ ( is_a @ SV396 ) )
= $true )
| ( ( is_fun949378684l_bool @ ( hAPP_a85458249l_bool @ SV3 @ SV396 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1716]) ).
thf(2174,plain,
! [SV4: $i,SV397: $i] :
( ( ( ~ ( is_pname @ SV397 ) )
= $true )
| ( ( is_a @ ( hAPP_pname_a @ SV4 @ SV397 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1717]) ).
thf(2175,plain,
! [SV5: $i,SV398: $i] :
( ( ( ~ ( is_pname @ SV398 ) )
= $true )
| ( ( is_fun1661590463l_bool @ ( hAPP_p338031245l_bool @ SV5 @ SV398 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1718]) ).
thf(2176,plain,
! [SV400: $i,SV7: $i] :
( ( ( ~ ( is_fun949378684l_bool @ SV7 )
| ~ ( is_fun_a_bool @ SV400 ) )
= $true )
| ( ( is_bool @ ( hAPP_fun_a_bool_bool @ SV7 @ SV400 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1720]) ).
thf(2177,plain,
! [SV8: $i,SV401: $i] :
( ( ( ~ ( is_fun_a_bool @ SV401 ) )
= $true )
| ( ( is_fun949378684l_bool @ ( hAPP_f1631501043l_bool @ SV8 @ SV401 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1721]) ).
thf(2178,plain,
! [SV402: $i,SV9: $i] :
( ( ( ~ ( is_fun1661590463l_bool @ SV9 )
| ~ ( is_fun_pname_bool @ SV402 ) )
= $true )
| ( ( is_bool @ ( hAPP_f1664156314l_bool @ SV9 @ SV402 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1722]) ).
thf(2179,plain,
! [SV10: $i,SV403: $i] :
( ( ( ~ ( is_fun_a_bool @ SV403 ) )
= $true )
| ( ( is_fun_a_bool @ ( cOMBB_bool_bool_a @ SV10 @ SV403 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1723]) ).
thf(2180,plain,
! [SV11: $i,SV404: $i] :
( ( ( ~ ( is_fun_pname_bool @ SV404 ) )
= $true )
| ( ( is_fun_pname_bool @ ( cOMBB_647938656_pname @ SV11 @ SV404 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1724]) ).
thf(2181,plain,
! [SV12: $i,SV405: $i] :
( ( ( ~ ( is_fun949378684l_bool @ SV405 ) )
= $true )
| ( ( is_fun949378684l_bool @ ( cOMBB_2140588453a_bool @ SV12 @ SV405 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1725]) ).
thf(2182,plain,
! [SV13: $i,SV406: $i] :
( ( ( ~ ( is_fun1661590463l_bool @ SV406 ) )
= $true )
| ( ( is_fun1661590463l_bool @ ( cOMBB_307249310e_bool @ SV13 @ SV406 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1726]) ).
thf(2183,plain,
! [SV14: $i,SV407: $i] :
( ( ( ~ ( is_fun_a_bool @ SV407 ) )
= $true )
| ( ( is_fun_a_bool @ ( cOMBS_a_bool_bool @ SV14 @ SV407 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1727]) ).
thf(2184,plain,
! [SV15: $i,SV408: $i] :
( ( ( ~ ( is_fun_pname_bool @ SV408 ) )
= $true )
| ( ( is_fun_pname_bool @ ( cOMBS_568398431l_bool @ SV15 @ SV408 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1728]) ).
thf(2185,plain,
! [SV16: $i,SV409: $i] :
( ( ( ~ ( is_fun949378684l_bool @ SV409 ) )
= $true )
| ( ( is_fun949378684l_bool @ ( cOMBS_1035972772l_bool @ SV16 @ SV409 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1729]) ).
thf(2186,plain,
! [SV17: $i,SV410: $i] :
( ( ( ~ ( is_fun1661590463l_bool @ SV410 ) )
= $true )
| ( ( is_fun1661590463l_bool @ ( cOMBS_350070575l_bool @ SV17 @ SV410 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1730]) ).
thf(2187,plain,
! [SV18: $i] :
( ( ( is_fun_a_bool @ SV18 )
= $false )
| ( ( is_fun_a_bool @ ( collect_a @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1731]) ).
thf(2188,plain,
! [SV19: $i] :
( ( ( is_fun_pname_bool @ SV19 )
= $false )
| ( ( is_fun_pname_bool @ ( collect_pname @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1732]) ).
thf(2189,plain,
! [SV20: $i] :
( ( ( is_fun949378684l_bool @ SV20 )
= $false )
| ( ( is_fun949378684l_bool @ ( collect_fun_a_bool @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1733]) ).
thf(2190,plain,
! [SV21: $i] :
( ( ( is_fun1661590463l_bool @ SV21 )
= $false )
| ( ( is_fun1661590463l_bool @ ( collec1974731493e_bool @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1734]) ).
thf(2191,plain,
! [SV22: $i,SV411: $i] :
( ( ( ~ ( is_fun_a_bool @ SV411 ) )
= $true )
| ( ( is_fun_a_bool @ ( image_a_a @ SV22 @ SV411 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1735]) ).
thf(2192,plain,
! [SV23: $i,SV412: $i] :
( ( ( ~ ( is_fun_a_bool @ SV412 ) )
= $true )
| ( ( is_fun_pname_bool @ ( image_a_pname @ SV23 @ SV412 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1736]) ).
thf(2193,plain,
! [SV24: $i,SV413: $i] :
( ( ( ~ ( is_fun_pname_bool @ SV413 ) )
= $true )
| ( ( is_fun_pname_bool @ ( image_pname_pname @ SV24 @ SV413 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1737]) ).
thf(2194,plain,
! [SV25: $i,SV414: $i] :
( ( ( ~ ( is_fun_pname_bool @ SV414 ) )
= $true )
| ( ( is_fun949378684l_bool @ ( image_112932426a_bool @ SV25 @ SV414 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1738]) ).
thf(2195,plain,
! [SV26: $i,SV415: $i] :
( ( ( ~ ( is_fun_pname_bool @ SV415 ) )
= $true )
| ( ( is_fun1661590463l_bool @ ( image_47868345e_bool @ SV26 @ SV415 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1739]) ).
thf(2196,plain,
! [SV31: $i,SV420: $i] :
( ( ( ~ ( is_fun949378684l_bool @ SV420 ) )
= $true )
| ( ( is_fun_a_bool @ ( image_fun_a_bool_a @ SV31 @ SV420 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1744]) ).
thf(2197,plain,
! [SV32: $i,SV421: $i] :
( ( ( ~ ( is_fun949378684l_bool @ SV421 ) )
= $true )
| ( ( is_fun_pname_bool @ ( image_1854862208_pname @ SV32 @ SV421 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1745]) ).
thf(2198,plain,
! [SV33: $i,SV422: $i] :
( ( ( ~ ( is_fun1661590463l_bool @ SV422 ) )
= $true )
| ( ( is_fun_a_bool @ ( image_876012084bool_a @ SV33 @ SV422 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1746]) ).
thf(2199,plain,
! [SV34: $i,SV423: $i] :
( ( ( ~ ( is_fun1661590463l_bool @ SV423 ) )
= $true )
| ( ( is_fun_pname_bool @ ( image_1283814551_pname @ SV34 @ SV423 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1747]) ).
thf(2200,plain,
! [SV43: $i,SV432: $i] :
( ( ( ~ ( is_fun_pname_bool @ SV432 )
| ~ ( is_pname @ SV43 ) )
= $true )
| ( ( is_fun_pname_bool @ ( insert_pname @ SV43 @ SV432 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1756]) ).
thf(2201,plain,
! [SV44: $i,SV433: $i] :
( ( ( ~ ( is_fun949378684l_bool @ SV433 )
| ~ ( is_fun_a_bool @ SV44 ) )
= $true )
| ( ( is_fun949378684l_bool @ ( insert_fun_a_bool @ SV44 @ SV433 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1757]) ).
thf(2202,plain,
! [SV45: $i,SV434: $i] :
( ( ( ~ ( is_fun1661590463l_bool @ SV434 )
| ~ ( is_fun_pname_bool @ SV45 ) )
= $true )
| ( ( is_fun1661590463l_bool @ ( insert1325755072e_bool @ SV45 @ SV434 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1758]) ).
thf(2203,plain,
! [SV46: $i,SV435: $i] :
( ( ( ~ ( is_a @ SV435 )
| ~ ( is_fun_a_bool @ SV46 ) )
= $true )
| ( ( is_bool @ ( hAPP_a_bool @ SV46 @ SV435 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1759]) ).
thf(2204,plain,
! [SV47: $i,SV436: $i] :
( ( ( ~ ( is_a @ SV436 ) )
= $true )
| ( ( is_fun_a_bool @ ( hAPP_a_fun_a_bool @ SV47 @ SV436 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1760]) ).
thf(2205,plain,
! [SV48: $i,SV437: $i] :
( ( ( ~ ( is_a @ SV437 ) )
= $true )
| ( ( is_fun_pname_bool @ ( hAPP_a93125764e_bool @ SV48 @ SV437 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1761]) ).
thf(2206,plain,
! [SV438: $i,SV49: $i] :
( ( ( ~ ( is_fun_pname_bool @ SV49 )
| ~ ( is_pname @ SV438 ) )
= $true )
| ( ( is_bool @ ( hAPP_pname_bool @ SV49 @ SV438 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1762]) ).
thf(2207,plain,
! [SV50: $i,SV439: $i] :
( ( ( ~ ( is_pname @ SV439 ) )
= $true )
| ( ( is_fun_a_bool @ ( hAPP_p1534023578a_bool @ SV50 @ SV439 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1763]) ).
thf(2208,plain,
! [SV51: $i,SV440: $i] :
( ( ( ~ ( is_pname @ SV440 ) )
= $true )
| ( ( is_fun_pname_bool @ ( hAPP_p61793385e_bool @ SV51 @ SV440 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1764]) ).
thf(2209,plain,
! [SV52: $i,SV441: $i] :
( ( ( ~ ( is_bool @ SV441 ) )
= $true )
| ( ( is_bool @ ( hAPP_bool_bool @ SV52 @ SV441 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1765]) ).
thf(2210,plain,
! [SV55: $i,SV444: $i] :
( ( ( ~ ( is_fun_a_bool @ SV444 ) )
= $true )
| ( ( is_fun_a_bool @ ( hAPP_f2050579477a_bool @ SV55 @ SV444 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1768]) ).
thf(2211,plain,
! [SV56: $i,SV445: $i] :
( ( ( ~ ( is_fun_pname_bool @ SV445 ) )
= $true )
| ( ( is_fun_pname_bool @ ( hAPP_f759274231e_bool @ SV56 @ SV445 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1769]) ).
thf(2212,plain,
! [SV57: $i,SV446: $i] :
( ( ( ~ ( is_fun_pname_bool @ SV446 ) )
= $true )
| ( ( is_fun1661590463l_bool @ ( hAPP_f434788991l_bool @ SV57 @ SV446 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1770]) ).
thf(2213,plain,
! [SV59: $i,SV448: $i] :
( ( ( ~ ( is_fun949378684l_bool @ SV448 ) )
= $true )
| ( ( is_bool @ ( hAPP_f621171935l_bool @ SV59 @ SV448 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1772]) ).
thf(2214,plain,
! [SV60: $i,SV449: $i] :
( ( ( ~ ( is_fun949378684l_bool @ SV449 ) )
= $true )
| ( ( is_fun949378684l_bool @ ( hAPP_f2117159681l_bool @ SV60 @ SV449 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1773]) ).
thf(2215,plain,
! [SV61: $i,SV450: $i] :
( ( ( ~ ( is_fun1661590463l_bool @ SV450 ) )
= $true )
| ( ( is_bool @ ( hAPP_f1935102916l_bool @ SV61 @ SV450 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1774]) ).
thf(2216,plain,
! [SV62: $i,SV451: $i] :
( ( ( ~ ( is_fun1661590463l_bool @ SV451 ) )
= $true )
| ( ( is_fun1661590463l_bool @ ( hAPP_f559147733l_bool @ SV62 @ SV451 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1775]) ).
thf(2217,plain,
! [SV70: $i] :
( ( ( is_fun_a_bool @ SV70 )
= $false )
| ( ( is_fun949378684l_bool @ ( p @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1783]) ).
thf(2218,plain,
! [SV459: $i,SV71: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV71 ) @ SV459 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( p @ SV459 ) @ SV71 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1784]) ).
thf(2219,plain,
! [SV72: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV72 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( hAPP_f103356543l_bool @ ( cOMBC_1693257480l_bool @ ord_le1568362934t_bool ) @ SV72 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1785]) ).
thf(2220,plain,
! [SV73: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV73 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ ord_le313189616e_bool ) @ SV73 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1786]) ).
thf(2221,plain,
! [SV74: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV74 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ ord_le1311769555a_bool ) @ SV74 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1787]) ).
thf(2222,plain,
! [SV75: $i] :
( ( ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ SV75 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1295398978l_bool @ finite719726885l_bool @ ( collec1874991203l_bool @ ( hAPP_f760187903l_bool @ ( cOMBC_1269652216l_bool @ ord_le65145710l_bool ) @ SV75 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1788]) ).
thf(2223,plain,
! [SV76: $i] :
( ( ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ SV76 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f595608956l_bool @ finite1491191519l_bool @ ( collec792590109l_bool @ ( hAPP_f1759205631l_bool @ ( cOMBC_336095980l_bool @ ord_le1375671464l_bool ) @ SV76 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1789]) ).
thf(2224,plain,
! [SV77: $i] :
( ( ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ SV77 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1363661463l_bool @ finite1343359508l_bool @ ( collec1635217238l_bool @ ( hAPP_f1050622307l_bool @ ( cOMBC_636888218l_bool @ ord_le967226251l_bool ) @ SV77 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1790]) ).
thf(2225,plain,
! [SV78: $i] :
( ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV78 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ ( collec707592106l_bool @ ( hAPP_f1434722111l_bool @ ( cOMBC_331553030l_bool @ ord_le1375614389l_bool ) @ SV78 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1791]) ).
thf(2226,plain,
! [SV79: $i] :
( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV79 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ ( collec1613912337l_bool @ ( hAPP_f510955609l_bool @ ( cOMBC_7971162l_bool @ ord_le675606854l_bool ) @ SV79 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1792]) ).
thf(2227,plain,
! [SV80: $i] :
( ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV80 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ ( collec1015864663l_bool @ ( hAPP_f1772781669l_bool @ ( cOMBC_595898202l_bool @ ord_le1454342156l_bool ) @ SV80 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1793]) ).
thf(2228,plain,
! [SV81: $i,SV460: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV460 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_pname_a @ SV81 @ SV460 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1794]) ).
thf(2229,plain,
! [SV82: $i,SV461: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ SV461 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_2089570637ol_nat @ SV82 @ SV461 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1795]) ).
thf(2230,plain,
! [SV83: $i,SV462: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ SV462 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_1079571347ol_nat @ SV83 @ SV462 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1796]) ).
thf(2231,plain,
! [SV84: $i,SV463: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ SV463 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_1802975832ol_nat @ SV84 @ SV463 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1797]) ).
thf(2232,plain,
! [SV85: $i,SV464: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV464 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_fun_a_bool_nat @ SV85 @ SV464 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1798]) ).
thf(2233,plain,
! [SV86: $i,SV465: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV465 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_1551609309ol_nat @ SV86 @ SV465 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1799]) ).
thf(2234,plain,
! [SV87: $i,SV466: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV466 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_496248727ol_nat @ SV87 @ SV466 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1800]) ).
thf(2235,plain,
! [SV88: $i,SV467: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV467 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_a_nat @ SV88 @ SV467 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1801]) ).
thf(2236,plain,
! [SV89: $i,SV468: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ SV468 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1604018183_pname @ SV89 @ SV468 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1802]) ).
thf(2237,plain,
! [SV90: $i,SV469: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ SV469 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1705983821_pname @ SV90 @ SV469 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1803]) ).
thf(2238,plain,
! [SV91: $i,SV470: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ SV470 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_990671762_pname @ SV91 @ SV470 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1804]) ).
thf(2239,plain,
! [SV92: $i,SV471: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV471 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1854862208_pname @ SV92 @ SV471 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1805]) ).
thf(2240,plain,
! [SV93: $i,SV472: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV472 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1283814551_pname @ SV93 @ SV472 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1806]) ).
thf(2241,plain,
! [SV94: $i,SV473: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV473 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1921560913_pname @ SV94 @ SV473 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1807]) ).
thf(2242,plain,
! [SV95: $i,SV474: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV474 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_a_pname @ SV95 @ SV474 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1808]) ).
thf(2243,plain,
! [SV96: $i,SV475: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV475 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ ( image_1607900221l_bool @ SV96 @ SV475 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1809]) ).
thf(2244,plain,
! [SV97: $i,SV476: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV476 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ ( image_1874789623l_bool @ SV97 @ SV476 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1810]) ).
thf(2245,plain,
! [SV98: $i,SV477: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV477 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ ( image_1208015684l_bool @ SV98 @ SV477 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1811]) ).
thf(2246,plain,
! [SV99: $i,SV478: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV478 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( image_nat_fun_a_bool @ SV99 @ SV478 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1812]) ).
thf(2247,plain,
! [SV100: $i,SV479: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV479 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( image_1655916159e_bool @ SV100 @ SV479 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1813]) ).
thf(2248,plain,
! [SV101: $i,SV480: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV480 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( image_26036933t_bool @ SV101 @ SV480 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1814]) ).
thf(2249,plain,
! [SV102: $i,SV481: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV481 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_nat_a @ SV102 @ SV481 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1815]) ).
thf(2250,plain,
! [SV103: $i,SV482: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV482 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ ( image_1154884483l_bool @ SV103 @ SV482 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1816]) ).
thf(2251,plain,
! [SV104: $i,SV483: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV483 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ ( image_1642285373l_bool @ SV104 @ SV483 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1817]) ).
thf(2252,plain,
! [SV105: $i,SV484: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV484 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ ( image_1420695166l_bool @ SV105 @ SV484 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1818]) ).
thf(2253,plain,
! [SV106: $i,SV485: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV485 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( image_112932426a_bool @ SV106 @ SV485 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1819]) ).
thf(2254,plain,
! [SV107: $i,SV486: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV486 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( image_47868345e_bool @ SV107 @ SV486 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1820]) ).
thf(2255,plain,
! [SV108: $i,SV487: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV487 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( image_2129980159t_bool @ SV108 @ SV487 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1821]) ).
thf(2256,plain,
! [SV109: $i,SV488: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV488 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_pname_pname @ SV109 @ SV488 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1822]) ).
thf(2257,plain,
! [SV110: $i,SV489: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV489 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_a_a @ SV110 @ SV489 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1823]) ).
thf(2258,plain,
! [SV111: $i,SV490: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV490 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_fun_nat_bool_a @ SV111 @ SV490 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1824]) ).
thf(2259,plain,
! [SV112: $i,SV491: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV491 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_876012084bool_a @ SV112 @ SV491 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1825]) ).
thf(2260,plain,
! [SV113: $i,SV492: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV492 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_fun_a_bool_a @ SV113 @ SV492 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1826]) ).
thf(2261,plain,
! [SV114: $i,SV493: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV493 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_pname_nat @ SV114 @ SV493 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1827]) ).
thf(2262,plain,
! [SV115: $i,SV494: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV494 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_nat_pname @ SV115 @ SV494 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1828]) ).
thf(2263,plain,
! [SV116: $i,SV495: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV495 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ SV116 @ SV495 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1829]) ).
thf(2264,plain,
! [SV117: $i,SV496: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV496 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ SV117 @ SV496 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1830]) ).
thf(2265,plain,
! [SV118: $i,SV497: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV497 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ SV118 @ SV497 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1831]) ).
thf(2266,plain,
! [SV119: $i,SV498: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ SV498 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ ( insert2003652156l_bool @ SV119 @ SV498 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1832]) ).
thf(2267,plain,
! [SV120: $i,SV499: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ SV499 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ ( insert1117693814l_bool @ SV120 @ SV499 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1833]) ).
thf(2268,plain,
! [SV121: $i,SV500: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ SV500 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ ( insert1457093509l_bool @ SV121 @ SV500 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1834]) ).
thf(2269,plain,
! [SV122: $i,SV501: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV501 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ SV122 @ SV501 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1835]) ).
thf(2270,plain,
! [SV123: $i,SV502: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV502 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SV123 @ SV502 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1836]) ).
thf(2271,plain,
! [SV124: $i,SV503: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV503 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ SV124 @ SV503 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1837]) ).
thf(2272,plain,
! [SV125: $i,SV504: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV504 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( image_pname_nat @ SV125 @ SV504 ) ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV504 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1838]) ).
thf(2273,plain,
! [SV126: $i,SV505: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV505 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( image_a_nat @ SV126 @ SV505 ) ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SV505 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1839]) ).
thf(2274,plain,
! [SV127: $i,SV506: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV506 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( image_496248727ol_nat @ SV127 @ SV506 ) ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SV506 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1840]) ).
thf(2275,plain,
! [SV128: $i,SV507: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV507 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( image_1551609309ol_nat @ SV128 @ SV507 ) ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SV507 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1841]) ).
thf(2276,plain,
! [SV129: $i,SV508: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV508 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( image_fun_a_bool_nat @ SV129 @ SV508 ) ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SV508 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1842]) ).
thf(2277,plain,
! [SV130: $i,SV509: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV509 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( image_a_pname @ SV130 @ SV509 ) ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SV509 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1843]) ).
thf(2278,plain,
! [SV131: $i,SV510: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV510 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( image_nat_pname @ SV131 @ SV510 ) ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SV510 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1844]) ).
thf(2279,plain,
! [SV132: $i,SV511: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV511 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_pname_a @ SV132 @ SV511 ) ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV511 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1845]) ).
thf(2280,plain,
! [SV133: $i,SV512: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ SV512 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_526090948bool_a @ SV133 @ SV512 ) ) ) @ ( hAPP_f1690079119ol_nat @ finite1352710292l_bool @ SV512 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1846]) ).
thf(2281,plain,
! [SV134: $i,SV513: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ SV513 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_349102846bool_a @ SV134 @ SV513 ) ) ) @ ( hAPP_f98387925ol_nat @ finite269641166l_bool @ SV513 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1847]) ).
thf(2282,plain,
! [SV135: $i,SV514: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ SV514 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_573985017bool_a @ SV135 @ SV514 ) ) ) @ ( hAPP_f1253658590ol_nat @ finite1659325229l_bool @ SV514 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1848]) ).
thf(2283,plain,
! [SV136: $i,SV515: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV515 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_fun_a_bool_a @ SV136 @ SV515 ) ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SV515 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1849]) ).
thf(2284,plain,
! [SV137: $i,SV516: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV516 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_876012084bool_a @ SV137 @ SV516 ) ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SV516 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1850]) ).
thf(2285,plain,
! [SV138: $i,SV517: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV517 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_fun_nat_bool_a @ SV138 @ SV517 ) ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SV517 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1851]) ).
thf(2286,plain,
! [SV139: $i,SV518: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV518 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_a_a @ SV139 @ SV518 ) ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SV518 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1852]) ).
thf(2287,plain,
! [SV140: $i,SV519: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV519 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( image_pname_pname @ SV140 @ SV519 ) ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV519 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1853]) ).
thf(2288,plain,
! [SV141: $i,SV520: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV520 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( image_2129980159t_bool @ SV141 @ SV520 ) ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV520 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1854]) ).
thf(2289,plain,
! [SV142: $i,SV521: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV521 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( image_47868345e_bool @ SV142 @ SV521 ) ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV521 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1855]) ).
thf(2290,plain,
! [SV143: $i,SV522: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV522 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( image_112932426a_bool @ SV143 @ SV522 ) ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV522 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1856]) ).
thf(2291,plain,
! [SV144: $i,SV523: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV523 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_nat_a @ SV144 @ SV523 ) ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SV523 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1857]) ).
thf(2292,plain,
! [SV145: $i,SV524: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV524 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( image_26036933t_bool @ SV145 @ SV524 ) ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SV524 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1858]) ).
thf(2293,plain,
! [SV146: $i,SV525: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV525 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( image_1655916159e_bool @ SV146 @ SV525 ) ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SV525 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1859]) ).
thf(2294,plain,
! [SV147: $i,SV526: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV526 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( image_nat_fun_a_bool @ SV147 @ SV526 ) ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SV526 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1860]) ).
thf(2295,plain,
! [SV148: $i,SV527: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV527 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( image_1921560913_pname @ SV148 @ SV527 ) ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SV527 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1861]) ).
thf(2296,plain,
! [SV149: $i,SV528: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV528 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( image_1283814551_pname @ SV149 @ SV528 ) ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SV528 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1862]) ).
thf(2297,plain,
! [SV150: $i,SV529: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV529 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( image_1854862208_pname @ SV150 @ SV529 ) ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SV529 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1863]) ).
thf(2298,plain,
! [SV151: $i,SV530: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV530 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ SV151 ) @ SV530 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SV151 ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SV530 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1864]) ).
thf(2299,plain,
! [SV152: $i,SV531: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV531 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ SV152 ) @ SV531 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SV152 ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SV531 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1865]) ).
thf(2300,plain,
! [SV153: $i,SV532: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV532 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ SV153 ) @ SV532 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SV153 ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SV532 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1866]) ).
thf(2301,plain,
! [SV154: $i,SV533: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV533 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV154 ) @ SV533 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV154 ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV533 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1867]) ).
thf(2302,plain,
! [SV155: $i,SV534: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV534 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV155 ) @ SV534 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SV155 ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SV534 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1868]) ).
thf(2303,plain,
! [SV156: $i,SV535: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV535 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV156 ) @ SV535 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SV156 ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SV535 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1869]) ).
thf(2304,plain,
! [SV157: $i,SV536: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV536 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ SV157 ) @ SV536 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SV536 ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SV157 ) ) )
| ( SV157 = SV536 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1870]) ).
thf(2305,plain,
! [SV537: $i,SV158: $i] :
( ( ( ~ ( is_fun1661590463l_bool @ SV158 )
| ~ ( is_fun1661590463l_bool @ SV537 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV537 ) )
| ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ SV158 ) @ SV537 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SV537 ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SV158 ) ) )
| ( SV158 = SV537 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1871]) ).
thf(2306,plain,
! [SV538: $i,SV159: $i] :
( ( ( ~ ( is_fun949378684l_bool @ SV159 )
| ~ ( is_fun949378684l_bool @ SV538 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV538 ) )
| ~ ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ SV159 ) @ SV538 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SV538 ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SV159 ) ) )
| ( SV159 = SV538 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1872]) ).
thf(2307,plain,
! [SV539: $i,SV160: $i] :
( ( ( ~ ( is_fun_pname_bool @ SV160 )
| ~ ( is_fun_pname_bool @ SV539 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV539 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV160 ) @ SV539 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV539 ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV160 ) ) )
| ( SV160 = SV539 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1873]) ).
thf(2308,plain,
! [SV540: $i,SV161: $i] :
( ( ( ~ ( is_fun_a_bool @ SV161 )
| ~ ( is_fun_a_bool @ SV540 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV540 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV161 ) @ SV540 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SV540 ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SV161 ) ) )
| ( SV161 = SV540 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1874]) ).
thf(2309,plain,
! [SV162: $i,SV541: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV541 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV162 ) @ SV541 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SV541 ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SV162 ) ) )
| ( SV162 = SV541 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1875]) ).
thf(2310,plain,
! [SV163: $i,SV542: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV542 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SV542 ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( insert_fun_nat_bool @ SV163 @ SV542 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1876]) ).
thf(2311,plain,
! [SV164: $i,SV543: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV543 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SV543 ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( insert1325755072e_bool @ SV164 @ SV543 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1877]) ).
thf(2312,plain,
! [SV165: $i,SV544: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV544 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SV544 ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( insert_fun_a_bool @ SV165 @ SV544 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1878]) ).
thf(2313,plain,
! [SV166: $i,SV545: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV545 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV545 ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( insert_pname @ SV166 @ SV545 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1879]) ).
thf(2314,plain,
! [SV167: $i,SV546: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV546 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SV546 ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( insert_nat @ SV167 @ SV546 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1880]) ).
thf(2315,plain,
! [SV168: $i,SV547: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV547 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SV547 ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( insert_a @ SV168 @ SV547 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1881]) ).
thf(2316,plain,
! [SV169: $i,SV548: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV548 ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ SV169 ) @ SV548 ) )
| ( ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( insert_fun_nat_bool @ SV169 @ SV548 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SV548 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1882]) ).
thf(2317,plain,
! [SV170: $i,SV549: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV549 ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ SV170 ) @ SV549 ) )
| ( ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( insert1325755072e_bool @ SV170 @ SV549 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SV549 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1883]) ).
thf(2318,plain,
! [SV171: $i,SV550: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV550 ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ SV171 ) @ SV550 ) )
| ( ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( insert_fun_a_bool @ SV171 @ SV550 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SV550 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1884]) ).
thf(2319,plain,
! [SV172: $i,SV551: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV551 ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV172 ) @ SV551 ) )
| ( ( hAPP_f22106695ol_nat @ finite_card_nat @ ( insert_nat @ SV172 @ SV551 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SV551 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1885]) ).
thf(2320,plain,
! [SV173: $i,SV552: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV552 ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV173 ) @ SV552 ) )
| ( ( hAPP_f921600141ol_nat @ finite_card_pname @ ( insert_pname @ SV173 @ SV552 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV552 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1886]) ).
thf(2321,plain,
! [SV174: $i,SV553: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV553 ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV174 ) @ SV553 ) )
| ( ( hAPP_fun_a_bool_nat @ finite_card_a @ ( insert_a @ SV174 @ SV553 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SV553 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1887]) ).
thf(2322,plain,
! [SV554: $i,SV175: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV175 ) @ SV554 ) ) )
= $true )
| ( ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ suc @ SV554 ) ) @ SV175 )
= ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV554 ) @ SV175 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1888]) ).
thf(2323,plain,
! [SV555: $i,SV178: $i] :
( ( ( ( ( hAPP_nat_nat @ suc @ SV178 )
!= ( hAPP_nat_nat @ suc @ SV555 ) ) )
= $true )
| ( ( SV178 = SV555 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1889]) ).
thf(2324,plain,
! [SV556: $i,SV181: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV181 ) @ SV556 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV556 ) @ SV181 ) )
| ( SV181 = SV556 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1892]) ).
thf(2325,plain,
! [SV182: $i,SV729: $i,SV557: $i] :
( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV557 ) @ SV729 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV729 ) @ SV182 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV557 ) @ SV182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1893]) ).
thf(2326,plain,
! [SV558: $i,SV183: $i] :
( ( ( ( SV183 != SV558 ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV183 ) @ SV558 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1894]) ).
thf(2327,plain,
! [SV559: $i,SV184: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV184 ) @ SV559 ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV559 ) @ SV184 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1895]) ).
thf(2328,plain,
! [SV730: $i,SV560: $i,SV186: $i] :
( ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV186 ) @ SV560 ) ) @ SV730 )
= ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV186 ) @ SV730 ) ) @ SV560 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1896]) ).
thf(2329,plain,
! [SV561: $i,SV187: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ SV187 ) @ SV561 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV561 ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV187 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1897]) ).
thf(2330,plain,
! [SV562: $i,SV188: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ SV188 ) @ SV562 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV562 ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV188 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1898]) ).
thf(2331,plain,
! [SV563: $i,SV189: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV189 ) @ SV563 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV563 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV189 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1899]) ).
thf(2332,plain,
! [SV564: $i,SV190: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ SV190 ) @ SV564 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV564 ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV190 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1900]) ).
thf(2333,plain,
! [SV565: $i,SV191: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV191 ) @ SV565 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV565 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV191 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1901]) ).
thf(2334,plain,
! [SV566: $i,SV192: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV192 ) @ SV566 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV566 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV192 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1902]) ).
thf(2335,plain,
! [SV193: $i,SV567: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV567 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ SV193 ) @ SV567 ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV193 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1903]) ).
thf(2336,plain,
! [SV194: $i,SV568: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV568 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ SV194 ) @ SV568 ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV194 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1904]) ).
thf(2337,plain,
! [SV195: $i,SV569: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV569 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV195 ) @ SV569 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV195 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1905]) ).
thf(2338,plain,
! [SV196: $i,SV570: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV570 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ SV196 ) @ SV570 ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV196 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1906]) ).
thf(2339,plain,
! [SV197: $i,SV571: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV571 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV197 ) @ SV571 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV197 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1907]) ).
thf(2340,plain,
! [SV198: $i,SV572: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV572 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV198 ) @ SV572 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV198 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1908]) ).
thf(2341,plain,
! [SV573: $i,SV199: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ SV199 ) ) @ SV573 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV199 ) @ SV573 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1909]) ).
thf(2342,plain,
! [SV574: $i,SV200: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV200 ) @ ( hAPP_nat_nat @ suc @ SV574 ) ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV200 ) @ SV574 ) )
| ( SV200
= ( hAPP_nat_nat @ suc @ SV574 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1910]) ).
thf(2343,plain,
! [SV575: $i,SV201: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV201 ) @ SV575 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV201 ) @ ( hAPP_nat_nat @ suc @ SV575 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1911]) ).
thf(2344,plain,
! [SV731: $i,SV576: $i,SV203: $i] :
( ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ suc @ SV203 ) ) @ SV576 ) ) @ ( hAPP_nat_nat @ suc @ SV731 ) )
= ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV203 ) @ SV576 ) ) @ SV731 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1913]) ).
thf(2345,plain,
! [SV205: $i,SV732: $i,SV578: $i] :
( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV578 ) @ SV732 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV578 ) @ SV205 ) )
| ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV732 ) @ SV578 ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV205 ) @ SV578 ) )
= ( hAPP_nat_nat @ ( minus_minus_nat @ SV732 ) @ SV205 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1915]) ).
thf(2346,plain,
! [SV579: $i,SV206: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV206 ) @ SV579 ) ) )
= $true )
| ( ( ( hAPP_nat_nat @ ( minus_minus_nat @ SV579 ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV579 ) @ SV206 ) )
= SV206 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1916]) ).
thf(2347,plain,
! [SV207: $i,SV733: $i,SV580: $i] :
( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV580 ) @ SV733 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV580 ) @ SV207 ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV733 ) @ SV207 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1917]) ).
thf(2348,plain,
! [SV208: $i,SV734: $i,SV581: $i] :
( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV581 ) @ SV734 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV208 ) @ SV734 ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV208 ) @ SV581 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1918]) ).
thf(2349,plain,
! [SV583: $i,SV210: $i,SV735: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV735 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV210 ) @ ( image_pname_a @ SV583 @ SV735 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV210 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1920]) ).
thf(2350,plain,
! [SV211: $i,SV584: $i,SV736: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( hAPP_n1699378549t_bool @ SV736 @ ( sK16_N_2 @ SV736 @ SV584 @ SV211 ) ) ) @ ( hAPP_n1699378549t_bool @ SV736 @ ( hAPP_nat_nat @ suc @ ( sK16_N_2 @ SV736 @ SV584 @ SV211 ) ) ) ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV211 ) @ SV584 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( hAPP_n1699378549t_bool @ SV736 @ SV211 ) ) @ ( hAPP_n1699378549t_bool @ SV736 @ SV584 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1921]) ).
thf(2351,plain,
! [SV212: $i,SV585: $i,SV737: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_n1025906991e_bool @ SV737 @ ( sK15_N_2 @ SV737 @ SV585 @ SV212 ) ) ) @ ( hAPP_n1025906991e_bool @ SV737 @ ( hAPP_nat_nat @ suc @ ( sK15_N_2 @ SV737 @ SV585 @ SV212 ) ) ) ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV212 ) @ SV585 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_n1025906991e_bool @ SV737 @ SV212 ) ) @ ( hAPP_n1025906991e_bool @ SV737 @ SV585 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1922]) ).
thf(2352,plain,
! [SV213: $i,SV586: $i,SV738: $i] :
( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ SV738 @ ( sK14_N_2 @ SV738 @ SV586 @ SV213 ) ) ) @ ( hAPP_nat_nat @ SV738 @ ( hAPP_nat_nat @ suc @ ( sK14_N_2 @ SV738 @ SV586 @ SV213 ) ) ) ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV213 ) @ SV586 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ SV738 @ SV213 ) ) @ ( hAPP_nat_nat @ SV738 @ SV586 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1923]) ).
thf(2353,plain,
! [SV214: $i,SV587: $i,SV739: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_nat_fun_a_bool @ SV739 @ ( sK13_N_2 @ SV739 @ SV587 @ SV214 ) ) ) @ ( hAPP_nat_fun_a_bool @ SV739 @ ( hAPP_nat_nat @ suc @ ( sK13_N_2 @ SV739 @ SV587 @ SV214 ) ) ) ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV214 ) @ SV587 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_nat_fun_a_bool @ SV739 @ SV214 ) ) @ ( hAPP_nat_fun_a_bool @ SV739 @ SV587 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1924]) ).
thf(2354,plain,
! [SV215: $i,SV740: $i,SV588: $i] :
( ( ! [SY1052: $i] :
( ( SV588
!= ( hAPP_pname_a @ SV740 @ SY1052 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SY1052 ) @ SV215 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV588 ) @ ( image_pname_a @ SV740 @ SV215 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1925]) ).
thf(2355,plain,
! [SV589: $i,SV216: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV216 ) @ SV589 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV589 ) @ SV216 ) )
| ( SV216 = SV589 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1926]) ).
thf(2356,plain,
! [SV590: $i,SV217: $i] :
( ( ( ~ ( is_fun_pname_bool @ SV217 )
| ~ ( is_fun_pname_bool @ SV590 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV217 ) @ SV590 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV590 ) @ SV217 ) )
| ( SV217 = SV590 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1927]) ).
thf(2357,plain,
! [SV591: $i,SV218: $i] :
( ( ( ~ ( is_fun_a_bool @ SV218 )
| ~ ( is_fun_a_bool @ SV591 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV218 ) @ SV591 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV591 ) @ SV218 ) )
| ( SV218 = SV591 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1928]) ).
thf(2358,plain,
! [SV219: $i,SV741: $i,SV592: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV592 ) @ SV741 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV219 ) @ SV592 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV219 ) @ SV741 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1929]) ).
thf(2359,plain,
! [SV220: $i,SV742: $i,SV593: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV593 ) @ SV742 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV220 ) @ SV593 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV220 ) @ SV742 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1930]) ).
thf(2360,plain,
! [SV221: $i,SV743: $i,SV594: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV594 ) @ SV743 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV221 ) @ SV594 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV221 ) @ SV743 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1931]) ).
thf(2361,plain,
! [SV744: $i,SV595: $i,SV222: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV222 ) @ ( insert_nat @ SV595 @ SV744 ) ) )
| ( SV222 = SV595 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV222 ) @ SV744 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1932]) ).
thf(2362,plain,
! [SV596: $i,SV223: $i] :
( ( ( ~ ( is_pname @ SV223 )
| ~ ( is_pname @ SV596 ) )
= $true )
| ( ( ! [SY979: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV223 ) @ ( insert_pname @ SV596 @ SY979 ) ) )
| ( SV223 = SV596 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV223 ) @ SY979 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1933]) ).
thf(2363,plain,
! [SV597: $i,SV224: $i] :
( ( ( ~ ( is_a @ SV224 )
| ~ ( is_a @ SV597 ) )
= $true )
| ( ( ! [SY980: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV224 ) @ ( insert_a @ SV597 @ SY980 ) ) )
| ( SV224 = SV597 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV224 ) @ SY980 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1934]) ).
thf(2364,plain,
! [SV745: $i,SV616: $i,SV243: $i] :
( ( ( insert_nat @ SV243 @ ( insert_nat @ SV616 @ SV745 ) )
= ( insert_nat @ SV616 @ ( insert_nat @ SV243 @ SV745 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1953]) ).
thf(2365,plain,
! [SV746: $i,SV617: $i,SV244: $i] :
( ( ( insert_pname @ SV244 @ ( insert_pname @ SV617 @ SV746 ) )
= ( insert_pname @ SV617 @ ( insert_pname @ SV244 @ SV746 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1954]) ).
thf(2366,plain,
! [SV747: $i,SV618: $i,SV245: $i] :
( ( ( insert_a @ SV245 @ ( insert_a @ SV618 @ SV747 ) )
= ( insert_a @ SV618 @ ( insert_a @ SV245 @ SV747 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1955]) ).
thf(2367,plain,
! [SV246: $i,SV748: $i,SV619: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV619 ) @ SV748 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV619 ) @ ( insert_nat @ SV246 @ SV748 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1956]) ).
thf(2368,plain,
! [SV247: $i,SV749: $i,SV620: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV620 ) @ SV749 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV620 ) @ ( insert_pname @ SV247 @ SV749 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1957]) ).
thf(2369,plain,
! [SV248: $i,SV750: $i,SV621: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV621 ) @ SV750 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV621 ) @ ( insert_a @ SV248 @ SV750 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1958]) ).
thf(2370,plain,
! [SV622: $i,SV249: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV249 ) @ SV622 ) ) )
= $true )
| ( ( ( insert_nat @ SV249 @ SV622 )
= SV622 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1959]) ).
thf(2371,plain,
! [SV250: $i,SV623: $i] :
( ( ( ~ ( is_fun_pname_bool @ SV623 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV250 ) @ SV623 ) )
| ( ( insert_pname @ SV250 @ SV623 )
= SV623 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1960]) ).
thf(2372,plain,
! [SV251: $i,SV624: $i] :
( ( ( ~ ( is_fun_a_bool @ SV624 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV251 ) @ SV624 ) )
| ( ( insert_a @ SV251 @ SV624 )
= SV624 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1961]) ).
thf(2373,plain,
! [SV625: $i,SV255: $i] :
( ( ( ( SV255 != SV625 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV255 ) @ SV625 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1962]) ).
thf(2374,plain,
! [SV626: $i,SV256: $i] :
( ( ( ( SV256 != SV626 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV256 ) @ SV626 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1963]) ).
thf(2375,plain,
! [SV627: $i,SV257: $i] :
( ( ( ( SV257 != SV627 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV257 ) @ SV627 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1964]) ).
thf(2376,plain,
! [SV628: $i,SV258: $i] :
( ( ( ( SV258 != SV628 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV628 ) @ SV258 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1965]) ).
thf(2377,plain,
! [SV629: $i,SV259: $i] :
( ( ( ( SV259 != SV629 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV629 ) @ SV259 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1966]) ).
thf(2378,plain,
! [SV630: $i,SV260: $i] :
( ( ( ( SV260 != SV630 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV630 ) @ SV260 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1967]) ).
thf(2379,plain,
! [SV261: $i,SV751: $i,SV631: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV631 ) @ SV751 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV261 ) @ SV631 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV261 ) @ SV751 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1968]) ).
thf(2380,plain,
! [SV262: $i,SV752: $i,SV632: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV632 ) @ SV752 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV262 ) @ SV632 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV262 ) @ SV752 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1969]) ).
thf(2381,plain,
! [SV263: $i,SV753: $i,SV633: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV633 ) @ SV753 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV263 ) @ SV633 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV263 ) @ SV753 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1970]) ).
thf(2382,plain,
! [SV264: $i,SV754: $i,SV634: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV634 ) @ SV754 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV754 ) @ SV264 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV634 ) @ SV264 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1971]) ).
thf(2383,plain,
! [SV265: $i,SV755: $i,SV635: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV635 ) @ SV755 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV755 ) @ SV265 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV635 ) @ SV265 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1972]) ).
thf(2384,plain,
! [SV266: $i,SV756: $i,SV636: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV636 ) @ SV756 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV756 ) @ SV266 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV636 ) @ SV266 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1973]) ).
thf(2385,plain,
! [SV267: $i,SV757: $i,SV637: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV637 ) @ SV757 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV267 ) @ SV637 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV267 ) @ SV757 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1974]) ).
thf(2386,plain,
! [SV268: $i,SV758: $i,SV638: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV638 ) @ SV758 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV268 ) @ SV638 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV268 ) @ SV758 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1975]) ).
thf(2387,plain,
! [SV269: $i,SV759: $i,SV639: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV639 ) @ SV759 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV269 ) @ SV639 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV269 ) @ SV759 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1976]) ).
thf(2388,plain,
! [SV270: $i,SV760: $i,SV640: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV640 ) @ SV760 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV760 ) @ SV270 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV640 ) @ SV270 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1977]) ).
thf(2389,plain,
! [SV271: $i,SV761: $i,SV641: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV641 ) @ SV761 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV761 ) @ SV271 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV641 ) @ SV271 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1978]) ).
thf(2390,plain,
! [SV272: $i,SV762: $i,SV642: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV642 ) @ SV762 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV762 ) @ SV272 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV642 ) @ SV272 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1979]) ).
thf(2391,plain,
! [SV273: $i] :
( ( ( is_fun_pname_bool @ SV273 )
= $false )
| ( ( ( collect_pname @ SV273 )
= SV273 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1980]) ).
thf(2392,plain,
! [SV275: $i] :
( ( ( is_fun1661590463l_bool @ SV275 )
= $false )
| ( ( ( collec1974731493e_bool @ SV275 )
= SV275 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1981]) ).
thf(2393,plain,
! [SV276: $i] :
( ( ( is_fun949378684l_bool @ SV276 )
= $false )
| ( ( ( collect_fun_a_bool @ SV276 )
= SV276 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1982]) ).
thf(2394,plain,
! [SV278: $i,SV763: $i,SV643: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV643 ) @ SV763 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( hAPP_pname_a @ SV278 @ SV643 ) ) @ ( image_pname_a @ SV278 @ SV763 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1983]) ).
thf(2395,plain,
! [SV644: $i,SV279: $i,SV764: $i] :
( ( ! [SY1053: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV764 ) @ SY1053 ) )
| ( SV279
!= ( hAPP_pname_a @ SV644 @ SV764 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV279 ) @ ( image_pname_a @ SV644 @ SY1053 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1984]) ).
thf(2396,plain,
! [SV289: $i,SV765: $i,SV654: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV654 ) @ SV765 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV654 ) @ ( insert_nat @ SV289 @ SV765 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1994]) ).
thf(2397,plain,
! [SV290: $i,SV766: $i,SV655: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV655 ) @ SV766 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV655 ) @ ( insert_pname @ SV290 @ SV766 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1995]) ).
thf(2398,plain,
! [SV291: $i,SV767: $i,SV656: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV656 ) @ SV767 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV656 ) @ ( insert_a @ SV291 @ SV767 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1996]) ).
thf(2399,plain,
! [SV292: $i,SV768: $i,SV657: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV657 ) @ SV768 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( insert_nat @ SV292 @ SV657 ) ) @ ( insert_nat @ SV292 @ SV768 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1997]) ).
thf(2400,plain,
! [SV293: $i,SV769: $i,SV658: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV658 ) @ SV769 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ SV293 @ SV658 ) ) @ ( insert_pname @ SV293 @ SV769 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1998]) ).
thf(2401,plain,
! [SV294: $i,SV770: $i,SV659: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV659 ) @ SV770 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV294 @ SV659 ) ) @ ( insert_a @ SV294 @ SV770 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1999]) ).
thf(2402,plain,
! [SV771: $i,SV660: $i,SV295: $i] :
( ( ( image_pname_a @ SV295 @ ( insert_pname @ SV660 @ SV771 ) )
= ( insert_a @ ( hAPP_pname_a @ SV295 @ SV660 ) @ ( image_pname_a @ SV295 @ SV771 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2000]) ).
thf(2403,plain,
! [SV296: $i,SV772: $i,SV661: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV661 ) @ SV772 ) )
| ( ( insert_a @ ( hAPP_pname_a @ SV296 @ SV661 ) @ ( image_pname_a @ SV296 @ SV772 ) )
= ( image_pname_a @ SV296 @ SV772 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2001]) ).
thf(2404,plain,
! [SV297: $i,SV773: $i,SV662: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV662 ) @ SV773 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_pname_a @ SV297 @ SV662 ) ) @ ( image_pname_a @ SV297 @ SV773 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2002]) ).
thf(2405,plain,
! [SV663: $i,SV298: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ SV298 ) ) @ SV663 ) ) )
= $true )
| ( ( SV663
= ( hAPP_nat_nat @ suc @ ( sK4_M @ SV663 @ SV298 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2003]) ).
thf(2406,plain,
! [SV303: $i] :
( ( ( hBOOL @ ( hAPP_bool_bool @ fNot @ SV303 ) )
= $false )
| ( ( ~ ( hBOOL @ SV303 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2004]) ).
thf(2407,plain,
! [SV305: $i,SV664: $i] :
( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ SV664 ) @ SV305 ) )
= $true )
| ( ( ~ ( hBOOL @ SV664 )
| ~ ( hBOOL @ SV305 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2006]) ).
thf(2408,plain,
! [SV774: $i,SV306: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ SV306 ) @ SV774 ) ) )
= $true )
| ( ( hBOOL @ SV306 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2007]) ).
thf(2409,plain,
! [SV665: $i,SV307: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ SV307 ) @ SV665 ) ) )
= $true )
| ( ( hBOOL @ SV665 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2008]) ).
thf(2410,plain,
! [SV308: $i,SV666: $i] :
( ( ( ~ ( hBOOL @ SV666 ) )
= $true )
| ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ SV666 ) @ SV308 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2009]) ).
thf(2411,plain,
! [SV309: $i,SV667: $i] :
( ( ( ~ ( hBOOL @ SV667 ) )
= $true )
| ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ SV309 ) @ SV667 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2010]) ).
thf(2412,plain,
! [SV310: $i,SV668: $i] :
( ( ( hBOOL @ SV668 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ SV310 ) @ SV668 ) )
| ( hBOOL @ SV310 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2011]) ).
thf(2413,plain,
! [SV311: $i,SV669: $i] :
( ( ( hBOOL @ SV669 )
= $true )
| ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ SV669 ) @ SV311 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2012]) ).
thf(2414,plain,
! [SV312: $i,SV670: $i] :
( ( ( ~ ( hBOOL @ SV670 ) )
= $true )
| ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ SV312 ) @ SV670 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2013]) ).
thf(2415,plain,
! [SV313: $i,SV671: $i] :
( ( ( hBOOL @ SV671 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ SV313 ) @ SV671 ) )
| ~ ( hBOOL @ SV313 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2014]) ).
thf(2416,plain,
! [SV672: $i,SV314: $i] :
( ( ( ~ ( is_a @ SV314 )
| ~ ( is_a @ SV672 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_a_bool @ ( hAPP_a_fun_a_bool @ fequal_a @ SV314 ) @ SV672 ) )
| ( SV314 = SV672 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2015]) ).
thf(2417,plain,
! [SV673: $i,SV315: $i] :
( ( ( ( SV315 != SV673 ) )
= $true )
| ( ( hBOOL @ ( hAPP_a_bool @ ( hAPP_a_fun_a_bool @ fequal_a @ SV315 ) @ SV673 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2016]) ).
thf(2418,plain,
! [SV674: $i,SV316: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ SV316 ) @ SV674 ) ) )
= $true )
| ( ( SV316 = SV674 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2017]) ).
thf(2419,plain,
! [SV675: $i,SV317: $i] :
( ( ( ( SV317 != SV675 ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ SV317 ) @ SV675 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2018]) ).
thf(2420,plain,
! [SV676: $i,SV318: $i] :
( ( ( ~ ( is_pname @ SV318 )
| ~ ( is_pname @ SV676 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ fequal_pname @ SV318 ) @ SV676 ) )
| ( SV318 = SV676 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2019]) ).
thf(2421,plain,
! [SV677: $i,SV319: $i] :
( ( ( ( SV319 != SV677 ) )
= $true )
| ( ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ fequal_pname @ SV319 ) @ SV677 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2020]) ).
thf(2422,plain,
! [SV775: $i,SV678: $i,SV320: $i] :
( ( ( hAPP_a_bool @ ( hAPP_a_fun_a_bool @ ( cOMBC_a_a_bool @ SV320 ) @ SV678 ) @ SV775 )
= ( hAPP_a_bool @ ( hAPP_a_fun_a_bool @ SV320 @ SV775 ) @ SV678 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2021]) ).
thf(2423,plain,
! [SV679: $i,SV321: $i] :
( ( ( ~ ( is_fun_a_bool @ SV321 )
| ~ ( is_fun_a_bool @ SV679 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ SV321 ) @ SV679 ) )
| ( SV321 = SV679 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2022]) ).
thf(2424,plain,
! [SV680: $i,SV322: $i] :
( ( ( ( SV322 != SV680 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ SV322 ) @ SV680 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2023]) ).
thf(2425,plain,
! [SV776: $i,SV681: $i,SV323: $i] :
( ( ( hAPP_a_bool @ ( cOMBB_bool_bool_a @ SV323 @ SV681 ) @ SV776 )
= ( hAPP_bool_bool @ SV323 @ ( hAPP_a_bool @ SV681 @ SV776 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2024]) ).
thf(2426,plain,
! [SV777: $i,SV682: $i,SV324: $i] :
( ( ( hAPP_a_bool @ ( cOMBS_a_bool_bool @ SV324 @ SV682 ) @ SV777 )
= ( hAPP_bool_bool @ ( hAPP_a_fun_bool_bool @ SV324 @ SV777 ) @ ( hAPP_a_bool @ SV682 @ SV777 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2025]) ).
thf(2427,plain,
! [SV778: $i,SV683: $i,SV325: $i] :
( ( ( hAPP_pname_bool @ ( hAPP_a93125764e_bool @ ( cOMBC_pname_a_bool @ SV325 ) @ SV683 ) @ SV778 )
= ( hAPP_a_bool @ ( hAPP_p1534023578a_bool @ SV325 @ SV778 ) @ SV683 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2026]) ).
thf(2428,plain,
! [SV684: $i,SV326: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ SV326 ) @ SV684 ) ) )
= $true )
| ( ( SV326 = SV684 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2027]) ).
thf(2429,plain,
! [SV685: $i,SV327: $i] :
( ( ( ( SV327 != SV685 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ SV327 ) @ SV685 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2028]) ).
thf(2430,plain,
! [SV686: $i,SV328: $i] :
( ( ( ~ ( is_fun_pname_bool @ SV328 )
| ~ ( is_fun_pname_bool @ SV686 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ SV328 ) @ SV686 ) )
| ( SV328 = SV686 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2029]) ).
thf(2431,plain,
! [SV687: $i,SV329: $i] :
( ( ( ( SV329 != SV687 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ SV329 ) @ SV687 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2030]) ).
thf(2432,plain,
! [SV779: $i,SV688: $i,SV330: $i] :
( ( ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ SV330 ) @ SV688 ) @ SV779 )
= ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV330 @ SV779 ) @ SV688 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2031]) ).
thf(2433,plain,
! [SV780: $i,SV689: $i,SV331: $i] :
( ( ( hAPP_nat_bool @ ( cOMBB_bool_bool_nat @ SV331 @ SV689 ) @ SV780 )
= ( hAPP_bool_bool @ SV331 @ ( hAPP_nat_bool @ SV689 @ SV780 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2032]) ).
thf(2434,plain,
! [SV781: $i,SV690: $i,SV332: $i] :
( ( ( hAPP_nat_bool @ ( cOMBS_nat_bool_bool @ SV332 @ SV690 ) @ SV781 )
= ( hAPP_bool_bool @ ( hAPP_n1006566506l_bool @ SV332 @ SV781 ) @ ( hAPP_nat_bool @ SV690 @ SV781 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2033]) ).
thf(2435,plain,
! [SV782: $i,SV691: $i,SV333: $i] :
( ( ( hAPP_pname_bool @ ( cOMBB_647938656_pname @ SV333 @ SV691 ) @ SV782 )
= ( hAPP_bool_bool @ SV333 @ ( hAPP_pname_bool @ SV691 @ SV782 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2034]) ).
thf(2436,plain,
! [SV783: $i,SV692: $i,SV334: $i] :
( ( ( hAPP_pname_bool @ ( cOMBS_568398431l_bool @ SV334 @ SV692 ) @ SV783 )
= ( hAPP_bool_bool @ ( hAPP_p393069232l_bool @ SV334 @ SV783 ) @ ( hAPP_pname_bool @ SV692 @ SV783 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2035]) ).
thf(2437,plain,
! [SV784: $i,SV693: $i,SV335: $i] :
( ( ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ SV335 ) @ SV693 ) @ SV784 )
= ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ SV335 @ SV784 ) @ SV693 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2036]) ).
thf(2438,plain,
! [SV785: $i,SV694: $i,SV336: $i] :
( ( ( hAPP_a_bool @ ( hAPP_f2050579477a_bool @ ( cOMBC_1355376034l_bool @ SV336 ) @ SV694 ) @ SV785 )
= ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ SV336 @ SV785 ) @ SV694 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2037]) ).
thf(2439,plain,
! [SV786: $i,SV695: $i,SV337: $i] :
( ( ( hAPP_p1534023578a_bool @ ( cOMBB_1897541054_pname @ SV337 @ SV695 ) @ SV786 )
= ( hAPP_a_fun_a_bool @ SV337 @ ( hAPP_pname_a @ SV695 @ SV786 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2038]) ).
thf(2440,plain,
! [SV787: $i,SV696: $i,SV338: $i] :
( ( ( hAPP_fun_a_bool_bool @ ( cOMBB_2140588453a_bool @ SV338 @ SV696 ) @ SV787 )
= ( hAPP_bool_bool @ SV338 @ ( hAPP_fun_a_bool_bool @ SV696 @ SV787 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2039]) ).
thf(2441,plain,
! [SV788: $i,SV697: $i,SV339: $i] :
( ( ( hAPP_a_fun_bool_bool @ ( cOMBB_1972296269bool_a @ SV339 @ SV697 ) @ SV788 )
= ( hAPP_b589554111l_bool @ SV339 @ ( hAPP_a_bool @ SV697 @ SV788 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2040]) ).
thf(2442,plain,
! [SV789: $i,SV698: $i,SV340: $i] :
( ( ( hAPP_fun_a_bool_bool @ ( cOMBS_1035972772l_bool @ SV340 @ SV698 ) @ SV789 )
= ( hAPP_bool_bool @ ( hAPP_f198738859l_bool @ SV340 @ SV789 ) @ ( hAPP_fun_a_bool_bool @ SV698 @ SV789 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2041]) ).
thf(2443,plain,
! [SV790: $i,SV699: $i,SV341: $i] :
( ( ( hAPP_nat_bool @ ( hAPP_f800510211t_bool @ ( cOMBC_226598744l_bool @ SV341 ) @ SV699 ) @ SV790 )
= ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ SV341 @ SV790 ) @ SV699 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2042]) ).
thf(2444,plain,
! [SV791: $i,SV700: $i,SV342: $i] :
( ( ( hAPP_f54304608l_bool @ ( cOMBB_238756964t_bool @ SV342 @ SV700 ) @ SV791 )
= ( hAPP_bool_bool @ SV342 @ ( hAPP_f54304608l_bool @ SV700 @ SV791 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2043]) ).
thf(2445,plain,
! [SV792: $i,SV701: $i,SV343: $i] :
( ( ( hAPP_n1006566506l_bool @ ( cOMBB_1015721476ol_nat @ SV343 @ SV701 ) @ SV792 )
= ( hAPP_b589554111l_bool @ SV343 @ ( hAPP_nat_bool @ SV701 @ SV792 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2044]) ).
thf(2446,plain,
! [SV793: $i,SV702: $i,SV344: $i] :
( ( ( hAPP_f54304608l_bool @ ( cOMBS_1187019125l_bool @ SV344 @ SV702 ) @ SV793 )
= ( hAPP_bool_bool @ ( hAPP_f1748468828l_bool @ SV344 @ SV793 ) @ ( hAPP_f54304608l_bool @ SV702 @ SV793 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2045]) ).
thf(2447,plain,
! [SV794: $i,SV703: $i,SV345: $i] :
( ( ( hAPP_f1664156314l_bool @ ( cOMBB_307249310e_bool @ SV345 @ SV703 ) @ SV794 )
= ( hAPP_bool_bool @ SV345 @ ( hAPP_f1664156314l_bool @ SV703 @ SV794 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2046]) ).
thf(2448,plain,
! [SV795: $i,SV704: $i,SV346: $i] :
( ( ( hAPP_p393069232l_bool @ ( cOMBB_675860798_pname @ SV346 @ SV704 ) @ SV795 )
= ( hAPP_b589554111l_bool @ SV346 @ ( hAPP_pname_bool @ SV704 @ SV795 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2047]) ).
thf(2449,plain,
! [SV796: $i,SV705: $i,SV347: $i] :
( ( ( hAPP_f1664156314l_bool @ ( cOMBS_350070575l_bool @ SV347 @ SV705 ) @ SV796 )
= ( hAPP_bool_bool @ ( hAPP_f1476298914l_bool @ SV347 @ SV796 ) @ ( hAPP_f1664156314l_bool @ SV705 @ SV796 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2048]) ).
thf(2450,plain,
! [SV797: $i,SV706: $i,SV348: $i] :
( ( ( hAPP_pname_bool @ ( hAPP_f759274231e_bool @ ( cOMBC_1058051404l_bool @ SV348 ) @ SV706 ) @ SV797 )
= ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ SV348 @ SV797 ) @ SV706 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2049]) ).
thf(2451,plain,
! [SV798: $i,SV707: $i,SV349: $i] :
( ( ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ SV349 ) @ SV707 ) @ SV798 )
= ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ SV349 @ SV798 ) @ SV707 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2050]) ).
thf(2452,plain,
! [SV799: $i,SV708: $i,SV350: $i] :
( ( ( hAPP_f198738859l_bool @ ( cOMBB_338059395a_bool @ SV350 @ SV708 ) @ SV799 )
= ( hAPP_b589554111l_bool @ SV350 @ ( hAPP_fun_a_bool_bool @ SV708 @ SV799 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2051]) ).
thf(2453,plain,
! [SV800: $i,SV709: $i,SV351: $i] :
( ( ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ( cOMBC_1693257480l_bool @ SV351 ) @ SV709 ) @ SV800 )
= ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ SV351 @ SV800 ) @ SV709 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2052]) ).
thf(2454,plain,
! [SV801: $i,SV710: $i,SV352: $i] :
( ( ( hAPP_f1748468828l_bool @ ( cOMBB_444170502t_bool @ SV352 @ SV710 ) @ SV801 )
= ( hAPP_b589554111l_bool @ SV352 @ ( hAPP_f54304608l_bool @ SV710 @ SV801 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2053]) ).
thf(2455,plain,
! [SV802: $i,SV711: $i,SV353: $i] :
( ( ( hAPP_f1476298914l_bool @ ( cOMBB_2095475776e_bool @ SV353 @ SV711 ) @ SV802 )
= ( hAPP_b589554111l_bool @ SV353 @ ( hAPP_f1664156314l_bool @ SV711 @ SV802 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2054]) ).
thf(2456,plain,
! [SV803: $i,SV712: $i,SV354: $i] :
( ( ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ SV354 ) @ SV712 ) @ SV803 )
= ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ SV354 @ SV803 ) @ SV712 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2055]) ).
thf(2457,plain,
! [SV804: $i,SV713: $i,SV355: $i] :
( ( ( hAPP_fun_a_bool_bool @ ( hAPP_f2117159681l_bool @ ( cOMBC_1880041174l_bool @ SV355 ) @ SV713 ) @ SV804 )
= ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ SV355 @ SV804 ) @ SV713 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2056]) ).
thf(2458,plain,
! [SV805: $i,SV714: $i,SV356: $i] :
( ( ( hAPP_f54304608l_bool @ ( hAPP_f1246832597l_bool @ ( cOMBC_1245412066l_bool @ SV356 ) @ SV714 ) @ SV805 )
= ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ SV356 @ SV805 ) @ SV714 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2057]) ).
thf(2459,plain,
! [SV806: $i,SV715: $i,SV357: $i] :
( ( ( hAPP_f1664156314l_bool @ ( hAPP_f559147733l_bool @ ( cOMBC_1988546018l_bool @ SV357 ) @ SV715 ) @ SV806 )
= ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ SV357 @ SV806 ) @ SV715 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2058]) ).
thf(2460,plain,
! [SV807: $i,SV716: $i,SV358: $i] :
( ( ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ( cOMBC_331553030l_bool @ SV358 ) @ SV716 ) @ SV807 )
= ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ SV358 @ SV807 ) @ SV716 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2059]) ).
thf(2461,plain,
! [SV808: $i,SV717: $i,SV359: $i] :
( ( ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ( cOMBC_595898202l_bool @ SV359 ) @ SV717 ) @ SV808 )
= ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ SV359 @ SV808 ) @ SV717 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2060]) ).
thf(2462,plain,
! [SV809: $i,SV718: $i,SV360: $i] :
( ( ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ( cOMBC_7971162l_bool @ SV360 ) @ SV718 ) @ SV809 )
= ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ SV360 @ SV809 ) @ SV718 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2061]) ).
thf(2463,plain,
! [SV810: $i,SV719: $i,SV361: $i] :
( ( ( hAPP_f292226953l_bool @ ( hAPP_f1050622307l_bool @ ( cOMBC_636888218l_bool @ SV361 ) @ SV719 ) @ SV810 )
= ( hAPP_f292226953l_bool @ ( hAPP_f1050622307l_bool @ SV361 @ SV810 ) @ SV719 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2062]) ).
thf(2464,plain,
! [SV811: $i,SV720: $i,SV362: $i] :
( ( ( hAPP_f937997336l_bool @ ( hAPP_f760187903l_bool @ ( cOMBC_1269652216l_bool @ SV362 ) @ SV720 ) @ SV811 )
= ( hAPP_f937997336l_bool @ ( hAPP_f760187903l_bool @ SV362 @ SV811 ) @ SV720 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2063]) ).
thf(2465,plain,
! [SV812: $i,SV721: $i,SV363: $i] :
( ( ( hAPP_f389811538l_bool @ ( hAPP_f1759205631l_bool @ ( cOMBC_336095980l_bool @ SV363 ) @ SV721 ) @ SV812 )
= ( hAPP_f389811538l_bool @ ( hAPP_f1759205631l_bool @ SV363 @ SV812 ) @ SV721 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2064]) ).
thf(2466,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SX0 ) @ SX1 ) )
| ( hBOOL @ ( hAPP_nat_bool @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2065]) ).
thf(2467,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ SX1 @ SX0 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2066]) ).
thf(2468,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SX0 ) @ SX1 ) )
| ( hBOOL @ ( hAPP_pname_bool @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2067]) ).
thf(2469,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_pname_bool @ SX1 @ SX0 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2068]) ).
thf(2470,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fconj @ SX1 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2069]) ).
thf(2471,plain,
( ( ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ SX0 ) ) )
| ! [SX1: $i] : ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fconj @ SX1 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2070]) ).
thf(2472,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2071]) ).
thf(2473,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2072]) ).
thf(2474,plain,
! [SV364: $i] :
( ( ~ ( ~ ( is_fun_a_bool @ SV364 )
| ! [SY842: $i,SY843: $i] :
( ! [SY844: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY844 ) @ SY843 ) )
| ~ ( is_fun_pname_bool @ SY844 )
| ( SV364
!= ( image_pname_a @ SY842 @ SY844 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV364 ) @ ( image_pname_a @ SY842 @ SY843 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2073]) ).
thf(2475,plain,
! [SV364: $i] :
( ( ~ ( ~ ( is_fun_a_bool @ SV364 )
| ! [SY845: $i,SY846: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV364 ) @ ( image_pname_a @ SY845 @ SY846 ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( sK10_AA @ SY846 @ SY845 @ SV364 ) ) @ SY846 ) )
| ~ ( is_fun_pname_bool @ ( sK10_AA @ SY846 @ SY845 @ SV364 ) ) )
| ( SV364
!= ( image_pname_a @ SY845 @ ( sK10_AA @ SY846 @ SY845 @ SV364 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2073]) ).
thf(2476,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX0 ) @ ( hAPP_nat_nat @ suc @ SX1 ) ) )
| ( SX0
= ( hAPP_nat_nat @ suc @ SX1 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2074]) ).
thf(2477,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( hAPP_nat_nat @ suc @ SX1 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX0 ) @ ( hAPP_nat_nat @ suc @ SX1 ) ) ) )
| ~ ! [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 @ SX0 ) @ ( hAPP_nat_nat @ suc @ SX1 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2075]) ).
thf(2478,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(extcnf_not_neg,[status(thm)],[2076]) ).
thf(2479,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX0 ) @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2077]) ).
thf(2480,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SX1 ) )
| ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ SX0 ) @ SX1 ) )
| ( ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( insert_fun_nat_bool @ SX0 @ SX1 ) )
= ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2078]) ).
thf(2481,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SX1 ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ SX0 ) @ SX1 ) )
| ( ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( insert_fun_nat_bool @ SX0 @ SX1 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2079]) ).
thf(2482,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( is_fun_pname_bool @ SX0 )
| ~ ( is_fun_pname_bool @ 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 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2080]) ).
thf(2483,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( is_fun_pname_bool @ SX0 )
| ~ ( is_fun_pname_bool @ SX1 )
| ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SX0 ) @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( is_fun_pname_bool @ SX0 )
| ~ ( is_fun_pname_bool @ SX1 )
| ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2081]) ).
thf(2484,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ SX1 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2082]) ).
thf(2485,plain,
( ( ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ SX0 ) ) )
| ! [SX1: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ SX1 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2083]) ).
thf(2486,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( hAPP_nat_nat @ suc @ SX0 )
!= ( hAPP_nat_nat @ suc @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2084]) ).
thf(2487,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( hAPP_nat_nat @ suc @ SX0 )
= ( hAPP_nat_nat @ suc @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2085]) ).
thf(2488,plain,
! [SV365: $i] :
( ( ~ ! [SY847: $i,SY848: $i] :
( ~ ( is_pname @ SV365 )
| ~ ( is_pname @ SY848 )
| ~ ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV365 @ SY847 ) @ SY848 ) )
| ( SV365 = SY848 )
| ( hBOOL @ ( hAPP_pname_bool @ SY847 @ SY848 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2086]) ).
thf(2489,plain,
! [SV365: $i] :
( ( ~ ~ ( ~ ! [SY849: $i,SY850: $i] :
( ~ ( is_pname @ SV365 )
| ~ ( is_pname @ SY850 )
| ( SV365 != SY850 )
| ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV365 @ SY849 ) @ SY850 ) ) )
| ~ ! [SY851: $i,SY852: $i] :
( ~ ( is_pname @ SV365 )
| ~ ( is_pname @ SY852 )
| ~ ( hBOOL @ ( hAPP_pname_bool @ SY851 @ SY852 ) )
| ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV365 @ SY851 ) @ SY852 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2086]) ).
thf(2490,plain,
! [SV366: $i] :
( ( ~ ! [SY853: $i,SY854: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV366 ) @ ( insert_nat @ SY853 @ SY854 ) ) )
| ( SV366 = SY853 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV366 ) @ SY854 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2087]) ).
thf(2491,plain,
! [SV366: $i] :
( ( ~ ~ ( ~ ! [SY855: $i] :
( ( SV366 != SY855 )
| ! [SY856: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV366 ) @ ( insert_nat @ SY855 @ SY856 ) ) ) )
| ~ ! [SY857: $i,SY858: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV366 ) @ SY858 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV366 ) @ ( insert_nat @ SY857 @ SY858 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2087]) ).
thf(2492,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ SX0 @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2088]) ).
thf(2493,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(extcnf_not_neg,[status(thm)],[2089]) ).
thf(2494,plain,
! [SV367: $i] :
( ( ~ ! [SY859: $i] :
( ~ ( is_a @ SV367 )
| ~ ( is_a @ SY859 )
| ! [SY860: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ ( insert_a @ SY859 @ SY860 ) ) )
| ( SV367 = SY859 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ SY860 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2090]) ).
thf(2495,plain,
! [SV367: $i] :
( ( ~ ~ ( ~ ! [SY861: $i] :
( ~ ( is_a @ SV367 )
| ~ ( is_a @ SY861 )
| ( SV367 != SY861 )
| ! [SY862: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ ( insert_a @ SY861 @ SY862 ) ) ) )
| ~ ! [SY863: $i] :
( ~ ( is_a @ SV367 )
| ~ ( is_a @ SY863 )
| ! [SY864: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ SY864 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ ( insert_a @ SY863 @ SY864 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2090]) ).
thf(2496,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ SX1 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ SX1 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2091]) ).
thf(2497,plain,
( ( ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ SX0 ) ) )
| ! [SX1: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ SX1 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2092]) ).
thf(2498,plain,
! [SV368: $i] :
( ( ~ ! [SY865: $i,SY866: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY865 ) @ SY866 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY866 ) @ ( insert_a @ SY865 @ SV368 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY866 ) @ SV368 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2093]) ).
thf(2499,plain,
! [SV368: $i] :
( ( ~ ! [SY867: $i,SY868: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY867 ) @ SY868 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY868 ) @ SV368 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY868 ) @ ( insert_a @ SY867 @ SV368 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2093]) ).
thf(2500,plain,
! [SV369: $i] :
( ( ~ ( ~ ( is_a @ SV369 )
| ! [SY869: $i,SY870: $i] :
( ! [SY871: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SY871 ) @ SY870 ) )
| ~ ( is_pname @ SY871 )
| ( SV369
!= ( hAPP_pname_a @ SY869 @ SY871 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV369 ) @ ( image_pname_a @ SY869 @ SY870 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2094]) ).
thf(2501,plain,
! [SV369: $i] :
( ( ~ ( ~ ( is_a @ SV369 )
| ! [SY872: $i,SY873: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV369 ) @ ( image_pname_a @ SY872 @ SY873 ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK11_X_1 @ SY873 @ SY872 @ SV369 ) ) @ SY873 ) )
| ~ ( is_pname @ ( sK11_X_1 @ SY873 @ SY872 @ SV369 ) ) )
| ( SV369
!= ( hAPP_pname_a @ SY872 @ ( sK11_X_1 @ SY873 @ SY872 @ SV369 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2094]) ).
thf(2502,plain,
! [SV370: $i] :
( ( ~ ! [SY874: $i,SY875: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SY874 ) @ SY875 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY875 ) @ ( insert_nat @ SY874 @ SV370 ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY875 ) @ SV370 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2095]) ).
thf(2503,plain,
! [SV370: $i] :
( ( ~ ! [SY876: $i,SY877: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SY876 ) @ SY877 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY877 ) @ SV370 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY877 ) @ ( insert_nat @ SY876 @ SV370 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2095]) ).
thf(2504,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fconj @ SX1 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2096]) ).
thf(2505,plain,
( ( ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ SX0 ) ) )
| ! [SX1: $i] : ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fconj @ SX1 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2097]) ).
thf(2506,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SX0 @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2098]) ).
thf(2507,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SX1 ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2099]) ).
thf(2508,plain,
! [SV371: $i] :
( ( ~ ! [SY878: $i,SY879: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SY878 ) @ SY879 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SY878 ) @ ( insert_nat @ SV371 @ SY879 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2100]) ).
thf(2509,plain,
! [SV371: $i] :
( ( ~ ! [SY880: $i] :
( ( SY880 != SV371 )
| ! [SY881: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SY880 ) @ ( insert_nat @ SV371 @ SY881 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2100]) ).
thf(2510,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(extcnf_not_neg,[status(thm)],[2101]) ).
thf(2511,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 ) ) )
| ~ ! [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 @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2102]) ).
thf(2512,plain,
! [SV722: $i,SV372: $i,SV813: $i] :
( ( ~ ( is_fun_a_bool @ SV813 )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV813 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV813 ) @ ( image_pname_a @ SV372 @ SV722 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( sK17_C_2 @ SV813 @ SV722 @ SV372 ) ) @ SV722 ) )
| ~ ( is_fun_pname_bool @ ( sK17_C_2 @ SV813 @ SV722 @ SV372 ) ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( sK17_C_2 @ SV813 @ SV722 @ SV372 ) ) ) )
| ( SV813
!= ( image_pname_a @ SV372 @ ( sK17_C_2 @ SV813 @ SV722 @ SV372 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2103]) ).
thf(2513,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ SX1 ) ) @ SX0 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2104]) ).
thf(2514,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 @ ( hAPP_nat_nat @ suc @ SX1 ) ) @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2105]) ).
thf(2515,plain,
! [SV373: $i] :
( ( ~ ! [SY884: $i,SY885: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SY884 ) @ SY885 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SY884 ) @ ( insert_pname @ SV373 @ SY885 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2106]) ).
thf(2516,plain,
! [SV373: $i] :
( ( ~ ! [SY886: $i] :
( ( SY886 != SV373 )
| ! [SY887: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SY886 ) @ ( insert_pname @ SV373 @ SY887 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2106]) ).
thf(2517,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ SX0 ) ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ SX1 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ SX0 ) @ SX1 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2107]) ).
thf(2518,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ SX0 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ SX1 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2108]) ).
thf(2519,plain,
! [SV374: $i] :
( ( ~ ! [SY888: $i,SY889: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV374 ) @ SY889 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY888 ) @ SY889 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV374 @ SY888 ) ) @ SY889 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2109]) ).
thf(2520,plain,
! [SV374: $i] :
( ( ~ ~ ( ~ ! [SY890: $i,SY891: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV374 @ SY890 ) ) @ SY891 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV374 ) @ SY891 ) ) )
| ~ ! [SY892: $i,SY893: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV374 @ SY892 ) ) @ SY893 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY892 ) @ SY893 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2109]) ).
thf(2521,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ SX0 ) ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ SX0 ) @ SX1 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2110]) ).
thf(2522,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ SX0 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ SX1 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2111]) ).
thf(2523,plain,
! [SV375: $i,SV723: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV723 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_pname_a @ SV375 @ SV723 ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK12_X_1 @ SV723 @ SV375 ) ) @ SV723 ) )
| ~ ( is_pname @ ( sK12_X_1 @ SV723 @ SV375 ) ) )
| ~ ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ ( hAPP_f759274231e_bool @ ( cOMBC_1058051404l_bool @ member_pname ) @ SV723 ) ) @ ( hAPP_a93125764e_bool @ ( cOMBC_pname_a_bool @ ( cOMBB_1897541054_pname @ fequal_a @ SV375 ) ) @ ( hAPP_pname_a @ SV375 @ ( sK12_X_1 @ SV723 @ SV375 ) ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2112]) ).
thf(2524,plain,
! [SV376: $i] :
( ( ~ ! [SY895: $i,SY896: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV376 ) @ SY896 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY895 ) @ SY896 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( insert_nat @ SV376 @ SY895 ) ) @ SY896 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2113]) ).
thf(2525,plain,
! [SV376: $i] :
( ( ~ ~ ( ~ ! [SY897: $i,SY898: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( insert_nat @ SV376 @ SY897 ) ) @ SY898 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV376 ) @ SY898 ) ) )
| ~ ! [SY899: $i,SY900: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( insert_nat @ SV376 @ SY899 ) ) @ SY900 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY899 ) @ SY900 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2113]) ).
thf(2526,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SX1 ) )
| ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ SX0 ) @ SX1 ) )
| ( ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( insert1325755072e_bool @ SX0 @ SX1 ) )
= ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2114]) ).
thf(2527,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SX1 ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ SX0 ) @ SX1 ) )
| ( ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( insert1325755072e_bool @ SX0 @ SX1 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2115]) ).
thf(2528,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ SX0 @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2116]) ).
thf(2529,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(extcnf_not_neg,[status(thm)],[2117]) ).
thf(2530,plain,
! [SV377: $i] :
( ( ~ ! [SY901: $i,SY902: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SY901 ) @ SY902 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SY901 ) @ SV377 ) )
| ( ( insert_nat @ SY901 @ SY902 )
!= ( insert_nat @ SY901 @ SV377 ) )
| ( SY902 = SV377 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2118]) ).
thf(2531,plain,
! [SV377: $i] :
( ( ~ ! [SY903: $i,SY904: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SY903 ) @ SY904 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SY903 ) @ SV377 ) )
| ( SY904 != SV377 )
| ( ( insert_nat @ SY903 @ SY904 )
= ( insert_nat @ SY903 @ SV377 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2118]) ).
thf(2532,plain,
! [SV378: $i,SV724: $i] :
( ( ( ~ ( ~ ( is_a @ ( sK7_X_1 @ SV724 @ SV378 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( sK7_X_1 @ SV724 @ SV378 ) ) @ SV724 ) )
| ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( sK7_X_1 @ SV724 @ SV378 ) ) @ SV378 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV724 ) @ SV378 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2119]) ).
thf(2533,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX0 ) @ SX1 ) )
| ( hBOOL @ ( hAPP_a_bool @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2120]) ).
thf(2534,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_a_bool @ SX1 @ SX0 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2121]) ).
thf(2535,plain,
! [SV379: $i] :
( ( ~ ! [SY906: $i,SY907: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY906 ) @ SY907 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY906 ) @ ( insert_a @ SV379 @ SY907 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2122]) ).
thf(2536,plain,
! [SV379: $i] :
( ( ~ ! [SY908: $i] :
( ( SY908 != SV379 )
| ! [SY909: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY908 ) @ ( insert_a @ SV379 @ SY909 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2122]) ).
thf(2537,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SX1 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SX0 ) @ SX1 ) )
| ( ( hAPP_f22106695ol_nat @ finite_card_nat @ ( insert_nat @ SX0 @ SX1 ) )
= ( hAPP_f22106695ol_nat @ finite_card_nat @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2123]) ).
thf(2538,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SX1 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SX0 ) @ SX1 ) )
| ( ( hAPP_f22106695ol_nat @ finite_card_nat @ ( insert_nat @ SX0 @ SX1 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2124]) ).
thf(2539,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ SX0 @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2125]) ).
thf(2540,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(extcnf_not_neg,[status(thm)],[2126]) ).
thf(2541,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SX1 ) )
| ~ ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ SX0 ) @ SX1 ) )
| ( ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( insert_fun_a_bool @ SX0 @ SX1 ) )
= ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2127]) ).
thf(2542,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SX1 ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ SX0 ) @ SX1 ) )
| ( ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( insert_fun_a_bool @ SX0 @ SX1 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2128]) ).
thf(2543,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2129]) ).
thf(2544,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2130]) ).
thf(2545,plain,
! [SV380: $i,SV725: $i,SV814: $i] :
( ( ~ ( ~ ( is_pname @ ( sK3_X_1 @ SV814 @ SV725 @ SV380 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK3_X_1 @ SV814 @ SV725 @ SV380 ) ) @ SV814 ) )
| ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( hAPP_pname_a @ SV380 @ ( sK3_X_1 @ SV814 @ SV725 @ SV380 ) ) ) @ SV725 ) ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_pname_a @ SV380 @ SV814 ) ) @ SV725 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2131]) ).
thf(2546,plain,
! [SV381: $i] :
( ( ~ ! [SY912: $i,SY913: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY912 ) @ SY913 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY912 ) @ SV381 ) )
| ( ( hAPP_nat_nat @ ( minus_minus_nat @ SY913 ) @ SY912 )
!= ( hAPP_nat_nat @ ( minus_minus_nat @ SV381 ) @ SY912 ) )
| ( SY913 = SV381 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2132]) ).
thf(2547,plain,
! [SV381: $i] :
( ( ~ ! [SY914: $i,SY915: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY914 ) @ SY915 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY914 ) @ SV381 ) )
| ( SY915 != SV381 )
| ( ( hAPP_nat_nat @ ( minus_minus_nat @ SY915 ) @ SY914 )
= ( hAPP_nat_nat @ ( minus_minus_nat @ SV381 ) @ SY914 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2132]) ).
thf(2548,plain,
! [SV382: $i,SV726: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ ( sK8_X_1 @ SV726 @ SV382 ) ) @ SV726 ) )
| ~ ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ ( sK8_X_1 @ SV726 @ SV382 ) ) @ SV382 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV726 ) @ SV382 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2133]) ).
thf(2549,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ SX0 ) ) )
| ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ SX0 ) @ SX1 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2134]) ).
thf(2550,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ SX0 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ SX1 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2135]) ).
thf(2551,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fconj @ SX1 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2136]) ).
thf(2552,plain,
( ( ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ SX0 ) ) )
| ! [SX1: $i] : ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fconj @ SX1 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2137]) ).
thf(2553,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SX1 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX0 ) @ SX1 ) )
| ( ( hAPP_fun_a_bool_nat @ finite_card_a @ ( insert_a @ SX0 @ SX1 ) )
= ( hAPP_fun_a_bool_nat @ finite_card_a @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2138]) ).
thf(2554,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SX1 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX0 ) @ SX1 ) )
| ( ( hAPP_fun_a_bool_nat @ finite_card_a @ ( insert_a @ SX0 @ SX1 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2139]) ).
thf(2555,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SX1 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SX0 ) @ SX1 ) )
| ( ( hAPP_f921600141ol_nat @ finite_card_pname @ ( insert_pname @ SX0 @ SX1 ) )
= ( hAPP_f921600141ol_nat @ finite_card_pname @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2140]) ).
thf(2556,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SX1 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SX0 ) @ SX1 ) )
| ( ( hAPP_f921600141ol_nat @ finite_card_pname @ ( insert_pname @ SX0 @ SX1 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2141]) ).
thf(2557,plain,
! [SV383: $i] :
( ( ~ ! [SY917: $i] :
( ~ ( is_pname @ SV383 )
| ~ ( is_pname @ SY917 )
| ! [SY918: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ ( insert_pname @ SY917 @ SY918 ) ) )
| ( SV383 = SY917 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ SY918 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2142]) ).
thf(2558,plain,
! [SV383: $i] :
( ( ~ ~ ( ~ ! [SY919: $i] :
( ~ ( is_pname @ SV383 )
| ~ ( is_pname @ SY919 )
| ( SV383 != SY919 )
| ! [SY920: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ ( insert_pname @ SY919 @ SY920 ) ) ) )
| ~ ! [SY921: $i] :
( ~ ( is_pname @ SV383 )
| ~ ( is_pname @ SY921 )
| ! [SY922: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ SY922 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ ( insert_pname @ SY921 @ SY922 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2142]) ).
thf(2559,plain,
! [SV384: $i] :
( ( ~ ! [SY923: $i,SY924: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV384 ) @ SY924 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY923 ) @ SY924 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ SV384 @ SY923 ) ) @ SY924 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2143]) ).
thf(2560,plain,
! [SV384: $i] :
( ( ~ ~ ( ~ ! [SY925: $i,SY926: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ SV384 @ SY925 ) ) @ SY926 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV384 ) @ SY926 ) ) )
| ~ ! [SY927: $i,SY928: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ SV384 @ SY927 ) ) @ SY928 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY927 ) @ SY928 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2143]) ).
thf(2561,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ SX0 ) ) )
| ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ SX0 ) @ SX1 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2144]) ).
thf(2562,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ SX0 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ SX1 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2145]) ).
thf(2563,plain,
! [SV385: $i] :
( ( ~ ! [SY929: $i,SY930: $i] :
( ~ ( is_fun_a_bool @ SV385 )
| ~ ( is_fun_a_bool @ SY930 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY929 ) @ SY930 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY929 ) @ SV385 ) )
| ( ( insert_a @ SY929 @ SY930 )
!= ( insert_a @ SY929 @ SV385 ) )
| ( SY930 = SV385 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2146]) ).
thf(2564,plain,
! [SV385: $i] :
( ( ~ ! [SY931: $i,SY932: $i] :
( ~ ( is_fun_a_bool @ SV385 )
| ~ ( is_fun_a_bool @ SY932 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY931 ) @ SY932 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY931 ) @ SV385 ) )
| ( SY932 != SV385 )
| ( ( insert_a @ SY931 @ SY932 )
= ( insert_a @ SY931 @ SV385 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2146]) ).
thf(2565,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2147]) ).
thf(2566,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2148]) ).
thf(2567,plain,
! [SV386: $i] :
( ( ~ ! [SY933: $i,SY934: $i] :
( ~ ( is_a @ SV386 )
| ~ ( is_a @ SY934 )
| ~ ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV386 @ SY933 ) @ SY934 ) )
| ( SV386 = SY934 )
| ( hBOOL @ ( hAPP_a_bool @ SY933 @ SY934 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2149]) ).
thf(2568,plain,
! [SV386: $i] :
( ( ~ ~ ( ~ ! [SY935: $i,SY936: $i] :
( ~ ( is_a @ SV386 )
| ~ ( is_a @ SY936 )
| ( SV386 != SY936 )
| ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV386 @ SY935 ) @ SY936 ) ) )
| ~ ! [SY937: $i,SY938: $i] :
( ~ ( is_a @ SV386 )
| ~ ( is_a @ SY938 )
| ~ ( hBOOL @ ( hAPP_a_bool @ SY937 @ SY938 ) )
| ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV386 @ SY937 ) @ SY938 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2149]) ).
thf(2569,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ SX1 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2150]) ).
thf(2570,plain,
( ( ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ SX0 ) ) )
| ! [SX1: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ SX1 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2151]) ).
thf(2571,plain,
! [SV387: $i] :
( ( ( is_a @ SV387 )
= $false )
| ( ( ! [SY939: $i,SY940: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV387 ) @ ( image_pname_a @ SY939 @ SY940 ) ) )
| ~ ( ~ ( is_pname @ ( sK9_X_1 @ SY940 @ SY939 @ SV387 ) )
| ~ ~ ( ( SV387
!= ( hAPP_pname_a @ SY939 @ ( sK9_X_1 @ SY940 @ SY939 @ SV387 ) ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK9_X_1 @ SY940 @ SY939 @ SV387 ) ) @ SY940 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2152]) ).
thf(2572,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ SX0 @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2153]) ).
thf(2573,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(extcnf_not_neg,[status(thm)],[2154]) ).
thf(2574,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ SX0 ) ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ SX0 ) @ SX1 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2155]) ).
thf(2575,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ SX0 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ SX1 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2156]) ).
thf(2576,plain,
! [SV388: $i,SV815: $i,SV727: $i] :
( ( ~ ( hBOOL @ ( hAPP_nat_bool @ SV727 @ SV815 ) )
| ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ SV727 @ ( hAPP_nat_nat @ suc @ ( sK5_N_2 @ SV815 @ SV727 @ SV388 ) ) ) )
| ~ ~ ( hBOOL @ ( hAPP_nat_bool @ SV727 @ ( sK5_N_2 @ SV815 @ SV727 @ SV388 ) ) ) )
| ( hBOOL @ ( hAPP_nat_bool @ SV727 @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV815 ) @ SV388 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2157]) ).
thf(2577,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ SX0 ) ) )
| ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ SX0 ) @ SX1 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2158]) ).
thf(2578,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ SX0 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ SX1 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2159]) ).
thf(2579,plain,
! [SV389: $i] :
( ( ~ ! [SY943: $i,SY944: $i] :
( ~ ( is_fun_pname_bool @ SV389 )
| ~ ( is_fun_pname_bool @ SY944 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SY943 ) @ SY944 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SY943 ) @ SV389 ) )
| ( ( insert_pname @ SY943 @ SY944 )
!= ( insert_pname @ SY943 @ SV389 ) )
| ( SY944 = SV389 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2160]) ).
thf(2580,plain,
! [SV389: $i] :
( ( ~ ! [SY945: $i,SY946: $i] :
( ~ ( is_fun_pname_bool @ SV389 )
| ~ ( is_fun_pname_bool @ SY946 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SY945 ) @ SY946 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SY945 ) @ SV389 ) )
| ( SY946 != SV389 )
| ( ( insert_pname @ SY945 @ SY946 )
= ( insert_pname @ SY945 @ SV389 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2160]) ).
thf(2581,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ SX0 ) ) @ ( hAPP_nat_nat @ suc @ SX1 ) ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2161]) ).
thf(2582,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 @ ( hAPP_nat_nat @ suc @ SX0 ) ) @ ( hAPP_nat_nat @ suc @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2162]) ).
thf(2583,plain,
! [SV390: $i] :
( ( ~ ! [SY947: $i,SY948: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SY947 ) @ SY948 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY948 ) @ ( insert_pname @ SY947 @ SV390 ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY948 ) @ SV390 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2163]) ).
thf(2584,plain,
! [SV390: $i] :
( ( ~ ! [SY949: $i,SY950: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SY949 ) @ SY950 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY950 ) @ SV390 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY950 ) @ ( insert_pname @ SY949 @ SV390 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2163]) ).
thf(2585,plain,
! [SV391: $i] :
( ( ~ ! [SY951: $i,SY952: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY951 ) @ SY952 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY951 ) @ SV391 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ SY952 ) @ SY951 ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV391 ) @ SY951 ) ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY952 ) @ SV391 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2164]) ).
thf(2586,plain,
! [SV391: $i] :
( ( ~ ! [SY953: $i,SY954: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY953 ) @ SY954 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY953 ) @ SV391 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY954 ) @ SV391 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ SY954 ) @ SY953 ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV391 ) @ SY953 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2164]) ).
thf(2587,plain,
! [SV392: $i,SV728: $i] :
( ( ( ~ ( ~ ( is_pname @ ( sK6_X_1 @ SV728 @ SV392 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK6_X_1 @ SV728 @ SV392 ) ) @ SV728 ) )
| ~ ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK6_X_1 @ SV728 @ SV392 ) ) @ SV392 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV728 ) @ SV392 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2165]) ).
thf(2588,plain,
! [SV393: $i] :
( ( ~ ! [SY956: $i,SY957: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV393 @ SY956 ) @ SY957 ) )
| ( SV393 = SY957 )
| ( hBOOL @ ( hAPP_nat_bool @ SY956 @ SY957 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2166]) ).
thf(2589,plain,
! [SV393: $i] :
( ( ~ ~ ( ~ ! [SY958: $i,SY959: $i] :
( ( SV393 != SY959 )
| ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV393 @ SY958 ) @ SY959 ) ) )
| ~ ! [SY960: $i,SY961: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ SY960 @ SY961 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV393 @ SY960 ) @ SY961 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2166]) ).
thf(2590,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ ( sK2_X_1 @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( sK2_X_1 @ SX1 @ SX0 ) ) @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2167]) ).
thf(2591,plain,
( ( ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SX0 ) )
| ! [SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX1 ) @ ( sK1_M @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2168]) ).
thf(2592,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 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2169]) ).
thf(2593,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(extcnf_not_neg,[status(thm)],[2170]) ).
thf(2594,plain,
! [SV1: $i,SV394: $i] :
( ( ( is_fun_pname_bool @ SV394 )
= $false )
| ( ( is_fun_a_bool @ ( image_pname_a @ SV1 @ SV394 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2171]) ).
thf(2595,plain,
! [SV395: $i,SV2: $i] :
( ( ( ~ ( is_a @ SV2 ) )
= $true )
| ( ( ~ ( is_fun_a_bool @ SV395 ) )
= $true )
| ( ( is_fun_a_bool @ ( insert_a @ SV2 @ SV395 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2172]) ).
thf(2596,plain,
! [SV3: $i,SV396: $i] :
( ( ( is_a @ SV396 )
= $false )
| ( ( is_fun949378684l_bool @ ( hAPP_a85458249l_bool @ SV3 @ SV396 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2173]) ).
thf(2597,plain,
! [SV4: $i,SV397: $i] :
( ( ( is_pname @ SV397 )
= $false )
| ( ( is_a @ ( hAPP_pname_a @ SV4 @ SV397 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2174]) ).
thf(2598,plain,
! [SV5: $i,SV398: $i] :
( ( ( is_pname @ SV398 )
= $false )
| ( ( is_fun1661590463l_bool @ ( hAPP_p338031245l_bool @ SV5 @ SV398 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2175]) ).
thf(2599,plain,
! [SV400: $i,SV7: $i] :
( ( ( ~ ( is_fun949378684l_bool @ SV7 ) )
= $true )
| ( ( ~ ( is_fun_a_bool @ SV400 ) )
= $true )
| ( ( is_bool @ ( hAPP_fun_a_bool_bool @ SV7 @ SV400 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2176]) ).
thf(2600,plain,
! [SV8: $i,SV401: $i] :
( ( ( is_fun_a_bool @ SV401 )
= $false )
| ( ( is_fun949378684l_bool @ ( hAPP_f1631501043l_bool @ SV8 @ SV401 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2177]) ).
thf(2601,plain,
! [SV402: $i,SV9: $i] :
( ( ( ~ ( is_fun1661590463l_bool @ SV9 ) )
= $true )
| ( ( ~ ( is_fun_pname_bool @ SV402 ) )
= $true )
| ( ( is_bool @ ( hAPP_f1664156314l_bool @ SV9 @ SV402 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2178]) ).
thf(2602,plain,
! [SV10: $i,SV403: $i] :
( ( ( is_fun_a_bool @ SV403 )
= $false )
| ( ( is_fun_a_bool @ ( cOMBB_bool_bool_a @ SV10 @ SV403 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2179]) ).
thf(2603,plain,
! [SV11: $i,SV404: $i] :
( ( ( is_fun_pname_bool @ SV404 )
= $false )
| ( ( is_fun_pname_bool @ ( cOMBB_647938656_pname @ SV11 @ SV404 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2180]) ).
thf(2604,plain,
! [SV12: $i,SV405: $i] :
( ( ( is_fun949378684l_bool @ SV405 )
= $false )
| ( ( is_fun949378684l_bool @ ( cOMBB_2140588453a_bool @ SV12 @ SV405 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2181]) ).
thf(2605,plain,
! [SV13: $i,SV406: $i] :
( ( ( is_fun1661590463l_bool @ SV406 )
= $false )
| ( ( is_fun1661590463l_bool @ ( cOMBB_307249310e_bool @ SV13 @ SV406 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2182]) ).
thf(2606,plain,
! [SV14: $i,SV407: $i] :
( ( ( is_fun_a_bool @ SV407 )
= $false )
| ( ( is_fun_a_bool @ ( cOMBS_a_bool_bool @ SV14 @ SV407 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2183]) ).
thf(2607,plain,
! [SV15: $i,SV408: $i] :
( ( ( is_fun_pname_bool @ SV408 )
= $false )
| ( ( is_fun_pname_bool @ ( cOMBS_568398431l_bool @ SV15 @ SV408 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2184]) ).
thf(2608,plain,
! [SV16: $i,SV409: $i] :
( ( ( is_fun949378684l_bool @ SV409 )
= $false )
| ( ( is_fun949378684l_bool @ ( cOMBS_1035972772l_bool @ SV16 @ SV409 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2185]) ).
thf(2609,plain,
! [SV17: $i,SV410: $i] :
( ( ( is_fun1661590463l_bool @ SV410 )
= $false )
| ( ( is_fun1661590463l_bool @ ( cOMBS_350070575l_bool @ SV17 @ SV410 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2186]) ).
thf(2610,plain,
! [SV22: $i,SV411: $i] :
( ( ( is_fun_a_bool @ SV411 )
= $false )
| ( ( is_fun_a_bool @ ( image_a_a @ SV22 @ SV411 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2191]) ).
thf(2611,plain,
! [SV23: $i,SV412: $i] :
( ( ( is_fun_a_bool @ SV412 )
= $false )
| ( ( is_fun_pname_bool @ ( image_a_pname @ SV23 @ SV412 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2192]) ).
thf(2612,plain,
! [SV24: $i,SV413: $i] :
( ( ( is_fun_pname_bool @ SV413 )
= $false )
| ( ( is_fun_pname_bool @ ( image_pname_pname @ SV24 @ SV413 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2193]) ).
thf(2613,plain,
! [SV25: $i,SV414: $i] :
( ( ( is_fun_pname_bool @ SV414 )
= $false )
| ( ( is_fun949378684l_bool @ ( image_112932426a_bool @ SV25 @ SV414 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2194]) ).
thf(2614,plain,
! [SV26: $i,SV415: $i] :
( ( ( is_fun_pname_bool @ SV415 )
= $false )
| ( ( is_fun1661590463l_bool @ ( image_47868345e_bool @ SV26 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2195]) ).
thf(2615,plain,
! [SV31: $i,SV420: $i] :
( ( ( is_fun949378684l_bool @ SV420 )
= $false )
| ( ( is_fun_a_bool @ ( image_fun_a_bool_a @ SV31 @ SV420 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2196]) ).
thf(2616,plain,
! [SV32: $i,SV421: $i] :
( ( ( is_fun949378684l_bool @ SV421 )
= $false )
| ( ( is_fun_pname_bool @ ( image_1854862208_pname @ SV32 @ SV421 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2197]) ).
thf(2617,plain,
! [SV33: $i,SV422: $i] :
( ( ( is_fun1661590463l_bool @ SV422 )
= $false )
| ( ( is_fun_a_bool @ ( image_876012084bool_a @ SV33 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2198]) ).
thf(2618,plain,
! [SV34: $i,SV423: $i] :
( ( ( is_fun1661590463l_bool @ SV423 )
= $false )
| ( ( is_fun_pname_bool @ ( image_1283814551_pname @ SV34 @ SV423 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2199]) ).
thf(2619,plain,
! [SV43: $i,SV432: $i] :
( ( ( ~ ( is_fun_pname_bool @ SV432 ) )
= $true )
| ( ( ~ ( is_pname @ SV43 ) )
= $true )
| ( ( is_fun_pname_bool @ ( insert_pname @ SV43 @ SV432 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2200]) ).
thf(2620,plain,
! [SV44: $i,SV433: $i] :
( ( ( ~ ( is_fun949378684l_bool @ SV433 ) )
= $true )
| ( ( ~ ( is_fun_a_bool @ SV44 ) )
= $true )
| ( ( is_fun949378684l_bool @ ( insert_fun_a_bool @ SV44 @ SV433 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2201]) ).
thf(2621,plain,
! [SV45: $i,SV434: $i] :
( ( ( ~ ( is_fun1661590463l_bool @ SV434 ) )
= $true )
| ( ( ~ ( is_fun_pname_bool @ SV45 ) )
= $true )
| ( ( is_fun1661590463l_bool @ ( insert1325755072e_bool @ SV45 @ SV434 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2202]) ).
thf(2622,plain,
! [SV46: $i,SV435: $i] :
( ( ( ~ ( is_a @ SV435 ) )
= $true )
| ( ( ~ ( is_fun_a_bool @ SV46 ) )
= $true )
| ( ( is_bool @ ( hAPP_a_bool @ SV46 @ SV435 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2203]) ).
thf(2623,plain,
! [SV47: $i,SV436: $i] :
( ( ( is_a @ SV436 )
= $false )
| ( ( is_fun_a_bool @ ( hAPP_a_fun_a_bool @ SV47 @ SV436 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2204]) ).
thf(2624,plain,
! [SV48: $i,SV437: $i] :
( ( ( is_a @ SV437 )
= $false )
| ( ( is_fun_pname_bool @ ( hAPP_a93125764e_bool @ SV48 @ SV437 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2205]) ).
thf(2625,plain,
! [SV438: $i,SV49: $i] :
( ( ( ~ ( is_fun_pname_bool @ SV49 ) )
= $true )
| ( ( ~ ( is_pname @ SV438 ) )
= $true )
| ( ( is_bool @ ( hAPP_pname_bool @ SV49 @ SV438 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2206]) ).
thf(2626,plain,
! [SV50: $i,SV439: $i] :
( ( ( is_pname @ SV439 )
= $false )
| ( ( is_fun_a_bool @ ( hAPP_p1534023578a_bool @ SV50 @ SV439 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2207]) ).
thf(2627,plain,
! [SV51: $i,SV440: $i] :
( ( ( is_pname @ SV440 )
= $false )
| ( ( is_fun_pname_bool @ ( hAPP_p61793385e_bool @ SV51 @ SV440 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2208]) ).
thf(2628,plain,
! [SV52: $i,SV441: $i] :
( ( ( is_bool @ SV441 )
= $false )
| ( ( is_bool @ ( hAPP_bool_bool @ SV52 @ SV441 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2209]) ).
thf(2629,plain,
! [SV55: $i,SV444: $i] :
( ( ( is_fun_a_bool @ SV444 )
= $false )
| ( ( is_fun_a_bool @ ( hAPP_f2050579477a_bool @ SV55 @ SV444 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2210]) ).
thf(2630,plain,
! [SV56: $i,SV445: $i] :
( ( ( is_fun_pname_bool @ SV445 )
= $false )
| ( ( is_fun_pname_bool @ ( hAPP_f759274231e_bool @ SV56 @ SV445 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2211]) ).
thf(2631,plain,
! [SV57: $i,SV446: $i] :
( ( ( is_fun_pname_bool @ SV446 )
= $false )
| ( ( is_fun1661590463l_bool @ ( hAPP_f434788991l_bool @ SV57 @ SV446 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2212]) ).
thf(2632,plain,
! [SV59: $i,SV448: $i] :
( ( ( is_fun949378684l_bool @ SV448 )
= $false )
| ( ( is_bool @ ( hAPP_f621171935l_bool @ SV59 @ SV448 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2213]) ).
thf(2633,plain,
! [SV60: $i,SV449: $i] :
( ( ( is_fun949378684l_bool @ SV449 )
= $false )
| ( ( is_fun949378684l_bool @ ( hAPP_f2117159681l_bool @ SV60 @ SV449 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2214]) ).
thf(2634,plain,
! [SV61: $i,SV450: $i] :
( ( ( is_fun1661590463l_bool @ SV450 )
= $false )
| ( ( is_bool @ ( hAPP_f1935102916l_bool @ SV61 @ SV450 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2215]) ).
thf(2635,plain,
! [SV62: $i,SV451: $i] :
( ( ( is_fun1661590463l_bool @ SV451 )
= $false )
| ( ( is_fun1661590463l_bool @ ( hAPP_f559147733l_bool @ SV62 @ SV451 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2216]) ).
thf(2636,plain,
! [SV459: $i,SV71: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV71 ) @ SV459 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( p @ SV459 ) @ SV71 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2218]) ).
thf(2637,plain,
! [SV81: $i,SV460: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV460 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_pname_a @ SV81 @ SV460 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2228]) ).
thf(2638,plain,
! [SV82: $i,SV461: $i] :
( ( ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ SV461 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_2089570637ol_nat @ SV82 @ SV461 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2229]) ).
thf(2639,plain,
! [SV83: $i,SV462: $i] :
( ( ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ SV462 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_1079571347ol_nat @ SV83 @ SV462 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2230]) ).
thf(2640,plain,
! [SV84: $i,SV463: $i] :
( ( ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ SV463 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_1802975832ol_nat @ SV84 @ SV463 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2231]) ).
thf(2641,plain,
! [SV85: $i,SV464: $i] :
( ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV464 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_fun_a_bool_nat @ SV85 @ SV464 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2232]) ).
thf(2642,plain,
! [SV86: $i,SV465: $i] :
( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV465 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_1551609309ol_nat @ SV86 @ SV465 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2233]) ).
thf(2643,plain,
! [SV87: $i,SV466: $i] :
( ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV466 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_496248727ol_nat @ SV87 @ SV466 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2234]) ).
thf(2644,plain,
! [SV88: $i,SV467: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV467 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_a_nat @ SV88 @ SV467 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2235]) ).
thf(2645,plain,
! [SV89: $i,SV468: $i] :
( ( ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ SV468 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1604018183_pname @ SV89 @ SV468 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2236]) ).
thf(2646,plain,
! [SV90: $i,SV469: $i] :
( ( ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ SV469 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1705983821_pname @ SV90 @ SV469 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2237]) ).
thf(2647,plain,
! [SV91: $i,SV470: $i] :
( ( ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ SV470 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_990671762_pname @ SV91 @ SV470 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2238]) ).
thf(2648,plain,
! [SV92: $i,SV471: $i] :
( ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV471 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1854862208_pname @ SV92 @ SV471 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2239]) ).
thf(2649,plain,
! [SV93: $i,SV472: $i] :
( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV472 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1283814551_pname @ SV93 @ SV472 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2240]) ).
thf(2650,plain,
! [SV94: $i,SV473: $i] :
( ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV473 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1921560913_pname @ SV94 @ SV473 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2241]) ).
thf(2651,plain,
! [SV95: $i,SV474: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV474 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_a_pname @ SV95 @ SV474 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2242]) ).
thf(2652,plain,
! [SV96: $i,SV475: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV475 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ ( image_1607900221l_bool @ SV96 @ SV475 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2243]) ).
thf(2653,plain,
! [SV97: $i,SV476: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV476 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ ( image_1874789623l_bool @ SV97 @ SV476 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2244]) ).
thf(2654,plain,
! [SV98: $i,SV477: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV477 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ ( image_1208015684l_bool @ SV98 @ SV477 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2245]) ).
thf(2655,plain,
! [SV99: $i,SV478: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV478 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( image_nat_fun_a_bool @ SV99 @ SV478 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2246]) ).
thf(2656,plain,
! [SV100: $i,SV479: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV479 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( image_1655916159e_bool @ SV100 @ SV479 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2247]) ).
thf(2657,plain,
! [SV101: $i,SV480: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV480 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( image_26036933t_bool @ SV101 @ SV480 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2248]) ).
thf(2658,plain,
! [SV102: $i,SV481: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV481 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_nat_a @ SV102 @ SV481 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2249]) ).
thf(2659,plain,
! [SV103: $i,SV482: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV482 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ ( image_1154884483l_bool @ SV103 @ SV482 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2250]) ).
thf(2660,plain,
! [SV104: $i,SV483: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV483 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ ( image_1642285373l_bool @ SV104 @ SV483 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2251]) ).
thf(2661,plain,
! [SV105: $i,SV484: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV484 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ ( image_1420695166l_bool @ SV105 @ SV484 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2252]) ).
thf(2662,plain,
! [SV106: $i,SV485: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV485 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( image_112932426a_bool @ SV106 @ SV485 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2253]) ).
thf(2663,plain,
! [SV107: $i,SV486: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV486 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( image_47868345e_bool @ SV107 @ SV486 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2254]) ).
thf(2664,plain,
! [SV108: $i,SV487: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV487 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( image_2129980159t_bool @ SV108 @ SV487 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2255]) ).
thf(2665,plain,
! [SV109: $i,SV488: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV488 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_pname_pname @ SV109 @ SV488 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2256]) ).
thf(2666,plain,
! [SV110: $i,SV489: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV489 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_a_a @ SV110 @ SV489 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2257]) ).
thf(2667,plain,
! [SV111: $i,SV490: $i] :
( ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV490 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_fun_nat_bool_a @ SV111 @ SV490 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2258]) ).
thf(2668,plain,
! [SV112: $i,SV491: $i] :
( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV491 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_876012084bool_a @ SV112 @ SV491 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2259]) ).
thf(2669,plain,
! [SV113: $i,SV492: $i] :
( ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV492 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_fun_a_bool_a @ SV113 @ SV492 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2260]) ).
thf(2670,plain,
! [SV114: $i,SV493: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV493 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_pname_nat @ SV114 @ SV493 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2261]) ).
thf(2671,plain,
! [SV115: $i,SV494: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV494 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_nat_pname @ SV115 @ SV494 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2262]) ).
thf(2672,plain,
! [SV116: $i,SV495: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV495 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ SV116 @ SV495 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2263]) ).
thf(2673,plain,
! [SV117: $i,SV496: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV496 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ SV117 @ SV496 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2264]) ).
thf(2674,plain,
! [SV118: $i,SV497: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV497 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ SV118 @ SV497 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2265]) ).
thf(2675,plain,
! [SV119: $i,SV498: $i] :
( ( ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ SV498 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ ( insert2003652156l_bool @ SV119 @ SV498 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2266]) ).
thf(2676,plain,
! [SV120: $i,SV499: $i] :
( ( ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ SV499 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ ( insert1117693814l_bool @ SV120 @ SV499 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2267]) ).
thf(2677,plain,
! [SV121: $i,SV500: $i] :
( ( ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ SV500 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ ( insert1457093509l_bool @ SV121 @ SV500 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2268]) ).
thf(2678,plain,
! [SV122: $i,SV501: $i] :
( ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV501 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ SV122 @ SV501 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2269]) ).
thf(2679,plain,
! [SV123: $i,SV502: $i] :
( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV502 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SV123 @ SV502 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2270]) ).
thf(2680,plain,
! [SV124: $i,SV503: $i] :
( ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV503 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ SV124 @ SV503 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2271]) ).
thf(2681,plain,
! [SV125: $i,SV504: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV504 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( image_pname_nat @ SV125 @ SV504 ) ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV504 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2272]) ).
thf(2682,plain,
! [SV126: $i,SV505: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV505 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( image_a_nat @ SV126 @ SV505 ) ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SV505 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2273]) ).
thf(2683,plain,
! [SV127: $i,SV506: $i] :
( ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV506 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( image_496248727ol_nat @ SV127 @ SV506 ) ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SV506 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2274]) ).
thf(2684,plain,
! [SV128: $i,SV507: $i] :
( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV507 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( image_1551609309ol_nat @ SV128 @ SV507 ) ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SV507 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2275]) ).
thf(2685,plain,
! [SV129: $i,SV508: $i] :
( ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV508 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( image_fun_a_bool_nat @ SV129 @ SV508 ) ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SV508 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2276]) ).
thf(2686,plain,
! [SV130: $i,SV509: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV509 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( image_a_pname @ SV130 @ SV509 ) ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SV509 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2277]) ).
thf(2687,plain,
! [SV131: $i,SV510: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV510 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( image_nat_pname @ SV131 @ SV510 ) ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SV510 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2278]) ).
thf(2688,plain,
! [SV132: $i,SV511: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV511 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_pname_a @ SV132 @ SV511 ) ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV511 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2279]) ).
thf(2689,plain,
! [SV133: $i,SV512: $i] :
( ( ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ SV512 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_526090948bool_a @ SV133 @ SV512 ) ) ) @ ( hAPP_f1690079119ol_nat @ finite1352710292l_bool @ SV512 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2280]) ).
thf(2690,plain,
! [SV134: $i,SV513: $i] :
( ( ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ SV513 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_349102846bool_a @ SV134 @ SV513 ) ) ) @ ( hAPP_f98387925ol_nat @ finite269641166l_bool @ SV513 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2281]) ).
thf(2691,plain,
! [SV135: $i,SV514: $i] :
( ( ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ SV514 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_573985017bool_a @ SV135 @ SV514 ) ) ) @ ( hAPP_f1253658590ol_nat @ finite1659325229l_bool @ SV514 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2282]) ).
thf(2692,plain,
! [SV136: $i,SV515: $i] :
( ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV515 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_fun_a_bool_a @ SV136 @ SV515 ) ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SV515 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2283]) ).
thf(2693,plain,
! [SV137: $i,SV516: $i] :
( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV516 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_876012084bool_a @ SV137 @ SV516 ) ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SV516 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2284]) ).
thf(2694,plain,
! [SV138: $i,SV517: $i] :
( ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV517 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_fun_nat_bool_a @ SV138 @ SV517 ) ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SV517 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2285]) ).
thf(2695,plain,
! [SV139: $i,SV518: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV518 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_a_a @ SV139 @ SV518 ) ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SV518 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2286]) ).
thf(2696,plain,
! [SV140: $i,SV519: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV519 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( image_pname_pname @ SV140 @ SV519 ) ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV519 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2287]) ).
thf(2697,plain,
! [SV141: $i,SV520: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV520 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( image_2129980159t_bool @ SV141 @ SV520 ) ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV520 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2288]) ).
thf(2698,plain,
! [SV142: $i,SV521: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV521 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( image_47868345e_bool @ SV142 @ SV521 ) ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV521 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2289]) ).
thf(2699,plain,
! [SV143: $i,SV522: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV522 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( image_112932426a_bool @ SV143 @ SV522 ) ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV522 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2290]) ).
thf(2700,plain,
! [SV144: $i,SV523: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV523 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_nat_a @ SV144 @ SV523 ) ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SV523 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2291]) ).
thf(2701,plain,
! [SV145: $i,SV524: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV524 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( image_26036933t_bool @ SV145 @ SV524 ) ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SV524 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2292]) ).
thf(2702,plain,
! [SV146: $i,SV525: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV525 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( image_1655916159e_bool @ SV146 @ SV525 ) ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SV525 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2293]) ).
thf(2703,plain,
! [SV147: $i,SV526: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV526 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( image_nat_fun_a_bool @ SV147 @ SV526 ) ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SV526 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2294]) ).
thf(2704,plain,
! [SV148: $i,SV527: $i] :
( ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV527 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( image_1921560913_pname @ SV148 @ SV527 ) ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SV527 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2295]) ).
thf(2705,plain,
! [SV149: $i,SV528: $i] :
( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV528 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( image_1283814551_pname @ SV149 @ SV528 ) ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SV528 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2296]) ).
thf(2706,plain,
! [SV150: $i,SV529: $i] :
( ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV529 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( image_1854862208_pname @ SV150 @ SV529 ) ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SV529 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2297]) ).
thf(2707,plain,
! [SV151: $i,SV530: $i] :
( ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV530 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ SV151 ) @ SV530 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SV151 ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SV530 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2298]) ).
thf(2708,plain,
! [SV152: $i,SV531: $i] :
( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV531 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ SV152 ) @ SV531 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SV152 ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SV531 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2299]) ).
thf(2709,plain,
! [SV153: $i,SV532: $i] :
( ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV532 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ SV153 ) @ SV532 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SV153 ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SV532 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2300]) ).
thf(2710,plain,
! [SV154: $i,SV533: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV533 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV154 ) @ SV533 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV154 ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV533 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2301]) ).
thf(2711,plain,
! [SV155: $i,SV534: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV534 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV155 ) @ SV534 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SV155 ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SV534 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2302]) ).
thf(2712,plain,
! [SV156: $i,SV535: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV535 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV156 ) @ SV535 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SV156 ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SV535 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2303]) ).
thf(2713,plain,
! [SV157: $i,SV536: $i] :
( ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV536 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ SV157 ) @ SV536 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SV536 ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SV157 ) ) )
| ( SV157 = SV536 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2304]) ).
thf(2714,plain,
! [SV537: $i,SV158: $i] :
( ( ( ~ ( is_fun1661590463l_bool @ SV158 ) )
= $true )
| ( ( ~ ( is_fun1661590463l_bool @ SV537 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV537 ) )
| ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ SV158 ) @ SV537 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SV537 ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SV158 ) ) )
| ( SV158 = SV537 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2305]) ).
thf(2715,plain,
! [SV538: $i,SV159: $i] :
( ( ( ~ ( is_fun949378684l_bool @ SV159 ) )
= $true )
| ( ( ~ ( is_fun949378684l_bool @ SV538 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV538 ) )
| ~ ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ SV159 ) @ SV538 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SV538 ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SV159 ) ) )
| ( SV159 = SV538 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2306]) ).
thf(2716,plain,
! [SV539: $i,SV160: $i] :
( ( ( ~ ( is_fun_pname_bool @ SV160 ) )
= $true )
| ( ( ~ ( is_fun_pname_bool @ SV539 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV539 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV160 ) @ SV539 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV539 ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV160 ) ) )
| ( SV160 = SV539 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2307]) ).
thf(2717,plain,
! [SV540: $i,SV161: $i] :
( ( ( ~ ( is_fun_a_bool @ SV161 ) )
= $true )
| ( ( ~ ( is_fun_a_bool @ SV540 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV540 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV161 ) @ SV540 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SV540 ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SV161 ) ) )
| ( SV161 = SV540 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2308]) ).
thf(2718,plain,
! [SV162: $i,SV541: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV541 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV162 ) @ SV541 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SV541 ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SV162 ) ) )
| ( SV162 = SV541 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2309]) ).
thf(2719,plain,
! [SV163: $i,SV542: $i] :
( ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV542 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SV542 ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( insert_fun_nat_bool @ SV163 @ SV542 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2310]) ).
thf(2720,plain,
! [SV164: $i,SV543: $i] :
( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV543 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SV543 ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( insert1325755072e_bool @ SV164 @ SV543 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2311]) ).
thf(2721,plain,
! [SV165: $i,SV544: $i] :
( ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV544 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SV544 ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( insert_fun_a_bool @ SV165 @ SV544 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2312]) ).
thf(2722,plain,
! [SV166: $i,SV545: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV545 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV545 ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( insert_pname @ SV166 @ SV545 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2313]) ).
thf(2723,plain,
! [SV167: $i,SV546: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV546 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SV546 ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( insert_nat @ SV167 @ SV546 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2314]) ).
thf(2724,plain,
! [SV168: $i,SV547: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV547 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SV547 ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( insert_a @ SV168 @ SV547 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2315]) ).
thf(2725,plain,
! [SV169: $i,SV548: $i] :
( ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV548 ) )
= $false )
| ( ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ SV169 ) @ SV548 ) )
| ( ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( insert_fun_nat_bool @ SV169 @ SV548 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SV548 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2316]) ).
thf(2726,plain,
! [SV170: $i,SV549: $i] :
( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV549 ) )
= $false )
| ( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ SV170 ) @ SV549 ) )
| ( ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( insert1325755072e_bool @ SV170 @ SV549 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SV549 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2317]) ).
thf(2727,plain,
! [SV171: $i,SV550: $i] :
( ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV550 ) )
= $false )
| ( ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ SV171 ) @ SV550 ) )
| ( ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( insert_fun_a_bool @ SV171 @ SV550 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SV550 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2318]) ).
thf(2728,plain,
! [SV172: $i,SV551: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV551 ) )
= $false )
| ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV172 ) @ SV551 ) )
| ( ( hAPP_f22106695ol_nat @ finite_card_nat @ ( insert_nat @ SV172 @ SV551 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SV551 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2319]) ).
thf(2729,plain,
! [SV173: $i,SV552: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV552 ) )
= $false )
| ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV173 ) @ SV552 ) )
| ( ( hAPP_f921600141ol_nat @ finite_card_pname @ ( insert_pname @ SV173 @ SV552 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV552 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2320]) ).
thf(2730,plain,
! [SV174: $i,SV553: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV553 ) )
= $false )
| ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV174 ) @ SV553 ) )
| ( ( hAPP_fun_a_bool_nat @ finite_card_a @ ( insert_a @ SV174 @ SV553 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SV553 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2321]) ).
thf(2731,plain,
! [SV554: $i,SV175: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV175 ) @ SV554 ) )
= $false )
| ( ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ suc @ SV554 ) ) @ SV175 )
= ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV554 ) @ SV175 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2322]) ).
thf(2732,plain,
! [SV555: $i,SV178: $i] :
( ( ( ( hAPP_nat_nat @ suc @ SV178 )
= ( hAPP_nat_nat @ suc @ SV555 ) )
= $false )
| ( ( SV178 = SV555 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2323]) ).
thf(2733,plain,
! [SV556: $i,SV181: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV181 ) @ SV556 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV556 ) @ SV181 ) )
| ( SV181 = SV556 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2324]) ).
thf(2734,plain,
! [SV182: $i,SV729: $i,SV557: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV557 ) @ SV729 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV729 ) @ SV182 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV557 ) @ SV182 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2325]) ).
thf(2735,plain,
! [SV558: $i,SV183: $i] :
( ( ( SV183 = SV558 )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV183 ) @ SV558 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2326]) ).
thf(2736,plain,
! [SV561: $i,SV187: $i] :
( ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ SV187 ) @ SV561 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV561 ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV187 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2329]) ).
thf(2737,plain,
! [SV562: $i,SV188: $i] :
( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ SV188 ) @ SV562 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV562 ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV188 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2330]) ).
thf(2738,plain,
! [SV563: $i,SV189: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV189 ) @ SV563 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV563 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV189 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2331]) ).
thf(2739,plain,
! [SV564: $i,SV190: $i] :
( ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ SV190 ) @ SV564 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV564 ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV190 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2332]) ).
thf(2740,plain,
! [SV565: $i,SV191: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV191 ) @ SV565 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV565 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV191 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2333]) ).
thf(2741,plain,
! [SV566: $i,SV192: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV192 ) @ SV566 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV566 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV192 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2334]) ).
thf(2742,plain,
! [SV193: $i,SV567: $i] :
( ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV567 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ SV193 ) @ SV567 ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV193 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2335]) ).
thf(2743,plain,
! [SV194: $i,SV568: $i] :
( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV568 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ SV194 ) @ SV568 ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV194 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2336]) ).
thf(2744,plain,
! [SV195: $i,SV569: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV569 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV195 ) @ SV569 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV195 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2337]) ).
thf(2745,plain,
! [SV196: $i,SV570: $i] :
( ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV570 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ SV196 ) @ SV570 ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV196 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2338]) ).
thf(2746,plain,
! [SV197: $i,SV571: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV571 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV197 ) @ SV571 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV197 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2339]) ).
thf(2747,plain,
! [SV198: $i,SV572: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV572 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV198 ) @ SV572 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV198 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2340]) ).
thf(2748,plain,
! [SV573: $i,SV199: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ SV199 ) ) @ SV573 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV199 ) @ SV573 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2341]) ).
thf(2749,plain,
! [SV574: $i,SV200: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV200 ) @ ( hAPP_nat_nat @ suc @ SV574 ) ) )
= $false )
| ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV200 ) @ SV574 ) )
| ( SV200
= ( hAPP_nat_nat @ suc @ SV574 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2342]) ).
thf(2750,plain,
! [SV575: $i,SV201: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV201 ) @ SV575 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV201 ) @ ( hAPP_nat_nat @ suc @ SV575 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2343]) ).
thf(2751,plain,
! [SV205: $i,SV732: $i,SV578: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV578 ) @ SV732 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV578 ) @ SV205 ) )
| ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV732 ) @ SV578 ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV205 ) @ SV578 ) )
= ( hAPP_nat_nat @ ( minus_minus_nat @ SV732 ) @ SV205 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2345]) ).
thf(2752,plain,
! [SV579: $i,SV206: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV206 ) @ SV579 ) )
= $false )
| ( ( ( hAPP_nat_nat @ ( minus_minus_nat @ SV579 ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV579 ) @ SV206 ) )
= SV206 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2346]) ).
thf(2753,plain,
! [SV207: $i,SV733: $i,SV580: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV580 ) @ SV733 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV580 ) @ SV207 ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV733 ) @ SV207 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2347]) ).
thf(2754,plain,
! [SV208: $i,SV734: $i,SV581: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV581 ) @ SV734 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV208 ) @ SV734 ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV208 ) @ SV581 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2348]) ).
thf(2755,plain,
! [SV583: $i,SV210: $i,SV735: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV735 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV210 ) @ ( image_pname_a @ SV583 @ SV735 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV210 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2349]) ).
thf(2756,plain,
! [SV211: $i,SV584: $i,SV736: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( hAPP_n1699378549t_bool @ SV736 @ ( sK16_N_2 @ SV736 @ SV584 @ SV211 ) ) ) @ ( hAPP_n1699378549t_bool @ SV736 @ ( hAPP_nat_nat @ suc @ ( sK16_N_2 @ SV736 @ SV584 @ SV211 ) ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV211 ) @ SV584 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( hAPP_n1699378549t_bool @ SV736 @ SV211 ) ) @ ( hAPP_n1699378549t_bool @ SV736 @ SV584 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2350]) ).
thf(2757,plain,
! [SV212: $i,SV585: $i,SV737: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_n1025906991e_bool @ SV737 @ ( sK15_N_2 @ SV737 @ SV585 @ SV212 ) ) ) @ ( hAPP_n1025906991e_bool @ SV737 @ ( hAPP_nat_nat @ suc @ ( sK15_N_2 @ SV737 @ SV585 @ SV212 ) ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV212 ) @ SV585 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_n1025906991e_bool @ SV737 @ SV212 ) ) @ ( hAPP_n1025906991e_bool @ SV737 @ SV585 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2351]) ).
thf(2758,plain,
! [SV213: $i,SV586: $i,SV738: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ SV738 @ ( sK14_N_2 @ SV738 @ SV586 @ SV213 ) ) ) @ ( hAPP_nat_nat @ SV738 @ ( hAPP_nat_nat @ suc @ ( sK14_N_2 @ SV738 @ SV586 @ SV213 ) ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV213 ) @ SV586 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ SV738 @ SV213 ) ) @ ( hAPP_nat_nat @ SV738 @ SV586 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2352]) ).
thf(2759,plain,
! [SV214: $i,SV587: $i,SV739: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_nat_fun_a_bool @ SV739 @ ( sK13_N_2 @ SV739 @ SV587 @ SV214 ) ) ) @ ( hAPP_nat_fun_a_bool @ SV739 @ ( hAPP_nat_nat @ suc @ ( sK13_N_2 @ SV739 @ SV587 @ SV214 ) ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV214 ) @ SV587 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_nat_fun_a_bool @ SV739 @ SV214 ) ) @ ( hAPP_nat_fun_a_bool @ SV739 @ SV587 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2353]) ).
thf(2760,plain,
! [SV215: $i,SV816: $i,SV740: $i,SV588: $i] :
( ( ( SV588
!= ( hAPP_pname_a @ SV740 @ SV816 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV816 ) @ SV215 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV588 ) @ ( image_pname_a @ SV740 @ SV215 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2354]) ).
thf(2761,plain,
! [SV589: $i,SV216: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV216 ) @ SV589 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV589 ) @ SV216 ) )
| ( SV216 = SV589 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2355]) ).
thf(2762,plain,
! [SV590: $i,SV217: $i] :
( ( ( ~ ( is_fun_pname_bool @ SV217 ) )
= $true )
| ( ( ~ ( is_fun_pname_bool @ SV590 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV217 ) @ SV590 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV590 ) @ SV217 ) )
| ( SV217 = SV590 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2356]) ).
thf(2763,plain,
! [SV591: $i,SV218: $i] :
( ( ( ~ ( is_fun_a_bool @ SV218 ) )
= $true )
| ( ( ~ ( is_fun_a_bool @ SV591 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV218 ) @ SV591 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV591 ) @ SV218 ) )
| ( SV218 = SV591 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2357]) ).
thf(2764,plain,
! [SV219: $i,SV741: $i,SV592: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV592 ) @ SV741 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV219 ) @ SV592 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV219 ) @ SV741 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2358]) ).
thf(2765,plain,
! [SV220: $i,SV742: $i,SV593: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV593 ) @ SV742 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV220 ) @ SV593 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV220 ) @ SV742 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2359]) ).
thf(2766,plain,
! [SV221: $i,SV743: $i,SV594: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV594 ) @ SV743 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV221 ) @ SV594 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV221 ) @ SV743 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2360]) ).
thf(2767,plain,
! [SV744: $i,SV595: $i,SV222: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV222 ) @ ( insert_nat @ SV595 @ SV744 ) ) ) )
= $true )
| ( ( ( SV222 = SV595 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV222 ) @ SV744 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2361]) ).
thf(2768,plain,
! [SV596: $i,SV223: $i] :
( ( ( ~ ( is_pname @ SV223 ) )
= $true )
| ( ( ~ ( is_pname @ SV596 ) )
= $true )
| ( ( ! [SY979: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV223 ) @ ( insert_pname @ SV596 @ SY979 ) ) )
| ( SV223 = SV596 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV223 ) @ SY979 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2362]) ).
thf(2769,plain,
! [SV597: $i,SV224: $i] :
( ( ( ~ ( is_a @ SV224 ) )
= $true )
| ( ( ~ ( is_a @ SV597 ) )
= $true )
| ( ( ! [SY980: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV224 ) @ ( insert_a @ SV597 @ SY980 ) ) )
| ( SV224 = SV597 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV224 ) @ SY980 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2363]) ).
thf(2770,plain,
! [SV246: $i,SV748: $i,SV619: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV619 ) @ SV748 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV619 ) @ ( insert_nat @ SV246 @ SV748 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2367]) ).
thf(2771,plain,
! [SV247: $i,SV749: $i,SV620: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV620 ) @ SV749 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV620 ) @ ( insert_pname @ SV247 @ SV749 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2368]) ).
thf(2772,plain,
! [SV248: $i,SV750: $i,SV621: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV621 ) @ SV750 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV621 ) @ ( insert_a @ SV248 @ SV750 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2369]) ).
thf(2773,plain,
! [SV622: $i,SV249: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV249 ) @ SV622 ) )
= $false )
| ( ( ( insert_nat @ SV249 @ SV622 )
= SV622 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2370]) ).
thf(2774,plain,
! [SV250: $i,SV623: $i] :
( ( ( is_fun_pname_bool @ SV623 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV250 ) @ SV623 ) )
| ( ( insert_pname @ SV250 @ SV623 )
= SV623 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2371]) ).
thf(2775,plain,
! [SV251: $i,SV624: $i] :
( ( ( is_fun_a_bool @ SV624 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV251 ) @ SV624 ) )
| ( ( insert_a @ SV251 @ SV624 )
= SV624 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2372]) ).
thf(2776,plain,
! [SV625: $i,SV255: $i] :
( ( ( SV255 = SV625 )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV255 ) @ SV625 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2373]) ).
thf(2777,plain,
! [SV626: $i,SV256: $i] :
( ( ( SV256 = SV626 )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV256 ) @ SV626 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2374]) ).
thf(2778,plain,
! [SV627: $i,SV257: $i] :
( ( ( SV257 = SV627 )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV257 ) @ SV627 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2375]) ).
thf(2779,plain,
! [SV628: $i,SV258: $i] :
( ( ( SV258 = SV628 )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV628 ) @ SV258 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2376]) ).
thf(2780,plain,
! [SV629: $i,SV259: $i] :
( ( ( SV259 = SV629 )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV629 ) @ SV259 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2377]) ).
thf(2781,plain,
! [SV630: $i,SV260: $i] :
( ( ( SV260 = SV630 )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV630 ) @ SV260 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2378]) ).
thf(2782,plain,
! [SV261: $i,SV751: $i,SV631: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV631 ) @ SV751 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV261 ) @ SV631 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV261 ) @ SV751 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2379]) ).
thf(2783,plain,
! [SV262: $i,SV752: $i,SV632: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV632 ) @ SV752 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV262 ) @ SV632 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV262 ) @ SV752 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2380]) ).
thf(2784,plain,
! [SV263: $i,SV753: $i,SV633: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV633 ) @ SV753 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV263 ) @ SV633 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV263 ) @ SV753 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2381]) ).
thf(2785,plain,
! [SV264: $i,SV754: $i,SV634: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV634 ) @ SV754 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV754 ) @ SV264 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV634 ) @ SV264 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2382]) ).
thf(2786,plain,
! [SV265: $i,SV755: $i,SV635: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV635 ) @ SV755 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV755 ) @ SV265 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV635 ) @ SV265 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2383]) ).
thf(2787,plain,
! [SV266: $i,SV756: $i,SV636: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV636 ) @ SV756 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV756 ) @ SV266 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV636 ) @ SV266 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2384]) ).
thf(2788,plain,
! [SV267: $i,SV757: $i,SV637: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV637 ) @ SV757 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV267 ) @ SV637 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV267 ) @ SV757 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2385]) ).
thf(2789,plain,
! [SV268: $i,SV758: $i,SV638: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV638 ) @ SV758 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV268 ) @ SV638 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV268 ) @ SV758 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2386]) ).
thf(2790,plain,
! [SV269: $i,SV759: $i,SV639: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV639 ) @ SV759 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV269 ) @ SV639 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV269 ) @ SV759 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2387]) ).
thf(2791,plain,
! [SV270: $i,SV760: $i,SV640: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV640 ) @ SV760 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV760 ) @ SV270 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV640 ) @ SV270 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2388]) ).
thf(2792,plain,
! [SV271: $i,SV761: $i,SV641: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV641 ) @ SV761 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV761 ) @ SV271 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV641 ) @ SV271 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2389]) ).
thf(2793,plain,
! [SV272: $i,SV762: $i,SV642: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV642 ) @ SV762 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV762 ) @ SV272 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV642 ) @ SV272 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2390]) ).
thf(2794,plain,
! [SV278: $i,SV763: $i,SV643: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV643 ) @ SV763 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( hAPP_pname_a @ SV278 @ SV643 ) ) @ ( image_pname_a @ SV278 @ SV763 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2394]) ).
thf(2795,plain,
! [SV644: $i,SV279: $i,SV817: $i,SV764: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV764 ) @ SV817 ) )
| ( SV279
!= ( hAPP_pname_a @ SV644 @ SV764 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV279 ) @ ( image_pname_a @ SV644 @ SV817 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2395]) ).
thf(2796,plain,
! [SV289: $i,SV765: $i,SV654: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV654 ) @ SV765 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV654 ) @ ( insert_nat @ SV289 @ SV765 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2396]) ).
thf(2797,plain,
! [SV290: $i,SV766: $i,SV655: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV655 ) @ SV766 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV655 ) @ ( insert_pname @ SV290 @ SV766 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2397]) ).
thf(2798,plain,
! [SV291: $i,SV767: $i,SV656: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV656 ) @ SV767 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV656 ) @ ( insert_a @ SV291 @ SV767 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2398]) ).
thf(2799,plain,
! [SV292: $i,SV768: $i,SV657: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV657 ) @ SV768 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( insert_nat @ SV292 @ SV657 ) ) @ ( insert_nat @ SV292 @ SV768 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2399]) ).
thf(2800,plain,
! [SV293: $i,SV769: $i,SV658: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV658 ) @ SV769 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ SV293 @ SV658 ) ) @ ( insert_pname @ SV293 @ SV769 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2400]) ).
thf(2801,plain,
! [SV294: $i,SV770: $i,SV659: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV659 ) @ SV770 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV294 @ SV659 ) ) @ ( insert_a @ SV294 @ SV770 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2401]) ).
thf(2802,plain,
! [SV296: $i,SV772: $i,SV661: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV661 ) @ SV772 ) ) )
= $true )
| ( ( ( insert_a @ ( hAPP_pname_a @ SV296 @ SV661 ) @ ( image_pname_a @ SV296 @ SV772 ) )
= ( image_pname_a @ SV296 @ SV772 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2403]) ).
thf(2803,plain,
! [SV297: $i,SV773: $i,SV662: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV662 ) @ SV773 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_pname_a @ SV297 @ SV662 ) ) @ ( image_pname_a @ SV297 @ SV773 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2404]) ).
thf(2804,plain,
! [SV663: $i,SV298: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ SV298 ) ) @ SV663 ) )
= $false )
| ( ( SV663
= ( hAPP_nat_nat @ suc @ ( sK4_M @ SV663 @ SV298 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2405]) ).
thf(2805,plain,
! [SV303: $i] :
( ( ( hBOOL @ SV303 )
= $false )
| ( ( hBOOL @ ( hAPP_bool_bool @ fNot @ SV303 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2406]) ).
thf(2806,plain,
! [SV305: $i,SV664: $i] :
( ( ( ~ ( hBOOL @ SV664 ) )
= $true )
| ( ( ~ ( hBOOL @ SV305 ) )
= $true )
| ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ SV664 ) @ SV305 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2407]) ).
thf(2807,plain,
! [SV774: $i,SV306: $i] :
( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ SV306 ) @ SV774 ) )
= $false )
| ( ( hBOOL @ SV306 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2408]) ).
thf(2808,plain,
! [SV665: $i,SV307: $i] :
( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ SV307 ) @ SV665 ) )
= $false )
| ( ( hBOOL @ SV665 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2409]) ).
thf(2809,plain,
! [SV308: $i,SV666: $i] :
( ( ( hBOOL @ SV666 )
= $false )
| ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ SV666 ) @ SV308 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2410]) ).
thf(2810,plain,
! [SV309: $i,SV667: $i] :
( ( ( hBOOL @ SV667 )
= $false )
| ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ SV309 ) @ SV667 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2411]) ).
thf(2811,plain,
! [SV668: $i,SV310: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ SV310 ) @ SV668 ) ) )
= $true )
| ( ( hBOOL @ SV310 )
= $true )
| ( ( hBOOL @ SV668 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2412]) ).
thf(2812,plain,
! [SV312: $i,SV670: $i] :
( ( ( hBOOL @ SV670 )
= $false )
| ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ SV312 ) @ SV670 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2414]) ).
thf(2813,plain,
! [SV671: $i,SV313: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ SV313 ) @ SV671 ) ) )
= $true )
| ( ( ~ ( hBOOL @ SV313 ) )
= $true )
| ( ( hBOOL @ SV671 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2415]) ).
thf(2814,plain,
! [SV672: $i,SV314: $i] :
( ( ( ~ ( is_a @ SV314 ) )
= $true )
| ( ( ~ ( is_a @ SV672 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_a_bool @ ( hAPP_a_fun_a_bool @ fequal_a @ SV314 ) @ SV672 ) )
| ( SV314 = SV672 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2416]) ).
thf(2815,plain,
! [SV673: $i,SV315: $i] :
( ( ( SV315 = SV673 )
= $false )
| ( ( hBOOL @ ( hAPP_a_bool @ ( hAPP_a_fun_a_bool @ fequal_a @ SV315 ) @ SV673 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2417]) ).
thf(2816,plain,
! [SV674: $i,SV316: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ SV316 ) @ SV674 ) )
= $false )
| ( ( SV316 = SV674 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2418]) ).
thf(2817,plain,
! [SV675: $i,SV317: $i] :
( ( ( SV317 = SV675 )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ SV317 ) @ SV675 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2419]) ).
thf(2818,plain,
! [SV676: $i,SV318: $i] :
( ( ( ~ ( is_pname @ SV318 ) )
= $true )
| ( ( ~ ( is_pname @ SV676 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ fequal_pname @ SV318 ) @ SV676 ) )
| ( SV318 = SV676 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2420]) ).
thf(2819,plain,
! [SV677: $i,SV319: $i] :
( ( ( SV319 = SV677 )
= $false )
| ( ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ fequal_pname @ SV319 ) @ SV677 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2421]) ).
thf(2820,plain,
! [SV679: $i,SV321: $i] :
( ( ( ~ ( is_fun_a_bool @ SV321 ) )
= $true )
| ( ( ~ ( is_fun_a_bool @ SV679 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ SV321 ) @ SV679 ) )
| ( SV321 = SV679 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2423]) ).
thf(2821,plain,
! [SV680: $i,SV322: $i] :
( ( ( SV322 = SV680 )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ SV322 ) @ SV680 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2424]) ).
thf(2822,plain,
! [SV684: $i,SV326: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ SV326 ) @ SV684 ) )
= $false )
| ( ( SV326 = SV684 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2428]) ).
thf(2823,plain,
! [SV685: $i,SV327: $i] :
( ( ( SV327 = SV685 )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ SV327 ) @ SV685 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2429]) ).
thf(2824,plain,
! [SV686: $i,SV328: $i] :
( ( ( ~ ( is_fun_pname_bool @ SV328 ) )
= $true )
| ( ( ~ ( is_fun_pname_bool @ SV686 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ SV328 ) @ SV686 ) )
| ( SV328 = SV686 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2430]) ).
thf(2825,plain,
! [SV687: $i,SV329: $i] :
( ( ( SV329 = SV687 )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ SV329 ) @ SV687 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2431]) ).
thf(2826,plain,
! [SV818: $i] :
( ( ! [SY1054: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV818 ) @ SY1054 ) )
| ( hBOOL @ ( hAPP_nat_bool @ SY1054 @ SV818 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2466]) ).
thf(2827,plain,
! [SV819: $i] :
( ( ! [SY1055: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ SY1055 @ SV819 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV819 ) @ SY1055 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2467]) ).
thf(2828,plain,
! [SV820: $i] :
( ( ! [SY1056: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV820 ) @ SY1056 ) )
| ( hBOOL @ ( hAPP_pname_bool @ SY1056 @ SV820 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2468]) ).
thf(2829,plain,
! [SV821: $i] :
( ( ! [SY1057: $i] :
( ~ ( hBOOL @ ( hAPP_pname_bool @ SY1057 @ SV821 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV821 ) @ SY1057 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2469]) ).
thf(2830,plain,
! [SV822: $i] :
( ( ! [SY1058: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ SY1058 ) ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fconj @ SY1058 ) @ SV822 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2470]) ).
thf(2831,plain,
! [SV823: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ SV823 ) ) )
| ! [SY1059: $i] : ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fconj @ SY1059 ) @ SV823 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2471]) ).
thf(2832,plain,
! [SV824: $i] :
( ( ! [SY1060: $i] :
( ( SV824 != SY1060 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV824 ) @ SY1060 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2472]) ).
thf(2833,plain,
! [SV825: $i] :
( ( ! [SY1061: $i] :
( ( SV825 != SY1061 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY1061 ) @ SV825 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2473]) ).
thf(2834,plain,
! [SV364: $i] :
( ( ~ ( is_fun_a_bool @ SV364 )
| ! [SY842: $i,SY843: $i] :
( ! [SY844: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY844 ) @ SY843 ) )
| ~ ( is_fun_pname_bool @ SY844 )
| ( SV364
!= ( image_pname_a @ SY842 @ SY844 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV364 ) @ ( image_pname_a @ SY842 @ SY843 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2474]) ).
thf(2835,plain,
! [SV364: $i] :
( ( ~ ( is_fun_a_bool @ SV364 )
| ! [SY845: $i,SY846: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV364 ) @ ( image_pname_a @ SY845 @ SY846 ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( sK10_AA @ SY846 @ SY845 @ SV364 ) ) @ SY846 ) )
| ~ ( is_fun_pname_bool @ ( sK10_AA @ SY846 @ SY845 @ SV364 ) ) )
| ( SV364
!= ( image_pname_a @ SY845 @ ( sK10_AA @ SY846 @ SY845 @ SV364 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2475]) ).
thf(2836,plain,
! [SV826: $i] :
( ( ! [SY1062: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV826 ) @ ( hAPP_nat_nat @ suc @ SY1062 ) ) )
| ( SV826
= ( hAPP_nat_nat @ suc @ SY1062 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV826 ) @ SY1062 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2476]) ).
thf(2837,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( hAPP_nat_nat @ suc @ SX1 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX0 ) @ ( hAPP_nat_nat @ suc @ SX1 ) ) ) )
| ~ ! [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 @ SX0 ) @ ( hAPP_nat_nat @ suc @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2477]) ).
thf(2838,plain,
! [SV827: $i] :
( ( ! [SY1063: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV827 ) @ SY1063 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY1063 ) @ SV827 ) )
| ( SV827 = SY1063 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2478]) ).
thf(2839,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX0 ) @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX1 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2479]) ).
thf(2840,plain,
! [SV828: $i] :
( ( ! [SY1064: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SY1064 ) )
| ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ SV828 ) @ SY1064 ) )
| ( ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( insert_fun_nat_bool @ SV828 @ SY1064 ) )
= ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SY1064 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2480]) ).
thf(2841,plain,
! [SV829: $i] :
( ( ! [SY1065: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SY1065 ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ SV829 ) @ SY1065 ) )
| ( ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( insert_fun_nat_bool @ SV829 @ SY1065 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SY1065 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2481]) ).
thf(2842,plain,
! [SV830: $i] :
( ( ! [SY1066: $i] :
( ~ ( is_fun_pname_bool @ SV830 )
| ~ ( is_fun_pname_bool @ SY1066 )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV830 ) @ SY1066 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY1066 ) @ SV830 ) )
| ( SV830 = SY1066 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2482]) ).
thf(2843,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( is_fun_pname_bool @ SX0 )
| ~ ( is_fun_pname_bool @ SX1 )
| ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SX0 ) @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( is_fun_pname_bool @ SX0 )
| ~ ( is_fun_pname_bool @ SX1 )
| ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SX1 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2483]) ).
thf(2844,plain,
! [SV831: $i] :
( ( ! [SY1067: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ SY1067 ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ SY1067 ) @ SV831 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2484]) ).
thf(2845,plain,
! [SV832: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ SV832 ) ) )
| ! [SY1068: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ SY1068 ) @ SV832 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2485]) ).
thf(2846,plain,
! [SV833: $i] :
( ( ! [SY1069: $i] :
( ( ( hAPP_nat_nat @ suc @ SV833 )
!= ( hAPP_nat_nat @ suc @ SY1069 ) )
| ( SV833 = SY1069 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2486]) ).
thf(2847,plain,
! [SV834: $i] :
( ( ! [SY1070: $i] :
( ( SV834 != SY1070 )
| ( ( hAPP_nat_nat @ suc @ SV834 )
= ( hAPP_nat_nat @ suc @ SY1070 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2487]) ).
thf(2848,plain,
! [SV365: $i] :
( ( ! [SY847: $i,SY848: $i] :
( ~ ( is_pname @ SV365 )
| ~ ( is_pname @ SY848 )
| ~ ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV365 @ SY847 ) @ SY848 ) )
| ( SV365 = SY848 )
| ( hBOOL @ ( hAPP_pname_bool @ SY847 @ SY848 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2488]) ).
thf(2849,plain,
! [SV365: $i] :
( ( ~ ( ~ ! [SY849: $i,SY850: $i] :
( ~ ( is_pname @ SV365 )
| ~ ( is_pname @ SY850 )
| ( SV365 != SY850 )
| ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV365 @ SY849 ) @ SY850 ) ) )
| ~ ! [SY851: $i,SY852: $i] :
( ~ ( is_pname @ SV365 )
| ~ ( is_pname @ SY852 )
| ~ ( hBOOL @ ( hAPP_pname_bool @ SY851 @ SY852 ) )
| ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV365 @ SY851 ) @ SY852 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2489]) ).
thf(2850,plain,
! [SV366: $i] :
( ( ! [SY853: $i,SY854: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV366 ) @ ( insert_nat @ SY853 @ SY854 ) ) )
| ( SV366 = SY853 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV366 ) @ SY854 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2490]) ).
thf(2851,plain,
! [SV366: $i] :
( ( ~ ( ~ ! [SY855: $i] :
( ( SV366 != SY855 )
| ! [SY856: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV366 ) @ ( insert_nat @ SY855 @ SY856 ) ) ) )
| ~ ! [SY857: $i,SY858: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV366 ) @ SY858 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV366 ) @ ( insert_nat @ SY857 @ SY858 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2491]) ).
thf(2852,plain,
! [SV835: $i] :
( ( ! [SY1071: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ SV835 @ SY1071 ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SY1071 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2492]) ).
thf(2853,plain,
! [SV836: $i] :
( ( ! [SY1072: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SY1072 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ SV836 @ SY1072 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2493]) ).
thf(2854,plain,
! [SV367: $i] :
( ( ! [SY859: $i] :
( ~ ( is_a @ SV367 )
| ~ ( is_a @ SY859 )
| ! [SY860: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ ( insert_a @ SY859 @ SY860 ) ) )
| ( SV367 = SY859 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ SY860 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2494]) ).
thf(2855,plain,
! [SV367: $i] :
( ( ~ ( ~ ! [SY861: $i] :
( ~ ( is_a @ SV367 )
| ~ ( is_a @ SY861 )
| ( SV367 != SY861 )
| ! [SY862: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ ( insert_a @ SY861 @ SY862 ) ) ) )
| ~ ! [SY863: $i] :
( ~ ( is_a @ SV367 )
| ~ ( is_a @ SY863 )
| ! [SY864: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ SY864 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ ( insert_a @ SY863 @ SY864 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2495]) ).
thf(2856,plain,
! [SV837: $i] :
( ( ! [SY1073: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ SY1073 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ SY1073 ) @ SV837 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2496]) ).
thf(2857,plain,
! [SV838: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ SV838 ) ) )
| ! [SY1074: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ SY1074 ) @ SV838 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2497]) ).
thf(2858,plain,
! [SV368: $i] :
( ( ! [SY865: $i,SY866: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY865 ) @ SY866 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY866 ) @ ( insert_a @ SY865 @ SV368 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY866 ) @ SV368 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2498]) ).
thf(2859,plain,
! [SV368: $i] :
( ( ! [SY867: $i,SY868: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY867 ) @ SY868 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY868 ) @ SV368 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY868 ) @ ( insert_a @ SY867 @ SV368 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2499]) ).
thf(2860,plain,
! [SV369: $i] :
( ( ~ ( is_a @ SV369 )
| ! [SY869: $i,SY870: $i] :
( ! [SY871: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SY871 ) @ SY870 ) )
| ~ ( is_pname @ SY871 )
| ( SV369
!= ( hAPP_pname_a @ SY869 @ SY871 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV369 ) @ ( image_pname_a @ SY869 @ SY870 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2500]) ).
thf(2861,plain,
! [SV369: $i] :
( ( ~ ( is_a @ SV369 )
| ! [SY872: $i,SY873: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV369 ) @ ( image_pname_a @ SY872 @ SY873 ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK11_X_1 @ SY873 @ SY872 @ SV369 ) ) @ SY873 ) )
| ~ ( is_pname @ ( sK11_X_1 @ SY873 @ SY872 @ SV369 ) ) )
| ( SV369
!= ( hAPP_pname_a @ SY872 @ ( sK11_X_1 @ SY873 @ SY872 @ SV369 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2501]) ).
thf(2862,plain,
! [SV370: $i] :
( ( ! [SY874: $i,SY875: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SY874 ) @ SY875 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY875 ) @ ( insert_nat @ SY874 @ SV370 ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY875 ) @ SV370 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2502]) ).
thf(2863,plain,
! [SV370: $i] :
( ( ! [SY876: $i,SY877: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SY876 ) @ SY877 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY877 ) @ SV370 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY877 ) @ ( insert_nat @ SY876 @ SV370 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2503]) ).
thf(2864,plain,
! [SV839: $i] :
( ( ! [SY1075: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ SY1075 ) ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fconj @ SY1075 ) @ SV839 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2504]) ).
thf(2865,plain,
! [SV840: $i] :
( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ SV840 ) ) )
| ! [SY1076: $i] : ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fconj @ SY1076 ) @ SV840 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2505]) ).
thf(2866,plain,
! [SV841: $i] :
( ( ! [SY1077: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SV841 @ SY1077 ) ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SY1077 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2506]) ).
thf(2867,plain,
! [SV842: $i] :
( ( ! [SY1078: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SY1078 ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SV842 @ SY1078 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2507]) ).
thf(2868,plain,
! [SV371: $i] :
( ( ! [SY878: $i,SY879: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SY878 ) @ SY879 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SY878 ) @ ( insert_nat @ SV371 @ SY879 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2508]) ).
thf(2869,plain,
! [SV371: $i] :
( ( ! [SY880: $i] :
( ( SY880 != SV371 )
| ! [SY881: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SY880 ) @ ( insert_nat @ SV371 @ SY881 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2509]) ).
thf(2870,plain,
! [SV843: $i] :
( ( ! [SY1079: $i] :
( ~ ( is_fun_a_bool @ SV843 )
| ~ ( is_fun_a_bool @ SY1079 )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV843 ) @ SY1079 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY1079 ) @ SV843 ) )
| ( SV843 = SY1079 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2510]) ).
thf(2871,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 ) ) )
| ~ ! [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 @ SX1 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2511]) ).
thf(2872,plain,
! [SV722: $i,SV372: $i,SV813: $i] :
( ( ( ~ ( is_fun_a_bool @ SV813 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV813 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV813 ) @ ( image_pname_a @ SV372 @ SV722 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( sK17_C_2 @ SV813 @ SV722 @ SV372 ) ) @ SV722 ) )
| ~ ( is_fun_pname_bool @ ( sK17_C_2 @ SV813 @ SV722 @ SV372 ) ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( sK17_C_2 @ SV813 @ SV722 @ SV372 ) ) ) )
| ( SV813
!= ( image_pname_a @ SV372 @ ( sK17_C_2 @ SV813 @ SV722 @ SV372 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2512]) ).
thf(2873,plain,
! [SV844: $i] :
( ( ! [SY1080: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ SY1080 ) ) @ SV844 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV844 ) @ SY1080 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2513]) ).
thf(2874,plain,
! [SV845: $i] :
( ( ! [SY1081: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV845 ) @ SY1081 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ SY1081 ) ) @ SV845 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2514]) ).
thf(2875,plain,
! [SV373: $i] :
( ( ! [SY884: $i,SY885: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SY884 ) @ SY885 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SY884 ) @ ( insert_pname @ SV373 @ SY885 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2515]) ).
thf(2876,plain,
! [SV373: $i] :
( ( ! [SY886: $i] :
( ( SY886 != SV373 )
| ! [SY887: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SY886 ) @ ( insert_pname @ SV373 @ SY887 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2516]) ).
thf(2877,plain,
! [SV846: $i] :
( ( ! [SY1082: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ SV846 ) ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ SY1082 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ SV846 ) @ SY1082 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2517]) ).
thf(2878,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ SX0 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2518]) ).
thf(2879,plain,
! [SV374: $i] :
( ( ! [SY888: $i,SY889: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV374 ) @ SY889 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY888 ) @ SY889 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV374 @ SY888 ) ) @ SY889 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2519]) ).
thf(2880,plain,
! [SV374: $i] :
( ( ~ ( ~ ! [SY890: $i,SY891: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV374 @ SY890 ) ) @ SY891 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV374 ) @ SY891 ) ) )
| ~ ! [SY892: $i,SY893: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV374 @ SY892 ) ) @ SY893 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY892 ) @ SY893 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2520]) ).
thf(2881,plain,
! [SV847: $i] :
( ( ! [SY1083: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ SV847 ) ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ SY1083 ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ SV847 ) @ SY1083 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2521]) ).
thf(2882,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ SX0 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2522]) ).
thf(2883,plain,
! [SV723: $i,SV375: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_pname_a @ SV375 @ SV723 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK12_X_1 @ SV723 @ SV375 ) ) @ SV723 ) )
| ~ ( is_pname @ ( sK12_X_1 @ SV723 @ SV375 ) ) )
| ~ ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ ( hAPP_f759274231e_bool @ ( cOMBC_1058051404l_bool @ member_pname ) @ SV723 ) ) @ ( hAPP_a93125764e_bool @ ( cOMBC_pname_a_bool @ ( cOMBB_1897541054_pname @ fequal_a @ SV375 ) ) @ ( hAPP_pname_a @ SV375 @ ( sK12_X_1 @ SV723 @ SV375 ) ) ) ) ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV723 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2523]) ).
thf(2884,plain,
! [SV376: $i] :
( ( ! [SY895: $i,SY896: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV376 ) @ SY896 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY895 ) @ SY896 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( insert_nat @ SV376 @ SY895 ) ) @ SY896 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2524]) ).
thf(2885,plain,
! [SV376: $i] :
( ( ~ ( ~ ! [SY897: $i,SY898: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( insert_nat @ SV376 @ SY897 ) ) @ SY898 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV376 ) @ SY898 ) ) )
| ~ ! [SY899: $i,SY900: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( insert_nat @ SV376 @ SY899 ) ) @ SY900 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY899 ) @ SY900 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2525]) ).
thf(2886,plain,
! [SV848: $i] :
( ( ! [SY1084: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SY1084 ) )
| ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ SV848 ) @ SY1084 ) )
| ( ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( insert1325755072e_bool @ SV848 @ SY1084 ) )
= ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SY1084 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2526]) ).
thf(2887,plain,
! [SV849: $i] :
( ( ! [SY1085: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SY1085 ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ SV849 ) @ SY1085 ) )
| ( ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( insert1325755072e_bool @ SV849 @ SY1085 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SY1085 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2527]) ).
thf(2888,plain,
! [SV850: $i] :
( ( ! [SY1086: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ SV850 @ SY1086 ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SY1086 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2528]) ).
thf(2889,plain,
! [SV851: $i] :
( ( ! [SY1087: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SY1087 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ SV851 @ SY1087 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2529]) ).
thf(2890,plain,
! [SV377: $i] :
( ( ! [SY901: $i,SY902: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SY901 ) @ SY902 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SY901 ) @ SV377 ) )
| ( ( insert_nat @ SY901 @ SY902 )
!= ( insert_nat @ SY901 @ SV377 ) )
| ( SY902 = SV377 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2530]) ).
thf(2891,plain,
! [SV377: $i] :
( ( ! [SY903: $i,SY904: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SY903 ) @ SY904 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SY903 ) @ SV377 ) )
| ( SY904 != SV377 )
| ( ( insert_nat @ SY903 @ SY904 )
= ( insert_nat @ SY903 @ SV377 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2531]) ).
thf(2892,plain,
! [SV378: $i,SV724: $i] :
( ( ( ~ ( is_a @ ( sK7_X_1 @ SV724 @ SV378 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( sK7_X_1 @ SV724 @ SV378 ) ) @ SV724 ) )
| ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( sK7_X_1 @ SV724 @ SV378 ) ) @ SV378 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV724 ) @ SV378 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2532]) ).
thf(2893,plain,
! [SV852: $i] :
( ( ! [SY1088: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV852 ) @ SY1088 ) )
| ( hBOOL @ ( hAPP_a_bool @ SY1088 @ SV852 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2533]) ).
thf(2894,plain,
! [SV853: $i] :
( ( ! [SY1089: $i] :
( ~ ( hBOOL @ ( hAPP_a_bool @ SY1089 @ SV853 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV853 ) @ SY1089 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2534]) ).
thf(2895,plain,
! [SV379: $i] :
( ( ! [SY906: $i,SY907: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY906 ) @ SY907 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY906 ) @ ( insert_a @ SV379 @ SY907 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2535]) ).
thf(2896,plain,
! [SV379: $i] :
( ( ! [SY908: $i] :
( ( SY908 != SV379 )
| ! [SY909: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY908 ) @ ( insert_a @ SV379 @ SY909 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2536]) ).
thf(2897,plain,
! [SV854: $i] :
( ( ! [SY1090: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SY1090 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV854 ) @ SY1090 ) )
| ( ( hAPP_f22106695ol_nat @ finite_card_nat @ ( insert_nat @ SV854 @ SY1090 ) )
= ( hAPP_f22106695ol_nat @ finite_card_nat @ SY1090 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2537]) ).
thf(2898,plain,
! [SV855: $i] :
( ( ! [SY1091: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SY1091 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV855 ) @ SY1091 ) )
| ( ( hAPP_f22106695ol_nat @ finite_card_nat @ ( insert_nat @ SV855 @ SY1091 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SY1091 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2538]) ).
thf(2899,plain,
! [SV856: $i] :
( ( ! [SY1092: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ SV856 @ SY1092 ) ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SY1092 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2539]) ).
thf(2900,plain,
! [SV857: $i] :
( ( ! [SY1093: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SY1093 ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ SV857 @ SY1093 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2540]) ).
thf(2901,plain,
! [SV858: $i] :
( ( ! [SY1094: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SY1094 ) )
| ~ ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ SV858 ) @ SY1094 ) )
| ( ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( insert_fun_a_bool @ SV858 @ SY1094 ) )
= ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SY1094 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2541]) ).
thf(2902,plain,
! [SV859: $i] :
( ( ! [SY1095: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SY1095 ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ SV859 ) @ SY1095 ) )
| ( ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( insert_fun_a_bool @ SV859 @ SY1095 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SY1095 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2542]) ).
thf(2903,plain,
! [SV860: $i] :
( ( ! [SY1096: $i] :
( ( SV860 != SY1096 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV860 ) @ SY1096 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2543]) ).
thf(2904,plain,
! [SV861: $i] :
( ( ! [SY1097: $i] :
( ( SV861 != SY1097 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY1097 ) @ SV861 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2544]) ).
thf(2905,plain,
! [SV380: $i,SV725: $i,SV814: $i] :
( ( ( ~ ( ~ ( is_pname @ ( sK3_X_1 @ SV814 @ SV725 @ SV380 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK3_X_1 @ SV814 @ SV725 @ SV380 ) ) @ SV814 ) )
| ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( hAPP_pname_a @ SV380 @ ( sK3_X_1 @ SV814 @ SV725 @ SV380 ) ) ) @ SV725 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_pname_a @ SV380 @ SV814 ) ) @ SV725 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2545]) ).
thf(2906,plain,
! [SV381: $i] :
( ( ! [SY912: $i,SY913: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY912 ) @ SY913 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY912 ) @ SV381 ) )
| ( ( hAPP_nat_nat @ ( minus_minus_nat @ SY913 ) @ SY912 )
!= ( hAPP_nat_nat @ ( minus_minus_nat @ SV381 ) @ SY912 ) )
| ( SY913 = SV381 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2546]) ).
thf(2907,plain,
! [SV381: $i] :
( ( ! [SY914: $i,SY915: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY914 ) @ SY915 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY914 ) @ SV381 ) )
| ( SY915 != SV381 )
| ( ( hAPP_nat_nat @ ( minus_minus_nat @ SY915 ) @ SY914 )
= ( hAPP_nat_nat @ ( minus_minus_nat @ SV381 ) @ SY914 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2547]) ).
thf(2908,plain,
! [SV382: $i,SV726: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ ( sK8_X_1 @ SV726 @ SV382 ) ) @ SV726 ) )
| ~ ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ ( sK8_X_1 @ SV726 @ SV382 ) ) @ SV382 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV726 ) @ SV382 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2548]) ).
thf(2909,plain,
! [SV862: $i] :
( ( ! [SY1098: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ SV862 ) ) )
| ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ SY1098 ) ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ SV862 ) @ SY1098 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2549]) ).
thf(2910,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ SX0 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2550]) ).
thf(2911,plain,
! [SV863: $i] :
( ( ! [SY1099: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ SY1099 ) ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fconj @ SY1099 ) @ SV863 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2551]) ).
thf(2912,plain,
! [SV864: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ SV864 ) ) )
| ! [SY1100: $i] : ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fconj @ SY1100 ) @ SV864 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2552]) ).
thf(2913,plain,
! [SV865: $i] :
( ( ! [SY1101: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY1101 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV865 ) @ SY1101 ) )
| ( ( hAPP_fun_a_bool_nat @ finite_card_a @ ( insert_a @ SV865 @ SY1101 ) )
= ( hAPP_fun_a_bool_nat @ finite_card_a @ SY1101 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2553]) ).
thf(2914,plain,
! [SV866: $i] :
( ( ! [SY1102: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY1102 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV866 ) @ SY1102 ) )
| ( ( hAPP_fun_a_bool_nat @ finite_card_a @ ( insert_a @ SV866 @ SY1102 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SY1102 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2554]) ).
thf(2915,plain,
! [SV867: $i] :
( ( ! [SY1103: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SY1103 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV867 ) @ SY1103 ) )
| ( ( hAPP_f921600141ol_nat @ finite_card_pname @ ( insert_pname @ SV867 @ SY1103 ) )
= ( hAPP_f921600141ol_nat @ finite_card_pname @ SY1103 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2555]) ).
thf(2916,plain,
! [SV868: $i] :
( ( ! [SY1104: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SY1104 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV868 ) @ SY1104 ) )
| ( ( hAPP_f921600141ol_nat @ finite_card_pname @ ( insert_pname @ SV868 @ SY1104 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SY1104 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2556]) ).
thf(2917,plain,
! [SV383: $i] :
( ( ! [SY917: $i] :
( ~ ( is_pname @ SV383 )
| ~ ( is_pname @ SY917 )
| ! [SY918: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ ( insert_pname @ SY917 @ SY918 ) ) )
| ( SV383 = SY917 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ SY918 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2557]) ).
thf(2918,plain,
! [SV383: $i] :
( ( ~ ( ~ ! [SY919: $i] :
( ~ ( is_pname @ SV383 )
| ~ ( is_pname @ SY919 )
| ( SV383 != SY919 )
| ! [SY920: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ ( insert_pname @ SY919 @ SY920 ) ) ) )
| ~ ! [SY921: $i] :
( ~ ( is_pname @ SV383 )
| ~ ( is_pname @ SY921 )
| ! [SY922: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ SY922 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ ( insert_pname @ SY921 @ SY922 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2558]) ).
thf(2919,plain,
! [SV384: $i] :
( ( ! [SY923: $i,SY924: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV384 ) @ SY924 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY923 ) @ SY924 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ SV384 @ SY923 ) ) @ SY924 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2559]) ).
thf(2920,plain,
! [SV384: $i] :
( ( ~ ( ~ ! [SY925: $i,SY926: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ SV384 @ SY925 ) ) @ SY926 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV384 ) @ SY926 ) ) )
| ~ ! [SY927: $i,SY928: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ SV384 @ SY927 ) ) @ SY928 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY927 ) @ SY928 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2560]) ).
thf(2921,plain,
! [SV869: $i] :
( ( ! [SY1105: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ SV869 ) ) )
| ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ SY1105 ) ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ SV869 ) @ SY1105 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2561]) ).
thf(2922,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ SX0 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2562]) ).
thf(2923,plain,
! [SV385: $i] :
( ( ! [SY929: $i,SY930: $i] :
( ~ ( is_fun_a_bool @ SV385 )
| ~ ( is_fun_a_bool @ SY930 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY929 ) @ SY930 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY929 ) @ SV385 ) )
| ( ( insert_a @ SY929 @ SY930 )
!= ( insert_a @ SY929 @ SV385 ) )
| ( SY930 = SV385 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2563]) ).
thf(2924,plain,
! [SV385: $i] :
( ( ! [SY931: $i,SY932: $i] :
( ~ ( is_fun_a_bool @ SV385 )
| ~ ( is_fun_a_bool @ SY932 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY931 ) @ SY932 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY931 ) @ SV385 ) )
| ( SY932 != SV385 )
| ( ( insert_a @ SY931 @ SY932 )
= ( insert_a @ SY931 @ SV385 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2564]) ).
thf(2925,plain,
! [SV870: $i] :
( ( ! [SY1106: $i] :
( ( SV870 != SY1106 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV870 ) @ SY1106 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2565]) ).
thf(2926,plain,
! [SV871: $i] :
( ( ! [SY1107: $i] :
( ( SV871 != SY1107 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY1107 ) @ SV871 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2566]) ).
thf(2927,plain,
! [SV386: $i] :
( ( ! [SY933: $i,SY934: $i] :
( ~ ( is_a @ SV386 )
| ~ ( is_a @ SY934 )
| ~ ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV386 @ SY933 ) @ SY934 ) )
| ( SV386 = SY934 )
| ( hBOOL @ ( hAPP_a_bool @ SY933 @ SY934 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2567]) ).
thf(2928,plain,
! [SV386: $i] :
( ( ~ ( ~ ! [SY935: $i,SY936: $i] :
( ~ ( is_a @ SV386 )
| ~ ( is_a @ SY936 )
| ( SV386 != SY936 )
| ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV386 @ SY935 ) @ SY936 ) ) )
| ~ ! [SY937: $i,SY938: $i] :
( ~ ( is_a @ SV386 )
| ~ ( is_a @ SY938 )
| ~ ( hBOOL @ ( hAPP_a_bool @ SY937 @ SY938 ) )
| ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV386 @ SY937 ) @ SY938 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2568]) ).
thf(2929,plain,
! [SV872: $i] :
( ( ! [SY1108: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ SY1108 ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ SY1108 ) @ SV872 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2569]) ).
thf(2930,plain,
! [SV873: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ SV873 ) ) )
| ! [SY1109: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ SY1109 ) @ SV873 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2570]) ).
thf(2931,plain,
! [SV874: $i,SV387: $i] :
( ( ( ! [SY1110: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV387 ) @ ( image_pname_a @ SV874 @ SY1110 ) ) )
| ~ ( ~ ( is_pname @ ( sK9_X_1 @ SY1110 @ SV874 @ SV387 ) )
| ~ ~ ( ( SV387
!= ( hAPP_pname_a @ SV874 @ ( sK9_X_1 @ SY1110 @ SV874 @ SV387 ) ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK9_X_1 @ SY1110 @ SV874 @ SV387 ) ) @ SY1110 ) ) ) ) ) )
= $true )
| ( ( is_a @ SV387 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2571]) ).
thf(2932,plain,
! [SV875: $i] :
( ( ! [SY1111: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ SV875 @ SY1111 ) ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SY1111 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2572]) ).
thf(2933,plain,
! [SV876: $i] :
( ( ! [SY1112: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SY1112 ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ SV876 @ SY1112 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2573]) ).
thf(2934,plain,
! [SV877: $i] :
( ( ! [SY1113: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ SV877 ) ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ SY1113 ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ SV877 ) @ SY1113 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2574]) ).
thf(2935,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ SX0 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2575]) ).
thf(2936,plain,
! [SV388: $i,SV815: $i,SV727: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ SV727 @ SV815 ) ) )
= $true )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ SV727 @ ( hAPP_nat_nat @ suc @ ( sK5_N_2 @ SV815 @ SV727 @ SV388 ) ) ) )
| ~ ~ ( hBOOL @ ( hAPP_nat_bool @ SV727 @ ( sK5_N_2 @ SV815 @ SV727 @ SV388 ) ) ) )
| ( hBOOL @ ( hAPP_nat_bool @ SV727 @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV815 ) @ SV388 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2576]) ).
thf(2937,plain,
! [SV878: $i] :
( ( ! [SY1114: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ SV878 ) ) )
| ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ SY1114 ) ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ SV878 ) @ SY1114 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2577]) ).
thf(2938,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ SX0 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2578]) ).
thf(2939,plain,
! [SV389: $i] :
( ( ! [SY943: $i,SY944: $i] :
( ~ ( is_fun_pname_bool @ SV389 )
| ~ ( is_fun_pname_bool @ SY944 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SY943 ) @ SY944 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SY943 ) @ SV389 ) )
| ( ( insert_pname @ SY943 @ SY944 )
!= ( insert_pname @ SY943 @ SV389 ) )
| ( SY944 = SV389 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2579]) ).
thf(2940,plain,
! [SV389: $i] :
( ( ! [SY945: $i,SY946: $i] :
( ~ ( is_fun_pname_bool @ SV389 )
| ~ ( is_fun_pname_bool @ SY946 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SY945 ) @ SY946 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SY945 ) @ SV389 ) )
| ( SY946 != SV389 )
| ( ( insert_pname @ SY945 @ SY946 )
= ( insert_pname @ SY945 @ SV389 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2580]) ).
thf(2941,plain,
! [SV879: $i] :
( ( ! [SY1115: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ SV879 ) ) @ ( hAPP_nat_nat @ suc @ SY1115 ) ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV879 ) @ SY1115 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2581]) ).
thf(2942,plain,
! [SV880: $i] :
( ( ! [SY1116: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV880 ) @ SY1116 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ SV880 ) ) @ ( hAPP_nat_nat @ suc @ SY1116 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2582]) ).
thf(2943,plain,
! [SV390: $i] :
( ( ! [SY947: $i,SY948: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SY947 ) @ SY948 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY948 ) @ ( insert_pname @ SY947 @ SV390 ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY948 ) @ SV390 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2583]) ).
thf(2944,plain,
! [SV390: $i] :
( ( ! [SY949: $i,SY950: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SY949 ) @ SY950 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY950 ) @ SV390 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY950 ) @ ( insert_pname @ SY949 @ SV390 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2584]) ).
thf(2945,plain,
! [SV391: $i] :
( ( ! [SY951: $i,SY952: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY951 ) @ SY952 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY951 ) @ SV391 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ SY952 ) @ SY951 ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV391 ) @ SY951 ) ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY952 ) @ SV391 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2585]) ).
thf(2946,plain,
! [SV391: $i] :
( ( ! [SY953: $i,SY954: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY953 ) @ SY954 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY953 ) @ SV391 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY954 ) @ SV391 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ SY954 ) @ SY953 ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV391 ) @ SY953 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2586]) ).
thf(2947,plain,
! [SV392: $i,SV728: $i] :
( ( ( ~ ( is_pname @ ( sK6_X_1 @ SV728 @ SV392 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK6_X_1 @ SV728 @ SV392 ) ) @ SV728 ) )
| ~ ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK6_X_1 @ SV728 @ SV392 ) ) @ SV392 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV728 ) @ SV392 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2587]) ).
thf(2948,plain,
! [SV393: $i] :
( ( ! [SY956: $i,SY957: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV393 @ SY956 ) @ SY957 ) )
| ( SV393 = SY957 )
| ( hBOOL @ ( hAPP_nat_bool @ SY956 @ SY957 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2588]) ).
thf(2949,plain,
! [SV393: $i] :
( ( ~ ( ~ ! [SY958: $i,SY959: $i] :
( ( SV393 != SY959 )
| ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV393 @ SY958 ) @ SY959 ) ) )
| ~ ! [SY960: $i,SY961: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ SY960 @ SY961 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV393 @ SY960 ) @ SY961 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2589]) ).
thf(2950,plain,
! [SV881: $i] :
( ( ! [SY1117: $i] :
~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ ( sK2_X_1 @ SY1117 @ SV881 ) ) @ SV881 ) )
| ~ ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( sK2_X_1 @ SY1117 @ SV881 ) ) @ SY1117 ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV881 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2590]) ).
thf(2951,plain,
! [SV882: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV882 ) )
| ! [SY1118: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SY1118 ) @ SV882 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY1118 ) @ ( sK1_M @ SV882 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2591]) ).
thf(2952,plain,
! [SV883: $i] :
( ( ! [SY1119: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ SV883 @ SY1119 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY1119 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2592]) ).
thf(2953,plain,
! [SV884: $i] :
( ( ! [SY1120: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY1120 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ SV884 @ SY1120 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2593]) ).
thf(2954,plain,
! [SV395: $i,SV2: $i] :
( ( ( is_a @ SV2 )
= $false )
| ( ( ~ ( is_fun_a_bool @ SV395 ) )
= $true )
| ( ( is_fun_a_bool @ ( insert_a @ SV2 @ SV395 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2595]) ).
thf(2955,plain,
! [SV400: $i,SV7: $i] :
( ( ( is_fun949378684l_bool @ SV7 )
= $false )
| ( ( ~ ( is_fun_a_bool @ SV400 ) )
= $true )
| ( ( is_bool @ ( hAPP_fun_a_bool_bool @ SV7 @ SV400 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2599]) ).
thf(2956,plain,
! [SV402: $i,SV9: $i] :
( ( ( is_fun1661590463l_bool @ SV9 )
= $false )
| ( ( ~ ( is_fun_pname_bool @ SV402 ) )
= $true )
| ( ( is_bool @ ( hAPP_f1664156314l_bool @ SV9 @ SV402 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2601]) ).
thf(2957,plain,
! [SV43: $i,SV432: $i] :
( ( ( is_fun_pname_bool @ SV432 )
= $false )
| ( ( ~ ( is_pname @ SV43 ) )
= $true )
| ( ( is_fun_pname_bool @ ( insert_pname @ SV43 @ SV432 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2619]) ).
thf(2958,plain,
! [SV44: $i,SV433: $i] :
( ( ( is_fun949378684l_bool @ SV433 )
= $false )
| ( ( ~ ( is_fun_a_bool @ SV44 ) )
= $true )
| ( ( is_fun949378684l_bool @ ( insert_fun_a_bool @ SV44 @ SV433 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2620]) ).
thf(2959,plain,
! [SV45: $i,SV434: $i] :
( ( ( is_fun1661590463l_bool @ SV434 )
= $false )
| ( ( ~ ( is_fun_pname_bool @ SV45 ) )
= $true )
| ( ( is_fun1661590463l_bool @ ( insert1325755072e_bool @ SV45 @ SV434 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2621]) ).
thf(2960,plain,
! [SV46: $i,SV435: $i] :
( ( ( is_a @ SV435 )
= $false )
| ( ( ~ ( is_fun_a_bool @ SV46 ) )
= $true )
| ( ( is_bool @ ( hAPP_a_bool @ SV46 @ SV435 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2622]) ).
thf(2961,plain,
! [SV438: $i,SV49: $i] :
( ( ( is_fun_pname_bool @ SV49 )
= $false )
| ( ( ~ ( is_pname @ SV438 ) )
= $true )
| ( ( is_bool @ ( hAPP_pname_bool @ SV49 @ SV438 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2625]) ).
thf(2962,plain,
! [SV530: $i,SV151: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ SV151 ) @ SV530 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SV151 ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SV530 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV530 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2707]) ).
thf(2963,plain,
! [SV531: $i,SV152: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ SV152 ) @ SV531 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SV152 ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SV531 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV531 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2708]) ).
thf(2964,plain,
! [SV532: $i,SV153: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ SV153 ) @ SV532 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SV153 ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SV532 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV532 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2709]) ).
thf(2965,plain,
! [SV533: $i,SV154: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV154 ) @ SV533 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV154 ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV533 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV533 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2710]) ).
thf(2966,plain,
! [SV534: $i,SV155: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV155 ) @ SV534 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SV155 ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SV534 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV534 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2711]) ).
thf(2967,plain,
! [SV535: $i,SV156: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV156 ) @ SV535 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SV156 ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SV535 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV535 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2712]) ).
thf(2968,plain,
! [SV536: $i,SV157: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ SV157 ) @ SV536 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SV536 ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SV157 ) ) )
| ( SV157 = SV536 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV536 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2713]) ).
thf(2969,plain,
! [SV537: $i,SV158: $i] :
( ( ( is_fun1661590463l_bool @ SV158 )
= $false )
| ( ( ~ ( is_fun1661590463l_bool @ SV537 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV537 ) )
| ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ SV158 ) @ SV537 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SV537 ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SV158 ) ) )
| ( SV158 = SV537 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2714]) ).
thf(2970,plain,
! [SV538: $i,SV159: $i] :
( ( ( is_fun949378684l_bool @ SV159 )
= $false )
| ( ( ~ ( is_fun949378684l_bool @ SV538 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV538 ) )
| ~ ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ SV159 ) @ SV538 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SV538 ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SV159 ) ) )
| ( SV159 = SV538 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2715]) ).
thf(2971,plain,
! [SV539: $i,SV160: $i] :
( ( ( is_fun_pname_bool @ SV160 )
= $false )
| ( ( ~ ( is_fun_pname_bool @ SV539 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV539 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV160 ) @ SV539 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV539 ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV160 ) ) )
| ( SV160 = SV539 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2716]) ).
thf(2972,plain,
! [SV540: $i,SV161: $i] :
( ( ( is_fun_a_bool @ SV161 )
= $false )
| ( ( ~ ( is_fun_a_bool @ SV540 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV540 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV161 ) @ SV540 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SV540 ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SV161 ) ) )
| ( SV161 = SV540 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2717]) ).
thf(2973,plain,
! [SV541: $i,SV162: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV162 ) @ SV541 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SV541 ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SV162 ) ) )
| ( SV162 = SV541 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV541 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2718]) ).
thf(2974,plain,
! [SV548: $i,SV169: $i] :
( ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ SV169 ) @ SV548 ) )
= $true )
| ( ( ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( insert_fun_nat_bool @ SV169 @ SV548 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SV548 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV548 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2725]) ).
thf(2975,plain,
! [SV549: $i,SV170: $i] :
( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ SV170 ) @ SV549 ) )
= $true )
| ( ( ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( insert1325755072e_bool @ SV170 @ SV549 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SV549 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV549 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2726]) ).
thf(2976,plain,
! [SV550: $i,SV171: $i] :
( ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ SV171 ) @ SV550 ) )
= $true )
| ( ( ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( insert_fun_a_bool @ SV171 @ SV550 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SV550 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV550 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2727]) ).
thf(2977,plain,
! [SV551: $i,SV172: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV172 ) @ SV551 ) )
= $true )
| ( ( ( hAPP_f22106695ol_nat @ finite_card_nat @ ( insert_nat @ SV172 @ SV551 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SV551 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV551 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2728]) ).
thf(2978,plain,
! [SV552: $i,SV173: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV173 ) @ SV552 ) )
= $true )
| ( ( ( hAPP_f921600141ol_nat @ finite_card_pname @ ( insert_pname @ SV173 @ SV552 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV552 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV552 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2729]) ).
thf(2979,plain,
! [SV553: $i,SV174: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV174 ) @ SV553 ) )
= $true )
| ( ( ( hAPP_fun_a_bool_nat @ finite_card_a @ ( insert_a @ SV174 @ SV553 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SV553 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV553 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2730]) ).
thf(2980,plain,
! [SV181: $i,SV556: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV556 ) @ SV181 ) ) )
= $true )
| ( ( SV181 = SV556 )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV181 ) @ SV556 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2733]) ).
thf(2981,plain,
! [SV182: $i,SV729: $i,SV557: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV557 ) @ SV729 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV729 ) @ SV182 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV557 ) @ SV182 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2734]) ).
thf(2982,plain,
! [SV187: $i,SV561: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV561 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV187 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ SV187 ) @ SV561 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2736]) ).
thf(2983,plain,
! [SV188: $i,SV562: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV562 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV188 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ SV188 ) @ SV562 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2737]) ).
thf(2984,plain,
! [SV189: $i,SV563: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV563 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV189 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV189 ) @ SV563 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2738]) ).
thf(2985,plain,
! [SV190: $i,SV564: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV564 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV190 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ SV190 ) @ SV564 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2739]) ).
thf(2986,plain,
! [SV191: $i,SV565: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV565 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV191 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV191 ) @ SV565 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2740]) ).
thf(2987,plain,
! [SV192: $i,SV566: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV566 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV192 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV192 ) @ SV566 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2741]) ).
thf(2988,plain,
! [SV567: $i,SV193: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ SV193 ) @ SV567 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV193 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV567 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2742]) ).
thf(2989,plain,
! [SV568: $i,SV194: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ SV194 ) @ SV568 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV194 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV568 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2743]) ).
thf(2990,plain,
! [SV569: $i,SV195: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV195 ) @ SV569 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV195 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV569 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2744]) ).
thf(2991,plain,
! [SV570: $i,SV196: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ SV196 ) @ SV570 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV196 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV570 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2745]) ).
thf(2992,plain,
! [SV571: $i,SV197: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV197 ) @ SV571 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV197 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV571 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2746]) ).
thf(2993,plain,
! [SV572: $i,SV198: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV198 ) @ SV572 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV198 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV572 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2747]) ).
thf(2994,plain,
! [SV574: $i,SV200: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV200 ) @ SV574 ) )
= $true )
| ( ( SV200
= ( hAPP_nat_nat @ suc @ SV574 ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV200 ) @ ( hAPP_nat_nat @ suc @ SV574 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2749]) ).
thf(2995,plain,
! [SV205: $i,SV732: $i,SV578: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV578 ) @ SV732 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV578 ) @ SV205 ) )
| ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV732 ) @ SV578 ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV205 ) @ SV578 ) )
= ( hAPP_nat_nat @ ( minus_minus_nat @ SV732 ) @ SV205 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2751]) ).
thf(2996,plain,
! [SV207: $i,SV733: $i,SV580: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV580 ) @ SV733 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV580 ) @ SV207 ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV733 ) @ SV207 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2753]) ).
thf(2997,plain,
! [SV208: $i,SV734: $i,SV581: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV581 ) @ SV734 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV208 ) @ SV734 ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV208 ) @ SV581 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2754]) ).
thf(2998,plain,
! [SV583: $i,SV210: $i,SV735: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV735 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV210 ) @ ( image_pname_a @ SV583 @ SV735 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV210 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2755]) ).
thf(2999,plain,
! [SV211: $i,SV584: $i,SV736: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( hAPP_n1699378549t_bool @ SV736 @ ( sK16_N_2 @ SV736 @ SV584 @ SV211 ) ) ) @ ( hAPP_n1699378549t_bool @ SV736 @ ( hAPP_nat_nat @ suc @ ( sK16_N_2 @ SV736 @ SV584 @ SV211 ) ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV211 ) @ SV584 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( hAPP_n1699378549t_bool @ SV736 @ SV211 ) ) @ ( hAPP_n1699378549t_bool @ SV736 @ SV584 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2756]) ).
thf(3000,plain,
! [SV212: $i,SV585: $i,SV737: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_n1025906991e_bool @ SV737 @ ( sK15_N_2 @ SV737 @ SV585 @ SV212 ) ) ) @ ( hAPP_n1025906991e_bool @ SV737 @ ( hAPP_nat_nat @ suc @ ( sK15_N_2 @ SV737 @ SV585 @ SV212 ) ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV212 ) @ SV585 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_n1025906991e_bool @ SV737 @ SV212 ) ) @ ( hAPP_n1025906991e_bool @ SV737 @ SV585 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2757]) ).
thf(3001,plain,
! [SV213: $i,SV586: $i,SV738: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ SV738 @ ( sK14_N_2 @ SV738 @ SV586 @ SV213 ) ) ) @ ( hAPP_nat_nat @ SV738 @ ( hAPP_nat_nat @ suc @ ( sK14_N_2 @ SV738 @ SV586 @ SV213 ) ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV213 ) @ SV586 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ SV738 @ SV213 ) ) @ ( hAPP_nat_nat @ SV738 @ SV586 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2758]) ).
thf(3002,plain,
! [SV214: $i,SV587: $i,SV739: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_nat_fun_a_bool @ SV739 @ ( sK13_N_2 @ SV739 @ SV587 @ SV214 ) ) ) @ ( hAPP_nat_fun_a_bool @ SV739 @ ( hAPP_nat_nat @ suc @ ( sK13_N_2 @ SV739 @ SV587 @ SV214 ) ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV214 ) @ SV587 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_nat_fun_a_bool @ SV739 @ SV214 ) ) @ ( hAPP_nat_fun_a_bool @ SV739 @ SV587 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2759]) ).
thf(3003,plain,
! [SV215: $i,SV816: $i,SV740: $i,SV588: $i] :
( ( ( ( SV588
!= ( hAPP_pname_a @ SV740 @ SV816 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV816 ) @ SV215 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV588 ) @ ( image_pname_a @ SV740 @ SV215 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2760]) ).
thf(3004,plain,
! [SV216: $i,SV589: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV589 ) @ SV216 ) ) )
= $true )
| ( ( SV216 = SV589 )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV216 ) @ SV589 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2761]) ).
thf(3005,plain,
! [SV590: $i,SV217: $i] :
( ( ( is_fun_pname_bool @ SV217 )
= $false )
| ( ( ~ ( is_fun_pname_bool @ SV590 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV217 ) @ SV590 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV590 ) @ SV217 ) )
| ( SV217 = SV590 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2762]) ).
thf(3006,plain,
! [SV591: $i,SV218: $i] :
( ( ( is_fun_a_bool @ SV218 )
= $false )
| ( ( ~ ( is_fun_a_bool @ SV591 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV218 ) @ SV591 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV591 ) @ SV218 ) )
| ( SV218 = SV591 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2763]) ).
thf(3007,plain,
! [SV219: $i,SV741: $i,SV592: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV592 ) @ SV741 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV219 ) @ SV592 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV219 ) @ SV741 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2764]) ).
thf(3008,plain,
! [SV220: $i,SV742: $i,SV593: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV593 ) @ SV742 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV220 ) @ SV593 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV220 ) @ SV742 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2765]) ).
thf(3009,plain,
! [SV221: $i,SV743: $i,SV594: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV594 ) @ SV743 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV221 ) @ SV594 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV221 ) @ SV743 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2766]) ).
thf(3010,plain,
! [SV744: $i,SV595: $i,SV222: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV222 ) @ ( insert_nat @ SV595 @ SV744 ) ) )
= $false )
| ( ( ( SV222 = SV595 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV222 ) @ SV744 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2767]) ).
thf(3011,plain,
! [SV596: $i,SV223: $i] :
( ( ( is_pname @ SV223 )
= $false )
| ( ( ~ ( is_pname @ SV596 ) )
= $true )
| ( ( ! [SY979: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV223 ) @ ( insert_pname @ SV596 @ SY979 ) ) )
| ( SV223 = SV596 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV223 ) @ SY979 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2768]) ).
thf(3012,plain,
! [SV597: $i,SV224: $i] :
( ( ( is_a @ SV224 )
= $false )
| ( ( ~ ( is_a @ SV597 ) )
= $true )
| ( ( ! [SY980: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV224 ) @ ( insert_a @ SV597 @ SY980 ) ) )
| ( SV224 = SV597 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV224 ) @ SY980 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2769]) ).
thf(3013,plain,
! [SV246: $i,SV748: $i,SV619: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV619 ) @ SV748 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV619 ) @ ( insert_nat @ SV246 @ SV748 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2770]) ).
thf(3014,plain,
! [SV247: $i,SV749: $i,SV620: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV620 ) @ SV749 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV620 ) @ ( insert_pname @ SV247 @ SV749 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2771]) ).
thf(3015,plain,
! [SV248: $i,SV750: $i,SV621: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV621 ) @ SV750 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV621 ) @ ( insert_a @ SV248 @ SV750 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2772]) ).
thf(3016,plain,
! [SV623: $i,SV250: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV250 ) @ SV623 ) ) )
= $true )
| ( ( ( insert_pname @ SV250 @ SV623 )
= SV623 )
= $true )
| ( ( is_fun_pname_bool @ SV623 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2774]) ).
thf(3017,plain,
! [SV624: $i,SV251: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV251 ) @ SV624 ) ) )
= $true )
| ( ( ( insert_a @ SV251 @ SV624 )
= SV624 )
= $true )
| ( ( is_fun_a_bool @ SV624 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2775]) ).
thf(3018,plain,
! [SV261: $i,SV751: $i,SV631: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV631 ) @ SV751 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV261 ) @ SV631 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV261 ) @ SV751 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2782]) ).
thf(3019,plain,
! [SV262: $i,SV752: $i,SV632: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV632 ) @ SV752 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV262 ) @ SV632 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV262 ) @ SV752 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2783]) ).
thf(3020,plain,
! [SV263: $i,SV753: $i,SV633: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV633 ) @ SV753 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV263 ) @ SV633 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV263 ) @ SV753 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2784]) ).
thf(3021,plain,
! [SV264: $i,SV754: $i,SV634: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV634 ) @ SV754 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV754 ) @ SV264 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV634 ) @ SV264 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2785]) ).
thf(3022,plain,
! [SV265: $i,SV755: $i,SV635: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV635 ) @ SV755 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV755 ) @ SV265 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV635 ) @ SV265 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2786]) ).
thf(3023,plain,
! [SV266: $i,SV756: $i,SV636: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV636 ) @ SV756 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV756 ) @ SV266 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV636 ) @ SV266 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2787]) ).
thf(3024,plain,
! [SV267: $i,SV757: $i,SV637: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV637 ) @ SV757 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV267 ) @ SV637 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV267 ) @ SV757 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2788]) ).
thf(3025,plain,
! [SV268: $i,SV758: $i,SV638: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV638 ) @ SV758 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV268 ) @ SV638 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV268 ) @ SV758 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2789]) ).
thf(3026,plain,
! [SV269: $i,SV759: $i,SV639: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV639 ) @ SV759 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV269 ) @ SV639 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV269 ) @ SV759 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2790]) ).
thf(3027,plain,
! [SV270: $i,SV760: $i,SV640: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV640 ) @ SV760 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV760 ) @ SV270 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV640 ) @ SV270 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2791]) ).
thf(3028,plain,
! [SV271: $i,SV761: $i,SV641: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV641 ) @ SV761 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV761 ) @ SV271 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV641 ) @ SV271 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2792]) ).
thf(3029,plain,
! [SV272: $i,SV762: $i,SV642: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV642 ) @ SV762 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV762 ) @ SV272 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV642 ) @ SV272 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2793]) ).
thf(3030,plain,
! [SV278: $i,SV763: $i,SV643: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV643 ) @ SV763 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( hAPP_pname_a @ SV278 @ SV643 ) ) @ ( image_pname_a @ SV278 @ SV763 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2794]) ).
thf(3031,plain,
! [SV644: $i,SV279: $i,SV817: $i,SV764: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV764 ) @ SV817 ) ) )
= $true )
| ( ( ( SV279
!= ( hAPP_pname_a @ SV644 @ SV764 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV279 ) @ ( image_pname_a @ SV644 @ SV817 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2795]) ).
thf(3032,plain,
! [SV289: $i,SV765: $i,SV654: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV654 ) @ SV765 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV654 ) @ ( insert_nat @ SV289 @ SV765 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2796]) ).
thf(3033,plain,
! [SV290: $i,SV766: $i,SV655: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV655 ) @ SV766 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV655 ) @ ( insert_pname @ SV290 @ SV766 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2797]) ).
thf(3034,plain,
! [SV291: $i,SV767: $i,SV656: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV656 ) @ SV767 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV656 ) @ ( insert_a @ SV291 @ SV767 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2798]) ).
thf(3035,plain,
! [SV292: $i,SV768: $i,SV657: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV657 ) @ SV768 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( insert_nat @ SV292 @ SV657 ) ) @ ( insert_nat @ SV292 @ SV768 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2799]) ).
thf(3036,plain,
! [SV293: $i,SV769: $i,SV658: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV658 ) @ SV769 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ SV293 @ SV658 ) ) @ ( insert_pname @ SV293 @ SV769 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2800]) ).
thf(3037,plain,
! [SV294: $i,SV770: $i,SV659: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV659 ) @ SV770 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV294 @ SV659 ) ) @ ( insert_a @ SV294 @ SV770 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2801]) ).
thf(3038,plain,
! [SV296: $i,SV772: $i,SV661: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV661 ) @ SV772 ) )
= $false )
| ( ( ( insert_a @ ( hAPP_pname_a @ SV296 @ SV661 ) @ ( image_pname_a @ SV296 @ SV772 ) )
= ( image_pname_a @ SV296 @ SV772 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2802]) ).
thf(3039,plain,
! [SV297: $i,SV773: $i,SV662: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV662 ) @ SV773 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_pname_a @ SV297 @ SV662 ) ) @ ( image_pname_a @ SV297 @ SV773 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2803]) ).
thf(3040,plain,
! [SV305: $i,SV664: $i] :
( ( ( hBOOL @ SV664 )
= $false )
| ( ( ~ ( hBOOL @ SV305 ) )
= $true )
| ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ SV664 ) @ SV305 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2806]) ).
thf(3041,plain,
! [SV668: $i,SV310: $i] :
( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ SV310 ) @ SV668 ) )
= $false )
| ( ( hBOOL @ SV310 )
= $true )
| ( ( hBOOL @ SV668 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2811]) ).
thf(3042,plain,
! [SV671: $i,SV313: $i] :
( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ SV313 ) @ SV671 ) )
= $false )
| ( ( ~ ( hBOOL @ SV313 ) )
= $true )
| ( ( hBOOL @ SV671 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2813]) ).
thf(3043,plain,
! [SV672: $i,SV314: $i] :
( ( ( is_a @ SV314 )
= $false )
| ( ( ~ ( is_a @ SV672 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_a_bool @ ( hAPP_a_fun_a_bool @ fequal_a @ SV314 ) @ SV672 ) )
| ( SV314 = SV672 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2814]) ).
thf(3044,plain,
! [SV676: $i,SV318: $i] :
( ( ( is_pname @ SV318 )
= $false )
| ( ( ~ ( is_pname @ SV676 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ fequal_pname @ SV318 ) @ SV676 ) )
| ( SV318 = SV676 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2818]) ).
thf(3045,plain,
! [SV679: $i,SV321: $i] :
( ( ( is_fun_a_bool @ SV321 )
= $false )
| ( ( ~ ( is_fun_a_bool @ SV679 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ SV321 ) @ SV679 ) )
| ( SV321 = SV679 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2820]) ).
thf(3046,plain,
! [SV686: $i,SV328: $i] :
( ( ( is_fun_pname_bool @ SV328 )
= $false )
| ( ( ~ ( is_fun_pname_bool @ SV686 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ SV328 ) @ SV686 ) )
| ( SV328 = SV686 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2824]) ).
thf(3047,plain,
! [SV885: $i,SV818: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV818 ) @ SV885 ) )
| ( hBOOL @ ( hAPP_nat_bool @ SV885 @ SV818 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2826]) ).
thf(3048,plain,
! [SV819: $i,SV886: $i] :
( ( ~ ( hBOOL @ ( hAPP_nat_bool @ SV886 @ SV819 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV819 ) @ SV886 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2827]) ).
thf(3049,plain,
! [SV887: $i,SV820: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV820 ) @ SV887 ) )
| ( hBOOL @ ( hAPP_pname_bool @ SV887 @ SV820 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2828]) ).
thf(3050,plain,
! [SV821: $i,SV888: $i] :
( ( ~ ( hBOOL @ ( hAPP_pname_bool @ SV888 @ SV821 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV821 ) @ SV888 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2829]) ).
thf(3051,plain,
! [SV822: $i,SV889: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ SV889 ) ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fconj @ SV889 ) @ SV822 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2830]) ).
thf(3052,plain,
! [SV823: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ SV823 ) ) ) )
= $true )
| ( ( ! [SY1059: $i] : ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fconj @ SY1059 ) @ SV823 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2831]) ).
thf(3053,plain,
! [SV890: $i,SV824: $i] :
( ( ( SV824 != SV890 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV824 ) @ SV890 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2832]) ).
thf(3054,plain,
! [SV891: $i,SV825: $i] :
( ( ( SV825 != SV891 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV891 ) @ SV825 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2833]) ).
thf(3055,plain,
! [SV364: $i] :
( ( ( ~ ( is_fun_a_bool @ SV364 ) )
= $true )
| ( ( ! [SY842: $i,SY843: $i] :
( ! [SY844: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY844 ) @ SY843 ) )
| ~ ( is_fun_pname_bool @ SY844 )
| ( SV364
!= ( image_pname_a @ SY842 @ SY844 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV364 ) @ ( image_pname_a @ SY842 @ SY843 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2834]) ).
thf(3056,plain,
! [SV364: $i] :
( ( ( ~ ( is_fun_a_bool @ SV364 ) )
= $true )
| ( ( ! [SY845: $i,SY846: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV364 ) @ ( image_pname_a @ SY845 @ SY846 ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( sK10_AA @ SY846 @ SY845 @ SV364 ) ) @ SY846 ) )
| ~ ( is_fun_pname_bool @ ( sK10_AA @ SY846 @ SY845 @ SV364 ) ) )
| ( SV364
!= ( image_pname_a @ SY845 @ ( sK10_AA @ SY846 @ SY845 @ SV364 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2835]) ).
thf(3057,plain,
! [SV892: $i,SV826: $i] :
( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV826 ) @ ( hAPP_nat_nat @ suc @ SV892 ) ) )
| ( SV826
= ( hAPP_nat_nat @ suc @ SV892 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV826 ) @ SV892 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2836]) ).
thf(3058,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( hAPP_nat_nat @ suc @ SX1 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX0 ) @ ( hAPP_nat_nat @ suc @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2837]) ).
thf(3059,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 @ SX0 ) @ ( hAPP_nat_nat @ suc @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2837]) ).
thf(3060,plain,
! [SV893: $i,SV827: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV827 ) @ SV893 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV893 ) @ SV827 ) )
| ( SV827 = SV893 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2838]) ).
thf(3061,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX0 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2839]) ).
thf(3062,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX1 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2839]) ).
thf(3063,plain,
! [SV828: $i,SV894: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV894 ) )
| ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ SV828 ) @ SV894 ) )
| ( ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( insert_fun_nat_bool @ SV828 @ SV894 ) )
= ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SV894 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2840]) ).
thf(3064,plain,
! [SV829: $i,SV895: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV895 ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ SV829 ) @ SV895 ) )
| ( ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( insert_fun_nat_bool @ SV829 @ SV895 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SV895 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2841]) ).
thf(3065,plain,
! [SV896: $i,SV830: $i] :
( ( ~ ( is_fun_pname_bool @ SV830 )
| ~ ( is_fun_pname_bool @ SV896 )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV830 ) @ SV896 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV896 ) @ SV830 ) )
| ( SV830 = SV896 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2842]) ).
thf(3066,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( is_fun_pname_bool @ SX0 )
| ~ ( is_fun_pname_bool @ SX1 )
| ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SX0 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2843]) ).
thf(3067,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( is_fun_pname_bool @ SX0 )
| ~ ( is_fun_pname_bool @ SX1 )
| ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SX1 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2843]) ).
thf(3068,plain,
! [SV831: $i,SV897: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ SV897 ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ SV897 ) @ SV831 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2844]) ).
thf(3069,plain,
! [SV832: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ SV832 ) ) ) )
= $true )
| ( ( ! [SY1068: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ SY1068 ) @ SV832 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2845]) ).
thf(3070,plain,
! [SV898: $i,SV833: $i] :
( ( ( ( hAPP_nat_nat @ suc @ SV833 )
!= ( hAPP_nat_nat @ suc @ SV898 ) )
| ( SV833 = SV898 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2846]) ).
thf(3071,plain,
! [SV899: $i,SV834: $i] :
( ( ( SV834 != SV899 )
| ( ( hAPP_nat_nat @ suc @ SV834 )
= ( hAPP_nat_nat @ suc @ SV899 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2847]) ).
thf(3072,plain,
! [SV900: $i,SV365: $i] :
( ( ! [SY1121: $i] :
( ~ ( is_pname @ SV365 )
| ~ ( is_pname @ SY1121 )
| ~ ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV365 @ SV900 ) @ SY1121 ) )
| ( SV365 = SY1121 )
| ( hBOOL @ ( hAPP_pname_bool @ SV900 @ SY1121 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2848]) ).
thf(3073,plain,
! [SV365: $i] :
( ( ~ ! [SY849: $i,SY850: $i] :
( ~ ( is_pname @ SV365 )
| ~ ( is_pname @ SY850 )
| ( SV365 != SY850 )
| ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV365 @ SY849 ) @ SY850 ) ) )
| ~ ! [SY851: $i,SY852: $i] :
( ~ ( is_pname @ SV365 )
| ~ ( is_pname @ SY852 )
| ~ ( hBOOL @ ( hAPP_pname_bool @ SY851 @ SY852 ) )
| ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV365 @ SY851 ) @ SY852 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2849]) ).
thf(3074,plain,
! [SV901: $i,SV366: $i] :
( ( ! [SY1122: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV366 ) @ ( insert_nat @ SV901 @ SY1122 ) ) )
| ( SV366 = SV901 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV366 ) @ SY1122 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2850]) ).
thf(3075,plain,
! [SV366: $i] :
( ( ~ ! [SY855: $i] :
( ( SV366 != SY855 )
| ! [SY856: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV366 ) @ ( insert_nat @ SY855 @ SY856 ) ) ) )
| ~ ! [SY857: $i,SY858: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV366 ) @ SY858 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV366 ) @ ( insert_nat @ SY857 @ SY858 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2851]) ).
thf(3076,plain,
! [SV902: $i,SV835: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ SV835 @ SV902 ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV902 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2852]) ).
thf(3077,plain,
! [SV836: $i,SV903: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV903 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ SV836 @ SV903 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2853]) ).
thf(3078,plain,
! [SV904: $i,SV367: $i] :
( ( ~ ( is_a @ SV367 )
| ~ ( is_a @ SV904 )
| ! [SY1123: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ ( insert_a @ SV904 @ SY1123 ) ) )
| ( SV367 = SV904 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ SY1123 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2854]) ).
thf(3079,plain,
! [SV367: $i] :
( ( ~ ! [SY861: $i] :
( ~ ( is_a @ SV367 )
| ~ ( is_a @ SY861 )
| ( SV367 != SY861 )
| ! [SY862: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ ( insert_a @ SY861 @ SY862 ) ) ) )
| ~ ! [SY863: $i] :
( ~ ( is_a @ SV367 )
| ~ ( is_a @ SY863 )
| ! [SY864: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ SY864 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ ( insert_a @ SY863 @ SY864 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2855]) ).
thf(3080,plain,
! [SV837: $i,SV905: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ SV905 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ SV905 ) @ SV837 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2856]) ).
thf(3081,plain,
! [SV838: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ SV838 ) ) ) )
= $true )
| ( ( ! [SY1074: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ SY1074 ) @ SV838 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2857]) ).
thf(3082,plain,
! [SV368: $i,SV906: $i] :
( ( ! [SY1124: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV906 ) @ SY1124 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY1124 ) @ ( insert_a @ SV906 @ SV368 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY1124 ) @ SV368 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2858]) ).
thf(3083,plain,
! [SV368: $i,SV907: $i] :
( ( ! [SY1125: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV907 ) @ SY1125 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY1125 ) @ SV368 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY1125 ) @ ( insert_a @ SV907 @ SV368 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2859]) ).
thf(3084,plain,
! [SV369: $i] :
( ( ( ~ ( is_a @ SV369 ) )
= $true )
| ( ( ! [SY869: $i,SY870: $i] :
( ! [SY871: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SY871 ) @ SY870 ) )
| ~ ( is_pname @ SY871 )
| ( SV369
!= ( hAPP_pname_a @ SY869 @ SY871 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV369 ) @ ( image_pname_a @ SY869 @ SY870 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2860]) ).
thf(3085,plain,
! [SV369: $i] :
( ( ( ~ ( is_a @ SV369 ) )
= $true )
| ( ( ! [SY872: $i,SY873: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV369 ) @ ( image_pname_a @ SY872 @ SY873 ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK11_X_1 @ SY873 @ SY872 @ SV369 ) ) @ SY873 ) )
| ~ ( is_pname @ ( sK11_X_1 @ SY873 @ SY872 @ SV369 ) ) )
| ( SV369
!= ( hAPP_pname_a @ SY872 @ ( sK11_X_1 @ SY873 @ SY872 @ SV369 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2861]) ).
thf(3086,plain,
! [SV370: $i,SV908: $i] :
( ( ! [SY1126: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV908 ) @ SY1126 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY1126 ) @ ( insert_nat @ SV908 @ SV370 ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY1126 ) @ SV370 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2862]) ).
thf(3087,plain,
! [SV370: $i,SV909: $i] :
( ( ! [SY1127: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV909 ) @ SY1127 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY1127 ) @ SV370 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY1127 ) @ ( insert_nat @ SV909 @ SV370 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2863]) ).
thf(3088,plain,
! [SV839: $i,SV910: $i] :
( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ SV910 ) ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fconj @ SV910 ) @ SV839 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2864]) ).
thf(3089,plain,
! [SV840: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ SV840 ) ) ) )
= $true )
| ( ( ! [SY1076: $i] : ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fconj @ SY1076 ) @ SV840 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2865]) ).
thf(3090,plain,
! [SV911: $i,SV841: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SV841 @ SV911 ) ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV911 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2866]) ).
thf(3091,plain,
! [SV842: $i,SV912: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV912 ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SV842 @ SV912 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2867]) ).
thf(3092,plain,
! [SV371: $i,SV913: $i] :
( ( ! [SY1128: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV913 ) @ SY1128 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV913 ) @ ( insert_nat @ SV371 @ SY1128 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2868]) ).
thf(3093,plain,
! [SV371: $i,SV914: $i] :
( ( ( SV914 != SV371 )
| ! [SY1129: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV914 ) @ ( insert_nat @ SV371 @ SY1129 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2869]) ).
thf(3094,plain,
! [SV915: $i,SV843: $i] :
( ( ~ ( is_fun_a_bool @ SV843 )
| ~ ( is_fun_a_bool @ SV915 )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV843 ) @ SV915 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV915 ) @ SV843 ) )
| ( SV843 = SV915 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2870]) ).
thf(3095,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 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2871]) ).
thf(3096,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 @ SX1 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2871]) ).
thf(3097,plain,
! [SV722: $i,SV372: $i,SV813: $i] :
( ( ( is_fun_a_bool @ SV813 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV813 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV813 ) @ ( image_pname_a @ SV372 @ SV722 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( sK17_C_2 @ SV813 @ SV722 @ SV372 ) ) @ SV722 ) )
| ~ ( is_fun_pname_bool @ ( sK17_C_2 @ SV813 @ SV722 @ SV372 ) ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( sK17_C_2 @ SV813 @ SV722 @ SV372 ) ) ) )
| ( SV813
!= ( image_pname_a @ SV372 @ ( sK17_C_2 @ SV813 @ SV722 @ SV372 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2872]) ).
thf(3098,plain,
! [SV844: $i,SV916: $i] :
( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ SV916 ) ) @ SV844 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV844 ) @ SV916 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2873]) ).
thf(3099,plain,
! [SV917: $i,SV845: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV845 ) @ SV917 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ SV917 ) ) @ SV845 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2874]) ).
thf(3100,plain,
! [SV373: $i,SV918: $i] :
( ( ! [SY1130: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV918 ) @ SY1130 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV918 ) @ ( insert_pname @ SV373 @ SY1130 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2875]) ).
thf(3101,plain,
! [SV373: $i,SV919: $i] :
( ( ( SV919 != SV373 )
| ! [SY1131: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV919 ) @ ( insert_pname @ SV373 @ SY1131 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2876]) ).
thf(3102,plain,
! [SV920: $i,SV846: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ SV846 ) ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ SV920 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ SV846 ) @ SV920 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2877]) ).
thf(3103,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2878]) ).
thf(3104,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2878]) ).
thf(3105,plain,
! [SV921: $i,SV374: $i] :
( ( ! [SY1132: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV374 ) @ SY1132 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV921 ) @ SY1132 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV374 @ SV921 ) ) @ SY1132 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2879]) ).
thf(3106,plain,
! [SV374: $i] :
( ( ~ ! [SY890: $i,SY891: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV374 @ SY890 ) ) @ SY891 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV374 ) @ SY891 ) ) )
| ~ ! [SY892: $i,SY893: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV374 @ SY892 ) ) @ SY893 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY892 ) @ SY893 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2880]) ).
thf(3107,plain,
! [SV922: $i,SV847: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ SV847 ) ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ SV922 ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ SV847 ) @ SV922 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2881]) ).
thf(3108,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2882]) ).
thf(3109,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2882]) ).
thf(3110,plain,
! [SV723: $i,SV375: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_pname_a @ SV375 @ SV723 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK12_X_1 @ SV723 @ SV375 ) ) @ SV723 ) )
| ~ ( is_pname @ ( sK12_X_1 @ SV723 @ SV375 ) ) )
| ~ ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ ( hAPP_f759274231e_bool @ ( cOMBC_1058051404l_bool @ member_pname ) @ SV723 ) ) @ ( hAPP_a93125764e_bool @ ( cOMBC_pname_a_bool @ ( cOMBB_1897541054_pname @ fequal_a @ SV375 ) ) @ ( hAPP_pname_a @ SV375 @ ( sK12_X_1 @ SV723 @ SV375 ) ) ) ) ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV723 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2883]) ).
thf(3111,plain,
! [SV923: $i,SV376: $i] :
( ( ! [SY1133: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV376 ) @ SY1133 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV923 ) @ SY1133 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( insert_nat @ SV376 @ SV923 ) ) @ SY1133 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2884]) ).
thf(3112,plain,
! [SV376: $i] :
( ( ~ ! [SY897: $i,SY898: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( insert_nat @ SV376 @ SY897 ) ) @ SY898 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV376 ) @ SY898 ) ) )
| ~ ! [SY899: $i,SY900: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( insert_nat @ SV376 @ SY899 ) ) @ SY900 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY899 ) @ SY900 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2885]) ).
thf(3113,plain,
! [SV848: $i,SV924: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV924 ) )
| ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ SV848 ) @ SV924 ) )
| ( ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( insert1325755072e_bool @ SV848 @ SV924 ) )
= ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SV924 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2886]) ).
thf(3114,plain,
! [SV849: $i,SV925: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV925 ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ SV849 ) @ SV925 ) )
| ( ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( insert1325755072e_bool @ SV849 @ SV925 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SV925 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2887]) ).
thf(3115,plain,
! [SV926: $i,SV850: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ SV850 @ SV926 ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV926 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2888]) ).
thf(3116,plain,
! [SV851: $i,SV927: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV927 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ SV851 @ SV927 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2889]) ).
thf(3117,plain,
! [SV377: $i,SV928: $i] :
( ( ! [SY1134: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV928 ) @ SY1134 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV928 ) @ SV377 ) )
| ( ( insert_nat @ SV928 @ SY1134 )
!= ( insert_nat @ SV928 @ SV377 ) )
| ( SY1134 = SV377 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2890]) ).
thf(3118,plain,
! [SV377: $i,SV929: $i] :
( ( ! [SY1135: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV929 ) @ SY1135 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV929 ) @ SV377 ) )
| ( SY1135 != SV377 )
| ( ( insert_nat @ SV929 @ SY1135 )
= ( insert_nat @ SV929 @ SV377 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2891]) ).
thf(3119,plain,
! [SV378: $i,SV724: $i] :
( ( ( ~ ( is_a @ ( sK7_X_1 @ SV724 @ SV378 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV724 ) @ SV378 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2892]) ).
thf(3120,plain,
! [SV378: $i,SV724: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( sK7_X_1 @ SV724 @ SV378 ) ) @ SV724 ) )
| ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( sK7_X_1 @ SV724 @ SV378 ) ) @ SV378 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV724 ) @ SV378 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2892]) ).
thf(3121,plain,
! [SV930: $i,SV852: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV852 ) @ SV930 ) )
| ( hBOOL @ ( hAPP_a_bool @ SV930 @ SV852 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2893]) ).
thf(3122,plain,
! [SV853: $i,SV931: $i] :
( ( ~ ( hBOOL @ ( hAPP_a_bool @ SV931 @ SV853 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV853 ) @ SV931 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2894]) ).
thf(3123,plain,
! [SV379: $i,SV932: $i] :
( ( ! [SY1136: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV932 ) @ SY1136 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV932 ) @ ( insert_a @ SV379 @ SY1136 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2895]) ).
thf(3124,plain,
! [SV379: $i,SV933: $i] :
( ( ( SV933 != SV379 )
| ! [SY1137: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV933 ) @ ( insert_a @ SV379 @ SY1137 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2896]) ).
thf(3125,plain,
! [SV854: $i,SV934: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV934 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV854 ) @ SV934 ) )
| ( ( hAPP_f22106695ol_nat @ finite_card_nat @ ( insert_nat @ SV854 @ SV934 ) )
= ( hAPP_f22106695ol_nat @ finite_card_nat @ SV934 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2897]) ).
thf(3126,plain,
! [SV855: $i,SV935: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV935 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV855 ) @ SV935 ) )
| ( ( hAPP_f22106695ol_nat @ finite_card_nat @ ( insert_nat @ SV855 @ SV935 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SV935 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2898]) ).
thf(3127,plain,
! [SV936: $i,SV856: $i] :
( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ SV856 @ SV936 ) ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV936 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2899]) ).
thf(3128,plain,
! [SV857: $i,SV937: $i] :
( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV937 ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ SV857 @ SV937 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2900]) ).
thf(3129,plain,
! [SV858: $i,SV938: $i] :
( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV938 ) )
| ~ ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ SV858 ) @ SV938 ) )
| ( ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( insert_fun_a_bool @ SV858 @ SV938 ) )
= ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SV938 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2901]) ).
thf(3130,plain,
! [SV859: $i,SV939: $i] :
( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV939 ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ SV859 ) @ SV939 ) )
| ( ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( insert_fun_a_bool @ SV859 @ SV939 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SV939 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2902]) ).
thf(3131,plain,
! [SV940: $i,SV860: $i] :
( ( ( SV860 != SV940 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV860 ) @ SV940 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2903]) ).
thf(3132,plain,
! [SV941: $i,SV861: $i] :
( ( ( SV861 != SV941 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV941 ) @ SV861 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2904]) ).
thf(3133,plain,
! [SV380: $i,SV725: $i,SV814: $i] :
( ( ( ~ ( is_pname @ ( sK3_X_1 @ SV814 @ SV725 @ SV380 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK3_X_1 @ SV814 @ SV725 @ SV380 ) ) @ SV814 ) )
| ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( hAPP_pname_a @ SV380 @ ( sK3_X_1 @ SV814 @ SV725 @ SV380 ) ) ) @ SV725 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_pname_a @ SV380 @ SV814 ) ) @ SV725 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2905]) ).
thf(3134,plain,
! [SV381: $i,SV942: $i] :
( ( ! [SY1138: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV942 ) @ SY1138 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV942 ) @ SV381 ) )
| ( ( hAPP_nat_nat @ ( minus_minus_nat @ SY1138 ) @ SV942 )
!= ( hAPP_nat_nat @ ( minus_minus_nat @ SV381 ) @ SV942 ) )
| ( SY1138 = SV381 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2906]) ).
thf(3135,plain,
! [SV381: $i,SV943: $i] :
( ( ! [SY1139: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV943 ) @ SY1139 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV943 ) @ SV381 ) )
| ( SY1139 != SV381 )
| ( ( hAPP_nat_nat @ ( minus_minus_nat @ SY1139 ) @ SV943 )
= ( hAPP_nat_nat @ ( minus_minus_nat @ SV381 ) @ SV943 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2907]) ).
thf(3136,plain,
! [SV382: $i,SV726: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ ( sK8_X_1 @ SV726 @ SV382 ) ) @ SV726 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV726 ) @ SV382 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2908]) ).
thf(3137,plain,
! [SV382: $i,SV726: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ ( sK8_X_1 @ SV726 @ SV382 ) ) @ SV382 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV726 ) @ SV382 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2908]) ).
thf(3138,plain,
! [SV944: $i,SV862: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ SV862 ) ) )
| ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ SV944 ) ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ SV862 ) @ SV944 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2909]) ).
thf(3139,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2910]) ).
thf(3140,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2910]) ).
thf(3141,plain,
! [SV863: $i,SV945: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ SV945 ) ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fconj @ SV945 ) @ SV863 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2911]) ).
thf(3142,plain,
! [SV864: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ SV864 ) ) ) )
= $true )
| ( ( ! [SY1100: $i] : ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fconj @ SY1100 ) @ SV864 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2912]) ).
thf(3143,plain,
! [SV865: $i,SV946: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV946 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV865 ) @ SV946 ) )
| ( ( hAPP_fun_a_bool_nat @ finite_card_a @ ( insert_a @ SV865 @ SV946 ) )
= ( hAPP_fun_a_bool_nat @ finite_card_a @ SV946 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2913]) ).
thf(3144,plain,
! [SV866: $i,SV947: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV947 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV866 ) @ SV947 ) )
| ( ( hAPP_fun_a_bool_nat @ finite_card_a @ ( insert_a @ SV866 @ SV947 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SV947 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2914]) ).
thf(3145,plain,
! [SV867: $i,SV948: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV948 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV867 ) @ SV948 ) )
| ( ( hAPP_f921600141ol_nat @ finite_card_pname @ ( insert_pname @ SV867 @ SV948 ) )
= ( hAPP_f921600141ol_nat @ finite_card_pname @ SV948 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2915]) ).
thf(3146,plain,
! [SV868: $i,SV949: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV949 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV868 ) @ SV949 ) )
| ( ( hAPP_f921600141ol_nat @ finite_card_pname @ ( insert_pname @ SV868 @ SV949 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV949 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2916]) ).
thf(3147,plain,
! [SV950: $i,SV383: $i] :
( ( ~ ( is_pname @ SV383 )
| ~ ( is_pname @ SV950 )
| ! [SY1140: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ ( insert_pname @ SV950 @ SY1140 ) ) )
| ( SV383 = SV950 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ SY1140 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2917]) ).
thf(3148,plain,
! [SV383: $i] :
( ( ~ ! [SY919: $i] :
( ~ ( is_pname @ SV383 )
| ~ ( is_pname @ SY919 )
| ( SV383 != SY919 )
| ! [SY920: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ ( insert_pname @ SY919 @ SY920 ) ) ) )
| ~ ! [SY921: $i] :
( ~ ( is_pname @ SV383 )
| ~ ( is_pname @ SY921 )
| ! [SY922: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ SY922 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ ( insert_pname @ SY921 @ SY922 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2918]) ).
thf(3149,plain,
! [SV951: $i,SV384: $i] :
( ( ! [SY1141: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV384 ) @ SY1141 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV951 ) @ SY1141 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ SV384 @ SV951 ) ) @ SY1141 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2919]) ).
thf(3150,plain,
! [SV384: $i] :
( ( ~ ! [SY925: $i,SY926: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ SV384 @ SY925 ) ) @ SY926 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV384 ) @ SY926 ) ) )
| ~ ! [SY927: $i,SY928: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ SV384 @ SY927 ) ) @ SY928 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY927 ) @ SY928 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2920]) ).
thf(3151,plain,
! [SV952: $i,SV869: $i] :
( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ SV869 ) ) )
| ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ SV952 ) ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ SV869 ) @ SV952 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2921]) ).
thf(3152,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2922]) ).
thf(3153,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2922]) ).
thf(3154,plain,
! [SV953: $i,SV385: $i] :
( ( ! [SY1142: $i] :
( ~ ( is_fun_a_bool @ SV385 )
| ~ ( is_fun_a_bool @ SY1142 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV953 ) @ SY1142 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV953 ) @ SV385 ) )
| ( ( insert_a @ SV953 @ SY1142 )
!= ( insert_a @ SV953 @ SV385 ) )
| ( SY1142 = SV385 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2923]) ).
thf(3155,plain,
! [SV954: $i,SV385: $i] :
( ( ! [SY1143: $i] :
( ~ ( is_fun_a_bool @ SV385 )
| ~ ( is_fun_a_bool @ SY1143 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV954 ) @ SY1143 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV954 ) @ SV385 ) )
| ( SY1143 != SV385 )
| ( ( insert_a @ SV954 @ SY1143 )
= ( insert_a @ SV954 @ SV385 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2924]) ).
thf(3156,plain,
! [SV955: $i,SV870: $i] :
( ( ( SV870 != SV955 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV870 ) @ SV955 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2925]) ).
thf(3157,plain,
! [SV956: $i,SV871: $i] :
( ( ( SV871 != SV956 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV956 ) @ SV871 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2926]) ).
thf(3158,plain,
! [SV957: $i,SV386: $i] :
( ( ! [SY1144: $i] :
( ~ ( is_a @ SV386 )
| ~ ( is_a @ SY1144 )
| ~ ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV386 @ SV957 ) @ SY1144 ) )
| ( SV386 = SY1144 )
| ( hBOOL @ ( hAPP_a_bool @ SV957 @ SY1144 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2927]) ).
thf(3159,plain,
! [SV386: $i] :
( ( ~ ! [SY935: $i,SY936: $i] :
( ~ ( is_a @ SV386 )
| ~ ( is_a @ SY936 )
| ( SV386 != SY936 )
| ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV386 @ SY935 ) @ SY936 ) ) )
| ~ ! [SY937: $i,SY938: $i] :
( ~ ( is_a @ SV386 )
| ~ ( is_a @ SY938 )
| ~ ( hBOOL @ ( hAPP_a_bool @ SY937 @ SY938 ) )
| ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV386 @ SY937 ) @ SY938 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2928]) ).
thf(3160,plain,
! [SV872: $i,SV958: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ SV958 ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ SV958 ) @ SV872 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2929]) ).
thf(3161,plain,
! [SV873: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ SV873 ) ) ) )
= $true )
| ( ( ! [SY1109: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ SY1109 ) @ SV873 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2930]) ).
thf(3162,plain,
! [SV959: $i,SV874: $i,SV387: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV387 ) @ ( image_pname_a @ SV874 @ SV959 ) ) )
| ~ ( ~ ( is_pname @ ( sK9_X_1 @ SV959 @ SV874 @ SV387 ) )
| ~ ~ ( ( SV387
!= ( hAPP_pname_a @ SV874 @ ( sK9_X_1 @ SV959 @ SV874 @ SV387 ) ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK9_X_1 @ SV959 @ SV874 @ SV387 ) ) @ SV959 ) ) ) ) )
= $true )
| ( ( is_a @ SV387 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2931]) ).
thf(3163,plain,
! [SV960: $i,SV875: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ SV875 @ SV960 ) ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV960 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2932]) ).
thf(3164,plain,
! [SV876: $i,SV961: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV961 ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ SV876 @ SV961 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2933]) ).
thf(3165,plain,
! [SV962: $i,SV877: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ SV877 ) ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ SV962 ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ SV877 ) @ SV962 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2934]) ).
thf(3166,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2935]) ).
thf(3167,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2935]) ).
thf(3168,plain,
! [SV388: $i,SV815: $i,SV727: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ SV727 @ SV815 ) )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ SV727 @ ( hAPP_nat_nat @ suc @ ( sK5_N_2 @ SV815 @ SV727 @ SV388 ) ) ) )
| ~ ~ ( hBOOL @ ( hAPP_nat_bool @ SV727 @ ( sK5_N_2 @ SV815 @ SV727 @ SV388 ) ) ) )
| ( hBOOL @ ( hAPP_nat_bool @ SV727 @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV815 ) @ SV388 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2936]) ).
thf(3169,plain,
! [SV963: $i,SV878: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ SV878 ) ) )
| ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ SV963 ) ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ SV878 ) @ SV963 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2937]) ).
thf(3170,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2938]) ).
thf(3171,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2938]) ).
thf(3172,plain,
! [SV964: $i,SV389: $i] :
( ( ! [SY1145: $i] :
( ~ ( is_fun_pname_bool @ SV389 )
| ~ ( is_fun_pname_bool @ SY1145 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV964 ) @ SY1145 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV964 ) @ SV389 ) )
| ( ( insert_pname @ SV964 @ SY1145 )
!= ( insert_pname @ SV964 @ SV389 ) )
| ( SY1145 = SV389 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2939]) ).
thf(3173,plain,
! [SV965: $i,SV389: $i] :
( ( ! [SY1146: $i] :
( ~ ( is_fun_pname_bool @ SV389 )
| ~ ( is_fun_pname_bool @ SY1146 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV965 ) @ SY1146 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV965 ) @ SV389 ) )
| ( SY1146 != SV389 )
| ( ( insert_pname @ SV965 @ SY1146 )
= ( insert_pname @ SV965 @ SV389 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2940]) ).
thf(3174,plain,
! [SV966: $i,SV879: $i] :
( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ SV879 ) ) @ ( hAPP_nat_nat @ suc @ SV966 ) ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV879 ) @ SV966 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2941]) ).
thf(3175,plain,
! [SV967: $i,SV880: $i] :
( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV880 ) @ SV967 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ SV880 ) ) @ ( hAPP_nat_nat @ suc @ SV967 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2942]) ).
thf(3176,plain,
! [SV390: $i,SV968: $i] :
( ( ! [SY1147: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV968 ) @ SY1147 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY1147 ) @ ( insert_pname @ SV968 @ SV390 ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY1147 ) @ SV390 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2943]) ).
thf(3177,plain,
! [SV390: $i,SV969: $i] :
( ( ! [SY1148: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV969 ) @ SY1148 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY1148 ) @ SV390 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY1148 ) @ ( insert_pname @ SV969 @ SV390 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2944]) ).
thf(3178,plain,
! [SV391: $i,SV970: $i] :
( ( ! [SY1149: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV970 ) @ SY1149 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV970 ) @ SV391 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ SY1149 ) @ SV970 ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV391 ) @ SV970 ) ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY1149 ) @ SV391 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2945]) ).
thf(3179,plain,
! [SV391: $i,SV971: $i] :
( ( ! [SY1150: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV971 ) @ SY1150 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV971 ) @ SV391 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY1150 ) @ SV391 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ SY1150 ) @ SV971 ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV391 ) @ SV971 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2946]) ).
thf(3180,plain,
! [SV392: $i,SV728: $i] :
( ( ( ~ ( is_pname @ ( sK6_X_1 @ SV728 @ SV392 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV728 ) @ SV392 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2947]) ).
thf(3181,plain,
! [SV392: $i,SV728: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK6_X_1 @ SV728 @ SV392 ) ) @ SV728 ) )
| ~ ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK6_X_1 @ SV728 @ SV392 ) ) @ SV392 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV728 ) @ SV392 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2947]) ).
thf(3182,plain,
! [SV972: $i,SV393: $i] :
( ( ! [SY1151: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV393 @ SV972 ) @ SY1151 ) )
| ( SV393 = SY1151 )
| ( hBOOL @ ( hAPP_nat_bool @ SV972 @ SY1151 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2948]) ).
thf(3183,plain,
! [SV393: $i] :
( ( ~ ! [SY958: $i,SY959: $i] :
( ( SV393 != SY959 )
| ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV393 @ SY958 ) @ SY959 ) ) )
| ~ ! [SY960: $i,SY961: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ SY960 @ SY961 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV393 @ SY960 ) @ SY961 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2949]) ).
thf(3184,plain,
! [SV881: $i] :
( ( ( ! [SY1117: $i] :
~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ ( sK2_X_1 @ SY1117 @ SV881 ) ) @ SV881 ) )
| ~ ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( sK2_X_1 @ SY1117 @ SV881 ) ) @ SY1117 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV881 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2950]) ).
thf(3185,plain,
! [SV882: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV882 ) ) )
= $true )
| ( ( ! [SY1118: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SY1118 ) @ SV882 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY1118 ) @ ( sK1_M @ SV882 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2951]) ).
thf(3186,plain,
! [SV973: $i,SV883: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ SV883 @ SV973 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV973 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2952]) ).
thf(3187,plain,
! [SV884: $i,SV974: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV974 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ SV884 @ SV974 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2953]) ).
thf(3188,plain,
! [SV2: $i,SV395: $i] :
( ( ( is_fun_a_bool @ SV395 )
= $false )
| ( ( is_a @ SV2 )
= $false )
| ( ( is_fun_a_bool @ ( insert_a @ SV2 @ SV395 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2954]) ).
thf(3189,plain,
! [SV7: $i,SV400: $i] :
( ( ( is_fun_a_bool @ SV400 )
= $false )
| ( ( is_fun949378684l_bool @ SV7 )
= $false )
| ( ( is_bool @ ( hAPP_fun_a_bool_bool @ SV7 @ SV400 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2955]) ).
thf(3190,plain,
! [SV9: $i,SV402: $i] :
( ( ( is_fun_pname_bool @ SV402 )
= $false )
| ( ( is_fun1661590463l_bool @ SV9 )
= $false )
| ( ( is_bool @ ( hAPP_f1664156314l_bool @ SV9 @ SV402 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2956]) ).
thf(3191,plain,
! [SV432: $i,SV43: $i] :
( ( ( is_pname @ SV43 )
= $false )
| ( ( is_fun_pname_bool @ SV432 )
= $false )
| ( ( is_fun_pname_bool @ ( insert_pname @ SV43 @ SV432 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2957]) ).
thf(3192,plain,
! [SV433: $i,SV44: $i] :
( ( ( is_fun_a_bool @ SV44 )
= $false )
| ( ( is_fun949378684l_bool @ SV433 )
= $false )
| ( ( is_fun949378684l_bool @ ( insert_fun_a_bool @ SV44 @ SV433 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2958]) ).
thf(3193,plain,
! [SV434: $i,SV45: $i] :
( ( ( is_fun_pname_bool @ SV45 )
= $false )
| ( ( is_fun1661590463l_bool @ SV434 )
= $false )
| ( ( is_fun1661590463l_bool @ ( insert1325755072e_bool @ SV45 @ SV434 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2959]) ).
thf(3194,plain,
! [SV435: $i,SV46: $i] :
( ( ( is_fun_a_bool @ SV46 )
= $false )
| ( ( is_a @ SV435 )
= $false )
| ( ( is_bool @ ( hAPP_a_bool @ SV46 @ SV435 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2960]) ).
thf(3195,plain,
! [SV49: $i,SV438: $i] :
( ( ( is_pname @ SV438 )
= $false )
| ( ( is_fun_pname_bool @ SV49 )
= $false )
| ( ( is_bool @ ( hAPP_pname_bool @ SV49 @ SV438 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2961]) ).
thf(3196,plain,
! [SV530: $i,SV151: $i] :
( ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ SV151 ) @ SV530 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SV151 ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SV530 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV530 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2962]) ).
thf(3197,plain,
! [SV531: $i,SV152: $i] :
( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ SV152 ) @ SV531 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SV152 ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SV531 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV531 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2963]) ).
thf(3198,plain,
! [SV532: $i,SV153: $i] :
( ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ SV153 ) @ SV532 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SV153 ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SV532 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV532 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2964]) ).
thf(3199,plain,
! [SV533: $i,SV154: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV154 ) @ SV533 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV154 ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV533 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV533 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2965]) ).
thf(3200,plain,
! [SV534: $i,SV155: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV155 ) @ SV534 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SV155 ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SV534 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV534 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2966]) ).
thf(3201,plain,
! [SV535: $i,SV156: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV156 ) @ SV535 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SV156 ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SV535 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV535 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2967]) ).
thf(3202,plain,
! [SV536: $i,SV157: $i] :
( ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ SV157 ) @ SV536 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SV536 ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SV157 ) ) )
| ( SV157 = SV536 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV536 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2968]) ).
thf(3203,plain,
! [SV158: $i,SV537: $i] :
( ( ( is_fun1661590463l_bool @ SV537 )
= $false )
| ( ( is_fun1661590463l_bool @ SV158 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV537 ) )
| ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ SV158 ) @ SV537 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SV537 ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SV158 ) ) )
| ( SV158 = SV537 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2969]) ).
thf(3204,plain,
! [SV159: $i,SV538: $i] :
( ( ( is_fun949378684l_bool @ SV538 )
= $false )
| ( ( is_fun949378684l_bool @ SV159 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV538 ) )
| ~ ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ SV159 ) @ SV538 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SV538 ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SV159 ) ) )
| ( SV159 = SV538 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2970]) ).
thf(3205,plain,
! [SV160: $i,SV539: $i] :
( ( ( is_fun_pname_bool @ SV539 )
= $false )
| ( ( is_fun_pname_bool @ SV160 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV539 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV160 ) @ SV539 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV539 ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV160 ) ) )
| ( SV160 = SV539 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2971]) ).
thf(3206,plain,
! [SV161: $i,SV540: $i] :
( ( ( is_fun_a_bool @ SV540 )
= $false )
| ( ( is_fun_a_bool @ SV161 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV540 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV161 ) @ SV540 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SV540 ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SV161 ) ) )
| ( SV161 = SV540 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2972]) ).
thf(3207,plain,
! [SV541: $i,SV162: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV162 ) @ SV541 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SV541 ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SV162 ) ) )
| ( SV162 = SV541 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV541 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2973]) ).
thf(3208,plain,
! [SV181: $i,SV556: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV556 ) @ SV181 ) )
= $false )
| ( ( SV181 = SV556 )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV181 ) @ SV556 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2980]) ).
thf(3209,plain,
! [SV557: $i,SV182: $i,SV729: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV729 ) @ SV182 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV557 ) @ SV182 ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV557 ) @ SV729 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2981]) ).
thf(3210,plain,
! [SV187: $i,SV561: $i] :
( ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV561 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV187 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ SV187 ) @ SV561 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2982]) ).
thf(3211,plain,
! [SV188: $i,SV562: $i] :
( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV562 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV188 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ SV188 ) @ SV562 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2983]) ).
thf(3212,plain,
! [SV189: $i,SV563: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV563 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV189 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV189 ) @ SV563 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2984]) ).
thf(3213,plain,
! [SV190: $i,SV564: $i] :
( ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV564 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV190 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ SV190 ) @ SV564 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2985]) ).
thf(3214,plain,
! [SV191: $i,SV565: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV565 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV191 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV191 ) @ SV565 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2986]) ).
thf(3215,plain,
! [SV192: $i,SV566: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV566 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV192 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV192 ) @ SV566 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2987]) ).
thf(3216,plain,
! [SV567: $i,SV193: $i] :
( ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ SV193 ) @ SV567 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV193 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV567 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2988]) ).
thf(3217,plain,
! [SV568: $i,SV194: $i] :
( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ SV194 ) @ SV568 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV194 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV568 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2989]) ).
thf(3218,plain,
! [SV569: $i,SV195: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV195 ) @ SV569 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV195 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV569 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2990]) ).
thf(3219,plain,
! [SV570: $i,SV196: $i] :
( ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ SV196 ) @ SV570 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV196 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV570 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2991]) ).
thf(3220,plain,
! [SV571: $i,SV197: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV197 ) @ SV571 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV197 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV571 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2992]) ).
thf(3221,plain,
! [SV572: $i,SV198: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV198 ) @ SV572 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV198 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV572 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2993]) ).
thf(3222,plain,
! [SV732: $i,SV205: $i,SV578: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV578 ) @ SV205 ) ) )
= $true )
| ( ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV732 ) @ SV578 ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV205 ) @ SV578 ) )
= ( hAPP_nat_nat @ ( minus_minus_nat @ SV732 ) @ SV205 ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV578 ) @ SV732 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2995]) ).
thf(3223,plain,
! [SV735: $i,SV583: $i,SV210: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV210 ) @ ( image_pname_a @ SV583 @ SV735 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV210 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV735 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2998]) ).
thf(3224,plain,
! [SV736: $i,SV584: $i,SV211: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV211 ) @ SV584 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( hAPP_n1699378549t_bool @ SV736 @ SV211 ) ) @ ( hAPP_n1699378549t_bool @ SV736 @ SV584 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( hAPP_n1699378549t_bool @ SV736 @ ( sK16_N_2 @ SV736 @ SV584 @ SV211 ) ) ) @ ( hAPP_n1699378549t_bool @ SV736 @ ( hAPP_nat_nat @ suc @ ( sK16_N_2 @ SV736 @ SV584 @ SV211 ) ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2999]) ).
thf(3225,plain,
! [SV737: $i,SV585: $i,SV212: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV212 ) @ SV585 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_n1025906991e_bool @ SV737 @ SV212 ) ) @ ( hAPP_n1025906991e_bool @ SV737 @ SV585 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_n1025906991e_bool @ SV737 @ ( sK15_N_2 @ SV737 @ SV585 @ SV212 ) ) ) @ ( hAPP_n1025906991e_bool @ SV737 @ ( hAPP_nat_nat @ suc @ ( sK15_N_2 @ SV737 @ SV585 @ SV212 ) ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3000]) ).
thf(3226,plain,
! [SV738: $i,SV586: $i,SV213: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV213 ) @ SV586 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ SV738 @ SV213 ) ) @ ( hAPP_nat_nat @ SV738 @ SV586 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ SV738 @ ( sK14_N_2 @ SV738 @ SV586 @ SV213 ) ) ) @ ( hAPP_nat_nat @ SV738 @ ( hAPP_nat_nat @ suc @ ( sK14_N_2 @ SV738 @ SV586 @ SV213 ) ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3001]) ).
thf(3227,plain,
! [SV739: $i,SV587: $i,SV214: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV214 ) @ SV587 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_nat_fun_a_bool @ SV739 @ SV214 ) ) @ ( hAPP_nat_fun_a_bool @ SV739 @ SV587 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_nat_fun_a_bool @ SV739 @ ( sK13_N_2 @ SV739 @ SV587 @ SV214 ) ) ) @ ( hAPP_nat_fun_a_bool @ SV739 @ ( hAPP_nat_nat @ suc @ ( sK13_N_2 @ SV739 @ SV587 @ SV214 ) ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3002]) ).
thf(3228,plain,
! [SV215: $i,SV816: $i,SV740: $i,SV588: $i] :
( ( ( SV588
= ( hAPP_pname_a @ SV740 @ SV816 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV816 ) @ SV215 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV588 ) @ ( image_pname_a @ SV740 @ SV215 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3003]) ).
thf(3229,plain,
! [SV216: $i,SV589: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV589 ) @ SV216 ) )
= $false )
| ( ( SV216 = SV589 )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV216 ) @ SV589 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3004]) ).
thf(3230,plain,
! [SV217: $i,SV590: $i] :
( ( ( is_fun_pname_bool @ SV590 )
= $false )
| ( ( is_fun_pname_bool @ SV217 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV217 ) @ SV590 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV590 ) @ SV217 ) )
| ( SV217 = SV590 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3005]) ).
thf(3231,plain,
! [SV218: $i,SV591: $i] :
( ( ( is_fun_a_bool @ SV591 )
= $false )
| ( ( is_fun_a_bool @ SV218 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV218 ) @ SV591 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV591 ) @ SV218 ) )
| ( SV218 = SV591 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3006]) ).
thf(3232,plain,
! [SV741: $i,SV592: $i,SV219: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV219 ) @ SV592 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV219 ) @ SV741 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV592 ) @ SV741 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3007]) ).
thf(3233,plain,
! [SV742: $i,SV593: $i,SV220: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV220 ) @ SV593 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV220 ) @ SV742 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV593 ) @ SV742 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3008]) ).
thf(3234,plain,
! [SV743: $i,SV594: $i,SV221: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV221 ) @ SV594 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV221 ) @ SV743 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV594 ) @ SV743 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3009]) ).
thf(3235,plain,
! [SV744: $i,SV595: $i,SV222: $i] :
( ( ( SV222 = SV595 )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV222 ) @ SV744 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV222 ) @ ( insert_nat @ SV595 @ SV744 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3010]) ).
thf(3236,plain,
! [SV223: $i,SV596: $i] :
( ( ( is_pname @ SV596 )
= $false )
| ( ( is_pname @ SV223 )
= $false )
| ( ( ! [SY979: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV223 ) @ ( insert_pname @ SV596 @ SY979 ) ) )
| ( SV223 = SV596 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV223 ) @ SY979 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3011]) ).
thf(3237,plain,
! [SV224: $i,SV597: $i] :
( ( ( is_a @ SV597 )
= $false )
| ( ( is_a @ SV224 )
= $false )
| ( ( ! [SY980: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV224 ) @ ( insert_a @ SV597 @ SY980 ) ) )
| ( SV224 = SV597 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV224 ) @ SY980 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3012]) ).
thf(3238,plain,
! [SV623: $i,SV250: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV250 ) @ SV623 ) )
= $false )
| ( ( ( insert_pname @ SV250 @ SV623 )
= SV623 )
= $true )
| ( ( is_fun_pname_bool @ SV623 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3016]) ).
thf(3239,plain,
! [SV624: $i,SV251: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV251 ) @ SV624 ) )
= $false )
| ( ( ( insert_a @ SV251 @ SV624 )
= SV624 )
= $true )
| ( ( is_fun_a_bool @ SV624 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3017]) ).
thf(3240,plain,
! [SV751: $i,SV631: $i,SV261: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV261 ) @ SV631 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV261 ) @ SV751 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV631 ) @ SV751 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3018]) ).
thf(3241,plain,
! [SV752: $i,SV632: $i,SV262: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV262 ) @ SV632 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV262 ) @ SV752 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV632 ) @ SV752 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3019]) ).
thf(3242,plain,
! [SV753: $i,SV633: $i,SV263: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV263 ) @ SV633 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV263 ) @ SV753 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV633 ) @ SV753 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3020]) ).
thf(3243,plain,
! [SV634: $i,SV264: $i,SV754: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV754 ) @ SV264 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV634 ) @ SV264 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV634 ) @ SV754 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3021]) ).
thf(3244,plain,
! [SV635: $i,SV265: $i,SV755: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV755 ) @ SV265 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV635 ) @ SV265 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV635 ) @ SV755 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3022]) ).
thf(3245,plain,
! [SV636: $i,SV266: $i,SV756: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV756 ) @ SV266 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV636 ) @ SV266 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV636 ) @ SV756 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3023]) ).
thf(3246,plain,
! [SV757: $i,SV637: $i,SV267: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV267 ) @ SV637 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV267 ) @ SV757 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV637 ) @ SV757 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3024]) ).
thf(3247,plain,
! [SV758: $i,SV638: $i,SV268: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV268 ) @ SV638 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV268 ) @ SV758 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV638 ) @ SV758 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3025]) ).
thf(3248,plain,
! [SV759: $i,SV639: $i,SV269: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV269 ) @ SV639 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV269 ) @ SV759 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV639 ) @ SV759 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3026]) ).
thf(3249,plain,
! [SV640: $i,SV270: $i,SV760: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV760 ) @ SV270 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV640 ) @ SV270 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV640 ) @ SV760 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3027]) ).
thf(3250,plain,
! [SV641: $i,SV271: $i,SV761: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV761 ) @ SV271 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV641 ) @ SV271 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV641 ) @ SV761 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3028]) ).
thf(3251,plain,
! [SV642: $i,SV272: $i,SV762: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV762 ) @ SV272 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV642 ) @ SV272 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV642 ) @ SV762 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3029]) ).
thf(3252,plain,
! [SV644: $i,SV279: $i,SV817: $i,SV764: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV764 ) @ SV817 ) )
= $false )
| ( ( ( SV279
!= ( hAPP_pname_a @ SV644 @ SV764 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV279 ) @ ( image_pname_a @ SV644 @ SV817 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3031]) ).
thf(3253,plain,
! [SV664: $i,SV305: $i] :
( ( ( hBOOL @ SV305 )
= $false )
| ( ( hBOOL @ SV664 )
= $false )
| ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ SV664 ) @ SV305 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3040]) ).
thf(3254,plain,
! [SV671: $i,SV313: $i] :
( ( ( hBOOL @ SV313 )
= $false )
| ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ SV313 ) @ SV671 ) )
= $false )
| ( ( hBOOL @ SV671 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3042]) ).
thf(3255,plain,
! [SV314: $i,SV672: $i] :
( ( ( is_a @ SV672 )
= $false )
| ( ( is_a @ SV314 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_a_bool @ ( hAPP_a_fun_a_bool @ fequal_a @ SV314 ) @ SV672 ) )
| ( SV314 = SV672 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3043]) ).
thf(3256,plain,
! [SV318: $i,SV676: $i] :
( ( ( is_pname @ SV676 )
= $false )
| ( ( is_pname @ SV318 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ fequal_pname @ SV318 ) @ SV676 ) )
| ( SV318 = SV676 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3044]) ).
thf(3257,plain,
! [SV321: $i,SV679: $i] :
( ( ( is_fun_a_bool @ SV679 )
= $false )
| ( ( is_fun_a_bool @ SV321 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ SV321 ) @ SV679 ) )
| ( SV321 = SV679 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3045]) ).
thf(3258,plain,
! [SV328: $i,SV686: $i] :
( ( ( is_fun_pname_bool @ SV686 )
= $false )
| ( ( is_fun_pname_bool @ SV328 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ SV328 ) @ SV686 ) )
| ( SV328 = SV686 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3046]) ).
thf(3259,plain,
! [SV885: $i,SV818: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV818 ) @ SV885 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ SV885 @ SV818 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3047]) ).
thf(3260,plain,
! [SV819: $i,SV886: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ SV886 @ SV819 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV819 ) @ SV886 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3048]) ).
thf(3261,plain,
! [SV887: $i,SV820: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV820 ) @ SV887 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_pname_bool @ SV887 @ SV820 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3049]) ).
thf(3262,plain,
! [SV821: $i,SV888: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_pname_bool @ SV888 @ SV821 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV821 ) @ SV888 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3050]) ).
thf(3263,plain,
! [SV822: $i,SV889: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ SV889 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fconj @ SV889 ) @ SV822 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3051]) ).
thf(3264,plain,
! [SV823: $i] :
( ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ SV823 ) ) )
= $false )
| ( ( ! [SY1059: $i] : ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fconj @ SY1059 ) @ SV823 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3052]) ).
thf(3265,plain,
! [SV890: $i,SV824: $i] :
( ( ( ( SV824 != SV890 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV824 ) @ SV890 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3053]) ).
thf(3266,plain,
! [SV891: $i,SV825: $i] :
( ( ( ( SV825 != SV891 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV891 ) @ SV825 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3054]) ).
thf(3267,plain,
! [SV364: $i] :
( ( ( is_fun_a_bool @ SV364 )
= $false )
| ( ( ! [SY842: $i,SY843: $i] :
( ! [SY844: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY844 ) @ SY843 ) )
| ~ ( is_fun_pname_bool @ SY844 )
| ( SV364
!= ( image_pname_a @ SY842 @ SY844 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV364 ) @ ( image_pname_a @ SY842 @ SY843 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3055]) ).
thf(3268,plain,
! [SV364: $i] :
( ( ( is_fun_a_bool @ SV364 )
= $false )
| ( ( ! [SY845: $i,SY846: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV364 ) @ ( image_pname_a @ SY845 @ SY846 ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( sK10_AA @ SY846 @ SY845 @ SV364 ) ) @ SY846 ) )
| ~ ( is_fun_pname_bool @ ( sK10_AA @ SY846 @ SY845 @ SV364 ) ) )
| ( SV364
!= ( image_pname_a @ SY845 @ ( sK10_AA @ SY846 @ SY845 @ SV364 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3056]) ).
thf(3269,plain,
! [SV892: $i,SV826: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV826 ) @ ( hAPP_nat_nat @ suc @ SV892 ) ) ) )
= $true )
| ( ( ( SV826
= ( hAPP_nat_nat @ suc @ SV892 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV826 ) @ SV892 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3057]) ).
thf(3270,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( hAPP_nat_nat @ suc @ SX1 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX0 ) @ ( hAPP_nat_nat @ suc @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3058]) ).
thf(3271,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 @ SX0 ) @ ( hAPP_nat_nat @ suc @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3059]) ).
thf(3272,plain,
! [SV893: $i,SV827: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV827 ) @ SV893 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV893 ) @ SV827 ) ) )
= $true )
| ( ( SV827 = SV893 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3060]) ).
thf(3273,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3061]) ).
thf(3274,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3062]) ).
thf(3275,plain,
! [SV828: $i,SV894: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV894 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ SV828 ) @ SV894 ) )
| ( ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( insert_fun_nat_bool @ SV828 @ SV894 ) )
= ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SV894 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3063]) ).
thf(3276,plain,
! [SV829: $i,SV895: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV895 ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ SV829 ) @ SV895 ) )
| ( ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( insert_fun_nat_bool @ SV829 @ SV895 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SV895 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3064]) ).
thf(3277,plain,
! [SV896: $i,SV830: $i] :
( ( ( ~ ( is_fun_pname_bool @ SV830 )
| ~ ( is_fun_pname_bool @ SV896 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV830 ) @ SV896 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV896 ) @ SV830 ) )
| ( SV830 = SV896 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3065]) ).
thf(3278,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( is_fun_pname_bool @ SX0 )
| ~ ( is_fun_pname_bool @ SX1 )
| ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3066]) ).
thf(3279,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( is_fun_pname_bool @ SX0 )
| ~ ( is_fun_pname_bool @ SX1 )
| ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3067]) ).
thf(3280,plain,
! [SV831: $i,SV897: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ SV897 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ SV897 ) @ SV831 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3068]) ).
thf(3281,plain,
! [SV832: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ SV832 ) ) )
= $false )
| ( ( ! [SY1068: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ SY1068 ) @ SV832 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3069]) ).
thf(3282,plain,
! [SV898: $i,SV833: $i] :
( ( ( ( ( hAPP_nat_nat @ suc @ SV833 )
!= ( hAPP_nat_nat @ suc @ SV898 ) ) )
= $true )
| ( ( SV833 = SV898 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3070]) ).
thf(3283,plain,
! [SV899: $i,SV834: $i] :
( ( ( ( SV834 != SV899 ) )
= $true )
| ( ( ( hAPP_nat_nat @ suc @ SV834 )
= ( hAPP_nat_nat @ suc @ SV899 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3071]) ).
thf(3284,plain,
! [SV900: $i,SV975: $i,SV365: $i] :
( ( ~ ( is_pname @ SV365 )
| ~ ( is_pname @ SV975 )
| ~ ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV365 @ SV900 ) @ SV975 ) )
| ( SV365 = SV975 )
| ( hBOOL @ ( hAPP_pname_bool @ SV900 @ SV975 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3072]) ).
thf(3285,plain,
! [SV365: $i] :
( ( ~ ! [SY849: $i,SY850: $i] :
( ~ ( is_pname @ SV365 )
| ~ ( is_pname @ SY850 )
| ( SV365 != SY850 )
| ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV365 @ SY849 ) @ SY850 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3073]) ).
thf(3286,plain,
! [SV365: $i] :
( ( ~ ! [SY851: $i,SY852: $i] :
( ~ ( is_pname @ SV365 )
| ~ ( is_pname @ SY852 )
| ~ ( hBOOL @ ( hAPP_pname_bool @ SY851 @ SY852 ) )
| ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV365 @ SY851 ) @ SY852 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3073]) ).
thf(3287,plain,
! [SV976: $i,SV901: $i,SV366: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV366 ) @ ( insert_nat @ SV901 @ SV976 ) ) )
| ( SV366 = SV901 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV366 ) @ SV976 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3074]) ).
thf(3288,plain,
! [SV366: $i] :
( ( ~ ! [SY855: $i] :
( ( SV366 != SY855 )
| ! [SY856: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV366 ) @ ( insert_nat @ SY855 @ SY856 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3075]) ).
thf(3289,plain,
! [SV366: $i] :
( ( ~ ! [SY857: $i,SY858: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV366 ) @ SY858 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV366 ) @ ( insert_nat @ SY857 @ SY858 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3075]) ).
thf(3290,plain,
! [SV902: $i,SV835: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ SV835 @ SV902 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV902 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3076]) ).
thf(3291,plain,
! [SV836: $i,SV903: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV903 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ SV836 @ SV903 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3077]) ).
thf(3292,plain,
! [SV904: $i,SV367: $i] :
( ( ( ~ ( is_a @ SV367 )
| ~ ( is_a @ SV904 ) )
= $true )
| ( ( ! [SY1123: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ ( insert_a @ SV904 @ SY1123 ) ) )
| ( SV367 = SV904 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ SY1123 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3078]) ).
thf(3293,plain,
! [SV367: $i] :
( ( ~ ! [SY861: $i] :
( ~ ( is_a @ SV367 )
| ~ ( is_a @ SY861 )
| ( SV367 != SY861 )
| ! [SY862: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ ( insert_a @ SY861 @ SY862 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3079]) ).
thf(3294,plain,
! [SV367: $i] :
( ( ~ ! [SY863: $i] :
( ~ ( is_a @ SV367 )
| ~ ( is_a @ SY863 )
| ! [SY864: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ SY864 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ ( insert_a @ SY863 @ SY864 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3079]) ).
thf(3295,plain,
! [SV837: $i,SV905: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ SV905 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ SV905 ) @ SV837 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3080]) ).
thf(3296,plain,
! [SV838: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ SV838 ) ) )
= $false )
| ( ( ! [SY1074: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ SY1074 ) @ SV838 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3081]) ).
thf(3297,plain,
! [SV368: $i,SV977: $i,SV906: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV906 ) @ SV977 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV977 ) @ ( insert_a @ SV906 @ SV368 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV977 ) @ SV368 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3082]) ).
thf(3298,plain,
! [SV368: $i,SV978: $i,SV907: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV907 ) @ SV978 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV978 ) @ SV368 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV978 ) @ ( insert_a @ SV907 @ SV368 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3083]) ).
thf(3299,plain,
! [SV369: $i] :
( ( ( is_a @ SV369 )
= $false )
| ( ( ! [SY869: $i,SY870: $i] :
( ! [SY871: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SY871 ) @ SY870 ) )
| ~ ( is_pname @ SY871 )
| ( SV369
!= ( hAPP_pname_a @ SY869 @ SY871 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV369 ) @ ( image_pname_a @ SY869 @ SY870 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3084]) ).
thf(3300,plain,
! [SV369: $i] :
( ( ( is_a @ SV369 )
= $false )
| ( ( ! [SY872: $i,SY873: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV369 ) @ ( image_pname_a @ SY872 @ SY873 ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK11_X_1 @ SY873 @ SY872 @ SV369 ) ) @ SY873 ) )
| ~ ( is_pname @ ( sK11_X_1 @ SY873 @ SY872 @ SV369 ) ) )
| ( SV369
!= ( hAPP_pname_a @ SY872 @ ( sK11_X_1 @ SY873 @ SY872 @ SV369 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3085]) ).
thf(3301,plain,
! [SV370: $i,SV979: $i,SV908: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV908 ) @ SV979 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV979 ) @ ( insert_nat @ SV908 @ SV370 ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV979 ) @ SV370 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3086]) ).
thf(3302,plain,
! [SV370: $i,SV980: $i,SV909: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV909 ) @ SV980 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV980 ) @ SV370 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV980 ) @ ( insert_nat @ SV909 @ SV370 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3087]) ).
thf(3303,plain,
! [SV839: $i,SV910: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ SV910 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fconj @ SV910 ) @ SV839 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3088]) ).
thf(3304,plain,
! [SV840: $i] :
( ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ SV840 ) ) )
= $false )
| ( ( ! [SY1076: $i] : ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fconj @ SY1076 ) @ SV840 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3089]) ).
thf(3305,plain,
! [SV911: $i,SV841: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SV841 @ SV911 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV911 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3090]) ).
thf(3306,plain,
! [SV842: $i,SV912: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV912 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SV842 @ SV912 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3091]) ).
thf(3307,plain,
! [SV371: $i,SV981: $i,SV913: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV913 ) @ SV981 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV913 ) @ ( insert_nat @ SV371 @ SV981 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3092]) ).
thf(3308,plain,
! [SV371: $i,SV914: $i] :
( ( ( ( SV914 != SV371 ) )
= $true )
| ( ( ! [SY1129: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV914 ) @ ( insert_nat @ SV371 @ SY1129 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3093]) ).
thf(3309,plain,
! [SV915: $i,SV843: $i] :
( ( ( ~ ( is_fun_a_bool @ SV843 )
| ~ ( is_fun_a_bool @ SV915 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV843 ) @ SV915 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV915 ) @ SV843 ) )
| ( SV843 = SV915 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3094]) ).
thf(3310,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 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3095]) ).
thf(3311,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 @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3096]) ).
thf(3312,plain,
! [SV722: $i,SV372: $i,SV813: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV813 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV813 ) @ ( image_pname_a @ SV372 @ SV722 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( sK17_C_2 @ SV813 @ SV722 @ SV372 ) ) @ SV722 ) )
| ~ ( is_fun_pname_bool @ ( sK17_C_2 @ SV813 @ SV722 @ SV372 ) ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( sK17_C_2 @ SV813 @ SV722 @ SV372 ) ) ) )
| ( SV813
!= ( image_pname_a @ SV372 @ ( sK17_C_2 @ SV813 @ SV722 @ SV372 ) ) ) ) )
= $true )
| ( ( is_fun_a_bool @ SV813 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3097]) ).
thf(3313,plain,
! [SV844: $i,SV916: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ SV916 ) ) @ SV844 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV844 ) @ SV916 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3098]) ).
thf(3314,plain,
! [SV917: $i,SV845: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV845 ) @ SV917 ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ SV917 ) ) @ SV845 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3099]) ).
thf(3315,plain,
! [SV373: $i,SV982: $i,SV918: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV918 ) @ SV982 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV918 ) @ ( insert_pname @ SV373 @ SV982 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3100]) ).
thf(3316,plain,
! [SV373: $i,SV919: $i] :
( ( ( ( SV919 != SV373 ) )
= $true )
| ( ( ! [SY1131: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV919 ) @ ( insert_pname @ SV373 @ SY1131 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3101]) ).
thf(3317,plain,
! [SV920: $i,SV846: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ SV846 ) ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ SV920 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ SV846 ) @ SV920 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3102]) ).
thf(3318,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3103]) ).
thf(3319,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3104]) ).
thf(3320,plain,
! [SV921: $i,SV983: $i,SV374: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV374 ) @ SV983 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV921 ) @ SV983 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV374 @ SV921 ) ) @ SV983 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3105]) ).
thf(3321,plain,
! [SV374: $i] :
( ( ~ ! [SY890: $i,SY891: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV374 @ SY890 ) ) @ SY891 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV374 ) @ SY891 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3106]) ).
thf(3322,plain,
! [SV374: $i] :
( ( ~ ! [SY892: $i,SY893: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV374 @ SY892 ) ) @ SY893 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY892 ) @ SY893 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3106]) ).
thf(3323,plain,
! [SV922: $i,SV847: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ SV847 ) ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ SV922 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ SV847 ) @ SV922 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3107]) ).
thf(3324,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3108]) ).
thf(3325,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3109]) ).
thf(3326,plain,
! [SV375: $i,SV723: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK12_X_1 @ SV723 @ SV375 ) ) @ SV723 ) )
| ~ ( is_pname @ ( sK12_X_1 @ SV723 @ SV375 ) ) )
| ~ ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ ( hAPP_f759274231e_bool @ ( cOMBC_1058051404l_bool @ member_pname ) @ SV723 ) ) @ ( hAPP_a93125764e_bool @ ( cOMBC_pname_a_bool @ ( cOMBB_1897541054_pname @ fequal_a @ SV375 ) ) @ ( hAPP_pname_a @ SV375 @ ( sK12_X_1 @ SV723 @ SV375 ) ) ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_pname_a @ SV375 @ SV723 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV723 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3110]) ).
thf(3327,plain,
! [SV923: $i,SV984: $i,SV376: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV376 ) @ SV984 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV923 ) @ SV984 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( insert_nat @ SV376 @ SV923 ) ) @ SV984 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3111]) ).
thf(3328,plain,
! [SV376: $i] :
( ( ~ ! [SY897: $i,SY898: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( insert_nat @ SV376 @ SY897 ) ) @ SY898 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV376 ) @ SY898 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3112]) ).
thf(3329,plain,
! [SV376: $i] :
( ( ~ ! [SY899: $i,SY900: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( insert_nat @ SV376 @ SY899 ) ) @ SY900 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY899 ) @ SY900 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3112]) ).
thf(3330,plain,
! [SV848: $i,SV924: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV924 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ SV848 ) @ SV924 ) )
| ( ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( insert1325755072e_bool @ SV848 @ SV924 ) )
= ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SV924 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3113]) ).
thf(3331,plain,
! [SV849: $i,SV925: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV925 ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ SV849 ) @ SV925 ) )
| ( ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( insert1325755072e_bool @ SV849 @ SV925 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SV925 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3114]) ).
thf(3332,plain,
! [SV926: $i,SV850: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ SV850 @ SV926 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV926 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3115]) ).
thf(3333,plain,
! [SV851: $i,SV927: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV927 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ SV851 @ SV927 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3116]) ).
thf(3334,plain,
! [SV377: $i,SV985: $i,SV928: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV928 ) @ SV985 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV928 ) @ SV377 ) )
| ( ( insert_nat @ SV928 @ SV985 )
!= ( insert_nat @ SV928 @ SV377 ) )
| ( SV985 = SV377 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3117]) ).
thf(3335,plain,
! [SV377: $i,SV986: $i,SV929: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV929 ) @ SV986 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV929 ) @ SV377 ) )
| ( SV986 != SV377 )
| ( ( insert_nat @ SV929 @ SV986 )
= ( insert_nat @ SV929 @ SV377 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3118]) ).
thf(3336,plain,
! [SV378: $i,SV724: $i] :
( ( ( is_a @ ( sK7_X_1 @ SV724 @ SV378 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV724 ) @ SV378 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3119]) ).
thf(3337,plain,
! [SV378: $i,SV724: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( sK7_X_1 @ SV724 @ SV378 ) ) @ SV724 ) )
| ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( sK7_X_1 @ SV724 @ SV378 ) ) @ SV378 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV724 ) @ SV378 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3120]) ).
thf(3338,plain,
! [SV930: $i,SV852: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV852 ) @ SV930 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_a_bool @ SV930 @ SV852 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3121]) ).
thf(3339,plain,
! [SV853: $i,SV931: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_a_bool @ SV931 @ SV853 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV853 ) @ SV931 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3122]) ).
thf(3340,plain,
! [SV379: $i,SV987: $i,SV932: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV932 ) @ SV987 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV932 ) @ ( insert_a @ SV379 @ SV987 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3123]) ).
thf(3341,plain,
! [SV379: $i,SV933: $i] :
( ( ( ( SV933 != SV379 ) )
= $true )
| ( ( ! [SY1137: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV933 ) @ ( insert_a @ SV379 @ SY1137 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3124]) ).
thf(3342,plain,
! [SV854: $i,SV934: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV934 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV854 ) @ SV934 ) )
| ( ( hAPP_f22106695ol_nat @ finite_card_nat @ ( insert_nat @ SV854 @ SV934 ) )
= ( hAPP_f22106695ol_nat @ finite_card_nat @ SV934 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3125]) ).
thf(3343,plain,
! [SV855: $i,SV935: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV935 ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV855 ) @ SV935 ) )
| ( ( hAPP_f22106695ol_nat @ finite_card_nat @ ( insert_nat @ SV855 @ SV935 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SV935 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3126]) ).
thf(3344,plain,
! [SV936: $i,SV856: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ SV856 @ SV936 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV936 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3127]) ).
thf(3345,plain,
! [SV857: $i,SV937: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV937 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ SV857 @ SV937 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3128]) ).
thf(3346,plain,
! [SV858: $i,SV938: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV938 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ SV858 ) @ SV938 ) )
| ( ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( insert_fun_a_bool @ SV858 @ SV938 ) )
= ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SV938 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3129]) ).
thf(3347,plain,
! [SV859: $i,SV939: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV939 ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ SV859 ) @ SV939 ) )
| ( ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( insert_fun_a_bool @ SV859 @ SV939 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SV939 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3130]) ).
thf(3348,plain,
! [SV940: $i,SV860: $i] :
( ( ( ( SV860 != SV940 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV860 ) @ SV940 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3131]) ).
thf(3349,plain,
! [SV941: $i,SV861: $i] :
( ( ( ( SV861 != SV941 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV941 ) @ SV861 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3132]) ).
thf(3350,plain,
! [SV380: $i,SV725: $i,SV814: $i] :
( ( ( ~ ( is_pname @ ( sK3_X_1 @ SV814 @ SV725 @ SV380 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_pname_a @ SV380 @ SV814 ) ) @ SV725 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3133]) ).
thf(3351,plain,
! [SV380: $i,SV725: $i,SV814: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK3_X_1 @ SV814 @ SV725 @ SV380 ) ) @ SV814 ) )
| ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( hAPP_pname_a @ SV380 @ ( sK3_X_1 @ SV814 @ SV725 @ SV380 ) ) ) @ SV725 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_pname_a @ SV380 @ SV814 ) ) @ SV725 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3133]) ).
thf(3352,plain,
! [SV381: $i,SV988: $i,SV942: $i] :
( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV942 ) @ SV988 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV942 ) @ SV381 ) )
| ( ( hAPP_nat_nat @ ( minus_minus_nat @ SV988 ) @ SV942 )
!= ( hAPP_nat_nat @ ( minus_minus_nat @ SV381 ) @ SV942 ) )
| ( SV988 = SV381 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3134]) ).
thf(3353,plain,
! [SV381: $i,SV989: $i,SV943: $i] :
( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV943 ) @ SV989 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV943 ) @ SV381 ) )
| ( SV989 != SV381 )
| ( ( hAPP_nat_nat @ ( minus_minus_nat @ SV989 ) @ SV943 )
= ( hAPP_nat_nat @ ( minus_minus_nat @ SV381 ) @ SV943 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3135]) ).
thf(3354,plain,
! [SV382: $i,SV726: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ ( sK8_X_1 @ SV726 @ SV382 ) ) @ SV726 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV726 ) @ SV382 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3136]) ).
thf(3355,plain,
! [SV382: $i,SV726: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ ( sK8_X_1 @ SV726 @ SV382 ) ) @ SV382 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV726 ) @ SV382 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3137]) ).
thf(3356,plain,
! [SV944: $i,SV862: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ SV862 ) ) )
| ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ SV944 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ SV862 ) @ SV944 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3138]) ).
thf(3357,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3139]) ).
thf(3358,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3140]) ).
thf(3359,plain,
! [SV863: $i,SV945: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ SV945 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fconj @ SV945 ) @ SV863 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3141]) ).
thf(3360,plain,
! [SV864: $i] :
( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ SV864 ) ) )
= $false )
| ( ( ! [SY1100: $i] : ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fconj @ SY1100 ) @ SV864 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3142]) ).
thf(3361,plain,
! [SV865: $i,SV946: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV946 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV865 ) @ SV946 ) )
| ( ( hAPP_fun_a_bool_nat @ finite_card_a @ ( insert_a @ SV865 @ SV946 ) )
= ( hAPP_fun_a_bool_nat @ finite_card_a @ SV946 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3143]) ).
thf(3362,plain,
! [SV866: $i,SV947: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV947 ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV866 ) @ SV947 ) )
| ( ( hAPP_fun_a_bool_nat @ finite_card_a @ ( insert_a @ SV866 @ SV947 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SV947 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3144]) ).
thf(3363,plain,
! [SV867: $i,SV948: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV948 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV867 ) @ SV948 ) )
| ( ( hAPP_f921600141ol_nat @ finite_card_pname @ ( insert_pname @ SV867 @ SV948 ) )
= ( hAPP_f921600141ol_nat @ finite_card_pname @ SV948 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3145]) ).
thf(3364,plain,
! [SV868: $i,SV949: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV949 ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV868 ) @ SV949 ) )
| ( ( hAPP_f921600141ol_nat @ finite_card_pname @ ( insert_pname @ SV868 @ SV949 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV949 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3146]) ).
thf(3365,plain,
! [SV950: $i,SV383: $i] :
( ( ( ~ ( is_pname @ SV383 )
| ~ ( is_pname @ SV950 ) )
= $true )
| ( ( ! [SY1140: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ ( insert_pname @ SV950 @ SY1140 ) ) )
| ( SV383 = SV950 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ SY1140 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3147]) ).
thf(3366,plain,
! [SV383: $i] :
( ( ~ ! [SY919: $i] :
( ~ ( is_pname @ SV383 )
| ~ ( is_pname @ SY919 )
| ( SV383 != SY919 )
| ! [SY920: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ ( insert_pname @ SY919 @ SY920 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3148]) ).
thf(3367,plain,
! [SV383: $i] :
( ( ~ ! [SY921: $i] :
( ~ ( is_pname @ SV383 )
| ~ ( is_pname @ SY921 )
| ! [SY922: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ SY922 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ ( insert_pname @ SY921 @ SY922 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3148]) ).
thf(3368,plain,
! [SV951: $i,SV990: $i,SV384: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV384 ) @ SV990 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV951 ) @ SV990 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ SV384 @ SV951 ) ) @ SV990 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3149]) ).
thf(3369,plain,
! [SV384: $i] :
( ( ~ ! [SY925: $i,SY926: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ SV384 @ SY925 ) ) @ SY926 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV384 ) @ SY926 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3150]) ).
thf(3370,plain,
! [SV384: $i] :
( ( ~ ! [SY927: $i,SY928: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ SV384 @ SY927 ) ) @ SY928 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY927 ) @ SY928 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3150]) ).
thf(3371,plain,
! [SV952: $i,SV869: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ SV869 ) ) )
| ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ SV952 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ SV869 ) @ SV952 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3151]) ).
thf(3372,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3152]) ).
thf(3373,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3153]) ).
thf(3374,plain,
! [SV953: $i,SV991: $i,SV385: $i] :
( ( ~ ( is_fun_a_bool @ SV385 )
| ~ ( is_fun_a_bool @ SV991 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV953 ) @ SV991 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV953 ) @ SV385 ) )
| ( ( insert_a @ SV953 @ SV991 )
!= ( insert_a @ SV953 @ SV385 ) )
| ( SV991 = SV385 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3154]) ).
thf(3375,plain,
! [SV954: $i,SV992: $i,SV385: $i] :
( ( ~ ( is_fun_a_bool @ SV385 )
| ~ ( is_fun_a_bool @ SV992 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV954 ) @ SV992 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV954 ) @ SV385 ) )
| ( SV992 != SV385 )
| ( ( insert_a @ SV954 @ SV992 )
= ( insert_a @ SV954 @ SV385 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3155]) ).
thf(3376,plain,
! [SV955: $i,SV870: $i] :
( ( ( ( SV870 != SV955 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV870 ) @ SV955 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3156]) ).
thf(3377,plain,
! [SV956: $i,SV871: $i] :
( ( ( ( SV871 != SV956 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV956 ) @ SV871 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3157]) ).
thf(3378,plain,
! [SV957: $i,SV993: $i,SV386: $i] :
( ( ~ ( is_a @ SV386 )
| ~ ( is_a @ SV993 )
| ~ ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV386 @ SV957 ) @ SV993 ) )
| ( SV386 = SV993 )
| ( hBOOL @ ( hAPP_a_bool @ SV957 @ SV993 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3158]) ).
thf(3379,plain,
! [SV386: $i] :
( ( ~ ! [SY935: $i,SY936: $i] :
( ~ ( is_a @ SV386 )
| ~ ( is_a @ SY936 )
| ( SV386 != SY936 )
| ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV386 @ SY935 ) @ SY936 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3159]) ).
thf(3380,plain,
! [SV386: $i] :
( ( ~ ! [SY937: $i,SY938: $i] :
( ~ ( is_a @ SV386 )
| ~ ( is_a @ SY938 )
| ~ ( hBOOL @ ( hAPP_a_bool @ SY937 @ SY938 ) )
| ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV386 @ SY937 ) @ SY938 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3159]) ).
thf(3381,plain,
! [SV872: $i,SV958: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ SV958 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ SV958 ) @ SV872 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3160]) ).
thf(3382,plain,
! [SV873: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ SV873 ) ) )
= $false )
| ( ( ! [SY1109: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ SY1109 ) @ SV873 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3161]) ).
thf(3383,plain,
! [SV959: $i,SV874: $i,SV387: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV387 ) @ ( image_pname_a @ SV874 @ SV959 ) ) ) )
= $true )
| ( ( ~ ( ~ ( is_pname @ ( sK9_X_1 @ SV959 @ SV874 @ SV387 ) )
| ~ ~ ( ( SV387
!= ( hAPP_pname_a @ SV874 @ ( sK9_X_1 @ SV959 @ SV874 @ SV387 ) ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK9_X_1 @ SV959 @ SV874 @ SV387 ) ) @ SV959 ) ) ) ) )
= $true )
| ( ( is_a @ SV387 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3162]) ).
thf(3384,plain,
! [SV960: $i,SV875: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ SV875 @ SV960 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV960 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3163]) ).
thf(3385,plain,
! [SV876: $i,SV961: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV961 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ SV876 @ SV961 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3164]) ).
thf(3386,plain,
! [SV962: $i,SV877: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ SV877 ) ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ SV962 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ SV877 ) @ SV962 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3165]) ).
thf(3387,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3166]) ).
thf(3388,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3167]) ).
thf(3389,plain,
! [SV388: $i,SV815: $i,SV727: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ SV727 @ ( hAPP_nat_nat @ suc @ ( sK5_N_2 @ SV815 @ SV727 @ SV388 ) ) ) )
| ~ ~ ( hBOOL @ ( hAPP_nat_bool @ SV727 @ ( sK5_N_2 @ SV815 @ SV727 @ SV388 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ SV727 @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV815 ) @ SV388 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ SV727 @ SV815 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3168]) ).
thf(3390,plain,
! [SV963: $i,SV878: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ SV878 ) ) )
| ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ SV963 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ SV878 ) @ SV963 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3169]) ).
thf(3391,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3170]) ).
thf(3392,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3171]) ).
thf(3393,plain,
! [SV964: $i,SV994: $i,SV389: $i] :
( ( ~ ( is_fun_pname_bool @ SV389 )
| ~ ( is_fun_pname_bool @ SV994 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV964 ) @ SV994 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV964 ) @ SV389 ) )
| ( ( insert_pname @ SV964 @ SV994 )
!= ( insert_pname @ SV964 @ SV389 ) )
| ( SV994 = SV389 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3172]) ).
thf(3394,plain,
! [SV965: $i,SV995: $i,SV389: $i] :
( ( ~ ( is_fun_pname_bool @ SV389 )
| ~ ( is_fun_pname_bool @ SV995 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV965 ) @ SV995 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV965 ) @ SV389 ) )
| ( SV995 != SV389 )
| ( ( insert_pname @ SV965 @ SV995 )
= ( insert_pname @ SV965 @ SV389 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3173]) ).
thf(3395,plain,
! [SV966: $i,SV879: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ SV879 ) ) @ ( hAPP_nat_nat @ suc @ SV966 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV879 ) @ SV966 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3174]) ).
thf(3396,plain,
! [SV967: $i,SV880: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV880 ) @ SV967 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ SV880 ) ) @ ( hAPP_nat_nat @ suc @ SV967 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3175]) ).
thf(3397,plain,
! [SV390: $i,SV996: $i,SV968: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV968 ) @ SV996 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV996 ) @ ( insert_pname @ SV968 @ SV390 ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV996 ) @ SV390 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3176]) ).
thf(3398,plain,
! [SV390: $i,SV997: $i,SV969: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV969 ) @ SV997 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV997 ) @ SV390 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV997 ) @ ( insert_pname @ SV969 @ SV390 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3177]) ).
thf(3399,plain,
! [SV391: $i,SV998: $i,SV970: $i] :
( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV970 ) @ SV998 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV970 ) @ SV391 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV998 ) @ SV970 ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV391 ) @ SV970 ) ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV998 ) @ SV391 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3178]) ).
thf(3400,plain,
! [SV391: $i,SV999: $i,SV971: $i] :
( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV971 ) @ SV999 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV971 ) @ SV391 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV999 ) @ SV391 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV999 ) @ SV971 ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV391 ) @ SV971 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3179]) ).
thf(3401,plain,
! [SV392: $i,SV728: $i] :
( ( ( is_pname @ ( sK6_X_1 @ SV728 @ SV392 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV728 ) @ SV392 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3180]) ).
thf(3402,plain,
! [SV392: $i,SV728: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK6_X_1 @ SV728 @ SV392 ) ) @ SV728 ) )
| ~ ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK6_X_1 @ SV728 @ SV392 ) ) @ SV392 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV728 ) @ SV392 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3181]) ).
thf(3403,plain,
! [SV1000: $i,SV972: $i,SV393: $i] :
( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV393 @ SV972 ) @ SV1000 ) )
| ( SV393 = SV1000 )
| ( hBOOL @ ( hAPP_nat_bool @ SV972 @ SV1000 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3182]) ).
thf(3404,plain,
! [SV393: $i] :
( ( ~ ! [SY958: $i,SY959: $i] :
( ( SV393 != SY959 )
| ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV393 @ SY958 ) @ SY959 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3183]) ).
thf(3405,plain,
! [SV393: $i] :
( ( ~ ! [SY960: $i,SY961: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ SY960 @ SY961 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV393 @ SY960 ) @ SY961 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3183]) ).
thf(3406,plain,
! [SV881: $i,SV1001: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ ( sK2_X_1 @ SV1001 @ SV881 ) ) @ SV881 ) )
| ~ ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( sK2_X_1 @ SV1001 @ SV881 ) ) @ SV1001 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV881 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3184]) ).
thf(3407,plain,
! [SV882: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV882 ) )
= $false )
| ( ( ! [SY1118: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SY1118 ) @ SV882 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY1118 ) @ ( sK1_M @ SV882 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3185]) ).
thf(3408,plain,
! [SV973: $i,SV883: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ SV883 @ SV973 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV973 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3186]) ).
thf(3409,plain,
! [SV884: $i,SV974: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV974 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ SV884 @ SV974 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3187]) ).
thf(3410,plain,
! [SV157: $i,SV536: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SV536 ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SV157 ) ) ) )
= $true )
| ( ( SV157 = SV536 )
= $true )
| ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ SV157 ) @ SV536 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV536 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3202]) ).
thf(3411,plain,
! [SV158: $i,SV537: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV537 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ SV158 ) @ SV537 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SV537 ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SV158 ) ) )
| ( SV158 = SV537 ) )
= $true )
| ( ( is_fun1661590463l_bool @ SV158 )
= $false )
| ( ( is_fun1661590463l_bool @ SV537 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3203]) ).
thf(3412,plain,
! [SV159: $i,SV538: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV538 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ SV159 ) @ SV538 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SV538 ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SV159 ) ) )
| ( SV159 = SV538 ) )
= $true )
| ( ( is_fun949378684l_bool @ SV159 )
= $false )
| ( ( is_fun949378684l_bool @ SV538 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3204]) ).
thf(3413,plain,
! [SV160: $i,SV539: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV539 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV160 ) @ SV539 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV539 ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV160 ) ) )
| ( SV160 = SV539 ) )
= $true )
| ( ( is_fun_pname_bool @ SV160 )
= $false )
| ( ( is_fun_pname_bool @ SV539 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3205]) ).
thf(3414,plain,
! [SV161: $i,SV540: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV540 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV161 ) @ SV540 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SV540 ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SV161 ) ) )
| ( SV161 = SV540 ) )
= $true )
| ( ( is_fun_a_bool @ SV161 )
= $false )
| ( ( is_fun_a_bool @ SV540 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3206]) ).
thf(3415,plain,
! [SV162: $i,SV541: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SV541 ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SV162 ) ) ) )
= $true )
| ( ( SV162 = SV541 )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV162 ) @ SV541 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV541 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3207]) ).
thf(3416,plain,
! [SV557: $i,SV182: $i,SV729: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV729 ) @ SV182 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV557 ) @ SV182 ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV557 ) @ SV729 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3209]) ).
thf(3417,plain,
! [SV732: $i,SV205: $i,SV578: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV578 ) @ SV205 ) )
= $false )
| ( ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV732 ) @ SV578 ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV205 ) @ SV578 ) )
= ( hAPP_nat_nat @ ( minus_minus_nat @ SV732 ) @ SV205 ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV578 ) @ SV732 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3222]) ).
thf(3418,plain,
! [SV735: $i,SV583: $i,SV210: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV210 ) @ ( image_pname_a @ SV583 @ SV735 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV210 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV735 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3223]) ).
thf(3419,plain,
! [SV736: $i,SV584: $i,SV211: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV211 ) @ SV584 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( hAPP_n1699378549t_bool @ SV736 @ SV211 ) ) @ ( hAPP_n1699378549t_bool @ SV736 @ SV584 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( hAPP_n1699378549t_bool @ SV736 @ ( sK16_N_2 @ SV736 @ SV584 @ SV211 ) ) ) @ ( hAPP_n1699378549t_bool @ SV736 @ ( hAPP_nat_nat @ suc @ ( sK16_N_2 @ SV736 @ SV584 @ SV211 ) ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3224]) ).
thf(3420,plain,
! [SV737: $i,SV585: $i,SV212: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV212 ) @ SV585 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_n1025906991e_bool @ SV737 @ SV212 ) ) @ ( hAPP_n1025906991e_bool @ SV737 @ SV585 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_n1025906991e_bool @ SV737 @ ( sK15_N_2 @ SV737 @ SV585 @ SV212 ) ) ) @ ( hAPP_n1025906991e_bool @ SV737 @ ( hAPP_nat_nat @ suc @ ( sK15_N_2 @ SV737 @ SV585 @ SV212 ) ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3225]) ).
thf(3421,plain,
! [SV738: $i,SV586: $i,SV213: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV213 ) @ SV586 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ SV738 @ SV213 ) ) @ ( hAPP_nat_nat @ SV738 @ SV586 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ SV738 @ ( sK14_N_2 @ SV738 @ SV586 @ SV213 ) ) ) @ ( hAPP_nat_nat @ SV738 @ ( hAPP_nat_nat @ suc @ ( sK14_N_2 @ SV738 @ SV586 @ SV213 ) ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3226]) ).
thf(3422,plain,
! [SV739: $i,SV587: $i,SV214: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV214 ) @ SV587 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_nat_fun_a_bool @ SV739 @ SV214 ) ) @ ( hAPP_nat_fun_a_bool @ SV739 @ SV587 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_nat_fun_a_bool @ SV739 @ ( sK13_N_2 @ SV739 @ SV587 @ SV214 ) ) ) @ ( hAPP_nat_fun_a_bool @ SV739 @ ( hAPP_nat_nat @ suc @ ( sK13_N_2 @ SV739 @ SV587 @ SV214 ) ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3227]) ).
thf(3423,plain,
! [SV740: $i,SV588: $i,SV215: $i,SV816: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV816 ) @ SV215 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV588 ) @ ( image_pname_a @ SV740 @ SV215 ) ) )
= $true )
| ( ( SV588
= ( hAPP_pname_a @ SV740 @ SV816 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3228]) ).
thf(3424,plain,
! [SV590: $i,SV217: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV217 ) @ SV590 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV590 ) @ SV217 ) )
| ( SV217 = SV590 ) )
= $true )
| ( ( is_fun_pname_bool @ SV217 )
= $false )
| ( ( is_fun_pname_bool @ SV590 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3230]) ).
thf(3425,plain,
! [SV591: $i,SV218: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV218 ) @ SV591 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV591 ) @ SV218 ) )
| ( SV218 = SV591 ) )
= $true )
| ( ( is_fun_a_bool @ SV218 )
= $false )
| ( ( is_fun_a_bool @ SV591 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3231]) ).
thf(3426,plain,
! [SV741: $i,SV592: $i,SV219: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV219 ) @ SV592 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV219 ) @ SV741 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV592 ) @ SV741 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3232]) ).
thf(3427,plain,
! [SV742: $i,SV593: $i,SV220: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV220 ) @ SV593 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV220 ) @ SV742 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV593 ) @ SV742 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3233]) ).
thf(3428,plain,
! [SV743: $i,SV594: $i,SV221: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV221 ) @ SV594 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV221 ) @ SV743 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV594 ) @ SV743 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3234]) ).
thf(3429,plain,
! [SV1002: $i,SV596: $i,SV223: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV223 ) @ ( insert_pname @ SV596 @ SV1002 ) ) )
| ( SV223 = SV596 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV223 ) @ SV1002 ) ) )
= $true )
| ( ( is_pname @ SV223 )
= $false )
| ( ( is_pname @ SV596 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3236]) ).
thf(3430,plain,
! [SV1003: $i,SV597: $i,SV224: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV224 ) @ ( insert_a @ SV597 @ SV1003 ) ) )
| ( SV224 = SV597 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV224 ) @ SV1003 ) ) )
= $true )
| ( ( is_a @ SV224 )
= $false )
| ( ( is_a @ SV597 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3237]) ).
thf(3431,plain,
! [SV751: $i,SV631: $i,SV261: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV261 ) @ SV631 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV261 ) @ SV751 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV631 ) @ SV751 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3240]) ).
thf(3432,plain,
! [SV752: $i,SV632: $i,SV262: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV262 ) @ SV632 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV262 ) @ SV752 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV632 ) @ SV752 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3241]) ).
thf(3433,plain,
! [SV753: $i,SV633: $i,SV263: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV263 ) @ SV633 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV263 ) @ SV753 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV633 ) @ SV753 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3242]) ).
thf(3434,plain,
! [SV634: $i,SV264: $i,SV754: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV754 ) @ SV264 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV634 ) @ SV264 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV634 ) @ SV754 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3243]) ).
thf(3435,plain,
! [SV635: $i,SV265: $i,SV755: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV755 ) @ SV265 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV635 ) @ SV265 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV635 ) @ SV755 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3244]) ).
thf(3436,plain,
! [SV636: $i,SV266: $i,SV756: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV756 ) @ SV266 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV636 ) @ SV266 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV636 ) @ SV756 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3245]) ).
thf(3437,plain,
! [SV757: $i,SV637: $i,SV267: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV267 ) @ SV637 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV267 ) @ SV757 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV637 ) @ SV757 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3246]) ).
thf(3438,plain,
! [SV758: $i,SV638: $i,SV268: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV268 ) @ SV638 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV268 ) @ SV758 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV638 ) @ SV758 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3247]) ).
thf(3439,plain,
! [SV759: $i,SV639: $i,SV269: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV269 ) @ SV639 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV269 ) @ SV759 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV639 ) @ SV759 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3248]) ).
thf(3440,plain,
! [SV640: $i,SV270: $i,SV760: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV760 ) @ SV270 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV640 ) @ SV270 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV640 ) @ SV760 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3249]) ).
thf(3441,plain,
! [SV641: $i,SV271: $i,SV761: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV761 ) @ SV271 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV641 ) @ SV271 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV641 ) @ SV761 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3250]) ).
thf(3442,plain,
! [SV642: $i,SV272: $i,SV762: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV762 ) @ SV272 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV642 ) @ SV272 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV642 ) @ SV762 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3251]) ).
thf(3443,plain,
! [SV817: $i,SV764: $i,SV644: $i,SV279: $i] :
( ( ( ( SV279
!= ( hAPP_pname_a @ SV644 @ SV764 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV279 ) @ ( image_pname_a @ SV644 @ SV817 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV764 ) @ SV817 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3252]) ).
thf(3444,plain,
! [SV672: $i,SV314: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_a_bool @ ( hAPP_a_fun_a_bool @ fequal_a @ SV314 ) @ SV672 ) ) )
= $true )
| ( ( SV314 = SV672 )
= $true )
| ( ( is_a @ SV314 )
= $false )
| ( ( is_a @ SV672 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3255]) ).
thf(3445,plain,
! [SV676: $i,SV318: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ fequal_pname @ SV318 ) @ SV676 ) ) )
= $true )
| ( ( SV318 = SV676 )
= $true )
| ( ( is_pname @ SV318 )
= $false )
| ( ( is_pname @ SV676 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3256]) ).
thf(3446,plain,
! [SV679: $i,SV321: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ SV321 ) @ SV679 ) ) )
= $true )
| ( ( SV321 = SV679 )
= $true )
| ( ( is_fun_a_bool @ SV321 )
= $false )
| ( ( is_fun_a_bool @ SV679 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3257]) ).
thf(3447,plain,
! [SV686: $i,SV328: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ SV328 ) @ SV686 ) ) )
= $true )
| ( ( SV328 = SV686 )
= $true )
| ( ( is_fun_pname_bool @ SV328 )
= $false )
| ( ( is_fun_pname_bool @ SV686 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3258]) ).
thf(3448,plain,
! [SV885: $i,SV818: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV818 ) @ SV885 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ SV885 @ SV818 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3259]) ).
thf(3449,plain,
! [SV819: $i,SV886: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ SV886 @ SV819 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV819 ) @ SV886 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3260]) ).
thf(3450,plain,
! [SV887: $i,SV820: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV820 ) @ SV887 ) )
= $false )
| ( ( hBOOL @ ( hAPP_pname_bool @ SV887 @ SV820 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3261]) ).
thf(3451,plain,
! [SV821: $i,SV888: $i] :
( ( ( hBOOL @ ( hAPP_pname_bool @ SV888 @ SV821 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV821 ) @ SV888 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3262]) ).
thf(3452,plain,
! [SV822: $i,SV889: $i] :
( ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ SV889 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fconj @ SV889 ) @ SV822 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3263]) ).
thf(3453,plain,
! [SV823: $i,SV1004: $i] :
( ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fconj @ SV1004 ) @ SV823 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ SV823 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3264]) ).
thf(3454,plain,
! [SV890: $i,SV824: $i] :
( ( ( SV824 = SV890 )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV824 ) @ SV890 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3265]) ).
thf(3455,plain,
! [SV891: $i,SV825: $i] :
( ( ( SV825 = SV891 )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV891 ) @ SV825 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3266]) ).
thf(3456,plain,
! [SV1005: $i,SV364: $i] :
( ( ( ! [SY1152: $i] :
( ! [SY1153: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY1153 ) @ SY1152 ) )
| ~ ( is_fun_pname_bool @ SY1153 )
| ( SV364
!= ( image_pname_a @ SV1005 @ SY1153 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV364 ) @ ( image_pname_a @ SV1005 @ SY1152 ) ) ) ) )
= $true )
| ( ( is_fun_a_bool @ SV364 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3267]) ).
thf(3457,plain,
! [SV1006: $i,SV364: $i] :
( ( ( ! [SY1154: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV364 ) @ ( image_pname_a @ SV1006 @ SY1154 ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( sK10_AA @ SY1154 @ SV1006 @ SV364 ) ) @ SY1154 ) )
| ~ ( is_fun_pname_bool @ ( sK10_AA @ SY1154 @ SV1006 @ SV364 ) ) )
| ( SV364
!= ( image_pname_a @ SV1006 @ ( sK10_AA @ SY1154 @ SV1006 @ SV364 ) ) ) ) ) )
= $true )
| ( ( is_fun_a_bool @ SV364 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3268]) ).
thf(3458,plain,
! [SV892: $i,SV826: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV826 ) @ ( hAPP_nat_nat @ suc @ SV892 ) ) )
= $false )
| ( ( ( SV826
= ( hAPP_nat_nat @ suc @ SV892 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV826 ) @ SV892 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3269]) ).
thf(3459,plain,
! [SV1007: $i] :
( ( ! [SY1155: $i] :
( ( SV1007
!= ( hAPP_nat_nat @ suc @ SY1155 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV1007 ) @ ( hAPP_nat_nat @ suc @ SY1155 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3270]) ).
thf(3460,plain,
! [SV1008: $i] :
( ( ! [SY1156: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV1008 ) @ SY1156 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV1008 ) @ ( hAPP_nat_nat @ suc @ SY1156 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3271]) ).
thf(3461,plain,
! [SV893: $i,SV827: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV827 ) @ SV893 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV893 ) @ SV827 ) ) )
= $true )
| ( ( SV827 = SV893 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3272]) ).
thf(3462,plain,
! [SV1009: $i] :
( ( ! [SY1157: $i] :
( ( SV1009 != SY1157 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV1009 ) @ SY1157 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3273]) ).
thf(3463,plain,
! [SV1010: $i] :
( ( ! [SY1158: $i] :
( ( SV1010 != SY1158 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY1158 ) @ SV1010 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3274]) ).
thf(3464,plain,
! [SV828: $i,SV894: $i] :
( ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV894 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ SV828 ) @ SV894 ) )
| ( ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( insert_fun_nat_bool @ SV828 @ SV894 ) )
= ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SV894 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3275]) ).
thf(3465,plain,
! [SV829: $i,SV895: $i] :
( ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV895 ) )
= $false )
| ( ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ SV829 ) @ SV895 ) )
| ( ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( insert_fun_nat_bool @ SV829 @ SV895 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SV895 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3276]) ).
thf(3466,plain,
! [SV896: $i,SV830: $i] :
( ( ( ~ ( is_fun_pname_bool @ SV830 ) )
= $true )
| ( ( ~ ( is_fun_pname_bool @ SV896 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV830 ) @ SV896 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV896 ) @ SV830 ) )
| ( SV830 = SV896 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3277]) ).
thf(3467,plain,
! [SV1011: $i] :
( ( ! [SY1159: $i] :
( ~ ( is_fun_pname_bool @ SV1011 )
| ~ ( is_fun_pname_bool @ SY1159 )
| ( SV1011 != SY1159 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV1011 ) @ SY1159 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3278]) ).
thf(3468,plain,
! [SV1012: $i] :
( ( ! [SY1160: $i] :
( ~ ( is_fun_pname_bool @ SV1012 )
| ~ ( is_fun_pname_bool @ SY1160 )
| ( SV1012 != SY1160 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY1160 ) @ SV1012 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3279]) ).
thf(3469,plain,
! [SV831: $i,SV897: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ SV897 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ SV897 ) @ SV831 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3280]) ).
thf(3470,plain,
! [SV832: $i,SV1013: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ SV1013 ) @ SV832 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ SV832 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3281]) ).
thf(3471,plain,
! [SV898: $i,SV833: $i] :
( ( ( ( hAPP_nat_nat @ suc @ SV833 )
= ( hAPP_nat_nat @ suc @ SV898 ) )
= $false )
| ( ( SV833 = SV898 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3282]) ).
thf(3472,plain,
! [SV899: $i,SV834: $i] :
( ( ( SV834 = SV899 )
= $false )
| ( ( ( hAPP_nat_nat @ suc @ SV834 )
= ( hAPP_nat_nat @ suc @ SV899 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3283]) ).
thf(3473,plain,
! [SV900: $i,SV975: $i,SV365: $i] :
( ( ( ~ ( is_pname @ SV365 )
| ~ ( is_pname @ SV975 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV365 @ SV900 ) @ SV975 ) )
| ( SV365 = SV975 )
| ( hBOOL @ ( hAPP_pname_bool @ SV900 @ SV975 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3284]) ).
thf(3474,plain,
! [SV365: $i] :
( ( ! [SY849: $i,SY850: $i] :
( ~ ( is_pname @ SV365 )
| ~ ( is_pname @ SY850 )
| ( SV365 != SY850 )
| ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV365 @ SY849 ) @ SY850 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3285]) ).
thf(3475,plain,
! [SV365: $i] :
( ( ! [SY851: $i,SY852: $i] :
( ~ ( is_pname @ SV365 )
| ~ ( is_pname @ SY852 )
| ~ ( hBOOL @ ( hAPP_pname_bool @ SY851 @ SY852 ) )
| ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV365 @ SY851 ) @ SY852 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3286]) ).
thf(3476,plain,
! [SV976: $i,SV901: $i,SV366: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV366 ) @ ( insert_nat @ SV901 @ SV976 ) ) ) )
= $true )
| ( ( ( SV366 = SV901 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV366 ) @ SV976 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3287]) ).
thf(3477,plain,
! [SV366: $i] :
( ( ! [SY855: $i] :
( ( SV366 != SY855 )
| ! [SY856: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV366 ) @ ( insert_nat @ SY855 @ SY856 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3288]) ).
thf(3478,plain,
! [SV366: $i] :
( ( ! [SY857: $i,SY858: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV366 ) @ SY858 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV366 ) @ ( insert_nat @ SY857 @ SY858 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3289]) ).
thf(3479,plain,
! [SV902: $i,SV835: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ SV835 @ SV902 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV902 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3290]) ).
thf(3480,plain,
! [SV836: $i,SV903: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV903 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ SV836 @ SV903 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3291]) ).
thf(3481,plain,
! [SV904: $i,SV367: $i] :
( ( ( ~ ( is_a @ SV367 ) )
= $true )
| ( ( ~ ( is_a @ SV904 ) )
= $true )
| ( ( ! [SY1123: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ ( insert_a @ SV904 @ SY1123 ) ) )
| ( SV367 = SV904 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ SY1123 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3292]) ).
thf(3482,plain,
! [SV367: $i] :
( ( ! [SY861: $i] :
( ~ ( is_a @ SV367 )
| ~ ( is_a @ SY861 )
| ( SV367 != SY861 )
| ! [SY862: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ ( insert_a @ SY861 @ SY862 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3293]) ).
thf(3483,plain,
! [SV367: $i] :
( ( ! [SY863: $i] :
( ~ ( is_a @ SV367 )
| ~ ( is_a @ SY863 )
| ! [SY864: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ SY864 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ ( insert_a @ SY863 @ SY864 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3294]) ).
thf(3484,plain,
! [SV837: $i,SV905: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ SV905 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ SV905 ) @ SV837 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3295]) ).
thf(3485,plain,
! [SV838: $i,SV1014: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ SV1014 ) @ SV838 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ SV838 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3296]) ).
thf(3486,plain,
! [SV368: $i,SV977: $i,SV906: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV906 ) @ SV977 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV977 ) @ ( insert_a @ SV906 @ SV368 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV977 ) @ SV368 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3297]) ).
thf(3487,plain,
! [SV368: $i,SV978: $i,SV907: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV907 ) @ SV978 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV978 ) @ SV368 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV978 ) @ ( insert_a @ SV907 @ SV368 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3298]) ).
thf(3488,plain,
! [SV1015: $i,SV369: $i] :
( ( ( ! [SY1161: $i] :
( ! [SY1162: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SY1162 ) @ SY1161 ) )
| ~ ( is_pname @ SY1162 )
| ( SV369
!= ( hAPP_pname_a @ SV1015 @ SY1162 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV369 ) @ ( image_pname_a @ SV1015 @ SY1161 ) ) ) ) )
= $true )
| ( ( is_a @ SV369 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3299]) ).
thf(3489,plain,
! [SV1016: $i,SV369: $i] :
( ( ( ! [SY1163: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV369 ) @ ( image_pname_a @ SV1016 @ SY1163 ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK11_X_1 @ SY1163 @ SV1016 @ SV369 ) ) @ SY1163 ) )
| ~ ( is_pname @ ( sK11_X_1 @ SY1163 @ SV1016 @ SV369 ) ) )
| ( SV369
!= ( hAPP_pname_a @ SV1016 @ ( sK11_X_1 @ SY1163 @ SV1016 @ SV369 ) ) ) ) ) )
= $true )
| ( ( is_a @ SV369 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3300]) ).
thf(3490,plain,
! [SV370: $i,SV979: $i,SV908: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV908 ) @ SV979 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV979 ) @ ( insert_nat @ SV908 @ SV370 ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV979 ) @ SV370 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3301]) ).
thf(3491,plain,
! [SV370: $i,SV980: $i,SV909: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV909 ) @ SV980 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV980 ) @ SV370 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV980 ) @ ( insert_nat @ SV909 @ SV370 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3302]) ).
thf(3492,plain,
! [SV839: $i,SV910: $i] :
( ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ SV910 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fconj @ SV910 ) @ SV839 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3303]) ).
thf(3493,plain,
! [SV840: $i,SV1017: $i] :
( ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fconj @ SV1017 ) @ SV840 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ SV840 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3304]) ).
thf(3494,plain,
! [SV911: $i,SV841: $i] :
( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SV841 @ SV911 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV911 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3305]) ).
thf(3495,plain,
! [SV842: $i,SV912: $i] :
( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV912 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SV842 @ SV912 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3306]) ).
thf(3496,plain,
! [SV371: $i,SV981: $i,SV913: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV913 ) @ SV981 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV913 ) @ ( insert_nat @ SV371 @ SV981 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3307]) ).
thf(3497,plain,
! [SV371: $i,SV914: $i] :
( ( ( SV914 = SV371 )
= $false )
| ( ( ! [SY1129: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV914 ) @ ( insert_nat @ SV371 @ SY1129 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3308]) ).
thf(3498,plain,
! [SV915: $i,SV843: $i] :
( ( ( ~ ( is_fun_a_bool @ SV843 ) )
= $true )
| ( ( ~ ( is_fun_a_bool @ SV915 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV843 ) @ SV915 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV915 ) @ SV843 ) )
| ( SV843 = SV915 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3309]) ).
thf(3499,plain,
! [SV1018: $i] :
( ( ! [SY1164: $i] :
( ~ ( is_fun_a_bool @ SV1018 )
| ~ ( is_fun_a_bool @ SY1164 )
| ( SV1018 != SY1164 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV1018 ) @ SY1164 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3310]) ).
thf(3500,plain,
! [SV1019: $i] :
( ( ! [SY1165: $i] :
( ~ ( is_fun_a_bool @ SV1019 )
| ~ ( is_fun_a_bool @ SY1165 )
| ( SV1019 != SY1165 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY1165 ) @ SV1019 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3311]) ).
thf(3501,plain,
! [SV722: $i,SV372: $i,SV813: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV813 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV813 ) @ ( image_pname_a @ SV372 @ SV722 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( sK17_C_2 @ SV813 @ SV722 @ SV372 ) ) @ SV722 ) )
| ~ ( is_fun_pname_bool @ ( sK17_C_2 @ SV813 @ SV722 @ SV372 ) ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( sK17_C_2 @ SV813 @ SV722 @ SV372 ) ) ) )
| ( SV813
!= ( image_pname_a @ SV372 @ ( sK17_C_2 @ SV813 @ SV722 @ SV372 ) ) ) ) )
= $true )
| ( ( is_fun_a_bool @ SV813 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3312]) ).
thf(3502,plain,
! [SV844: $i,SV916: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ SV916 ) ) @ SV844 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV844 ) @ SV916 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3313]) ).
thf(3503,plain,
! [SV373: $i,SV982: $i,SV918: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV918 ) @ SV982 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV918 ) @ ( insert_pname @ SV373 @ SV982 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3315]) ).
thf(3504,plain,
! [SV373: $i,SV919: $i] :
( ( ( SV919 = SV373 )
= $false )
| ( ( ! [SY1131: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV919 ) @ ( insert_pname @ SV373 @ SY1131 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3316]) ).
thf(3505,plain,
! [SV920: $i,SV846: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ SV846 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ SV920 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ SV846 ) @ SV920 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3317]) ).
thf(3506,plain,
! [SV1020: $i] :
( ( ! [SY1166: $i] :
~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ SV1020 ) @ SY1166 ) ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ SV1020 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3318]) ).
thf(3507,plain,
! [SV1021: $i] :
( ( ! [SY1167: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ SV1021 ) @ SY1167 ) ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ SY1167 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3319]) ).
thf(3508,plain,
! [SV921: $i,SV983: $i,SV374: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV374 ) @ SV983 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV921 ) @ SV983 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV374 @ SV921 ) ) @ SV983 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3320]) ).
thf(3509,plain,
! [SV374: $i] :
( ( ! [SY890: $i,SY891: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV374 @ SY890 ) ) @ SY891 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV374 ) @ SY891 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3321]) ).
thf(3510,plain,
! [SV374: $i] :
( ( ! [SY892: $i,SY893: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV374 @ SY892 ) ) @ SY893 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY892 ) @ SY893 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3322]) ).
thf(3511,plain,
! [SV922: $i,SV847: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ SV847 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ SV922 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ SV847 ) @ SV922 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3323]) ).
thf(3512,plain,
! [SV1022: $i] :
( ( ! [SY1168: $i] :
~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ SV1022 ) @ SY1168 ) ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ SV1022 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3324]) ).
thf(3513,plain,
! [SV1023: $i] :
( ( ! [SY1169: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ SV1023 ) @ SY1169 ) ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ SY1169 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3325]) ).
thf(3514,plain,
! [SV375: $i,SV723: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK12_X_1 @ SV723 @ SV375 ) ) @ SV723 ) )
| ~ ( is_pname @ ( sK12_X_1 @ SV723 @ SV375 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_pname_a @ SV375 @ SV723 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV723 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3326]) ).
thf(3515,plain,
! [SV375: $i,SV723: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ ( hAPP_f759274231e_bool @ ( cOMBC_1058051404l_bool @ member_pname ) @ SV723 ) ) @ ( hAPP_a93125764e_bool @ ( cOMBC_pname_a_bool @ ( cOMBB_1897541054_pname @ fequal_a @ SV375 ) ) @ ( hAPP_pname_a @ SV375 @ ( sK12_X_1 @ SV723 @ SV375 ) ) ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_pname_a @ SV375 @ SV723 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV723 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3326]) ).
thf(3516,plain,
! [SV923: $i,SV984: $i,SV376: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV376 ) @ SV984 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV923 ) @ SV984 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( insert_nat @ SV376 @ SV923 ) ) @ SV984 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3327]) ).
thf(3517,plain,
! [SV376: $i] :
( ( ! [SY897: $i,SY898: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( insert_nat @ SV376 @ SY897 ) ) @ SY898 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV376 ) @ SY898 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3328]) ).
thf(3518,plain,
! [SV376: $i] :
( ( ! [SY899: $i,SY900: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( insert_nat @ SV376 @ SY899 ) ) @ SY900 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY899 ) @ SY900 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3329]) ).
thf(3519,plain,
! [SV848: $i,SV924: $i] :
( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV924 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ SV848 ) @ SV924 ) )
| ( ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( insert1325755072e_bool @ SV848 @ SV924 ) )
= ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SV924 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3330]) ).
thf(3520,plain,
! [SV849: $i,SV925: $i] :
( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV925 ) )
= $false )
| ( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ SV849 ) @ SV925 ) )
| ( ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( insert1325755072e_bool @ SV849 @ SV925 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SV925 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3331]) ).
thf(3521,plain,
! [SV926: $i,SV850: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ SV850 @ SV926 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV926 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3332]) ).
thf(3522,plain,
! [SV851: $i,SV927: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV927 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ SV851 @ SV927 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3333]) ).
thf(3523,plain,
! [SV377: $i,SV985: $i,SV928: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV928 ) @ SV985 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV928 ) @ SV377 ) )
| ( ( insert_nat @ SV928 @ SV985 )
!= ( insert_nat @ SV928 @ SV377 ) )
| ( SV985 = SV377 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3334]) ).
thf(3524,plain,
! [SV377: $i,SV986: $i,SV929: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV929 ) @ SV986 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV929 ) @ SV377 ) )
| ( SV986 != SV377 )
| ( ( insert_nat @ SV929 @ SV986 )
= ( insert_nat @ SV929 @ SV377 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3335]) ).
thf(3525,plain,
! [SV378: $i,SV724: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( sK7_X_1 @ SV724 @ SV378 ) ) @ SV724 ) )
| ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( sK7_X_1 @ SV724 @ SV378 ) ) @ SV378 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV724 ) @ SV378 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3337]) ).
thf(3526,plain,
! [SV930: $i,SV852: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV852 ) @ SV930 ) )
= $false )
| ( ( hBOOL @ ( hAPP_a_bool @ SV930 @ SV852 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3338]) ).
thf(3527,plain,
! [SV853: $i,SV931: $i] :
( ( ( hBOOL @ ( hAPP_a_bool @ SV931 @ SV853 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV853 ) @ SV931 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3339]) ).
thf(3528,plain,
! [SV379: $i,SV987: $i,SV932: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV932 ) @ SV987 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV932 ) @ ( insert_a @ SV379 @ SV987 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3340]) ).
thf(3529,plain,
! [SV379: $i,SV933: $i] :
( ( ( SV933 = SV379 )
= $false )
| ( ( ! [SY1137: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV933 ) @ ( insert_a @ SV379 @ SY1137 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3341]) ).
thf(3530,plain,
! [SV854: $i,SV934: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV934 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV854 ) @ SV934 ) )
| ( ( hAPP_f22106695ol_nat @ finite_card_nat @ ( insert_nat @ SV854 @ SV934 ) )
= ( hAPP_f22106695ol_nat @ finite_card_nat @ SV934 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3342]) ).
thf(3531,plain,
! [SV855: $i,SV935: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV935 ) )
= $false )
| ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV855 ) @ SV935 ) )
| ( ( hAPP_f22106695ol_nat @ finite_card_nat @ ( insert_nat @ SV855 @ SV935 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SV935 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3343]) ).
thf(3532,plain,
! [SV936: $i,SV856: $i] :
( ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ SV856 @ SV936 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV936 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3344]) ).
thf(3533,plain,
! [SV857: $i,SV937: $i] :
( ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV937 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ SV857 @ SV937 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3345]) ).
thf(3534,plain,
! [SV858: $i,SV938: $i] :
( ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV938 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ SV858 ) @ SV938 ) )
| ( ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( insert_fun_a_bool @ SV858 @ SV938 ) )
= ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SV938 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3346]) ).
thf(3535,plain,
! [SV859: $i,SV939: $i] :
( ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV939 ) )
= $false )
| ( ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ SV859 ) @ SV939 ) )
| ( ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( insert_fun_a_bool @ SV859 @ SV939 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SV939 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3347]) ).
thf(3536,plain,
! [SV940: $i,SV860: $i] :
( ( ( SV860 = SV940 )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV860 ) @ SV940 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3348]) ).
thf(3537,plain,
! [SV941: $i,SV861: $i] :
( ( ( SV861 = SV941 )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV941 ) @ SV861 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3349]) ).
thf(3538,plain,
! [SV380: $i,SV725: $i,SV814: $i] :
( ( ( is_pname @ ( sK3_X_1 @ SV814 @ SV725 @ SV380 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_pname_a @ SV380 @ SV814 ) ) @ SV725 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3350]) ).
thf(3539,plain,
! [SV380: $i,SV725: $i,SV814: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK3_X_1 @ SV814 @ SV725 @ SV380 ) ) @ SV814 ) )
| ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( hAPP_pname_a @ SV380 @ ( sK3_X_1 @ SV814 @ SV725 @ SV380 ) ) ) @ SV725 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_pname_a @ SV380 @ SV814 ) ) @ SV725 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3351]) ).
thf(3540,plain,
! [SV381: $i,SV988: $i,SV942: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV942 ) @ SV988 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV942 ) @ SV381 ) )
| ( ( hAPP_nat_nat @ ( minus_minus_nat @ SV988 ) @ SV942 )
!= ( hAPP_nat_nat @ ( minus_minus_nat @ SV381 ) @ SV942 ) )
| ( SV988 = SV381 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3352]) ).
thf(3541,plain,
! [SV381: $i,SV989: $i,SV943: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV943 ) @ SV989 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV943 ) @ SV381 ) )
| ( SV989 != SV381 )
| ( ( hAPP_nat_nat @ ( minus_minus_nat @ SV989 ) @ SV943 )
= ( hAPP_nat_nat @ ( minus_minus_nat @ SV381 ) @ SV943 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3353]) ).
thf(3542,plain,
! [SV382: $i,SV726: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ ( sK8_X_1 @ SV726 @ SV382 ) ) @ SV382 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV726 ) @ SV382 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3355]) ).
thf(3543,plain,
! [SV944: $i,SV862: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ SV862 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ SV944 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ SV862 ) @ SV944 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3356]) ).
thf(3544,plain,
! [SV1024: $i] :
( ( ! [SY1170: $i] :
~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ SV1024 ) @ SY1170 ) ) ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ SV1024 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3357]) ).
thf(3545,plain,
! [SV1025: $i] :
( ( ! [SY1171: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ SV1025 ) @ SY1171 ) ) ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ SY1171 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3358]) ).
thf(3546,plain,
! [SV863: $i,SV945: $i] :
( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ SV945 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fconj @ SV945 ) @ SV863 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3359]) ).
thf(3547,plain,
! [SV864: $i,SV1026: $i] :
( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fconj @ SV1026 ) @ SV864 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ SV864 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3360]) ).
thf(3548,plain,
! [SV865: $i,SV946: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV946 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV865 ) @ SV946 ) )
| ( ( hAPP_fun_a_bool_nat @ finite_card_a @ ( insert_a @ SV865 @ SV946 ) )
= ( hAPP_fun_a_bool_nat @ finite_card_a @ SV946 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3361]) ).
thf(3549,plain,
! [SV866: $i,SV947: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV947 ) )
= $false )
| ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV866 ) @ SV947 ) )
| ( ( hAPP_fun_a_bool_nat @ finite_card_a @ ( insert_a @ SV866 @ SV947 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SV947 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3362]) ).
thf(3550,plain,
! [SV867: $i,SV948: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV948 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV867 ) @ SV948 ) )
| ( ( hAPP_f921600141ol_nat @ finite_card_pname @ ( insert_pname @ SV867 @ SV948 ) )
= ( hAPP_f921600141ol_nat @ finite_card_pname @ SV948 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3363]) ).
thf(3551,plain,
! [SV868: $i,SV949: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV949 ) )
= $false )
| ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV868 ) @ SV949 ) )
| ( ( hAPP_f921600141ol_nat @ finite_card_pname @ ( insert_pname @ SV868 @ SV949 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV949 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3364]) ).
thf(3552,plain,
! [SV950: $i,SV383: $i] :
( ( ( ~ ( is_pname @ SV383 ) )
= $true )
| ( ( ~ ( is_pname @ SV950 ) )
= $true )
| ( ( ! [SY1140: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ ( insert_pname @ SV950 @ SY1140 ) ) )
| ( SV383 = SV950 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ SY1140 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3365]) ).
thf(3553,plain,
! [SV383: $i] :
( ( ! [SY919: $i] :
( ~ ( is_pname @ SV383 )
| ~ ( is_pname @ SY919 )
| ( SV383 != SY919 )
| ! [SY920: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ ( insert_pname @ SY919 @ SY920 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3366]) ).
thf(3554,plain,
! [SV383: $i] :
( ( ! [SY921: $i] :
( ~ ( is_pname @ SV383 )
| ~ ( is_pname @ SY921 )
| ! [SY922: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ SY922 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ ( insert_pname @ SY921 @ SY922 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3367]) ).
thf(3555,plain,
! [SV951: $i,SV990: $i,SV384: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV384 ) @ SV990 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV951 ) @ SV990 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ SV384 @ SV951 ) ) @ SV990 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3368]) ).
thf(3556,plain,
! [SV384: $i] :
( ( ! [SY925: $i,SY926: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ SV384 @ SY925 ) ) @ SY926 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV384 ) @ SY926 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3369]) ).
thf(3557,plain,
! [SV384: $i] :
( ( ! [SY927: $i,SY928: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ SV384 @ SY927 ) ) @ SY928 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY927 ) @ SY928 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3370]) ).
thf(3558,plain,
! [SV952: $i,SV869: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ SV869 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ SV952 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ SV869 ) @ SV952 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3371]) ).
thf(3559,plain,
! [SV1027: $i] :
( ( ! [SY1172: $i] :
~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ SV1027 ) @ SY1172 ) ) ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ SV1027 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3372]) ).
thf(3560,plain,
! [SV1028: $i] :
( ( ! [SY1173: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ SV1028 ) @ SY1173 ) ) ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ SY1173 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3373]) ).
thf(3561,plain,
! [SV953: $i,SV991: $i,SV385: $i] :
( ( ( ~ ( is_fun_a_bool @ SV385 )
| ~ ( is_fun_a_bool @ SV991 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV953 ) @ SV991 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV953 ) @ SV385 ) )
| ( ( insert_a @ SV953 @ SV991 )
!= ( insert_a @ SV953 @ SV385 ) )
| ( SV991 = SV385 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3374]) ).
thf(3562,plain,
! [SV954: $i,SV992: $i,SV385: $i] :
( ( ( ~ ( is_fun_a_bool @ SV385 )
| ~ ( is_fun_a_bool @ SV992 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV954 ) @ SV992 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV954 ) @ SV385 ) )
| ( SV992 != SV385 )
| ( ( insert_a @ SV954 @ SV992 )
= ( insert_a @ SV954 @ SV385 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3375]) ).
thf(3563,plain,
! [SV955: $i,SV870: $i] :
( ( ( SV870 = SV955 )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV870 ) @ SV955 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3376]) ).
thf(3564,plain,
! [SV956: $i,SV871: $i] :
( ( ( SV871 = SV956 )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV956 ) @ SV871 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3377]) ).
thf(3565,plain,
! [SV957: $i,SV993: $i,SV386: $i] :
( ( ( ~ ( is_a @ SV386 )
| ~ ( is_a @ SV993 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV386 @ SV957 ) @ SV993 ) )
| ( SV386 = SV993 )
| ( hBOOL @ ( hAPP_a_bool @ SV957 @ SV993 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3378]) ).
thf(3566,plain,
! [SV386: $i] :
( ( ! [SY935: $i,SY936: $i] :
( ~ ( is_a @ SV386 )
| ~ ( is_a @ SY936 )
| ( SV386 != SY936 )
| ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV386 @ SY935 ) @ SY936 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3379]) ).
thf(3567,plain,
! [SV386: $i] :
( ( ! [SY937: $i,SY938: $i] :
( ~ ( is_a @ SV386 )
| ~ ( is_a @ SY938 )
| ~ ( hBOOL @ ( hAPP_a_bool @ SY937 @ SY938 ) )
| ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV386 @ SY937 ) @ SY938 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3380]) ).
thf(3568,plain,
! [SV872: $i,SV958: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ SV958 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ SV958 ) @ SV872 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3381]) ).
thf(3569,plain,
! [SV873: $i,SV1029: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ SV1029 ) @ SV873 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ SV873 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3382]) ).
thf(3570,plain,
! [SV959: $i,SV874: $i,SV387: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV387 ) @ ( image_pname_a @ SV874 @ SV959 ) ) )
= $false )
| ( ( ~ ( ~ ( is_pname @ ( sK9_X_1 @ SV959 @ SV874 @ SV387 ) )
| ~ ~ ( ( SV387
!= ( hAPP_pname_a @ SV874 @ ( sK9_X_1 @ SV959 @ SV874 @ SV387 ) ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK9_X_1 @ SV959 @ SV874 @ SV387 ) ) @ SV959 ) ) ) ) )
= $true )
| ( ( is_a @ SV387 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3383]) ).
thf(3571,plain,
! [SV960: $i,SV875: $i] :
( ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ SV875 @ SV960 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV960 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3384]) ).
thf(3572,plain,
! [SV876: $i,SV961: $i] :
( ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV961 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ SV876 @ SV961 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3385]) ).
thf(3573,plain,
! [SV962: $i,SV877: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ SV877 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ SV962 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ SV877 ) @ SV962 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3386]) ).
thf(3574,plain,
! [SV1030: $i] :
( ( ! [SY1174: $i] :
~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ SV1030 ) @ SY1174 ) ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ SV1030 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3387]) ).
thf(3575,plain,
! [SV1031: $i] :
( ( ! [SY1175: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ SV1031 ) @ SY1175 ) ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ SY1175 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3388]) ).
thf(3576,plain,
! [SV388: $i,SV815: $i,SV727: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ SV727 @ ( hAPP_nat_nat @ suc @ ( sK5_N_2 @ SV815 @ SV727 @ SV388 ) ) ) )
| ~ ~ ( hBOOL @ ( hAPP_nat_bool @ SV727 @ ( sK5_N_2 @ SV815 @ SV727 @ SV388 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ SV727 @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV815 ) @ SV388 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ SV727 @ SV815 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3389]) ).
thf(3577,plain,
! [SV963: $i,SV878: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ SV878 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ SV963 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ SV878 ) @ SV963 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3390]) ).
thf(3578,plain,
! [SV1032: $i] :
( ( ! [SY1176: $i] :
~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ SV1032 ) @ SY1176 ) ) ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ SV1032 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3391]) ).
thf(3579,plain,
! [SV1033: $i] :
( ( ! [SY1177: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ SV1033 ) @ SY1177 ) ) ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ SY1177 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3392]) ).
thf(3580,plain,
! [SV964: $i,SV994: $i,SV389: $i] :
( ( ( ~ ( is_fun_pname_bool @ SV389 )
| ~ ( is_fun_pname_bool @ SV994 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV964 ) @ SV994 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV964 ) @ SV389 ) )
| ( ( insert_pname @ SV964 @ SV994 )
!= ( insert_pname @ SV964 @ SV389 ) )
| ( SV994 = SV389 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3393]) ).
thf(3581,plain,
! [SV965: $i,SV995: $i,SV389: $i] :
( ( ( ~ ( is_fun_pname_bool @ SV389 )
| ~ ( is_fun_pname_bool @ SV995 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV965 ) @ SV995 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV965 ) @ SV389 ) )
| ( SV995 != SV389 )
| ( ( insert_pname @ SV965 @ SV995 )
= ( insert_pname @ SV965 @ SV389 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3394]) ).
thf(3582,plain,
! [SV966: $i,SV879: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ SV879 ) ) @ ( hAPP_nat_nat @ suc @ SV966 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV879 ) @ SV966 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3395]) ).
thf(3583,plain,
! [SV967: $i,SV880: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV880 ) @ SV967 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ SV880 ) ) @ ( hAPP_nat_nat @ suc @ SV967 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3396]) ).
thf(3584,plain,
! [SV390: $i,SV996: $i,SV968: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV968 ) @ SV996 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV996 ) @ ( insert_pname @ SV968 @ SV390 ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV996 ) @ SV390 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3397]) ).
thf(3585,plain,
! [SV390: $i,SV997: $i,SV969: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV969 ) @ SV997 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV997 ) @ SV390 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV997 ) @ ( insert_pname @ SV969 @ SV390 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3398]) ).
thf(3586,plain,
! [SV391: $i,SV998: $i,SV970: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV970 ) @ SV998 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV970 ) @ SV391 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV998 ) @ SV970 ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV391 ) @ SV970 ) ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV998 ) @ SV391 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3399]) ).
thf(3587,plain,
! [SV391: $i,SV999: $i,SV971: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV971 ) @ SV999 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV971 ) @ SV391 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV999 ) @ SV391 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV999 ) @ SV971 ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV391 ) @ SV971 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3400]) ).
thf(3588,plain,
! [SV392: $i,SV728: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK6_X_1 @ SV728 @ SV392 ) ) @ SV728 ) )
| ~ ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK6_X_1 @ SV728 @ SV392 ) ) @ SV392 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV728 ) @ SV392 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3402]) ).
thf(3589,plain,
! [SV1000: $i,SV972: $i,SV393: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV393 @ SV972 ) @ SV1000 ) ) )
= $true )
| ( ( ( SV393 = SV1000 )
| ( hBOOL @ ( hAPP_nat_bool @ SV972 @ SV1000 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3403]) ).
thf(3590,plain,
! [SV393: $i] :
( ( ! [SY958: $i,SY959: $i] :
( ( SV393 != SY959 )
| ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV393 @ SY958 ) @ SY959 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3404]) ).
thf(3591,plain,
! [SV393: $i] :
( ( ! [SY960: $i,SY961: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ SY960 @ SY961 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV393 @ SY960 ) @ SY961 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3405]) ).
thf(3592,plain,
! [SV881: $i,SV1001: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ ( sK2_X_1 @ SV1001 @ SV881 ) ) @ SV881 ) )
| ~ ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( sK2_X_1 @ SV1001 @ SV881 ) ) @ SV1001 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV881 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3406]) ).
thf(3593,plain,
! [SV882: $i,SV1034: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV1034 ) @ SV882 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV1034 ) @ ( sK1_M @ SV882 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV882 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3407]) ).
thf(3594,plain,
! [SV973: $i,SV883: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ SV883 @ SV973 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV973 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3408]) ).
thf(3595,plain,
! [SV884: $i,SV974: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV974 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ SV884 @ SV974 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3409]) ).
thf(3596,plain,
! [SV157: $i,SV536: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SV536 ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SV157 ) ) )
= $false )
| ( ( SV157 = SV536 )
= $true )
| ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ SV157 ) @ SV536 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV536 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3410]) ).
thf(3597,plain,
! [SV158: $i,SV537: $i] :
( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV537 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ SV158 ) @ SV537 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SV537 ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SV158 ) ) )
| ( SV158 = SV537 ) )
= $true )
| ( ( is_fun1661590463l_bool @ SV158 )
= $false )
| ( ( is_fun1661590463l_bool @ SV537 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3411]) ).
thf(3598,plain,
! [SV159: $i,SV538: $i] :
( ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV538 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ SV159 ) @ SV538 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SV538 ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SV159 ) ) )
| ( SV159 = SV538 ) )
= $true )
| ( ( is_fun949378684l_bool @ SV159 )
= $false )
| ( ( is_fun949378684l_bool @ SV538 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3412]) ).
thf(3599,plain,
! [SV160: $i,SV539: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV539 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV160 ) @ SV539 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV539 ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV160 ) ) )
| ( SV160 = SV539 ) )
= $true )
| ( ( is_fun_pname_bool @ SV160 )
= $false )
| ( ( is_fun_pname_bool @ SV539 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3413]) ).
thf(3600,plain,
! [SV161: $i,SV540: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV540 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV161 ) @ SV540 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SV540 ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SV161 ) ) )
| ( SV161 = SV540 ) )
= $true )
| ( ( is_fun_a_bool @ SV161 )
= $false )
| ( ( is_fun_a_bool @ SV540 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3414]) ).
thf(3601,plain,
! [SV162: $i,SV541: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SV541 ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SV162 ) ) )
= $false )
| ( ( SV162 = SV541 )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV162 ) @ SV541 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV541 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3415]) ).
thf(3602,plain,
! [SV740: $i,SV588: $i,SV215: $i,SV816: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV816 ) @ SV215 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV588 ) @ ( image_pname_a @ SV740 @ SV215 ) ) )
= $true )
| ( ( SV588
= ( hAPP_pname_a @ SV740 @ SV816 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3423]) ).
thf(3603,plain,
! [SV590: $i,SV217: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV217 ) @ SV590 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV590 ) @ SV217 ) )
| ( SV217 = SV590 ) )
= $true )
| ( ( is_fun_pname_bool @ SV217 )
= $false )
| ( ( is_fun_pname_bool @ SV590 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3424]) ).
thf(3604,plain,
! [SV591: $i,SV218: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV218 ) @ SV591 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV591 ) @ SV218 ) )
| ( SV218 = SV591 ) )
= $true )
| ( ( is_fun_a_bool @ SV218 )
= $false )
| ( ( is_fun_a_bool @ SV591 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3425]) ).
thf(3605,plain,
! [SV1002: $i,SV596: $i,SV223: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV223 ) @ ( insert_pname @ SV596 @ SV1002 ) ) ) )
= $true )
| ( ( ( SV223 = SV596 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV223 ) @ SV1002 ) ) )
= $true )
| ( ( is_pname @ SV223 )
= $false )
| ( ( is_pname @ SV596 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3429]) ).
thf(3606,plain,
! [SV1003: $i,SV597: $i,SV224: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV224 ) @ ( insert_a @ SV597 @ SV1003 ) ) ) )
= $true )
| ( ( ( SV224 = SV597 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV224 ) @ SV1003 ) ) )
= $true )
| ( ( is_a @ SV224 )
= $false )
| ( ( is_a @ SV597 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3430]) ).
thf(3607,plain,
! [SV817: $i,SV764: $i,SV644: $i,SV279: $i] :
( ( ( SV279
= ( hAPP_pname_a @ SV644 @ SV764 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV279 ) @ ( image_pname_a @ SV644 @ SV817 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV764 ) @ SV817 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3443]) ).
thf(3608,plain,
! [SV672: $i,SV314: $i] :
( ( ( hBOOL @ ( hAPP_a_bool @ ( hAPP_a_fun_a_bool @ fequal_a @ SV314 ) @ SV672 ) )
= $false )
| ( ( SV314 = SV672 )
= $true )
| ( ( is_a @ SV314 )
= $false )
| ( ( is_a @ SV672 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3444]) ).
thf(3609,plain,
! [SV676: $i,SV318: $i] :
( ( ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ fequal_pname @ SV318 ) @ SV676 ) )
= $false )
| ( ( SV318 = SV676 )
= $true )
| ( ( is_pname @ SV318 )
= $false )
| ( ( is_pname @ SV676 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3445]) ).
thf(3610,plain,
! [SV679: $i,SV321: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ SV321 ) @ SV679 ) )
= $false )
| ( ( SV321 = SV679 )
= $true )
| ( ( is_fun_a_bool @ SV321 )
= $false )
| ( ( is_fun_a_bool @ SV679 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3446]) ).
thf(3611,plain,
! [SV686: $i,SV328: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ SV328 ) @ SV686 ) )
= $false )
| ( ( SV328 = SV686 )
= $true )
| ( ( is_fun_pname_bool @ SV328 )
= $false )
| ( ( is_fun_pname_bool @ SV686 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3447]) ).
thf(3612,plain,
! [SV1005: $i,SV364: $i,SV1035: $i] :
( ( ( ! [SY1178: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY1178 ) @ SV1035 ) )
| ~ ( is_fun_pname_bool @ SY1178 )
| ( SV364
!= ( image_pname_a @ SV1005 @ SY1178 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV364 ) @ ( image_pname_a @ SV1005 @ SV1035 ) ) ) )
= $true )
| ( ( is_fun_a_bool @ SV364 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3456]) ).
thf(3613,plain,
! [SV1036: $i,SV1006: $i,SV364: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV364 ) @ ( image_pname_a @ SV1006 @ SV1036 ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( sK10_AA @ SV1036 @ SV1006 @ SV364 ) ) @ SV1036 ) )
| ~ ( is_fun_pname_bool @ ( sK10_AA @ SV1036 @ SV1006 @ SV364 ) ) )
| ( SV364
!= ( image_pname_a @ SV1006 @ ( sK10_AA @ SV1036 @ SV1006 @ SV364 ) ) ) ) )
= $true )
| ( ( is_fun_a_bool @ SV364 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3457]) ).
thf(3614,plain,
! [SV892: $i,SV826: $i] :
( ( ( SV826
= ( hAPP_nat_nat @ suc @ SV892 ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV826 ) @ SV892 ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV826 ) @ ( hAPP_nat_nat @ suc @ SV892 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3458]) ).
thf(3615,plain,
! [SV1037: $i,SV1007: $i] :
( ( ( SV1007
!= ( hAPP_nat_nat @ suc @ SV1037 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV1007 ) @ ( hAPP_nat_nat @ suc @ SV1037 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3459]) ).
thf(3616,plain,
! [SV1038: $i,SV1008: $i] :
( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV1008 ) @ SV1038 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV1008 ) @ ( hAPP_nat_nat @ suc @ SV1038 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3460]) ).
thf(3617,plain,
! [SV893: $i,SV827: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV827 ) @ SV893 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV893 ) @ SV827 ) ) )
= $true )
| ( ( SV827 = SV893 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3461]) ).
thf(3618,plain,
! [SV1039: $i,SV1009: $i] :
( ( ( SV1009 != SV1039 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV1009 ) @ SV1039 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3462]) ).
thf(3619,plain,
! [SV1040: $i,SV1010: $i] :
( ( ( SV1010 != SV1040 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV1040 ) @ SV1010 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3463]) ).
thf(3620,plain,
! [SV894: $i,SV828: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ SV828 ) @ SV894 ) ) )
= $true )
| ( ( ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( insert_fun_nat_bool @ SV828 @ SV894 ) )
= ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SV894 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV894 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3464]) ).
thf(3621,plain,
! [SV895: $i,SV829: $i] :
( ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ SV829 ) @ SV895 ) )
= $true )
| ( ( ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( insert_fun_nat_bool @ SV829 @ SV895 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SV895 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV895 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3465]) ).
thf(3622,plain,
! [SV896: $i,SV830: $i] :
( ( ( is_fun_pname_bool @ SV830 )
= $false )
| ( ( ~ ( is_fun_pname_bool @ SV896 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV830 ) @ SV896 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV896 ) @ SV830 ) )
| ( SV830 = SV896 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3466]) ).
thf(3623,plain,
! [SV1041: $i,SV1011: $i] :
( ( ~ ( is_fun_pname_bool @ SV1011 )
| ~ ( is_fun_pname_bool @ SV1041 )
| ( SV1011 != SV1041 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV1011 ) @ SV1041 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3467]) ).
thf(3624,plain,
! [SV1042: $i,SV1012: $i] :
( ( ~ ( is_fun_pname_bool @ SV1012 )
| ~ ( is_fun_pname_bool @ SV1042 )
| ( SV1012 != SV1042 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV1042 ) @ SV1012 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3468]) ).
thf(3625,plain,
! [SV900: $i,SV975: $i,SV365: $i] :
( ( ( ~ ( is_pname @ SV365 ) )
= $true )
| ( ( ~ ( is_pname @ SV975 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV365 @ SV900 ) @ SV975 ) )
| ( SV365 = SV975 )
| ( hBOOL @ ( hAPP_pname_bool @ SV900 @ SV975 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3473]) ).
thf(3626,plain,
! [SV1043: $i,SV365: $i] :
( ( ! [SY1179: $i] :
( ~ ( is_pname @ SV365 )
| ~ ( is_pname @ SY1179 )
| ( SV365 != SY1179 )
| ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV365 @ SV1043 ) @ SY1179 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3474]) ).
thf(3627,plain,
! [SV1044: $i,SV365: $i] :
( ( ! [SY1180: $i] :
( ~ ( is_pname @ SV365 )
| ~ ( is_pname @ SY1180 )
| ~ ( hBOOL @ ( hAPP_pname_bool @ SV1044 @ SY1180 ) )
| ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV365 @ SV1044 ) @ SY1180 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3475]) ).
thf(3628,plain,
! [SV976: $i,SV901: $i,SV366: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV366 ) @ ( insert_nat @ SV901 @ SV976 ) ) )
= $false )
| ( ( ( SV366 = SV901 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV366 ) @ SV976 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3476]) ).
thf(3629,plain,
! [SV1045: $i,SV366: $i] :
( ( ( SV366 != SV1045 )
| ! [SY1181: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV366 ) @ ( insert_nat @ SV1045 @ SY1181 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3477]) ).
thf(3630,plain,
! [SV1046: $i,SV366: $i] :
( ( ! [SY1182: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV366 ) @ SY1182 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV366 ) @ ( insert_nat @ SV1046 @ SY1182 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3478]) ).
thf(3631,plain,
! [SV904: $i,SV367: $i] :
( ( ( is_a @ SV367 )
= $false )
| ( ( ~ ( is_a @ SV904 ) )
= $true )
| ( ( ! [SY1123: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ ( insert_a @ SV904 @ SY1123 ) ) )
| ( SV367 = SV904 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ SY1123 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3481]) ).
thf(3632,plain,
! [SV1047: $i,SV367: $i] :
( ( ~ ( is_a @ SV367 )
| ~ ( is_a @ SV1047 )
| ( SV367 != SV1047 )
| ! [SY1183: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ ( insert_a @ SV1047 @ SY1183 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3482]) ).
thf(3633,plain,
! [SV1048: $i,SV367: $i] :
( ( ~ ( is_a @ SV367 )
| ~ ( is_a @ SV1048 )
| ! [SY1184: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ SY1184 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ ( insert_a @ SV1048 @ SY1184 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3483]) ).
thf(3634,plain,
! [SV368: $i,SV906: $i,SV977: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV977 ) @ ( insert_a @ SV906 @ SV368 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV977 ) @ SV368 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV906 ) @ SV977 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3486]) ).
thf(3635,plain,
! [SV907: $i,SV368: $i,SV978: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV978 ) @ SV368 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV978 ) @ ( insert_a @ SV907 @ SV368 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV907 ) @ SV978 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3487]) ).
thf(3636,plain,
! [SV1015: $i,SV369: $i,SV1049: $i] :
( ( ( ! [SY1185: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SY1185 ) @ SV1049 ) )
| ~ ( is_pname @ SY1185 )
| ( SV369
!= ( hAPP_pname_a @ SV1015 @ SY1185 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV369 ) @ ( image_pname_a @ SV1015 @ SV1049 ) ) ) )
= $true )
| ( ( is_a @ SV369 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3488]) ).
thf(3637,plain,
! [SV1050: $i,SV1016: $i,SV369: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV369 ) @ ( image_pname_a @ SV1016 @ SV1050 ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK11_X_1 @ SV1050 @ SV1016 @ SV369 ) ) @ SV1050 ) )
| ~ ( is_pname @ ( sK11_X_1 @ SV1050 @ SV1016 @ SV369 ) ) )
| ( SV369
!= ( hAPP_pname_a @ SV1016 @ ( sK11_X_1 @ SV1050 @ SV1016 @ SV369 ) ) ) ) )
= $true )
| ( ( is_a @ SV369 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3489]) ).
thf(3638,plain,
! [SV370: $i,SV908: $i,SV979: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV979 ) @ ( insert_nat @ SV908 @ SV370 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV979 ) @ SV370 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV908 ) @ SV979 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3490]) ).
thf(3639,plain,
! [SV909: $i,SV370: $i,SV980: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV980 ) @ SV370 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV980 ) @ ( insert_nat @ SV909 @ SV370 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV909 ) @ SV980 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3491]) ).
thf(3640,plain,
! [SV371: $i,SV981: $i,SV913: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV913 ) @ SV981 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV913 ) @ ( insert_nat @ SV371 @ SV981 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3496]) ).
thf(3641,plain,
! [SV1051: $i,SV371: $i,SV914: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV914 ) @ ( insert_nat @ SV371 @ SV1051 ) ) )
= $true )
| ( ( SV914 = SV371 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3497]) ).
thf(3642,plain,
! [SV915: $i,SV843: $i] :
( ( ( is_fun_a_bool @ SV843 )
= $false )
| ( ( ~ ( is_fun_a_bool @ SV915 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV843 ) @ SV915 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV915 ) @ SV843 ) )
| ( SV843 = SV915 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3498]) ).
thf(3643,plain,
! [SV1052: $i,SV1018: $i] :
( ( ~ ( is_fun_a_bool @ SV1018 )
| ~ ( is_fun_a_bool @ SV1052 )
| ( SV1018 != SV1052 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV1018 ) @ SV1052 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3499]) ).
thf(3644,plain,
! [SV1053: $i,SV1019: $i] :
( ( ~ ( is_fun_a_bool @ SV1019 )
| ~ ( is_fun_a_bool @ SV1053 )
| ( SV1019 != SV1053 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV1053 ) @ SV1019 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3500]) ).
thf(3645,plain,
! [SV722: $i,SV372: $i,SV813: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV813 ) @ ( image_pname_a @ SV372 @ SV722 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( sK17_C_2 @ SV813 @ SV722 @ SV372 ) ) @ SV722 ) )
| ~ ( is_fun_pname_bool @ ( sK17_C_2 @ SV813 @ SV722 @ SV372 ) ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( sK17_C_2 @ SV813 @ SV722 @ SV372 ) ) ) )
| ( SV813
!= ( image_pname_a @ SV372 @ ( sK17_C_2 @ SV813 @ SV722 @ SV372 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV813 ) )
= $false )
| ( ( is_fun_a_bool @ SV813 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3501]) ).
thf(3646,plain,
! [SV916: $i,SV844: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV844 ) @ SV916 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ SV916 ) ) @ SV844 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3502]) ).
thf(3647,plain,
! [SV373: $i,SV982: $i,SV918: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV918 ) @ SV982 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV918 ) @ ( insert_pname @ SV373 @ SV982 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3503]) ).
thf(3648,plain,
! [SV1054: $i,SV373: $i,SV919: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV919 ) @ ( insert_pname @ SV373 @ SV1054 ) ) )
= $true )
| ( ( SV919 = SV373 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3504]) ).
thf(3649,plain,
! [SV920: $i,SV846: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ SV846 ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ SV920 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ SV846 ) @ SV920 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3505]) ).
thf(3650,plain,
! [SV1020: $i] :
( ( ( ! [SY1166: $i] :
~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ SV1020 ) @ SY1166 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ SV1020 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3506]) ).
thf(3651,plain,
! [SV1055: $i,SV1021: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ SV1021 ) @ SV1055 ) ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ SV1055 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3507]) ).
thf(3652,plain,
! [SV921: $i,SV983: $i,SV374: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV374 ) @ SV983 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV921 ) @ SV983 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV374 @ SV921 ) ) @ SV983 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3508]) ).
thf(3653,plain,
! [SV1056: $i,SV374: $i] :
( ( ! [SY1186: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV374 @ SV1056 ) ) @ SY1186 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV374 ) @ SY1186 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3509]) ).
thf(3654,plain,
! [SV1057: $i,SV374: $i] :
( ( ! [SY1187: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV374 @ SV1057 ) ) @ SY1187 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV1057 ) @ SY1187 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3510]) ).
thf(3655,plain,
! [SV922: $i,SV847: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ SV847 ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ SV922 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ SV847 ) @ SV922 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3511]) ).
thf(3656,plain,
! [SV1022: $i] :
( ( ( ! [SY1168: $i] :
~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ SV1022 ) @ SY1168 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ SV1022 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3512]) ).
thf(3657,plain,
! [SV1058: $i,SV1023: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ SV1023 ) @ SV1058 ) ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ SV1058 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3513]) ).
thf(3658,plain,
! [SV375: $i,SV723: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK12_X_1 @ SV723 @ SV375 ) ) @ SV723 ) )
| ~ ( is_pname @ ( sK12_X_1 @ SV723 @ SV375 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_pname_a @ SV375 @ SV723 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV723 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3514]) ).
thf(3659,plain,
! [SV375: $i,SV723: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ ( hAPP_f759274231e_bool @ ( cOMBC_1058051404l_bool @ member_pname ) @ SV723 ) ) @ ( hAPP_a93125764e_bool @ ( cOMBC_pname_a_bool @ ( cOMBB_1897541054_pname @ fequal_a @ SV375 ) ) @ ( hAPP_pname_a @ SV375 @ ( sK12_X_1 @ SV723 @ SV375 ) ) ) ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_pname_a @ SV375 @ SV723 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV723 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3515]) ).
thf(3660,plain,
! [SV923: $i,SV984: $i,SV376: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV376 ) @ SV984 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV923 ) @ SV984 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( insert_nat @ SV376 @ SV923 ) ) @ SV984 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3516]) ).
thf(3661,plain,
! [SV1059: $i,SV376: $i] :
( ( ! [SY1188: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( insert_nat @ SV376 @ SV1059 ) ) @ SY1188 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV376 ) @ SY1188 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3517]) ).
thf(3662,plain,
! [SV1060: $i,SV376: $i] :
( ( ! [SY1189: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( insert_nat @ SV376 @ SV1060 ) ) @ SY1189 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV1060 ) @ SY1189 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3518]) ).
thf(3663,plain,
! [SV924: $i,SV848: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ SV848 ) @ SV924 ) ) )
= $true )
| ( ( ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( insert1325755072e_bool @ SV848 @ SV924 ) )
= ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SV924 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV924 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3519]) ).
thf(3664,plain,
! [SV925: $i,SV849: $i] :
( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ SV849 ) @ SV925 ) )
= $true )
| ( ( ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( insert1325755072e_bool @ SV849 @ SV925 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SV925 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV925 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3520]) ).
thf(3665,plain,
! [SV985: $i,SV377: $i,SV928: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV928 ) @ SV377 ) )
= $true )
| ( ( ( ( insert_nat @ SV928 @ SV985 )
!= ( insert_nat @ SV928 @ SV377 ) )
| ( SV985 = SV377 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV928 ) @ SV985 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3523]) ).
thf(3666,plain,
! [SV986: $i,SV377: $i,SV929: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV929 ) @ SV377 ) )
= $true )
| ( ( ( SV986 != SV377 )
| ( ( insert_nat @ SV929 @ SV986 )
= ( insert_nat @ SV929 @ SV377 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV929 ) @ SV986 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3524]) ).
thf(3667,plain,
! [SV378: $i,SV724: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( sK7_X_1 @ SV724 @ SV378 ) ) @ SV724 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV724 ) @ SV378 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3525]) ).
thf(3668,plain,
! [SV378: $i,SV724: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( sK7_X_1 @ SV724 @ SV378 ) ) @ SV378 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV724 ) @ SV378 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3525]) ).
thf(3669,plain,
! [SV379: $i,SV987: $i,SV932: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV932 ) @ SV987 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV932 ) @ ( insert_a @ SV379 @ SV987 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3528]) ).
thf(3670,plain,
! [SV1061: $i,SV379: $i,SV933: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV933 ) @ ( insert_a @ SV379 @ SV1061 ) ) )
= $true )
| ( ( SV933 = SV379 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3529]) ).
thf(3671,plain,
! [SV934: $i,SV854: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV854 ) @ SV934 ) ) )
= $true )
| ( ( ( hAPP_f22106695ol_nat @ finite_card_nat @ ( insert_nat @ SV854 @ SV934 ) )
= ( hAPP_f22106695ol_nat @ finite_card_nat @ SV934 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV934 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3530]) ).
thf(3672,plain,
! [SV935: $i,SV855: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV855 ) @ SV935 ) )
= $true )
| ( ( ( hAPP_f22106695ol_nat @ finite_card_nat @ ( insert_nat @ SV855 @ SV935 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f22106695ol_nat @ finite_card_nat @ SV935 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV935 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3531]) ).
thf(3673,plain,
! [SV938: $i,SV858: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ SV858 ) @ SV938 ) ) )
= $true )
| ( ( ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( insert_fun_a_bool @ SV858 @ SV938 ) )
= ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SV938 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV938 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3534]) ).
thf(3674,plain,
! [SV939: $i,SV859: $i] :
( ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ SV859 ) @ SV939 ) )
= $true )
| ( ( ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( insert_fun_a_bool @ SV859 @ SV939 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SV939 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV939 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3535]) ).
thf(3675,plain,
! [SV380: $i,SV725: $i,SV814: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK3_X_1 @ SV814 @ SV725 @ SV380 ) ) @ SV814 ) )
| ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( hAPP_pname_a @ SV380 @ ( sK3_X_1 @ SV814 @ SV725 @ SV380 ) ) ) @ SV725 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_pname_a @ SV380 @ SV814 ) ) @ SV725 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3539]) ).
thf(3676,plain,
! [SV381: $i,SV988: $i,SV942: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV942 ) @ SV988 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV942 ) @ SV381 ) )
| ( ( hAPP_nat_nat @ ( minus_minus_nat @ SV988 ) @ SV942 )
!= ( hAPP_nat_nat @ ( minus_minus_nat @ SV381 ) @ SV942 ) )
| ( SV988 = SV381 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3540]) ).
thf(3677,plain,
! [SV381: $i,SV989: $i,SV943: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV943 ) @ SV989 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV943 ) @ SV381 ) )
| ( SV989 != SV381 )
| ( ( hAPP_nat_nat @ ( minus_minus_nat @ SV989 ) @ SV943 )
= ( hAPP_nat_nat @ ( minus_minus_nat @ SV381 ) @ SV943 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3541]) ).
thf(3678,plain,
! [SV944: $i,SV862: $i] :
( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ SV862 ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ SV944 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ SV862 ) @ SV944 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3543]) ).
thf(3679,plain,
! [SV1024: $i] :
( ( ( ! [SY1170: $i] :
~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ SV1024 ) @ SY1170 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ SV1024 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3544]) ).
thf(3680,plain,
! [SV1062: $i,SV1025: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ SV1025 ) @ SV1062 ) ) ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ SV1062 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3545]) ).
thf(3681,plain,
! [SV946: $i,SV865: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV865 ) @ SV946 ) ) )
= $true )
| ( ( ( hAPP_fun_a_bool_nat @ finite_card_a @ ( insert_a @ SV865 @ SV946 ) )
= ( hAPP_fun_a_bool_nat @ finite_card_a @ SV946 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV946 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3548]) ).
thf(3682,plain,
! [SV947: $i,SV866: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV866 ) @ SV947 ) )
= $true )
| ( ( ( hAPP_fun_a_bool_nat @ finite_card_a @ ( insert_a @ SV866 @ SV947 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SV947 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV947 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3549]) ).
thf(3683,plain,
! [SV948: $i,SV867: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV867 ) @ SV948 ) ) )
= $true )
| ( ( ( hAPP_f921600141ol_nat @ finite_card_pname @ ( insert_pname @ SV867 @ SV948 ) )
= ( hAPP_f921600141ol_nat @ finite_card_pname @ SV948 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV948 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3550]) ).
thf(3684,plain,
! [SV949: $i,SV868: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV868 ) @ SV949 ) )
= $true )
| ( ( ( hAPP_f921600141ol_nat @ finite_card_pname @ ( insert_pname @ SV868 @ SV949 ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV949 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV949 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3551]) ).
thf(3685,plain,
! [SV950: $i,SV383: $i] :
( ( ( is_pname @ SV383 )
= $false )
| ( ( ~ ( is_pname @ SV950 ) )
= $true )
| ( ( ! [SY1140: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ ( insert_pname @ SV950 @ SY1140 ) ) )
| ( SV383 = SV950 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ SY1140 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3552]) ).
thf(3686,plain,
! [SV1063: $i,SV383: $i] :
( ( ~ ( is_pname @ SV383 )
| ~ ( is_pname @ SV1063 )
| ( SV383 != SV1063 )
| ! [SY1190: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ ( insert_pname @ SV1063 @ SY1190 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3553]) ).
thf(3687,plain,
! [SV1064: $i,SV383: $i] :
( ( ~ ( is_pname @ SV383 )
| ~ ( is_pname @ SV1064 )
| ! [SY1191: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ SY1191 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ ( insert_pname @ SV1064 @ SY1191 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3554]) ).
thf(3688,plain,
! [SV951: $i,SV990: $i,SV384: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV384 ) @ SV990 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV951 ) @ SV990 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ SV384 @ SV951 ) ) @ SV990 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3555]) ).
thf(3689,plain,
! [SV1065: $i,SV384: $i] :
( ( ! [SY1192: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ SV384 @ SV1065 ) ) @ SY1192 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV384 ) @ SY1192 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3556]) ).
thf(3690,plain,
! [SV1066: $i,SV384: $i] :
( ( ! [SY1193: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ SV384 @ SV1066 ) ) @ SY1193 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV1066 ) @ SY1193 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3557]) ).
thf(3691,plain,
! [SV952: $i,SV869: $i] :
( ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ SV869 ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ SV952 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ SV869 ) @ SV952 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3558]) ).
thf(3692,plain,
! [SV1027: $i] :
( ( ( ! [SY1172: $i] :
~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ SV1027 ) @ SY1172 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ SV1027 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3559]) ).
thf(3693,plain,
! [SV1067: $i,SV1028: $i] :
( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ SV1028 ) @ SV1067 ) ) ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ SV1067 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3560]) ).
thf(3694,plain,
! [SV953: $i,SV991: $i,SV385: $i] :
( ( ( ~ ( is_fun_a_bool @ SV385 ) )
= $true )
| ( ( ~ ( is_fun_a_bool @ SV991 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV953 ) @ SV991 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV953 ) @ SV385 ) )
| ( ( insert_a @ SV953 @ SV991 )
!= ( insert_a @ SV953 @ SV385 ) )
| ( SV991 = SV385 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3561]) ).
thf(3695,plain,
! [SV954: $i,SV992: $i,SV385: $i] :
( ( ( ~ ( is_fun_a_bool @ SV385 ) )
= $true )
| ( ( ~ ( is_fun_a_bool @ SV992 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV954 ) @ SV992 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV954 ) @ SV385 ) )
| ( SV992 != SV385 )
| ( ( insert_a @ SV954 @ SV992 )
= ( insert_a @ SV954 @ SV385 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3562]) ).
thf(3696,plain,
! [SV957: $i,SV993: $i,SV386: $i] :
( ( ( ~ ( is_a @ SV386 ) )
= $true )
| ( ( ~ ( is_a @ SV993 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV386 @ SV957 ) @ SV993 ) )
| ( SV386 = SV993 )
| ( hBOOL @ ( hAPP_a_bool @ SV957 @ SV993 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3565]) ).
thf(3697,plain,
! [SV1068: $i,SV386: $i] :
( ( ! [SY1194: $i] :
( ~ ( is_a @ SV386 )
| ~ ( is_a @ SY1194 )
| ( SV386 != SY1194 )
| ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV386 @ SV1068 ) @ SY1194 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3566]) ).
thf(3698,plain,
! [SV1069: $i,SV386: $i] :
( ( ! [SY1195: $i] :
( ~ ( is_a @ SV386 )
| ~ ( is_a @ SY1195 )
| ~ ( hBOOL @ ( hAPP_a_bool @ SV1069 @ SY1195 ) )
| ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV386 @ SV1069 ) @ SY1195 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3567]) ).
thf(3699,plain,
! [SV387: $i,SV874: $i,SV959: $i] :
( ( ( ~ ( is_pname @ ( sK9_X_1 @ SV959 @ SV874 @ SV387 ) )
| ~ ~ ( ( SV387
!= ( hAPP_pname_a @ SV874 @ ( sK9_X_1 @ SV959 @ SV874 @ SV387 ) ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK9_X_1 @ SV959 @ SV874 @ SV387 ) ) @ SV959 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV387 ) @ ( image_pname_a @ SV874 @ SV959 ) ) )
= $false )
| ( ( is_a @ SV387 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3570]) ).
thf(3700,plain,
! [SV962: $i,SV877: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ SV877 ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ SV962 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ SV877 ) @ SV962 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3573]) ).
thf(3701,plain,
! [SV1030: $i] :
( ( ( ! [SY1174: $i] :
~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ SV1030 ) @ SY1174 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ SV1030 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3574]) ).
thf(3702,plain,
! [SV1070: $i,SV1031: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ SV1031 ) @ SV1070 ) ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ SV1070 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3575]) ).
thf(3703,plain,
! [SV388: $i,SV815: $i,SV727: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ SV727 @ ( hAPP_nat_nat @ suc @ ( sK5_N_2 @ SV815 @ SV727 @ SV388 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ SV727 @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV815 ) @ SV388 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ SV727 @ SV815 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3576]) ).
thf(3704,plain,
! [SV388: $i,SV815: $i,SV727: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP_nat_bool @ SV727 @ ( sK5_N_2 @ SV815 @ SV727 @ SV388 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ SV727 @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV815 ) @ SV388 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ SV727 @ SV815 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3576]) ).
thf(3705,plain,
! [SV963: $i,SV878: $i] :
( ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ SV878 ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ SV963 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ SV878 ) @ SV963 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3577]) ).
thf(3706,plain,
! [SV1032: $i] :
( ( ( ! [SY1176: $i] :
~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ SV1032 ) @ SY1176 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ SV1032 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3578]) ).
thf(3707,plain,
! [SV1071: $i,SV1033: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ SV1033 ) @ SV1071 ) ) ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ SV1071 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3579]) ).
thf(3708,plain,
! [SV964: $i,SV994: $i,SV389: $i] :
( ( ( ~ ( is_fun_pname_bool @ SV389 ) )
= $true )
| ( ( ~ ( is_fun_pname_bool @ SV994 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV964 ) @ SV994 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV964 ) @ SV389 ) )
| ( ( insert_pname @ SV964 @ SV994 )
!= ( insert_pname @ SV964 @ SV389 ) )
| ( SV994 = SV389 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3580]) ).
thf(3709,plain,
! [SV965: $i,SV995: $i,SV389: $i] :
( ( ( ~ ( is_fun_pname_bool @ SV389 ) )
= $true )
| ( ( ~ ( is_fun_pname_bool @ SV995 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV965 ) @ SV995 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV965 ) @ SV389 ) )
| ( SV995 != SV389 )
| ( ( insert_pname @ SV965 @ SV995 )
= ( insert_pname @ SV965 @ SV389 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3581]) ).
thf(3710,plain,
! [SV390: $i,SV968: $i,SV996: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV996 ) @ ( insert_pname @ SV968 @ SV390 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV996 ) @ SV390 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV968 ) @ SV996 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3584]) ).
thf(3711,plain,
! [SV969: $i,SV390: $i,SV997: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV997 ) @ SV390 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV997 ) @ ( insert_pname @ SV969 @ SV390 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV969 ) @ SV997 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3585]) ).
thf(3712,plain,
! [SV391: $i,SV998: $i,SV970: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV970 ) @ SV998 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV970 ) @ SV391 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV998 ) @ SV970 ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV391 ) @ SV970 ) ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV998 ) @ SV391 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3586]) ).
thf(3713,plain,
! [SV391: $i,SV999: $i,SV971: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV971 ) @ SV999 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV971 ) @ SV391 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV999 ) @ SV391 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV999 ) @ SV971 ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV391 ) @ SV971 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3587]) ).
thf(3714,plain,
! [SV392: $i,SV728: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK6_X_1 @ SV728 @ SV392 ) ) @ SV728 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV728 ) @ SV392 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3588]) ).
thf(3715,plain,
! [SV392: $i,SV728: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK6_X_1 @ SV728 @ SV392 ) ) @ SV392 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV728 ) @ SV392 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3588]) ).
thf(3716,plain,
! [SV1000: $i,SV972: $i,SV393: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV393 @ SV972 ) @ SV1000 ) )
= $false )
| ( ( ( SV393 = SV1000 )
| ( hBOOL @ ( hAPP_nat_bool @ SV972 @ SV1000 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3589]) ).
thf(3717,plain,
! [SV1072: $i,SV393: $i] :
( ( ! [SY1196: $i] :
( ( SV393 != SY1196 )
| ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV393 @ SV1072 ) @ SY1196 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3590]) ).
thf(3718,plain,
! [SV393: $i,SV1073: $i] :
( ( ! [SY1197: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ SV1073 @ SY1197 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV393 @ SV1073 ) @ SY1197 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3591]) ).
thf(3719,plain,
! [SV881: $i,SV1001: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ ( sK2_X_1 @ SV1001 @ SV881 ) ) @ SV881 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV881 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3592]) ).
thf(3720,plain,
! [SV881: $i,SV1001: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( sK2_X_1 @ SV1001 @ SV881 ) ) @ SV1001 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV881 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3592]) ).
thf(3721,plain,
! [SV882: $i,SV1034: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV1034 ) @ SV882 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV1034 ) @ ( sK1_M @ SV882 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV882 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3593]) ).
thf(3722,plain,
! [SV537: $i,SV158: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ SV158 ) @ SV537 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SV537 ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SV158 ) ) )
| ( SV158 = SV537 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV537 ) )
= $false )
| ( ( is_fun1661590463l_bool @ SV158 )
= $false )
| ( ( is_fun1661590463l_bool @ SV537 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3597]) ).
thf(3723,plain,
! [SV538: $i,SV159: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ SV159 ) @ SV538 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SV538 ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SV159 ) ) )
| ( SV159 = SV538 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV538 ) )
= $false )
| ( ( is_fun949378684l_bool @ SV159 )
= $false )
| ( ( is_fun949378684l_bool @ SV538 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3598]) ).
thf(3724,plain,
! [SV539: $i,SV160: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV160 ) @ SV539 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV539 ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV160 ) ) )
| ( SV160 = SV539 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV539 ) )
= $false )
| ( ( is_fun_pname_bool @ SV160 )
= $false )
| ( ( is_fun_pname_bool @ SV539 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3599]) ).
thf(3725,plain,
! [SV540: $i,SV161: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV161 ) @ SV540 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SV540 ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SV161 ) ) )
| ( SV161 = SV540 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV540 ) )
= $false )
| ( ( is_fun_a_bool @ SV161 )
= $false )
| ( ( is_fun_a_bool @ SV540 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3600]) ).
thf(3726,plain,
! [SV217: $i,SV590: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV590 ) @ SV217 ) ) )
= $true )
| ( ( SV217 = SV590 )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV217 ) @ SV590 ) )
= $false )
| ( ( is_fun_pname_bool @ SV217 )
= $false )
| ( ( is_fun_pname_bool @ SV590 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3603]) ).
thf(3727,plain,
! [SV218: $i,SV591: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV591 ) @ SV218 ) ) )
= $true )
| ( ( SV218 = SV591 )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV218 ) @ SV591 ) )
= $false )
| ( ( is_fun_a_bool @ SV218 )
= $false )
| ( ( is_fun_a_bool @ SV591 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3604]) ).
thf(3728,plain,
! [SV1002: $i,SV596: $i,SV223: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV223 ) @ ( insert_pname @ SV596 @ SV1002 ) ) )
= $false )
| ( ( ( SV223 = SV596 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV223 ) @ SV1002 ) ) )
= $true )
| ( ( is_pname @ SV223 )
= $false )
| ( ( is_pname @ SV596 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3605]) ).
thf(3729,plain,
! [SV1003: $i,SV597: $i,SV224: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV224 ) @ ( insert_a @ SV597 @ SV1003 ) ) )
= $false )
| ( ( ( SV224 = SV597 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV224 ) @ SV1003 ) ) )
= $true )
| ( ( is_a @ SV224 )
= $false )
| ( ( is_a @ SV597 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3606]) ).
thf(3730,plain,
! [SV1005: $i,SV364: $i,SV1035: $i] :
( ( ( ! [SY1178: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY1178 ) @ SV1035 ) )
| ~ ( is_fun_pname_bool @ SY1178 )
| ( SV364
!= ( image_pname_a @ SV1005 @ SY1178 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV364 ) @ ( image_pname_a @ SV1005 @ SV1035 ) ) )
= $true )
| ( ( is_fun_a_bool @ SV364 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3612]) ).
thf(3731,plain,
! [SV1036: $i,SV1006: $i,SV364: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV364 ) @ ( image_pname_a @ SV1006 @ SV1036 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( sK10_AA @ SV1036 @ SV1006 @ SV364 ) ) @ SV1036 ) )
| ~ ( is_fun_pname_bool @ ( sK10_AA @ SV1036 @ SV1006 @ SV364 ) ) )
| ( SV364
!= ( image_pname_a @ SV1006 @ ( sK10_AA @ SV1036 @ SV1006 @ SV364 ) ) ) ) )
= $true )
| ( ( is_fun_a_bool @ SV364 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3613]) ).
thf(3732,plain,
! [SV1037: $i,SV1007: $i] :
( ( ( ( SV1007
!= ( hAPP_nat_nat @ suc @ SV1037 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV1007 ) @ ( hAPP_nat_nat @ suc @ SV1037 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3615]) ).
thf(3733,plain,
! [SV1038: $i,SV1008: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV1008 ) @ SV1038 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV1008 ) @ ( hAPP_nat_nat @ suc @ SV1038 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3616]) ).
thf(3734,plain,
! [SV827: $i,SV893: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV893 ) @ SV827 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV827 ) @ SV893 ) )
= $false )
| ( ( SV827 = SV893 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3617]) ).
thf(3735,plain,
! [SV1039: $i,SV1009: $i] :
( ( ( ( SV1009 != SV1039 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV1009 ) @ SV1039 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3618]) ).
thf(3736,plain,
! [SV1040: $i,SV1010: $i] :
( ( ( ( SV1010 != SV1040 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV1040 ) @ SV1010 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3619]) ).
thf(3737,plain,
! [SV894: $i,SV828: $i] :
( ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ SV828 ) @ SV894 ) )
= $false )
| ( ( ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( insert_fun_nat_bool @ SV828 @ SV894 ) )
= ( hAPP_f696928925ol_nat @ finite346522414t_bool @ SV894 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV894 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3620]) ).
thf(3738,plain,
! [SV830: $i,SV896: $i] :
( ( ( is_fun_pname_bool @ SV896 )
= $false )
| ( ( is_fun_pname_bool @ SV830 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV830 ) @ SV896 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV896 ) @ SV830 ) )
| ( SV830 = SV896 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3622]) ).
thf(3739,plain,
! [SV1041: $i,SV1011: $i] :
( ( ( ~ ( is_fun_pname_bool @ SV1011 )
| ~ ( is_fun_pname_bool @ SV1041 ) )
= $true )
| ( ( ( SV1011 != SV1041 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV1011 ) @ SV1041 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3623]) ).
thf(3740,plain,
! [SV1042: $i,SV1012: $i] :
( ( ( ~ ( is_fun_pname_bool @ SV1012 )
| ~ ( is_fun_pname_bool @ SV1042 ) )
= $true )
| ( ( ( SV1012 != SV1042 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV1042 ) @ SV1012 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3624]) ).
thf(3741,plain,
! [SV900: $i,SV975: $i,SV365: $i] :
( ( ( is_pname @ SV365 )
= $false )
| ( ( ~ ( is_pname @ SV975 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV365 @ SV900 ) @ SV975 ) )
| ( SV365 = SV975 )
| ( hBOOL @ ( hAPP_pname_bool @ SV900 @ SV975 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3625]) ).
thf(3742,plain,
! [SV1043: $i,SV1074: $i,SV365: $i] :
( ( ~ ( is_pname @ SV365 )
| ~ ( is_pname @ SV1074 )
| ( SV365 != SV1074 )
| ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV365 @ SV1043 ) @ SV1074 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3626]) ).
thf(3743,plain,
! [SV1044: $i,SV1075: $i,SV365: $i] :
( ( ~ ( is_pname @ SV365 )
| ~ ( is_pname @ SV1075 )
| ~ ( hBOOL @ ( hAPP_pname_bool @ SV1044 @ SV1075 ) )
| ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV365 @ SV1044 ) @ SV1075 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3627]) ).
thf(3744,plain,
! [SV976: $i,SV901: $i,SV366: $i] :
( ( ( SV366 = SV901 )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV366 ) @ SV976 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV366 ) @ ( insert_nat @ SV901 @ SV976 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3628]) ).
thf(3745,plain,
! [SV1045: $i,SV366: $i] :
( ( ( ( SV366 != SV1045 ) )
= $true )
| ( ( ! [SY1181: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV366 ) @ ( insert_nat @ SV1045 @ SY1181 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3629]) ).
thf(3746,plain,
! [SV1046: $i,SV1076: $i,SV366: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV366 ) @ SV1076 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV366 ) @ ( insert_nat @ SV1046 @ SV1076 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3630]) ).
thf(3747,plain,
! [SV367: $i,SV904: $i] :
( ( ( is_a @ SV904 )
= $false )
| ( ( is_a @ SV367 )
= $false )
| ( ( ! [SY1123: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ ( insert_a @ SV904 @ SY1123 ) ) )
| ( SV367 = SV904 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ SY1123 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3631]) ).
thf(3748,plain,
! [SV1047: $i,SV367: $i] :
( ( ( ~ ( is_a @ SV367 )
| ~ ( is_a @ SV1047 ) )
= $true )
| ( ( ( SV367 != SV1047 )
| ! [SY1183: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ ( insert_a @ SV1047 @ SY1183 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3632]) ).
thf(3749,plain,
! [SV1048: $i,SV367: $i] :
( ( ( ~ ( is_a @ SV367 )
| ~ ( is_a @ SV1048 ) )
= $true )
| ( ( ! [SY1184: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ SY1184 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ ( insert_a @ SV1048 @ SY1184 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3633]) ).
thf(3750,plain,
! [SV368: $i,SV906: $i,SV977: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV977 ) @ ( insert_a @ SV906 @ SV368 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV977 ) @ SV368 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV906 ) @ SV977 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3634]) ).
thf(3751,plain,
! [SV907: $i,SV368: $i,SV978: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV978 ) @ SV368 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV978 ) @ ( insert_a @ SV907 @ SV368 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV907 ) @ SV978 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3635]) ).
thf(3752,plain,
! [SV1015: $i,SV369: $i,SV1049: $i] :
( ( ( ! [SY1185: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SY1185 ) @ SV1049 ) )
| ~ ( is_pname @ SY1185 )
| ( SV369
!= ( hAPP_pname_a @ SV1015 @ SY1185 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV369 ) @ ( image_pname_a @ SV1015 @ SV1049 ) ) )
= $true )
| ( ( is_a @ SV369 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3636]) ).
thf(3753,plain,
! [SV1050: $i,SV1016: $i,SV369: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV369 ) @ ( image_pname_a @ SV1016 @ SV1050 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK11_X_1 @ SV1050 @ SV1016 @ SV369 ) ) @ SV1050 ) )
| ~ ( is_pname @ ( sK11_X_1 @ SV1050 @ SV1016 @ SV369 ) ) )
| ( SV369
!= ( hAPP_pname_a @ SV1016 @ ( sK11_X_1 @ SV1050 @ SV1016 @ SV369 ) ) ) ) )
= $true )
| ( ( is_a @ SV369 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3637]) ).
thf(3754,plain,
! [SV370: $i,SV908: $i,SV979: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV979 ) @ ( insert_nat @ SV908 @ SV370 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV979 ) @ SV370 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV908 ) @ SV979 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3638]) ).
thf(3755,plain,
! [SV909: $i,SV370: $i,SV980: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV980 ) @ SV370 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV980 ) @ ( insert_nat @ SV909 @ SV370 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV909 ) @ SV980 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3639]) ).
thf(3756,plain,
! [SV843: $i,SV915: $i] :
( ( ( is_fun_a_bool @ SV915 )
= $false )
| ( ( is_fun_a_bool @ SV843 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV843 ) @ SV915 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV915 ) @ SV843 ) )
| ( SV843 = SV915 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3642]) ).
thf(3757,plain,
! [SV1052: $i,SV1018: $i] :
( ( ( ~ ( is_fun_a_bool @ SV1018 )
| ~ ( is_fun_a_bool @ SV1052 ) )
= $true )
| ( ( ( SV1018 != SV1052 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV1018 ) @ SV1052 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3643]) ).
thf(3758,plain,
! [SV1053: $i,SV1019: $i] :
( ( ( ~ ( is_fun_a_bool @ SV1019 )
| ~ ( is_fun_a_bool @ SV1053 ) )
= $true )
| ( ( ( SV1019 != SV1053 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV1053 ) @ SV1019 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3644]) ).
thf(3759,plain,
! [SV722: $i,SV372: $i,SV813: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV813 ) @ ( image_pname_a @ SV372 @ SV722 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( sK17_C_2 @ SV813 @ SV722 @ SV372 ) ) @ SV722 ) )
| ~ ( is_fun_pname_bool @ ( sK17_C_2 @ SV813 @ SV722 @ SV372 ) ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( sK17_C_2 @ SV813 @ SV722 @ SV372 ) ) ) )
| ( SV813
!= ( image_pname_a @ SV372 @ ( sK17_C_2 @ SV813 @ SV722 @ SV372 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV813 ) )
= $false )
| ( ( is_fun_a_bool @ SV813 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3645]) ).
thf(3760,plain,
! [SV846: $i,SV920: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ SV920 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ SV846 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ SV846 ) @ SV920 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3649]) ).
thf(3761,plain,
! [SV1077: $i,SV1020: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ SV1020 ) @ SV1077 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ SV1020 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3650]) ).
thf(3762,plain,
! [SV1055: $i,SV1021: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ SV1021 ) @ SV1055 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ SV1055 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3651]) ).
thf(3763,plain,
! [SV921: $i,SV983: $i,SV374: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV374 ) @ SV983 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV921 ) @ SV983 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV374 @ SV921 ) ) @ SV983 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3652]) ).
thf(3764,plain,
! [SV1078: $i,SV1056: $i,SV374: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV374 @ SV1056 ) ) @ SV1078 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV374 ) @ SV1078 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3653]) ).
thf(3765,plain,
! [SV1079: $i,SV1057: $i,SV374: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV374 @ SV1057 ) ) @ SV1079 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV1057 ) @ SV1079 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3654]) ).
thf(3766,plain,
! [SV847: $i,SV922: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ SV922 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ SV847 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ SV847 ) @ SV922 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3655]) ).
thf(3767,plain,
! [SV1080: $i,SV1022: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ SV1022 ) @ SV1080 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ SV1022 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3656]) ).
thf(3768,plain,
! [SV1058: $i,SV1023: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ SV1023 ) @ SV1058 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ SV1058 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3657]) ).
thf(3769,plain,
! [SV375: $i,SV723: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK12_X_1 @ SV723 @ SV375 ) ) @ SV723 ) )
| ~ ( is_pname @ ( sK12_X_1 @ SV723 @ SV375 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_pname_a @ SV375 @ SV723 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV723 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3658]) ).
thf(3770,plain,
! [SV375: $i,SV723: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ ( hAPP_f759274231e_bool @ ( cOMBC_1058051404l_bool @ member_pname ) @ SV723 ) ) @ ( hAPP_a93125764e_bool @ ( cOMBC_pname_a_bool @ ( cOMBB_1897541054_pname @ fequal_a @ SV375 ) ) @ ( hAPP_pname_a @ SV375 @ ( sK12_X_1 @ SV723 @ SV375 ) ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_pname_a @ SV375 @ SV723 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV723 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3659]) ).
thf(3771,plain,
! [SV923: $i,SV984: $i,SV376: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV376 ) @ SV984 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV923 ) @ SV984 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( insert_nat @ SV376 @ SV923 ) ) @ SV984 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3660]) ).
thf(3772,plain,
! [SV1081: $i,SV1059: $i,SV376: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( insert_nat @ SV376 @ SV1059 ) ) @ SV1081 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV376 ) @ SV1081 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3661]) ).
thf(3773,plain,
! [SV1082: $i,SV1060: $i,SV376: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( insert_nat @ SV376 @ SV1060 ) ) @ SV1082 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV1060 ) @ SV1082 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3662]) ).
thf(3774,plain,
! [SV924: $i,SV848: $i] :
( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ SV848 ) @ SV924 ) )
= $false )
| ( ( ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( insert1325755072e_bool @ SV848 @ SV924 ) )
= ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SV924 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV924 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3663]) ).
thf(3775,plain,
! [SV377: $i,SV985: $i,SV928: $i] :
( ( ( ( ( insert_nat @ SV928 @ SV985 )
!= ( insert_nat @ SV928 @ SV377 ) ) )
= $true )
| ( ( SV985 = SV377 )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV928 ) @ SV377 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV928 ) @ SV985 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3665]) ).
thf(3776,plain,
! [SV929: $i,SV377: $i,SV986: $i] :
( ( ( ( SV986 != SV377 ) )
= $true )
| ( ( ( insert_nat @ SV929 @ SV986 )
= ( insert_nat @ SV929 @ SV377 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV929 ) @ SV377 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV929 ) @ SV986 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3666]) ).
thf(3777,plain,
! [SV378: $i,SV724: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( sK7_X_1 @ SV724 @ SV378 ) ) @ SV724 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV724 ) @ SV378 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3667]) ).
thf(3778,plain,
! [SV378: $i,SV724: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( sK7_X_1 @ SV724 @ SV378 ) ) @ SV378 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV724 ) @ SV378 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3668]) ).
thf(3779,plain,
! [SV934: $i,SV854: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV854 ) @ SV934 ) )
= $false )
| ( ( ( hAPP_f22106695ol_nat @ finite_card_nat @ ( insert_nat @ SV854 @ SV934 ) )
= ( hAPP_f22106695ol_nat @ finite_card_nat @ SV934 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV934 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3671]) ).
thf(3780,plain,
! [SV938: $i,SV858: $i] :
( ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ SV858 ) @ SV938 ) )
= $false )
| ( ( ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( insert_fun_a_bool @ SV858 @ SV938 ) )
= ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SV938 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV938 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3673]) ).
thf(3781,plain,
! [SV380: $i,SV725: $i,SV814: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK3_X_1 @ SV814 @ SV725 @ SV380 ) ) @ SV814 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_pname_a @ SV380 @ SV814 ) ) @ SV725 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3675]) ).
thf(3782,plain,
! [SV725: $i,SV814: $i,SV380: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( hAPP_pname_a @ SV380 @ ( sK3_X_1 @ SV814 @ SV725 @ SV380 ) ) ) @ SV725 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_pname_a @ SV380 @ SV814 ) ) @ SV725 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3675]) ).
thf(3783,plain,
! [SV988: $i,SV381: $i,SV942: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV942 ) @ SV381 ) ) )
= $true )
| ( ( ( ( hAPP_nat_nat @ ( minus_minus_nat @ SV988 ) @ SV942 )
!= ( hAPP_nat_nat @ ( minus_minus_nat @ SV381 ) @ SV942 ) )
| ( SV988 = SV381 ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV942 ) @ SV988 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3676]) ).
thf(3784,plain,
! [SV989: $i,SV381: $i,SV943: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV943 ) @ SV381 ) ) )
= $true )
| ( ( ( SV989 != SV381 )
| ( ( hAPP_nat_nat @ ( minus_minus_nat @ SV989 ) @ SV943 )
= ( hAPP_nat_nat @ ( minus_minus_nat @ SV381 ) @ SV943 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV943 ) @ SV989 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3677]) ).
thf(3785,plain,
! [SV862: $i,SV944: $i] :
( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ SV944 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ SV862 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ SV862 ) @ SV944 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3678]) ).
thf(3786,plain,
! [SV1083: $i,SV1024: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ SV1024 ) @ SV1083 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ SV1024 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3679]) ).
thf(3787,plain,
! [SV1062: $i,SV1025: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ SV1025 ) @ SV1062 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ SV1062 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3680]) ).
thf(3788,plain,
! [SV946: $i,SV865: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV865 ) @ SV946 ) )
= $false )
| ( ( ( hAPP_fun_a_bool_nat @ finite_card_a @ ( insert_a @ SV865 @ SV946 ) )
= ( hAPP_fun_a_bool_nat @ finite_card_a @ SV946 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV946 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3681]) ).
thf(3789,plain,
! [SV948: $i,SV867: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV867 ) @ SV948 ) )
= $false )
| ( ( ( hAPP_f921600141ol_nat @ finite_card_pname @ ( insert_pname @ SV867 @ SV948 ) )
= ( hAPP_f921600141ol_nat @ finite_card_pname @ SV948 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV948 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3683]) ).
thf(3790,plain,
! [SV383: $i,SV950: $i] :
( ( ( is_pname @ SV950 )
= $false )
| ( ( is_pname @ SV383 )
= $false )
| ( ( ! [SY1140: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ ( insert_pname @ SV950 @ SY1140 ) ) )
| ( SV383 = SV950 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ SY1140 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3685]) ).
thf(3791,plain,
! [SV1063: $i,SV383: $i] :
( ( ( ~ ( is_pname @ SV383 )
| ~ ( is_pname @ SV1063 ) )
= $true )
| ( ( ( SV383 != SV1063 )
| ! [SY1190: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ ( insert_pname @ SV1063 @ SY1190 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3686]) ).
thf(3792,plain,
! [SV1064: $i,SV383: $i] :
( ( ( ~ ( is_pname @ SV383 )
| ~ ( is_pname @ SV1064 ) )
= $true )
| ( ( ! [SY1191: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ SY1191 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ ( insert_pname @ SV1064 @ SY1191 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3687]) ).
thf(3793,plain,
! [SV951: $i,SV990: $i,SV384: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV384 ) @ SV990 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV951 ) @ SV990 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ SV384 @ SV951 ) ) @ SV990 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3688]) ).
thf(3794,plain,
! [SV1084: $i,SV1065: $i,SV384: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ SV384 @ SV1065 ) ) @ SV1084 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV384 ) @ SV1084 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3689]) ).
thf(3795,plain,
! [SV1085: $i,SV1066: $i,SV384: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ SV384 @ SV1066 ) ) @ SV1085 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV1066 ) @ SV1085 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3690]) ).
thf(3796,plain,
! [SV869: $i,SV952: $i] :
( ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ SV952 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ SV869 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ SV869 ) @ SV952 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3691]) ).
thf(3797,plain,
! [SV1086: $i,SV1027: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ SV1027 ) @ SV1086 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ SV1027 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3692]) ).
thf(3798,plain,
! [SV1067: $i,SV1028: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ SV1028 ) @ SV1067 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ SV1067 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3693]) ).
thf(3799,plain,
! [SV953: $i,SV991: $i,SV385: $i] :
( ( ( is_fun_a_bool @ SV385 )
= $false )
| ( ( ~ ( is_fun_a_bool @ SV991 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV953 ) @ SV991 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV953 ) @ SV385 ) )
| ( ( insert_a @ SV953 @ SV991 )
!= ( insert_a @ SV953 @ SV385 ) )
| ( SV991 = SV385 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3694]) ).
thf(3800,plain,
! [SV954: $i,SV992: $i,SV385: $i] :
( ( ( is_fun_a_bool @ SV385 )
= $false )
| ( ( ~ ( is_fun_a_bool @ SV992 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV954 ) @ SV992 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV954 ) @ SV385 ) )
| ( SV992 != SV385 )
| ( ( insert_a @ SV954 @ SV992 )
= ( insert_a @ SV954 @ SV385 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3695]) ).
thf(3801,plain,
! [SV957: $i,SV993: $i,SV386: $i] :
( ( ( is_a @ SV386 )
= $false )
| ( ( ~ ( is_a @ SV993 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV386 @ SV957 ) @ SV993 ) )
| ( SV386 = SV993 )
| ( hBOOL @ ( hAPP_a_bool @ SV957 @ SV993 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3696]) ).
thf(3802,plain,
! [SV1068: $i,SV1087: $i,SV386: $i] :
( ( ~ ( is_a @ SV386 )
| ~ ( is_a @ SV1087 )
| ( SV386 != SV1087 )
| ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV386 @ SV1068 ) @ SV1087 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3697]) ).
thf(3803,plain,
! [SV1069: $i,SV1088: $i,SV386: $i] :
( ( ~ ( is_a @ SV386 )
| ~ ( is_a @ SV1088 )
| ~ ( hBOOL @ ( hAPP_a_bool @ SV1069 @ SV1088 ) )
| ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV386 @ SV1069 ) @ SV1088 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3698]) ).
thf(3804,plain,
! [SV387: $i,SV874: $i,SV959: $i] :
( ( ( ~ ( is_pname @ ( sK9_X_1 @ SV959 @ SV874 @ SV387 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV387 ) @ ( image_pname_a @ SV874 @ SV959 ) ) )
= $false )
| ( ( is_a @ SV387 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3699]) ).
thf(3805,plain,
! [SV959: $i,SV874: $i,SV387: $i] :
( ( ( ~ ~ ( ( SV387
!= ( hAPP_pname_a @ SV874 @ ( sK9_X_1 @ SV959 @ SV874 @ SV387 ) ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK9_X_1 @ SV959 @ SV874 @ SV387 ) ) @ SV959 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV387 ) @ ( image_pname_a @ SV874 @ SV959 ) ) )
= $false )
| ( ( is_a @ SV387 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3699]) ).
thf(3806,plain,
! [SV877: $i,SV962: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ SV962 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ SV877 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ SV877 ) @ SV962 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3700]) ).
thf(3807,plain,
! [SV1089: $i,SV1030: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ SV1030 ) @ SV1089 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ SV1030 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3701]) ).
thf(3808,plain,
! [SV1070: $i,SV1031: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ SV1031 ) @ SV1070 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ SV1070 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3702]) ).
thf(3809,plain,
! [SV388: $i,SV815: $i,SV727: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ SV727 @ ( hAPP_nat_nat @ suc @ ( sK5_N_2 @ SV815 @ SV727 @ SV388 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ SV727 @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV815 ) @ SV388 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ SV727 @ SV815 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3703]) ).
thf(3810,plain,
! [SV388: $i,SV815: $i,SV727: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ SV727 @ ( sK5_N_2 @ SV815 @ SV727 @ SV388 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ SV727 @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV815 ) @ SV388 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ SV727 @ SV815 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3704]) ).
thf(3811,plain,
! [SV878: $i,SV963: $i] :
( ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ SV963 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ SV878 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ SV878 ) @ SV963 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3705]) ).
thf(3812,plain,
! [SV1090: $i,SV1032: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ SV1032 ) @ SV1090 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ SV1032 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3706]) ).
thf(3813,plain,
! [SV1071: $i,SV1033: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ SV1033 ) @ SV1071 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ SV1071 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3707]) ).
thf(3814,plain,
! [SV964: $i,SV994: $i,SV389: $i] :
( ( ( is_fun_pname_bool @ SV389 )
= $false )
| ( ( ~ ( is_fun_pname_bool @ SV994 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV964 ) @ SV994 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV964 ) @ SV389 ) )
| ( ( insert_pname @ SV964 @ SV994 )
!= ( insert_pname @ SV964 @ SV389 ) )
| ( SV994 = SV389 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3708]) ).
thf(3815,plain,
! [SV965: $i,SV995: $i,SV389: $i] :
( ( ( is_fun_pname_bool @ SV389 )
= $false )
| ( ( ~ ( is_fun_pname_bool @ SV995 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV965 ) @ SV995 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV965 ) @ SV389 ) )
| ( SV995 != SV389 )
| ( ( insert_pname @ SV965 @ SV995 )
= ( insert_pname @ SV965 @ SV389 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3709]) ).
thf(3816,plain,
! [SV390: $i,SV968: $i,SV996: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV996 ) @ ( insert_pname @ SV968 @ SV390 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV996 ) @ SV390 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV968 ) @ SV996 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3710]) ).
thf(3817,plain,
! [SV969: $i,SV390: $i,SV997: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV997 ) @ SV390 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV997 ) @ ( insert_pname @ SV969 @ SV390 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV969 ) @ SV997 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3711]) ).
thf(3818,plain,
! [SV998: $i,SV391: $i,SV970: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV970 ) @ SV391 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV998 ) @ SV970 ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV391 ) @ SV970 ) ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV998 ) @ SV391 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV970 ) @ SV998 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3712]) ).
thf(3819,plain,
! [SV999: $i,SV391: $i,SV971: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV971 ) @ SV391 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV999 ) @ SV391 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV999 ) @ SV971 ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV391 ) @ SV971 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV971 ) @ SV999 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3713]) ).
thf(3820,plain,
! [SV392: $i,SV728: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK6_X_1 @ SV728 @ SV392 ) ) @ SV728 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV728 ) @ SV392 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3714]) ).
thf(3821,plain,
! [SV392: $i,SV728: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK6_X_1 @ SV728 @ SV392 ) ) @ SV392 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV728 ) @ SV392 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3715]) ).
thf(3822,plain,
! [SV972: $i,SV1000: $i,SV393: $i] :
( ( ( SV393 = SV1000 )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ SV972 @ SV1000 ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV393 @ SV972 ) @ SV1000 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3716]) ).
thf(3823,plain,
! [SV1072: $i,SV1091: $i,SV393: $i] :
( ( ( SV393 != SV1091 )
| ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV393 @ SV1072 ) @ SV1091 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3717]) ).
thf(3824,plain,
! [SV393: $i,SV1092: $i,SV1073: $i] :
( ( ~ ( hBOOL @ ( hAPP_nat_bool @ SV1073 @ SV1092 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV393 @ SV1073 ) @ SV1092 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3718]) ).
thf(3825,plain,
! [SV881: $i,SV1001: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ ( sK2_X_1 @ SV1001 @ SV881 ) ) @ SV881 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV881 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3719]) ).
thf(3826,plain,
! [SV881: $i,SV1001: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( sK2_X_1 @ SV1001 @ SV881 ) ) @ SV1001 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV881 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3720]) ).
thf(3827,plain,
! [SV882: $i,SV1034: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV1034 ) @ SV882 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV1034 ) @ ( sK1_M @ SV882 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV882 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3721]) ).
thf(3828,plain,
! [SV537: $i,SV158: $i] :
( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ SV158 ) @ SV537 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SV537 ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SV158 ) ) )
| ( SV158 = SV537 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV537 ) )
= $false )
| ( ( is_fun1661590463l_bool @ SV158 )
= $false )
| ( ( is_fun1661590463l_bool @ SV537 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3722]) ).
thf(3829,plain,
! [SV538: $i,SV159: $i] :
( ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ SV159 ) @ SV538 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SV538 ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SV159 ) ) )
| ( SV159 = SV538 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV538 ) )
= $false )
| ( ( is_fun949378684l_bool @ SV159 )
= $false )
| ( ( is_fun949378684l_bool @ SV538 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3723]) ).
thf(3830,plain,
! [SV539: $i,SV160: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV160 ) @ SV539 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV539 ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV160 ) ) )
| ( SV160 = SV539 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV539 ) )
= $false )
| ( ( is_fun_pname_bool @ SV160 )
= $false )
| ( ( is_fun_pname_bool @ SV539 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3724]) ).
thf(3831,plain,
! [SV540: $i,SV161: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV161 ) @ SV540 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SV540 ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SV161 ) ) )
| ( SV161 = SV540 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV540 ) )
= $false )
| ( ( is_fun_a_bool @ SV161 )
= $false )
| ( ( is_fun_a_bool @ SV540 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3725]) ).
thf(3832,plain,
! [SV217: $i,SV590: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV590 ) @ SV217 ) )
= $false )
| ( ( SV217 = SV590 )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV217 ) @ SV590 ) )
= $false )
| ( ( is_fun_pname_bool @ SV217 )
= $false )
| ( ( is_fun_pname_bool @ SV590 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3726]) ).
thf(3833,plain,
! [SV218: $i,SV591: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV591 ) @ SV218 ) )
= $false )
| ( ( SV218 = SV591 )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV218 ) @ SV591 ) )
= $false )
| ( ( is_fun_a_bool @ SV218 )
= $false )
| ( ( is_fun_a_bool @ SV591 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3727]) ).
thf(3834,plain,
! [SV1002: $i,SV596: $i,SV223: $i] :
( ( ( SV223 = SV596 )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV223 ) @ SV1002 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV223 ) @ ( insert_pname @ SV596 @ SV1002 ) ) )
= $false )
| ( ( is_pname @ SV223 )
= $false )
| ( ( is_pname @ SV596 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3728]) ).
thf(3835,plain,
! [SV1003: $i,SV597: $i,SV224: $i] :
( ( ( SV224 = SV597 )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV224 ) @ SV1003 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV224 ) @ ( insert_a @ SV597 @ SV1003 ) ) )
= $false )
| ( ( is_a @ SV224 )
= $false )
| ( ( is_a @ SV597 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3729]) ).
thf(3836,plain,
! [SV1005: $i,SV364: $i,SV1035: $i,SV1093: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV1093 ) @ SV1035 ) )
| ~ ( is_fun_pname_bool @ SV1093 )
| ( SV364
!= ( image_pname_a @ SV1005 @ SV1093 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV364 ) @ ( image_pname_a @ SV1005 @ SV1035 ) ) )
= $true )
| ( ( is_fun_a_bool @ SV364 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3730]) ).
thf(3837,plain,
! [SV1036: $i,SV1006: $i,SV364: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV364 ) @ ( image_pname_a @ SV1006 @ SV1036 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( sK10_AA @ SV1036 @ SV1006 @ SV364 ) ) @ SV1036 ) )
| ~ ( is_fun_pname_bool @ ( sK10_AA @ SV1036 @ SV1006 @ SV364 ) ) )
| ( SV364
!= ( image_pname_a @ SV1006 @ ( sK10_AA @ SV1036 @ SV1006 @ SV364 ) ) ) ) )
= $true )
| ( ( is_fun_a_bool @ SV364 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3731]) ).
thf(3838,plain,
! [SV1037: $i,SV1007: $i] :
( ( ( SV1007
= ( hAPP_nat_nat @ suc @ SV1037 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV1007 ) @ ( hAPP_nat_nat @ suc @ SV1037 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3732]) ).
thf(3839,plain,
! [SV1038: $i,SV1008: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV1008 ) @ SV1038 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV1008 ) @ ( hAPP_nat_nat @ suc @ SV1038 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3733]) ).
thf(3840,plain,
! [SV1039: $i,SV1009: $i] :
( ( ( SV1009 = SV1039 )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV1009 ) @ SV1039 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3735]) ).
thf(3841,plain,
! [SV1040: $i,SV1010: $i] :
( ( ( SV1010 = SV1040 )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV1040 ) @ SV1010 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3736]) ).
thf(3842,plain,
! [SV896: $i,SV830: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV830 ) @ SV896 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV896 ) @ SV830 ) ) )
= $true )
| ( ( SV830 = SV896 )
= $true )
| ( ( is_fun_pname_bool @ SV830 )
= $false )
| ( ( is_fun_pname_bool @ SV896 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3738]) ).
thf(3843,plain,
! [SV1041: $i,SV1011: $i] :
( ( ( ~ ( is_fun_pname_bool @ SV1011 ) )
= $true )
| ( ( ~ ( is_fun_pname_bool @ SV1041 ) )
= $true )
| ( ( ( SV1011 != SV1041 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV1011 ) @ SV1041 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3739]) ).
thf(3844,plain,
! [SV1042: $i,SV1012: $i] :
( ( ( ~ ( is_fun_pname_bool @ SV1012 ) )
= $true )
| ( ( ~ ( is_fun_pname_bool @ SV1042 ) )
= $true )
| ( ( ( SV1012 != SV1042 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV1042 ) @ SV1012 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3740]) ).
thf(3845,plain,
! [SV900: $i,SV365: $i,SV975: $i] :
( ( ( is_pname @ SV975 )
= $false )
| ( ( is_pname @ SV365 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV365 @ SV900 ) @ SV975 ) )
| ( SV365 = SV975 )
| ( hBOOL @ ( hAPP_pname_bool @ SV900 @ SV975 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3741]) ).
thf(3846,plain,
! [SV1043: $i,SV1074: $i,SV365: $i] :
( ( ( ~ ( is_pname @ SV365 )
| ~ ( is_pname @ SV1074 ) )
= $true )
| ( ( ( SV365 != SV1074 )
| ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV365 @ SV1043 ) @ SV1074 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3742]) ).
thf(3847,plain,
! [SV1044: $i,SV1075: $i,SV365: $i] :
( ( ( ~ ( is_pname @ SV365 )
| ~ ( is_pname @ SV1075 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_pname_bool @ SV1044 @ SV1075 ) )
| ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV365 @ SV1044 ) @ SV1075 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3743]) ).
thf(3848,plain,
! [SV1045: $i,SV366: $i] :
( ( ( SV366 = SV1045 )
= $false )
| ( ( ! [SY1181: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV366 ) @ ( insert_nat @ SV1045 @ SY1181 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3745]) ).
thf(3849,plain,
! [SV1046: $i,SV1076: $i,SV366: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV366 ) @ SV1076 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV366 ) @ ( insert_nat @ SV1046 @ SV1076 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3746]) ).
thf(3850,plain,
! [SV1094: $i,SV904: $i,SV367: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ ( insert_a @ SV904 @ SV1094 ) ) )
| ( SV367 = SV904 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ SV1094 ) ) )
= $true )
| ( ( is_a @ SV367 )
= $false )
| ( ( is_a @ SV904 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3747]) ).
thf(3851,plain,
! [SV1047: $i,SV367: $i] :
( ( ( ~ ( is_a @ SV367 ) )
= $true )
| ( ( ~ ( is_a @ SV1047 ) )
= $true )
| ( ( ( SV367 != SV1047 )
| ! [SY1183: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ ( insert_a @ SV1047 @ SY1183 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3748]) ).
thf(3852,plain,
! [SV1048: $i,SV367: $i] :
( ( ( ~ ( is_a @ SV367 ) )
= $true )
| ( ( ~ ( is_a @ SV1048 ) )
= $true )
| ( ( ! [SY1184: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ SY1184 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ ( insert_a @ SV1048 @ SY1184 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3749]) ).
thf(3853,plain,
! [SV1015: $i,SV369: $i,SV1049: $i,SV1095: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV1095 ) @ SV1049 ) )
| ~ ( is_pname @ SV1095 )
| ( SV369
!= ( hAPP_pname_a @ SV1015 @ SV1095 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV369 ) @ ( image_pname_a @ SV1015 @ SV1049 ) ) )
= $true )
| ( ( is_a @ SV369 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3752]) ).
thf(3854,plain,
! [SV1050: $i,SV1016: $i,SV369: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV369 ) @ ( image_pname_a @ SV1016 @ SV1050 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK11_X_1 @ SV1050 @ SV1016 @ SV369 ) ) @ SV1050 ) )
| ~ ( is_pname @ ( sK11_X_1 @ SV1050 @ SV1016 @ SV369 ) ) )
| ( SV369
!= ( hAPP_pname_a @ SV1016 @ ( sK11_X_1 @ SV1050 @ SV1016 @ SV369 ) ) ) ) )
= $true )
| ( ( is_a @ SV369 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3753]) ).
thf(3855,plain,
! [SV915: $i,SV843: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV843 ) @ SV915 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV915 ) @ SV843 ) ) )
= $true )
| ( ( SV843 = SV915 )
= $true )
| ( ( is_fun_a_bool @ SV843 )
= $false )
| ( ( is_fun_a_bool @ SV915 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3756]) ).
thf(3856,plain,
! [SV1052: $i,SV1018: $i] :
( ( ( ~ ( is_fun_a_bool @ SV1018 ) )
= $true )
| ( ( ~ ( is_fun_a_bool @ SV1052 ) )
= $true )
| ( ( ( SV1018 != SV1052 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV1018 ) @ SV1052 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3757]) ).
thf(3857,plain,
! [SV1053: $i,SV1019: $i] :
( ( ( ~ ( is_fun_a_bool @ SV1019 ) )
= $true )
| ( ( ~ ( is_fun_a_bool @ SV1053 ) )
= $true )
| ( ( ( SV1019 != SV1053 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV1053 ) @ SV1019 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3758]) ).
thf(3858,plain,
! [SV372: $i,SV722: $i,SV813: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( sK17_C_2 @ SV813 @ SV722 @ SV372 ) ) @ SV722 ) )
| ~ ( is_fun_pname_bool @ ( sK17_C_2 @ SV813 @ SV722 @ SV372 ) ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( sK17_C_2 @ SV813 @ SV722 @ SV372 ) ) ) )
| ( SV813
!= ( image_pname_a @ SV372 @ ( sK17_C_2 @ SV813 @ SV722 @ SV372 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV813 ) @ ( image_pname_a @ SV372 @ SV722 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV813 ) )
= $false )
| ( ( is_fun_a_bool @ SV813 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3759]) ).
thf(3859,plain,
! [SV1077: $i,SV1020: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ SV1020 ) @ SV1077 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ SV1020 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3761]) ).
thf(3860,plain,
! [SV1055: $i,SV1021: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ SV1021 ) @ SV1055 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ SV1055 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3762]) ).
thf(3861,plain,
! [SV374: $i,SV983: $i,SV921: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV921 ) @ SV983 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV374 ) @ SV983 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV374 @ SV921 ) ) @ SV983 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3763]) ).
thf(3862,plain,
! [SV1078: $i,SV1056: $i,SV374: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV374 @ SV1056 ) ) @ SV1078 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV374 ) @ SV1078 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3764]) ).
thf(3863,plain,
! [SV1079: $i,SV1057: $i,SV374: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV374 @ SV1057 ) ) @ SV1079 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV1057 ) @ SV1079 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3765]) ).
thf(3864,plain,
! [SV1080: $i,SV1022: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ SV1022 ) @ SV1080 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ SV1022 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3767]) ).
thf(3865,plain,
! [SV1058: $i,SV1023: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ SV1023 ) @ SV1058 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ SV1058 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3768]) ).
thf(3866,plain,
! [SV375: $i,SV723: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK12_X_1 @ SV723 @ SV375 ) ) @ SV723 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_pname_a @ SV375 @ SV723 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV723 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3769]) ).
thf(3867,plain,
! [SV375: $i,SV723: $i] :
( ( ( ~ ( is_pname @ ( sK12_X_1 @ SV723 @ SV375 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_pname_a @ SV375 @ SV723 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV723 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3769]) ).
thf(3868,plain,
! [SV376: $i,SV984: $i,SV923: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV923 ) @ SV984 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV376 ) @ SV984 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( insert_nat @ SV376 @ SV923 ) ) @ SV984 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3771]) ).
thf(3869,plain,
! [SV1081: $i,SV1059: $i,SV376: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( insert_nat @ SV376 @ SV1059 ) ) @ SV1081 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV376 ) @ SV1081 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3772]) ).
thf(3870,plain,
! [SV1082: $i,SV1060: $i,SV376: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( insert_nat @ SV376 @ SV1060 ) ) @ SV1082 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV1060 ) @ SV1082 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3773]) ).
thf(3871,plain,
! [SV377: $i,SV985: $i,SV928: $i] :
( ( ( ( insert_nat @ SV928 @ SV985 )
= ( insert_nat @ SV928 @ SV377 ) )
= $false )
| ( ( SV985 = SV377 )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV928 ) @ SV377 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV928 ) @ SV985 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3775]) ).
thf(3872,plain,
! [SV929: $i,SV377: $i,SV986: $i] :
( ( ( SV986 = SV377 )
= $false )
| ( ( ( insert_nat @ SV929 @ SV986 )
= ( insert_nat @ SV929 @ SV377 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV929 ) @ SV377 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV929 ) @ SV986 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3776]) ).
thf(3873,plain,
! [SV378: $i,SV724: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( sK7_X_1 @ SV724 @ SV378 ) ) @ SV378 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV724 ) @ SV378 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3778]) ).
thf(3874,plain,
! [SV380: $i,SV725: $i,SV814: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK3_X_1 @ SV814 @ SV725 @ SV380 ) ) @ SV814 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_pname_a @ SV380 @ SV814 ) ) @ SV725 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3781]) ).
thf(3875,plain,
! [SV725: $i,SV814: $i,SV380: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( hAPP_pname_a @ SV380 @ ( sK3_X_1 @ SV814 @ SV725 @ SV380 ) ) ) @ SV725 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_pname_a @ SV380 @ SV814 ) ) @ SV725 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3782]) ).
thf(3876,plain,
! [SV988: $i,SV381: $i,SV942: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV942 ) @ SV381 ) )
= $false )
| ( ( ( ( hAPP_nat_nat @ ( minus_minus_nat @ SV988 ) @ SV942 )
!= ( hAPP_nat_nat @ ( minus_minus_nat @ SV381 ) @ SV942 ) )
| ( SV988 = SV381 ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV942 ) @ SV988 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3783]) ).
thf(3877,plain,
! [SV989: $i,SV381: $i,SV943: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV943 ) @ SV381 ) )
= $false )
| ( ( ( SV989 != SV381 )
| ( ( hAPP_nat_nat @ ( minus_minus_nat @ SV989 ) @ SV943 )
= ( hAPP_nat_nat @ ( minus_minus_nat @ SV381 ) @ SV943 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV943 ) @ SV989 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3784]) ).
thf(3878,plain,
! [SV1083: $i,SV1024: $i] :
( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ SV1024 ) @ SV1083 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ SV1024 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3786]) ).
thf(3879,plain,
! [SV1062: $i,SV1025: $i] :
( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ SV1025 ) @ SV1062 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ SV1062 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3787]) ).
thf(3880,plain,
! [SV1096: $i,SV950: $i,SV383: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ ( insert_pname @ SV950 @ SV1096 ) ) )
| ( SV383 = SV950 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ SV1096 ) ) )
= $true )
| ( ( is_pname @ SV383 )
= $false )
| ( ( is_pname @ SV950 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3790]) ).
thf(3881,plain,
! [SV1063: $i,SV383: $i] :
( ( ( ~ ( is_pname @ SV383 ) )
= $true )
| ( ( ~ ( is_pname @ SV1063 ) )
= $true )
| ( ( ( SV383 != SV1063 )
| ! [SY1190: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ ( insert_pname @ SV1063 @ SY1190 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3791]) ).
thf(3882,plain,
! [SV1064: $i,SV383: $i] :
( ( ( ~ ( is_pname @ SV383 ) )
= $true )
| ( ( ~ ( is_pname @ SV1064 ) )
= $true )
| ( ( ! [SY1191: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ SY1191 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ ( insert_pname @ SV1064 @ SY1191 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3792]) ).
thf(3883,plain,
! [SV384: $i,SV990: $i,SV951: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV951 ) @ SV990 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV384 ) @ SV990 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ SV384 @ SV951 ) ) @ SV990 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3793]) ).
thf(3884,plain,
! [SV1084: $i,SV1065: $i,SV384: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ SV384 @ SV1065 ) ) @ SV1084 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV384 ) @ SV1084 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3794]) ).
thf(3885,plain,
! [SV1085: $i,SV1066: $i,SV384: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ SV384 @ SV1066 ) ) @ SV1085 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV1066 ) @ SV1085 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3795]) ).
thf(3886,plain,
! [SV1086: $i,SV1027: $i] :
( ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ SV1027 ) @ SV1086 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ SV1027 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3797]) ).
thf(3887,plain,
! [SV1067: $i,SV1028: $i] :
( ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ SV1028 ) @ SV1067 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ SV1067 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3798]) ).
thf(3888,plain,
! [SV953: $i,SV385: $i,SV991: $i] :
( ( ( is_fun_a_bool @ SV991 )
= $false )
| ( ( is_fun_a_bool @ SV385 )
= $false )
| ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV953 ) @ SV991 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV953 ) @ SV385 ) )
| ( ( insert_a @ SV953 @ SV991 )
!= ( insert_a @ SV953 @ SV385 ) )
| ( SV991 = SV385 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3799]) ).
thf(3889,plain,
! [SV954: $i,SV385: $i,SV992: $i] :
( ( ( is_fun_a_bool @ SV992 )
= $false )
| ( ( is_fun_a_bool @ SV385 )
= $false )
| ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV954 ) @ SV992 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV954 ) @ SV385 ) )
| ( SV992 != SV385 )
| ( ( insert_a @ SV954 @ SV992 )
= ( insert_a @ SV954 @ SV385 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3800]) ).
thf(3890,plain,
! [SV957: $i,SV386: $i,SV993: $i] :
( ( ( is_a @ SV993 )
= $false )
| ( ( is_a @ SV386 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV386 @ SV957 ) @ SV993 ) )
| ( SV386 = SV993 )
| ( hBOOL @ ( hAPP_a_bool @ SV957 @ SV993 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3801]) ).
thf(3891,plain,
! [SV1068: $i,SV1087: $i,SV386: $i] :
( ( ( ~ ( is_a @ SV386 )
| ~ ( is_a @ SV1087 ) )
= $true )
| ( ( ( SV386 != SV1087 )
| ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV386 @ SV1068 ) @ SV1087 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3802]) ).
thf(3892,plain,
! [SV1069: $i,SV1088: $i,SV386: $i] :
( ( ( ~ ( is_a @ SV386 )
| ~ ( is_a @ SV1088 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_a_bool @ SV1069 @ SV1088 ) )
| ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV386 @ SV1069 ) @ SV1088 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3803]) ).
thf(3893,plain,
! [SV387: $i,SV874: $i,SV959: $i] :
( ( ( is_pname @ ( sK9_X_1 @ SV959 @ SV874 @ SV387 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV387 ) @ ( image_pname_a @ SV874 @ SV959 ) ) )
= $false )
| ( ( is_a @ SV387 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3804]) ).
thf(3894,plain,
! [SV959: $i,SV874: $i,SV387: $i] :
( ( ( ~ ( ( SV387
!= ( hAPP_pname_a @ SV874 @ ( sK9_X_1 @ SV959 @ SV874 @ SV387 ) ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK9_X_1 @ SV959 @ SV874 @ SV387 ) ) @ SV959 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV387 ) @ ( image_pname_a @ SV874 @ SV959 ) ) )
= $false )
| ( ( is_a @ SV387 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3805]) ).
thf(3895,plain,
! [SV1089: $i,SV1030: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ SV1030 ) @ SV1089 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ SV1030 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3807]) ).
thf(3896,plain,
! [SV1070: $i,SV1031: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ SV1031 ) @ SV1070 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ SV1070 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3808]) ).
thf(3897,plain,
! [SV388: $i,SV815: $i,SV727: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ SV727 @ ( sK5_N_2 @ SV815 @ SV727 @ SV388 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ SV727 @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV815 ) @ SV388 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ SV727 @ SV815 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3810]) ).
thf(3898,plain,
! [SV1090: $i,SV1032: $i] :
( ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ SV1032 ) @ SV1090 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ SV1032 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3812]) ).
thf(3899,plain,
! [SV1071: $i,SV1033: $i] :
( ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ SV1033 ) @ SV1071 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ SV1071 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3813]) ).
thf(3900,plain,
! [SV964: $i,SV389: $i,SV994: $i] :
( ( ( is_fun_pname_bool @ SV994 )
= $false )
| ( ( is_fun_pname_bool @ SV389 )
= $false )
| ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV964 ) @ SV994 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV964 ) @ SV389 ) )
| ( ( insert_pname @ SV964 @ SV994 )
!= ( insert_pname @ SV964 @ SV389 ) )
| ( SV994 = SV389 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3814]) ).
thf(3901,plain,
! [SV965: $i,SV389: $i,SV995: $i] :
( ( ( is_fun_pname_bool @ SV995 )
= $false )
| ( ( is_fun_pname_bool @ SV389 )
= $false )
| ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV965 ) @ SV995 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV965 ) @ SV389 ) )
| ( SV995 != SV389 )
| ( ( insert_pname @ SV965 @ SV995 )
= ( insert_pname @ SV965 @ SV389 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3815]) ).
thf(3902,plain,
! [SV998: $i,SV391: $i,SV970: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV970 ) @ SV391 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV998 ) @ SV970 ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV391 ) @ SV970 ) ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV998 ) @ SV391 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV970 ) @ SV998 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3818]) ).
thf(3903,plain,
! [SV999: $i,SV391: $i,SV971: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV971 ) @ SV391 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV999 ) @ SV391 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV999 ) @ SV971 ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV391 ) @ SV971 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV971 ) @ SV999 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3819]) ).
thf(3904,plain,
! [SV392: $i,SV728: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK6_X_1 @ SV728 @ SV392 ) ) @ SV392 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV728 ) @ SV392 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3821]) ).
thf(3905,plain,
! [SV1072: $i,SV1091: $i,SV393: $i] :
( ( ( ( SV393 != SV1091 ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV393 @ SV1072 ) @ SV1091 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3823]) ).
thf(3906,plain,
! [SV393: $i,SV1092: $i,SV1073: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ SV1073 @ SV1092 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV393 @ SV1073 ) @ SV1092 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3824]) ).
thf(3907,plain,
! [SV881: $i,SV1001: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( sK2_X_1 @ SV1001 @ SV881 ) ) @ SV1001 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV881 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3826]) ).
thf(3908,plain,
! [SV158: $i,SV537: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SV537 ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SV158 ) ) ) )
= $true )
| ( ( SV158 = SV537 )
= $true )
| ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ SV158 ) @ SV537 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV537 ) )
= $false )
| ( ( is_fun1661590463l_bool @ SV158 )
= $false )
| ( ( is_fun1661590463l_bool @ SV537 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3828]) ).
thf(3909,plain,
! [SV159: $i,SV538: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SV538 ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SV159 ) ) ) )
= $true )
| ( ( SV159 = SV538 )
= $true )
| ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ SV159 ) @ SV538 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV538 ) )
= $false )
| ( ( is_fun949378684l_bool @ SV159 )
= $false )
| ( ( is_fun949378684l_bool @ SV538 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3829]) ).
thf(3910,plain,
! [SV160: $i,SV539: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV539 ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV160 ) ) ) )
= $true )
| ( ( SV160 = SV539 )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV160 ) @ SV539 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV539 ) )
= $false )
| ( ( is_fun_pname_bool @ SV160 )
= $false )
| ( ( is_fun_pname_bool @ SV539 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3830]) ).
thf(3911,plain,
! [SV161: $i,SV540: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SV540 ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SV161 ) ) ) )
= $true )
| ( ( SV161 = SV540 )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV161 ) @ SV540 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV540 ) )
= $false )
| ( ( is_fun_a_bool @ SV161 )
= $false )
| ( ( is_fun_a_bool @ SV540 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3831]) ).
thf(3912,plain,
! [SV1005: $i,SV364: $i,SV1035: $i,SV1093: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV1093 ) @ SV1035 ) )
| ~ ( is_fun_pname_bool @ SV1093 ) )
= $true )
| ( ( ( SV364
!= ( image_pname_a @ SV1005 @ SV1093 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV364 ) @ ( image_pname_a @ SV1005 @ SV1035 ) ) )
= $true )
| ( ( is_fun_a_bool @ SV364 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3836]) ).
thf(3913,plain,
! [SV364: $i,SV1006: $i,SV1036: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( sK10_AA @ SV1036 @ SV1006 @ SV364 ) ) @ SV1036 ) )
| ~ ( is_fun_pname_bool @ ( sK10_AA @ SV1036 @ SV1006 @ SV364 ) ) )
| ( SV364
!= ( image_pname_a @ SV1006 @ ( sK10_AA @ SV1036 @ SV1006 @ SV364 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV364 ) @ ( image_pname_a @ SV1006 @ SV1036 ) ) )
= $false )
| ( ( is_fun_a_bool @ SV364 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3837]) ).
thf(3914,plain,
! [SV896: $i,SV830: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV830 ) @ SV896 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV896 ) @ SV830 ) ) )
= $true )
| ( ( SV830 = SV896 )
= $true )
| ( ( is_fun_pname_bool @ SV830 )
= $false )
| ( ( is_fun_pname_bool @ SV896 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3842]) ).
thf(3915,plain,
! [SV1041: $i,SV1011: $i] :
( ( ( is_fun_pname_bool @ SV1011 )
= $false )
| ( ( ~ ( is_fun_pname_bool @ SV1041 ) )
= $true )
| ( ( ( SV1011 != SV1041 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV1011 ) @ SV1041 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3843]) ).
thf(3916,plain,
! [SV1042: $i,SV1012: $i] :
( ( ( is_fun_pname_bool @ SV1012 )
= $false )
| ( ( ~ ( is_fun_pname_bool @ SV1042 ) )
= $true )
| ( ( ( SV1012 != SV1042 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV1042 ) @ SV1012 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3844]) ).
thf(3917,plain,
! [SV975: $i,SV900: $i,SV365: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV365 @ SV900 ) @ SV975 ) ) )
= $true )
| ( ( ( SV365 = SV975 )
| ( hBOOL @ ( hAPP_pname_bool @ SV900 @ SV975 ) ) )
= $true )
| ( ( is_pname @ SV365 )
= $false )
| ( ( is_pname @ SV975 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3845]) ).
thf(3918,plain,
! [SV1043: $i,SV1074: $i,SV365: $i] :
( ( ( ~ ( is_pname @ SV365 ) )
= $true )
| ( ( ~ ( is_pname @ SV1074 ) )
= $true )
| ( ( ( SV365 != SV1074 )
| ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV365 @ SV1043 ) @ SV1074 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3846]) ).
thf(3919,plain,
! [SV1044: $i,SV1075: $i,SV365: $i] :
( ( ( ~ ( is_pname @ SV365 ) )
= $true )
| ( ( ~ ( is_pname @ SV1075 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_pname_bool @ SV1044 @ SV1075 ) )
| ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV365 @ SV1044 ) @ SV1075 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3847]) ).
thf(3920,plain,
! [SV1097: $i,SV1045: $i,SV366: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV366 ) @ ( insert_nat @ SV1045 @ SV1097 ) ) )
= $true )
| ( ( SV366 = SV1045 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3848]) ).
thf(3921,plain,
! [SV1046: $i,SV1076: $i,SV366: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV366 ) @ SV1076 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV366 ) @ ( insert_nat @ SV1046 @ SV1076 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3849]) ).
thf(3922,plain,
! [SV1094: $i,SV904: $i,SV367: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ ( insert_a @ SV904 @ SV1094 ) ) ) )
= $true )
| ( ( ( SV367 = SV904 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ SV1094 ) ) )
= $true )
| ( ( is_a @ SV367 )
= $false )
| ( ( is_a @ SV904 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3850]) ).
thf(3923,plain,
! [SV1047: $i,SV367: $i] :
( ( ( is_a @ SV367 )
= $false )
| ( ( ~ ( is_a @ SV1047 ) )
= $true )
| ( ( ( SV367 != SV1047 )
| ! [SY1183: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ ( insert_a @ SV1047 @ SY1183 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3851]) ).
thf(3924,plain,
! [SV1048: $i,SV367: $i] :
( ( ( is_a @ SV367 )
= $false )
| ( ( ~ ( is_a @ SV1048 ) )
= $true )
| ( ( ! [SY1184: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ SY1184 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ ( insert_a @ SV1048 @ SY1184 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3852]) ).
thf(3925,plain,
! [SV1015: $i,SV369: $i,SV1049: $i,SV1095: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV1095 ) @ SV1049 ) )
| ~ ( is_pname @ SV1095 ) )
= $true )
| ( ( ( SV369
!= ( hAPP_pname_a @ SV1015 @ SV1095 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV369 ) @ ( image_pname_a @ SV1015 @ SV1049 ) ) )
= $true )
| ( ( is_a @ SV369 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3853]) ).
thf(3926,plain,
! [SV369: $i,SV1016: $i,SV1050: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK11_X_1 @ SV1050 @ SV1016 @ SV369 ) ) @ SV1050 ) )
| ~ ( is_pname @ ( sK11_X_1 @ SV1050 @ SV1016 @ SV369 ) ) )
| ( SV369
!= ( hAPP_pname_a @ SV1016 @ ( sK11_X_1 @ SV1050 @ SV1016 @ SV369 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV369 ) @ ( image_pname_a @ SV1016 @ SV1050 ) ) )
= $false )
| ( ( is_a @ SV369 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3854]) ).
thf(3927,plain,
! [SV915: $i,SV843: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV843 ) @ SV915 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV915 ) @ SV843 ) ) )
= $true )
| ( ( SV843 = SV915 )
= $true )
| ( ( is_fun_a_bool @ SV843 )
= $false )
| ( ( is_fun_a_bool @ SV915 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3855]) ).
thf(3928,plain,
! [SV1052: $i,SV1018: $i] :
( ( ( is_fun_a_bool @ SV1018 )
= $false )
| ( ( ~ ( is_fun_a_bool @ SV1052 ) )
= $true )
| ( ( ( SV1018 != SV1052 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV1018 ) @ SV1052 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3856]) ).
thf(3929,plain,
! [SV1053: $i,SV1019: $i] :
( ( ( is_fun_a_bool @ SV1019 )
= $false )
| ( ( ~ ( is_fun_a_bool @ SV1053 ) )
= $true )
| ( ( ( SV1019 != SV1053 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV1053 ) @ SV1019 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3857]) ).
thf(3930,plain,
! [SV372: $i,SV722: $i,SV813: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( sK17_C_2 @ SV813 @ SV722 @ SV372 ) ) @ SV722 ) )
| ~ ( is_fun_pname_bool @ ( sK17_C_2 @ SV813 @ SV722 @ SV372 ) ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( sK17_C_2 @ SV813 @ SV722 @ SV372 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV813 ) @ ( image_pname_a @ SV372 @ SV722 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV813 ) )
= $false )
| ( ( is_fun_a_bool @ SV813 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3858]) ).
thf(3931,plain,
! [SV722: $i,SV372: $i,SV813: $i] :
( ( ( ( SV813
!= ( image_pname_a @ SV372 @ ( sK17_C_2 @ SV813 @ SV722 @ SV372 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV813 ) @ ( image_pname_a @ SV372 @ SV722 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV813 ) )
= $false )
| ( ( is_fun_a_bool @ SV813 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3858]) ).
thf(3932,plain,
! [SV1078: $i,SV1056: $i,SV374: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV374 @ SV1056 ) ) @ SV1078 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV374 ) @ SV1078 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3862]) ).
thf(3933,plain,
! [SV1079: $i,SV1057: $i,SV374: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV374 @ SV1057 ) ) @ SV1079 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV1057 ) @ SV1079 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3863]) ).
thf(3934,plain,
! [SV375: $i,SV723: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK12_X_1 @ SV723 @ SV375 ) ) @ SV723 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_pname_a @ SV375 @ SV723 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV723 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3866]) ).
thf(3935,plain,
! [SV375: $i,SV723: $i] :
( ( ( is_pname @ ( sK12_X_1 @ SV723 @ SV375 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_pname_a @ SV375 @ SV723 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV723 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3867]) ).
thf(3936,plain,
! [SV1081: $i,SV1059: $i,SV376: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( insert_nat @ SV376 @ SV1059 ) ) @ SV1081 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ SV376 ) @ SV1081 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3869]) ).
thf(3937,plain,
! [SV1082: $i,SV1060: $i,SV376: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( insert_nat @ SV376 @ SV1060 ) ) @ SV1082 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV1060 ) @ SV1082 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3870]) ).
thf(3938,plain,
! [SV725: $i,SV814: $i,SV380: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( hAPP_pname_a @ SV380 @ ( sK3_X_1 @ SV814 @ SV725 @ SV380 ) ) ) @ SV725 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_pname_a @ SV380 @ SV814 ) ) @ SV725 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3875]) ).
thf(3939,plain,
! [SV381: $i,SV942: $i,SV988: $i] :
( ( ( ( ( hAPP_nat_nat @ ( minus_minus_nat @ SV988 ) @ SV942 )
!= ( hAPP_nat_nat @ ( minus_minus_nat @ SV381 ) @ SV942 ) ) )
= $true )
| ( ( SV988 = SV381 )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV942 ) @ SV381 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV942 ) @ SV988 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3876]) ).
thf(3940,plain,
! [SV943: $i,SV381: $i,SV989: $i] :
( ( ( ( SV989 != SV381 ) )
= $true )
| ( ( ( hAPP_nat_nat @ ( minus_minus_nat @ SV989 ) @ SV943 )
= ( hAPP_nat_nat @ ( minus_minus_nat @ SV381 ) @ SV943 ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV943 ) @ SV381 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV943 ) @ SV989 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3877]) ).
thf(3941,plain,
! [SV1096: $i,SV950: $i,SV383: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ ( insert_pname @ SV950 @ SV1096 ) ) ) )
= $true )
| ( ( ( SV383 = SV950 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ SV1096 ) ) )
= $true )
| ( ( is_pname @ SV383 )
= $false )
| ( ( is_pname @ SV950 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3880]) ).
thf(3942,plain,
! [SV1063: $i,SV383: $i] :
( ( ( is_pname @ SV383 )
= $false )
| ( ( ~ ( is_pname @ SV1063 ) )
= $true )
| ( ( ( SV383 != SV1063 )
| ! [SY1190: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ ( insert_pname @ SV1063 @ SY1190 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3881]) ).
thf(3943,plain,
! [SV1064: $i,SV383: $i] :
( ( ( is_pname @ SV383 )
= $false )
| ( ( ~ ( is_pname @ SV1064 ) )
= $true )
| ( ( ! [SY1191: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ SY1191 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ ( insert_pname @ SV1064 @ SY1191 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3882]) ).
thf(3944,plain,
! [SV1084: $i,SV1065: $i,SV384: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ SV384 @ SV1065 ) ) @ SV1084 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV384 ) @ SV1084 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3884]) ).
thf(3945,plain,
! [SV1085: $i,SV1066: $i,SV384: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ SV384 @ SV1066 ) ) @ SV1085 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV1066 ) @ SV1085 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3885]) ).
thf(3946,plain,
! [SV385: $i,SV991: $i,SV953: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV953 ) @ SV991 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV953 ) @ SV385 ) )
| ( ( insert_a @ SV953 @ SV991 )
!= ( insert_a @ SV953 @ SV385 ) )
| ( SV991 = SV385 ) )
= $true )
| ( ( is_fun_a_bool @ SV385 )
= $false )
| ( ( is_fun_a_bool @ SV991 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3888]) ).
thf(3947,plain,
! [SV385: $i,SV992: $i,SV954: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV954 ) @ SV992 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV954 ) @ SV385 ) )
| ( SV992 != SV385 )
| ( ( insert_a @ SV954 @ SV992 )
= ( insert_a @ SV954 @ SV385 ) ) )
= $true )
| ( ( is_fun_a_bool @ SV385 )
= $false )
| ( ( is_fun_a_bool @ SV992 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3889]) ).
thf(3948,plain,
! [SV993: $i,SV957: $i,SV386: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV386 @ SV957 ) @ SV993 ) ) )
= $true )
| ( ( ( SV386 = SV993 )
| ( hBOOL @ ( hAPP_a_bool @ SV957 @ SV993 ) ) )
= $true )
| ( ( is_a @ SV386 )
= $false )
| ( ( is_a @ SV993 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3890]) ).
thf(3949,plain,
! [SV1068: $i,SV1087: $i,SV386: $i] :
( ( ( ~ ( is_a @ SV386 ) )
= $true )
| ( ( ~ ( is_a @ SV1087 ) )
= $true )
| ( ( ( SV386 != SV1087 )
| ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV386 @ SV1068 ) @ SV1087 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3891]) ).
thf(3950,plain,
! [SV1069: $i,SV1088: $i,SV386: $i] :
( ( ( ~ ( is_a @ SV386 ) )
= $true )
| ( ( ~ ( is_a @ SV1088 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_a_bool @ SV1069 @ SV1088 ) )
| ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV386 @ SV1069 ) @ SV1088 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3892]) ).
thf(3951,plain,
! [SV959: $i,SV874: $i,SV387: $i] :
( ( ( ( SV387
!= ( hAPP_pname_a @ SV874 @ ( sK9_X_1 @ SV959 @ SV874 @ SV387 ) ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK9_X_1 @ SV959 @ SV874 @ SV387 ) ) @ SV959 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV387 ) @ ( image_pname_a @ SV874 @ SV959 ) ) )
= $false )
| ( ( is_a @ SV387 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3894]) ).
thf(3952,plain,
! [SV389: $i,SV994: $i,SV964: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV964 ) @ SV994 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV964 ) @ SV389 ) )
| ( ( insert_pname @ SV964 @ SV994 )
!= ( insert_pname @ SV964 @ SV389 ) )
| ( SV994 = SV389 ) )
= $true )
| ( ( is_fun_pname_bool @ SV389 )
= $false )
| ( ( is_fun_pname_bool @ SV994 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3900]) ).
thf(3953,plain,
! [SV389: $i,SV995: $i,SV965: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV965 ) @ SV995 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV965 ) @ SV389 ) )
| ( SV995 != SV389 )
| ( ( insert_pname @ SV965 @ SV995 )
= ( insert_pname @ SV965 @ SV389 ) ) )
= $true )
| ( ( is_fun_pname_bool @ SV389 )
= $false )
| ( ( is_fun_pname_bool @ SV995 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3901]) ).
thf(3954,plain,
! [SV391: $i,SV970: $i,SV998: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV998 ) @ SV970 ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV391 ) @ SV970 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV998 ) @ SV391 ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV970 ) @ SV391 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV970 ) @ SV998 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3902]) ).
thf(3955,plain,
! [SV971: $i,SV391: $i,SV999: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV999 ) @ SV391 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV999 ) @ SV971 ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV391 ) @ SV971 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV971 ) @ SV391 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV971 ) @ SV999 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3903]) ).
thf(3956,plain,
! [SV1072: $i,SV1091: $i,SV393: $i] :
( ( ( SV393 = SV1091 )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV393 @ SV1072 ) @ SV1091 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3905]) ).
thf(3957,plain,
! [SV393: $i,SV1092: $i,SV1073: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ SV1073 @ SV1092 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV393 @ SV1073 ) @ SV1092 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3906]) ).
thf(3958,plain,
! [SV158: $i,SV537: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SV537 ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ SV158 ) ) )
= $false )
| ( ( SV158 = SV537 )
= $true )
| ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ SV158 ) @ SV537 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV537 ) )
= $false )
| ( ( is_fun1661590463l_bool @ SV158 )
= $false )
| ( ( is_fun1661590463l_bool @ SV537 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3908]) ).
thf(3959,plain,
! [SV159: $i,SV538: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SV538 ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ SV159 ) ) )
= $false )
| ( ( SV159 = SV538 )
= $true )
| ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ SV159 ) @ SV538 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV538 ) )
= $false )
| ( ( is_fun949378684l_bool @ SV159 )
= $false )
| ( ( is_fun949378684l_bool @ SV538 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3909]) ).
thf(3960,plain,
! [SV160: $i,SV539: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV539 ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ SV160 ) ) )
= $false )
| ( ( SV160 = SV539 )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV160 ) @ SV539 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV539 ) )
= $false )
| ( ( is_fun_pname_bool @ SV160 )
= $false )
| ( ( is_fun_pname_bool @ SV539 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3910]) ).
thf(3961,plain,
! [SV161: $i,SV540: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SV540 ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ SV161 ) ) )
= $false )
| ( ( SV161 = SV540 )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV161 ) @ SV540 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV540 ) )
= $false )
| ( ( is_fun_a_bool @ SV161 )
= $false )
| ( ( is_fun_a_bool @ SV540 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3911]) ).
thf(3962,plain,
! [SV1005: $i,SV364: $i,SV1035: $i,SV1093: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV1093 ) @ SV1035 ) ) )
= $true )
| ( ( ~ ( is_fun_pname_bool @ SV1093 ) )
= $true )
| ( ( ( SV364
!= ( image_pname_a @ SV1005 @ SV1093 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV364 ) @ ( image_pname_a @ SV1005 @ SV1035 ) ) )
= $true )
| ( ( is_fun_a_bool @ SV364 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3912]) ).
thf(3963,plain,
! [SV364: $i,SV1006: $i,SV1036: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( sK10_AA @ SV1036 @ SV1006 @ SV364 ) ) @ SV1036 ) )
| ~ ( is_fun_pname_bool @ ( sK10_AA @ SV1036 @ SV1006 @ SV364 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV364 ) @ ( image_pname_a @ SV1006 @ SV1036 ) ) )
= $false )
| ( ( is_fun_a_bool @ SV364 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3913]) ).
thf(3964,plain,
! [SV1036: $i,SV1006: $i,SV364: $i] :
( ( ( ( SV364
!= ( image_pname_a @ SV1006 @ ( sK10_AA @ SV1036 @ SV1006 @ SV364 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV364 ) @ ( image_pname_a @ SV1006 @ SV1036 ) ) )
= $false )
| ( ( is_fun_a_bool @ SV364 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3913]) ).
thf(3965,plain,
! [SV896: $i,SV830: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV830 ) @ SV896 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV896 ) @ SV830 ) ) )
= $true )
| ( ( SV830 = SV896 )
= $true )
| ( ( is_fun_pname_bool @ SV830 )
= $false )
| ( ( is_fun_pname_bool @ SV896 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3914]) ).
thf(3966,plain,
! [SV1011: $i,SV1041: $i] :
( ( ( is_fun_pname_bool @ SV1041 )
= $false )
| ( ( is_fun_pname_bool @ SV1011 )
= $false )
| ( ( ( SV1011 != SV1041 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV1011 ) @ SV1041 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3915]) ).
thf(3967,plain,
! [SV1012: $i,SV1042: $i] :
( ( ( is_fun_pname_bool @ SV1042 )
= $false )
| ( ( is_fun_pname_bool @ SV1012 )
= $false )
| ( ( ( SV1012 != SV1042 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV1042 ) @ SV1012 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3916]) ).
thf(3968,plain,
! [SV975: $i,SV900: $i,SV365: $i] :
( ( ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV365 @ SV900 ) @ SV975 ) )
= $false )
| ( ( ( SV365 = SV975 )
| ( hBOOL @ ( hAPP_pname_bool @ SV900 @ SV975 ) ) )
= $true )
| ( ( is_pname @ SV365 )
= $false )
| ( ( is_pname @ SV975 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3917]) ).
thf(3969,plain,
! [SV1043: $i,SV1074: $i,SV365: $i] :
( ( ( is_pname @ SV365 )
= $false )
| ( ( ~ ( is_pname @ SV1074 ) )
= $true )
| ( ( ( SV365 != SV1074 )
| ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV365 @ SV1043 ) @ SV1074 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3918]) ).
thf(3970,plain,
! [SV1044: $i,SV1075: $i,SV365: $i] :
( ( ( is_pname @ SV365 )
= $false )
| ( ( ~ ( is_pname @ SV1075 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_pname_bool @ SV1044 @ SV1075 ) )
| ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV365 @ SV1044 ) @ SV1075 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3919]) ).
thf(3971,plain,
! [SV1094: $i,SV904: $i,SV367: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ ( insert_a @ SV904 @ SV1094 ) ) )
= $false )
| ( ( ( SV367 = SV904 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ SV1094 ) ) )
= $true )
| ( ( is_a @ SV367 )
= $false )
| ( ( is_a @ SV904 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3922]) ).
thf(3972,plain,
! [SV367: $i,SV1047: $i] :
( ( ( is_a @ SV1047 )
= $false )
| ( ( is_a @ SV367 )
= $false )
| ( ( ( SV367 != SV1047 )
| ! [SY1183: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ ( insert_a @ SV1047 @ SY1183 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3923]) ).
thf(3973,plain,
! [SV367: $i,SV1048: $i] :
( ( ( is_a @ SV1048 )
= $false )
| ( ( is_a @ SV367 )
= $false )
| ( ( ! [SY1184: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ SY1184 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ ( insert_a @ SV1048 @ SY1184 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3924]) ).
thf(3974,plain,
! [SV1015: $i,SV369: $i,SV1049: $i,SV1095: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV1095 ) @ SV1049 ) ) )
= $true )
| ( ( ~ ( is_pname @ SV1095 ) )
= $true )
| ( ( ( SV369
!= ( hAPP_pname_a @ SV1015 @ SV1095 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV369 ) @ ( image_pname_a @ SV1015 @ SV1049 ) ) )
= $true )
| ( ( is_a @ SV369 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3925]) ).
thf(3975,plain,
! [SV369: $i,SV1016: $i,SV1050: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK11_X_1 @ SV1050 @ SV1016 @ SV369 ) ) @ SV1050 ) )
| ~ ( is_pname @ ( sK11_X_1 @ SV1050 @ SV1016 @ SV369 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV369 ) @ ( image_pname_a @ SV1016 @ SV1050 ) ) )
= $false )
| ( ( is_a @ SV369 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3926]) ).
thf(3976,plain,
! [SV1050: $i,SV1016: $i,SV369: $i] :
( ( ( ( SV369
!= ( hAPP_pname_a @ SV1016 @ ( sK11_X_1 @ SV1050 @ SV1016 @ SV369 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV369 ) @ ( image_pname_a @ SV1016 @ SV1050 ) ) )
= $false )
| ( ( is_a @ SV369 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3926]) ).
thf(3977,plain,
! [SV915: $i,SV843: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV843 ) @ SV915 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV915 ) @ SV843 ) ) )
= $true )
| ( ( SV843 = SV915 )
= $true )
| ( ( is_fun_a_bool @ SV843 )
= $false )
| ( ( is_fun_a_bool @ SV915 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3927]) ).
thf(3978,plain,
! [SV1018: $i,SV1052: $i] :
( ( ( is_fun_a_bool @ SV1052 )
= $false )
| ( ( is_fun_a_bool @ SV1018 )
= $false )
| ( ( ( SV1018 != SV1052 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV1018 ) @ SV1052 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3928]) ).
thf(3979,plain,
! [SV1019: $i,SV1053: $i] :
( ( ( is_fun_a_bool @ SV1053 )
= $false )
| ( ( is_fun_a_bool @ SV1019 )
= $false )
| ( ( ( SV1019 != SV1053 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV1053 ) @ SV1019 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3929]) ).
thf(3980,plain,
! [SV372: $i,SV722: $i,SV813: $i] :
( ( ( ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( sK17_C_2 @ SV813 @ SV722 @ SV372 ) ) @ SV722 ) )
| ~ ( is_fun_pname_bool @ ( sK17_C_2 @ SV813 @ SV722 @ SV372 ) ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( sK17_C_2 @ SV813 @ SV722 @ SV372 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV813 ) @ ( image_pname_a @ SV372 @ SV722 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV813 ) )
= $false )
| ( ( is_fun_a_bool @ SV813 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3930]) ).
thf(3981,plain,
! [SV722: $i,SV372: $i,SV813: $i] :
( ( ( SV813
= ( image_pname_a @ SV372 @ ( sK17_C_2 @ SV813 @ SV722 @ SV372 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV813 ) @ ( image_pname_a @ SV372 @ SV722 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV813 ) )
= $false )
| ( ( is_fun_a_bool @ SV813 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3931]) ).
thf(3982,plain,
! [SV381: $i,SV942: $i,SV988: $i] :
( ( ( ( hAPP_nat_nat @ ( minus_minus_nat @ SV988 ) @ SV942 )
= ( hAPP_nat_nat @ ( minus_minus_nat @ SV381 ) @ SV942 ) )
= $false )
| ( ( SV988 = SV381 )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV942 ) @ SV381 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV942 ) @ SV988 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3939]) ).
thf(3983,plain,
! [SV943: $i,SV381: $i,SV989: $i] :
( ( ( SV989 = SV381 )
= $false )
| ( ( ( hAPP_nat_nat @ ( minus_minus_nat @ SV989 ) @ SV943 )
= ( hAPP_nat_nat @ ( minus_minus_nat @ SV381 ) @ SV943 ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV943 ) @ SV381 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV943 ) @ SV989 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3940]) ).
thf(3984,plain,
! [SV1096: $i,SV950: $i,SV383: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ ( insert_pname @ SV950 @ SV1096 ) ) )
= $false )
| ( ( ( SV383 = SV950 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ SV1096 ) ) )
= $true )
| ( ( is_pname @ SV383 )
= $false )
| ( ( is_pname @ SV950 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3941]) ).
thf(3985,plain,
! [SV383: $i,SV1063: $i] :
( ( ( is_pname @ SV1063 )
= $false )
| ( ( is_pname @ SV383 )
= $false )
| ( ( ( SV383 != SV1063 )
| ! [SY1190: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ ( insert_pname @ SV1063 @ SY1190 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3942]) ).
thf(3986,plain,
! [SV383: $i,SV1064: $i] :
( ( ( is_pname @ SV1064 )
= $false )
| ( ( is_pname @ SV383 )
= $false )
| ( ( ! [SY1191: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ SY1191 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ ( insert_pname @ SV1064 @ SY1191 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3943]) ).
thf(3987,plain,
! [SV991: $i,SV385: $i,SV953: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV953 ) @ SV385 ) )
= $true )
| ( ( ( ( insert_a @ SV953 @ SV991 )
!= ( insert_a @ SV953 @ SV385 ) )
| ( SV991 = SV385 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV953 ) @ SV991 ) )
= $true )
| ( ( is_fun_a_bool @ SV385 )
= $false )
| ( ( is_fun_a_bool @ SV991 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3946]) ).
thf(3988,plain,
! [SV992: $i,SV385: $i,SV954: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV954 ) @ SV385 ) )
= $true )
| ( ( ( SV992 != SV385 )
| ( ( insert_a @ SV954 @ SV992 )
= ( insert_a @ SV954 @ SV385 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV954 ) @ SV992 ) )
= $true )
| ( ( is_fun_a_bool @ SV385 )
= $false )
| ( ( is_fun_a_bool @ SV992 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3947]) ).
thf(3989,plain,
! [SV993: $i,SV957: $i,SV386: $i] :
( ( ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV386 @ SV957 ) @ SV993 ) )
= $false )
| ( ( ( SV386 = SV993 )
| ( hBOOL @ ( hAPP_a_bool @ SV957 @ SV993 ) ) )
= $true )
| ( ( is_a @ SV386 )
= $false )
| ( ( is_a @ SV993 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3948]) ).
thf(3990,plain,
! [SV1068: $i,SV1087: $i,SV386: $i] :
( ( ( is_a @ SV386 )
= $false )
| ( ( ~ ( is_a @ SV1087 ) )
= $true )
| ( ( ( SV386 != SV1087 )
| ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV386 @ SV1068 ) @ SV1087 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3949]) ).
thf(3991,plain,
! [SV1069: $i,SV1088: $i,SV386: $i] :
( ( ( is_a @ SV386 )
= $false )
| ( ( ~ ( is_a @ SV1088 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_a_bool @ SV1069 @ SV1088 ) )
| ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV386 @ SV1069 ) @ SV1088 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3950]) ).
thf(3992,plain,
! [SV959: $i,SV874: $i,SV387: $i] :
( ( ( ( SV387
!= ( hAPP_pname_a @ SV874 @ ( sK9_X_1 @ SV959 @ SV874 @ SV387 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV387 ) @ ( image_pname_a @ SV874 @ SV959 ) ) )
= $false )
| ( ( is_a @ SV387 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3951]) ).
thf(3993,plain,
! [SV387: $i,SV874: $i,SV959: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK9_X_1 @ SV959 @ SV874 @ SV387 ) ) @ SV959 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV387 ) @ ( image_pname_a @ SV874 @ SV959 ) ) )
= $false )
| ( ( is_a @ SV387 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3951]) ).
thf(3994,plain,
! [SV994: $i,SV389: $i,SV964: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV964 ) @ SV389 ) )
= $true )
| ( ( ( ( insert_pname @ SV964 @ SV994 )
!= ( insert_pname @ SV964 @ SV389 ) )
| ( SV994 = SV389 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV964 ) @ SV994 ) )
= $true )
| ( ( is_fun_pname_bool @ SV389 )
= $false )
| ( ( is_fun_pname_bool @ SV994 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3952]) ).
thf(3995,plain,
! [SV995: $i,SV389: $i,SV965: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV965 ) @ SV389 ) )
= $true )
| ( ( ( SV995 != SV389 )
| ( ( insert_pname @ SV965 @ SV995 )
= ( insert_pname @ SV965 @ SV389 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV965 ) @ SV995 ) )
= $true )
| ( ( is_fun_pname_bool @ SV389 )
= $false )
| ( ( is_fun_pname_bool @ SV995 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3953]) ).
thf(3996,plain,
! [SV391: $i,SV970: $i,SV998: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV998 ) @ SV970 ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV391 ) @ SV970 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV998 ) @ SV391 ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV970 ) @ SV391 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV970 ) @ SV998 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3954]) ).
thf(3997,plain,
! [SV971: $i,SV391: $i,SV999: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV999 ) @ SV391 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV999 ) @ SV971 ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ SV391 ) @ SV971 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV971 ) @ SV391 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV971 ) @ SV999 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3955]) ).
thf(3998,plain,
! [SV1005: $i,SV364: $i,SV1035: $i,SV1093: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV1093 ) @ SV1035 ) )
= $false )
| ( ( ~ ( is_fun_pname_bool @ SV1093 ) )
= $true )
| ( ( ( SV364
!= ( image_pname_a @ SV1005 @ SV1093 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV364 ) @ ( image_pname_a @ SV1005 @ SV1035 ) ) )
= $true )
| ( ( is_fun_a_bool @ SV364 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3962]) ).
thf(3999,plain,
! [SV364: $i,SV1006: $i,SV1036: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( sK10_AA @ SV1036 @ SV1006 @ SV364 ) ) @ SV1036 ) )
| ~ ( is_fun_pname_bool @ ( sK10_AA @ SV1036 @ SV1006 @ SV364 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV364 ) @ ( image_pname_a @ SV1006 @ SV1036 ) ) )
= $false )
| ( ( is_fun_a_bool @ SV364 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3963]) ).
thf(4000,plain,
! [SV1036: $i,SV1006: $i,SV364: $i] :
( ( ( SV364
= ( image_pname_a @ SV1006 @ ( sK10_AA @ SV1036 @ SV1006 @ SV364 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV364 ) @ ( image_pname_a @ SV1006 @ SV1036 ) ) )
= $false )
| ( ( is_fun_a_bool @ SV364 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3964]) ).
thf(4001,plain,
! [SV830: $i,SV896: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV896 ) @ SV830 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV830 ) @ SV896 ) )
= $false )
| ( ( SV830 = SV896 )
= $true )
| ( ( is_fun_pname_bool @ SV830 )
= $false )
| ( ( is_fun_pname_bool @ SV896 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3965]) ).
thf(4002,plain,
! [SV1041: $i,SV1011: $i] :
( ( ( ( SV1011 != SV1041 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV1011 ) @ SV1041 ) )
= $true )
| ( ( is_fun_pname_bool @ SV1011 )
= $false )
| ( ( is_fun_pname_bool @ SV1041 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3966]) ).
thf(4003,plain,
! [SV1042: $i,SV1012: $i] :
( ( ( ( SV1012 != SV1042 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV1042 ) @ SV1012 ) )
= $true )
| ( ( is_fun_pname_bool @ SV1012 )
= $false )
| ( ( is_fun_pname_bool @ SV1042 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3967]) ).
thf(4004,plain,
! [SV900: $i,SV975: $i,SV365: $i] :
( ( ( SV365 = SV975 )
= $true )
| ( ( hBOOL @ ( hAPP_pname_bool @ SV900 @ SV975 ) )
= $true )
| ( ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV365 @ SV900 ) @ SV975 ) )
= $false )
| ( ( is_pname @ SV365 )
= $false )
| ( ( is_pname @ SV975 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3968]) ).
thf(4005,plain,
! [SV1043: $i,SV365: $i,SV1074: $i] :
( ( ( is_pname @ SV1074 )
= $false )
| ( ( is_pname @ SV365 )
= $false )
| ( ( ( SV365 != SV1074 )
| ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV365 @ SV1043 ) @ SV1074 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3969]) ).
thf(4006,plain,
! [SV1044: $i,SV365: $i,SV1075: $i] :
( ( ( is_pname @ SV1075 )
= $false )
| ( ( is_pname @ SV365 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_pname_bool @ SV1044 @ SV1075 ) )
| ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV365 @ SV1044 ) @ SV1075 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3970]) ).
thf(4007,plain,
! [SV1094: $i,SV904: $i,SV367: $i] :
( ( ( SV367 = SV904 )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ SV1094 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ ( insert_a @ SV904 @ SV1094 ) ) )
= $false )
| ( ( is_a @ SV367 )
= $false )
| ( ( is_a @ SV904 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3971]) ).
thf(4008,plain,
! [SV1047: $i,SV367: $i] :
( ( ( ( SV367 != SV1047 ) )
= $true )
| ( ( ! [SY1183: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ ( insert_a @ SV1047 @ SY1183 ) ) ) )
= $true )
| ( ( is_a @ SV367 )
= $false )
| ( ( is_a @ SV1047 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3972]) ).
thf(4009,plain,
! [SV1048: $i,SV1098: $i,SV367: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ SV1098 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ ( insert_a @ SV1048 @ SV1098 ) ) ) )
= $true )
| ( ( is_a @ SV367 )
= $false )
| ( ( is_a @ SV1048 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3973]) ).
thf(4010,plain,
! [SV1015: $i,SV369: $i,SV1049: $i,SV1095: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV1095 ) @ SV1049 ) )
= $false )
| ( ( ~ ( is_pname @ SV1095 ) )
= $true )
| ( ( ( SV369
!= ( hAPP_pname_a @ SV1015 @ SV1095 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV369 ) @ ( image_pname_a @ SV1015 @ SV1049 ) ) )
= $true )
| ( ( is_a @ SV369 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3974]) ).
thf(4011,plain,
! [SV369: $i,SV1016: $i,SV1050: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK11_X_1 @ SV1050 @ SV1016 @ SV369 ) ) @ SV1050 ) )
| ~ ( is_pname @ ( sK11_X_1 @ SV1050 @ SV1016 @ SV369 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV369 ) @ ( image_pname_a @ SV1016 @ SV1050 ) ) )
= $false )
| ( ( is_a @ SV369 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3975]) ).
thf(4012,plain,
! [SV1050: $i,SV1016: $i,SV369: $i] :
( ( ( SV369
= ( hAPP_pname_a @ SV1016 @ ( sK11_X_1 @ SV1050 @ SV1016 @ SV369 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV369 ) @ ( image_pname_a @ SV1016 @ SV1050 ) ) )
= $false )
| ( ( is_a @ SV369 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3976]) ).
thf(4013,plain,
! [SV843: $i,SV915: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV915 ) @ SV843 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV843 ) @ SV915 ) )
= $false )
| ( ( SV843 = SV915 )
= $true )
| ( ( is_fun_a_bool @ SV843 )
= $false )
| ( ( is_fun_a_bool @ SV915 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3977]) ).
thf(4014,plain,
! [SV1052: $i,SV1018: $i] :
( ( ( ( SV1018 != SV1052 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV1018 ) @ SV1052 ) )
= $true )
| ( ( is_fun_a_bool @ SV1018 )
= $false )
| ( ( is_fun_a_bool @ SV1052 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3978]) ).
thf(4015,plain,
! [SV1053: $i,SV1019: $i] :
( ( ( ( SV1019 != SV1053 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV1053 ) @ SV1019 ) )
= $true )
| ( ( is_fun_a_bool @ SV1019 )
= $false )
| ( ( is_fun_a_bool @ SV1053 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3979]) ).
thf(4016,plain,
! [SV372: $i,SV722: $i,SV813: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( sK17_C_2 @ SV813 @ SV722 @ SV372 ) ) @ SV722 ) )
| ~ ( is_fun_pname_bool @ ( sK17_C_2 @ SV813 @ SV722 @ SV372 ) ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( sK17_C_2 @ SV813 @ SV722 @ SV372 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV813 ) @ ( image_pname_a @ SV372 @ SV722 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV813 ) )
= $false )
| ( ( is_fun_a_bool @ SV813 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3980]) ).
thf(4017,plain,
! [SV1096: $i,SV950: $i,SV383: $i] :
( ( ( SV383 = SV950 )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ SV1096 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ ( insert_pname @ SV950 @ SV1096 ) ) )
= $false )
| ( ( is_pname @ SV383 )
= $false )
| ( ( is_pname @ SV950 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3984]) ).
thf(4018,plain,
! [SV1063: $i,SV383: $i] :
( ( ( ( SV383 != SV1063 ) )
= $true )
| ( ( ! [SY1190: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ ( insert_pname @ SV1063 @ SY1190 ) ) ) )
= $true )
| ( ( is_pname @ SV383 )
= $false )
| ( ( is_pname @ SV1063 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3985]) ).
thf(4019,plain,
! [SV1064: $i,SV1099: $i,SV383: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ SV1099 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ ( insert_pname @ SV1064 @ SV1099 ) ) ) )
= $true )
| ( ( is_pname @ SV383 )
= $false )
| ( ( is_pname @ SV1064 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3986]) ).
thf(4020,plain,
! [SV385: $i,SV991: $i,SV953: $i] :
( ( ( ( ( insert_a @ SV953 @ SV991 )
!= ( insert_a @ SV953 @ SV385 ) ) )
= $true )
| ( ( SV991 = SV385 )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV953 ) @ SV385 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV953 ) @ SV991 ) )
= $true )
| ( ( is_fun_a_bool @ SV385 )
= $false )
| ( ( is_fun_a_bool @ SV991 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3987]) ).
thf(4021,plain,
! [SV954: $i,SV385: $i,SV992: $i] :
( ( ( ( SV992 != SV385 ) )
= $true )
| ( ( ( insert_a @ SV954 @ SV992 )
= ( insert_a @ SV954 @ SV385 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV954 ) @ SV385 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV954 ) @ SV992 ) )
= $true )
| ( ( is_fun_a_bool @ SV385 )
= $false )
| ( ( is_fun_a_bool @ SV992 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3988]) ).
thf(4022,plain,
! [SV957: $i,SV993: $i,SV386: $i] :
( ( ( SV386 = SV993 )
= $true )
| ( ( hBOOL @ ( hAPP_a_bool @ SV957 @ SV993 ) )
= $true )
| ( ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV386 @ SV957 ) @ SV993 ) )
= $false )
| ( ( is_a @ SV386 )
= $false )
| ( ( is_a @ SV993 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3989]) ).
thf(4023,plain,
! [SV1068: $i,SV386: $i,SV1087: $i] :
( ( ( is_a @ SV1087 )
= $false )
| ( ( is_a @ SV386 )
= $false )
| ( ( ( SV386 != SV1087 )
| ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV386 @ SV1068 ) @ SV1087 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3990]) ).
thf(4024,plain,
! [SV1069: $i,SV386: $i,SV1088: $i] :
( ( ( is_a @ SV1088 )
= $false )
| ( ( is_a @ SV386 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_a_bool @ SV1069 @ SV1088 ) )
| ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV386 @ SV1069 ) @ SV1088 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3991]) ).
thf(4025,plain,
! [SV959: $i,SV874: $i,SV387: $i] :
( ( ( SV387
= ( hAPP_pname_a @ SV874 @ ( sK9_X_1 @ SV959 @ SV874 @ SV387 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV387 ) @ ( image_pname_a @ SV874 @ SV959 ) ) )
= $false )
| ( ( is_a @ SV387 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3992]) ).
thf(4026,plain,
! [SV387: $i,SV874: $i,SV959: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK9_X_1 @ SV959 @ SV874 @ SV387 ) ) @ SV959 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV387 ) @ ( image_pname_a @ SV874 @ SV959 ) ) )
= $false )
| ( ( is_a @ SV387 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3993]) ).
thf(4027,plain,
! [SV389: $i,SV994: $i,SV964: $i] :
( ( ( ( ( insert_pname @ SV964 @ SV994 )
!= ( insert_pname @ SV964 @ SV389 ) ) )
= $true )
| ( ( SV994 = SV389 )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV964 ) @ SV389 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV964 ) @ SV994 ) )
= $true )
| ( ( is_fun_pname_bool @ SV389 )
= $false )
| ( ( is_fun_pname_bool @ SV994 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3994]) ).
thf(4028,plain,
! [SV965: $i,SV389: $i,SV995: $i] :
( ( ( ( SV995 != SV389 ) )
= $true )
| ( ( ( insert_pname @ SV965 @ SV995 )
= ( insert_pname @ SV965 @ SV389 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV965 ) @ SV389 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV965 ) @ SV995 ) )
= $true )
| ( ( is_fun_pname_bool @ SV389 )
= $false )
| ( ( is_fun_pname_bool @ SV995 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3995]) ).
thf(4029,plain,
! [SV1005: $i,SV364: $i,SV1035: $i,SV1093: $i] :
( ( ( is_fun_pname_bool @ SV1093 )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV1093 ) @ SV1035 ) )
= $false )
| ( ( ( SV364
!= ( image_pname_a @ SV1005 @ SV1093 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV364 ) @ ( image_pname_a @ SV1005 @ SV1035 ) ) )
= $true )
| ( ( is_fun_a_bool @ SV364 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3998]) ).
thf(4030,plain,
! [SV364: $i,SV1006: $i,SV1036: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( sK10_AA @ SV1036 @ SV1006 @ SV364 ) ) @ SV1036 ) )
| ~ ( is_fun_pname_bool @ ( sK10_AA @ SV1036 @ SV1006 @ SV364 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV364 ) @ ( image_pname_a @ SV1006 @ SV1036 ) ) )
= $false )
| ( ( is_fun_a_bool @ SV364 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3999]) ).
thf(4031,plain,
! [SV1041: $i,SV1011: $i] :
( ( ( SV1011 = SV1041 )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV1011 ) @ SV1041 ) )
= $true )
| ( ( is_fun_pname_bool @ SV1011 )
= $false )
| ( ( is_fun_pname_bool @ SV1041 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4002]) ).
thf(4032,plain,
! [SV1042: $i,SV1012: $i] :
( ( ( SV1012 = SV1042 )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV1042 ) @ SV1012 ) )
= $true )
| ( ( is_fun_pname_bool @ SV1012 )
= $false )
| ( ( is_fun_pname_bool @ SV1042 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4003]) ).
thf(4033,plain,
! [SV1043: $i,SV1074: $i,SV365: $i] :
( ( ( ( SV365 != SV1074 ) )
= $true )
| ( ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV365 @ SV1043 ) @ SV1074 ) )
= $true )
| ( ( is_pname @ SV365 )
= $false )
| ( ( is_pname @ SV1074 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4005]) ).
thf(4034,plain,
! [SV365: $i,SV1075: $i,SV1044: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_pname_bool @ SV1044 @ SV1075 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV365 @ SV1044 ) @ SV1075 ) )
= $true )
| ( ( is_pname @ SV365 )
= $false )
| ( ( is_pname @ SV1075 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4006]) ).
thf(4035,plain,
! [SV1047: $i,SV367: $i] :
( ( ( SV367 = SV1047 )
= $false )
| ( ( ! [SY1183: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ ( insert_a @ SV1047 @ SY1183 ) ) ) )
= $true )
| ( ( is_a @ SV367 )
= $false )
| ( ( is_a @ SV1047 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4008]) ).
thf(4036,plain,
! [SV1048: $i,SV1098: $i,SV367: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ SV1098 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ ( insert_a @ SV1048 @ SV1098 ) ) )
= $true )
| ( ( is_a @ SV367 )
= $false )
| ( ( is_a @ SV1048 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4009]) ).
thf(4037,plain,
! [SV1015: $i,SV369: $i,SV1049: $i,SV1095: $i] :
( ( ( is_pname @ SV1095 )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV1095 ) @ SV1049 ) )
= $false )
| ( ( ( SV369
!= ( hAPP_pname_a @ SV1015 @ SV1095 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV369 ) @ ( image_pname_a @ SV1015 @ SV1049 ) ) )
= $true )
| ( ( is_a @ SV369 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4010]) ).
thf(4038,plain,
! [SV369: $i,SV1016: $i,SV1050: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK11_X_1 @ SV1050 @ SV1016 @ SV369 ) ) @ SV1050 ) )
| ~ ( is_pname @ ( sK11_X_1 @ SV1050 @ SV1016 @ SV369 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV369 ) @ ( image_pname_a @ SV1016 @ SV1050 ) ) )
= $false )
| ( ( is_a @ SV369 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4011]) ).
thf(4039,plain,
! [SV1052: $i,SV1018: $i] :
( ( ( SV1018 = SV1052 )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV1018 ) @ SV1052 ) )
= $true )
| ( ( is_fun_a_bool @ SV1018 )
= $false )
| ( ( is_fun_a_bool @ SV1052 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4014]) ).
thf(4040,plain,
! [SV1053: $i,SV1019: $i] :
( ( ( SV1019 = SV1053 )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV1053 ) @ SV1019 ) )
= $true )
| ( ( is_fun_a_bool @ SV1019 )
= $false )
| ( ( is_fun_a_bool @ SV1053 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4015]) ).
thf(4041,plain,
! [SV372: $i,SV722: $i,SV813: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( sK17_C_2 @ SV813 @ SV722 @ SV372 ) ) @ SV722 ) )
| ~ ( is_fun_pname_bool @ ( sK17_C_2 @ SV813 @ SV722 @ SV372 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV813 ) @ ( image_pname_a @ SV372 @ SV722 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV813 ) )
= $false )
| ( ( is_fun_a_bool @ SV813 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4016]) ).
thf(4042,plain,
! [SV372: $i,SV722: $i,SV813: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( sK17_C_2 @ SV813 @ SV722 @ SV372 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV813 ) @ ( image_pname_a @ SV372 @ SV722 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV813 ) )
= $false )
| ( ( is_fun_a_bool @ SV813 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4016]) ).
thf(4043,plain,
! [SV1063: $i,SV383: $i] :
( ( ( SV383 = SV1063 )
= $false )
| ( ( ! [SY1190: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ ( insert_pname @ SV1063 @ SY1190 ) ) ) )
= $true )
| ( ( is_pname @ SV383 )
= $false )
| ( ( is_pname @ SV1063 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4018]) ).
thf(4044,plain,
! [SV1064: $i,SV1099: $i,SV383: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ SV1099 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ ( insert_pname @ SV1064 @ SV1099 ) ) )
= $true )
| ( ( is_pname @ SV383 )
= $false )
| ( ( is_pname @ SV1064 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4019]) ).
thf(4045,plain,
! [SV385: $i,SV991: $i,SV953: $i] :
( ( ( ( insert_a @ SV953 @ SV991 )
= ( insert_a @ SV953 @ SV385 ) )
= $false )
| ( ( SV991 = SV385 )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV953 ) @ SV385 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV953 ) @ SV991 ) )
= $true )
| ( ( is_fun_a_bool @ SV385 )
= $false )
| ( ( is_fun_a_bool @ SV991 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4020]) ).
thf(4046,plain,
! [SV954: $i,SV385: $i,SV992: $i] :
( ( ( SV992 = SV385 )
= $false )
| ( ( ( insert_a @ SV954 @ SV992 )
= ( insert_a @ SV954 @ SV385 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV954 ) @ SV385 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV954 ) @ SV992 ) )
= $true )
| ( ( is_fun_a_bool @ SV385 )
= $false )
| ( ( is_fun_a_bool @ SV992 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4021]) ).
thf(4047,plain,
! [SV1068: $i,SV1087: $i,SV386: $i] :
( ( ( ( SV386 != SV1087 ) )
= $true )
| ( ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV386 @ SV1068 ) @ SV1087 ) )
= $true )
| ( ( is_a @ SV386 )
= $false )
| ( ( is_a @ SV1087 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4023]) ).
thf(4048,plain,
! [SV386: $i,SV1088: $i,SV1069: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_a_bool @ SV1069 @ SV1088 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV386 @ SV1069 ) @ SV1088 ) )
= $true )
| ( ( is_a @ SV386 )
= $false )
| ( ( is_a @ SV1088 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4024]) ).
thf(4049,plain,
! [SV389: $i,SV994: $i,SV964: $i] :
( ( ( ( insert_pname @ SV964 @ SV994 )
= ( insert_pname @ SV964 @ SV389 ) )
= $false )
| ( ( SV994 = SV389 )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV964 ) @ SV389 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV964 ) @ SV994 ) )
= $true )
| ( ( is_fun_pname_bool @ SV389 )
= $false )
| ( ( is_fun_pname_bool @ SV994 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4027]) ).
thf(4050,plain,
! [SV965: $i,SV389: $i,SV995: $i] :
( ( ( SV995 = SV389 )
= $false )
| ( ( ( insert_pname @ SV965 @ SV995 )
= ( insert_pname @ SV965 @ SV389 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV965 ) @ SV389 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV965 ) @ SV995 ) )
= $true )
| ( ( is_fun_pname_bool @ SV389 )
= $false )
| ( ( is_fun_pname_bool @ SV995 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4028]) ).
thf(4051,plain,
! [SV1035: $i,SV1093: $i,SV1005: $i,SV364: $i] :
( ( ( SV364
= ( image_pname_a @ SV1005 @ SV1093 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV1093 ) @ SV1035 ) )
= $false )
| ( ( is_fun_pname_bool @ SV1093 )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV364 ) @ ( image_pname_a @ SV1005 @ SV1035 ) ) )
= $true )
| ( ( is_fun_a_bool @ SV364 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4029]) ).
thf(4052,plain,
! [SV364: $i,SV1006: $i,SV1036: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( sK10_AA @ SV1036 @ SV1006 @ SV364 ) ) @ SV1036 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV364 ) @ ( image_pname_a @ SV1006 @ SV1036 ) ) )
= $false )
| ( ( is_fun_a_bool @ SV364 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4030]) ).
thf(4053,plain,
! [SV364: $i,SV1006: $i,SV1036: $i] :
( ( ( ~ ( is_fun_pname_bool @ ( sK10_AA @ SV1036 @ SV1006 @ SV364 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV364 ) @ ( image_pname_a @ SV1006 @ SV1036 ) ) )
= $false )
| ( ( is_fun_a_bool @ SV364 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4030]) ).
thf(4054,plain,
! [SV1043: $i,SV1074: $i,SV365: $i] :
( ( ( SV365 = SV1074 )
= $false )
| ( ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV365 @ SV1043 ) @ SV1074 ) )
= $true )
| ( ( is_pname @ SV365 )
= $false )
| ( ( is_pname @ SV1074 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4033]) ).
thf(4055,plain,
! [SV365: $i,SV1075: $i,SV1044: $i] :
( ( ( hBOOL @ ( hAPP_pname_bool @ SV1044 @ SV1075 ) )
= $false )
| ( ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV365 @ SV1044 ) @ SV1075 ) )
= $true )
| ( ( is_pname @ SV365 )
= $false )
| ( ( is_pname @ SV1075 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4034]) ).
thf(4056,plain,
! [SV1100: $i,SV1047: $i,SV367: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ ( insert_a @ SV1047 @ SV1100 ) ) )
= $true )
| ( ( SV367 = SV1047 )
= $false )
| ( ( is_a @ SV367 )
= $false )
| ( ( is_a @ SV1047 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4035]) ).
thf(4057,plain,
! [SV1048: $i,SV1098: $i,SV367: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ SV1098 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV367 ) @ ( insert_a @ SV1048 @ SV1098 ) ) )
= $true )
| ( ( is_a @ SV367 )
= $false )
| ( ( is_a @ SV1048 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4036]) ).
thf(4058,plain,
! [SV1049: $i,SV1095: $i,SV1015: $i,SV369: $i] :
( ( ( SV369
= ( hAPP_pname_a @ SV1015 @ SV1095 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV1095 ) @ SV1049 ) )
= $false )
| ( ( is_pname @ SV1095 )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV369 ) @ ( image_pname_a @ SV1015 @ SV1049 ) ) )
= $true )
| ( ( is_a @ SV369 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4037]) ).
thf(4059,plain,
! [SV369: $i,SV1016: $i,SV1050: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK11_X_1 @ SV1050 @ SV1016 @ SV369 ) ) @ SV1050 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV369 ) @ ( image_pname_a @ SV1016 @ SV1050 ) ) )
= $false )
| ( ( is_a @ SV369 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4038]) ).
thf(4060,plain,
! [SV369: $i,SV1016: $i,SV1050: $i] :
( ( ( ~ ( is_pname @ ( sK11_X_1 @ SV1050 @ SV1016 @ SV369 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV369 ) @ ( image_pname_a @ SV1016 @ SV1050 ) ) )
= $false )
| ( ( is_a @ SV369 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4038]) ).
thf(4061,plain,
! [SV372: $i,SV722: $i,SV813: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( sK17_C_2 @ SV813 @ SV722 @ SV372 ) ) @ SV722 ) )
| ~ ( is_fun_pname_bool @ ( sK17_C_2 @ SV813 @ SV722 @ SV372 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV813 ) @ ( image_pname_a @ SV372 @ SV722 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV813 ) )
= $false )
| ( ( is_fun_a_bool @ SV813 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4041]) ).
thf(4062,plain,
! [SV372: $i,SV722: $i,SV813: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( sK17_C_2 @ SV813 @ SV722 @ SV372 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV813 ) @ ( image_pname_a @ SV372 @ SV722 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV813 ) )
= $false )
| ( ( is_fun_a_bool @ SV813 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4042]) ).
thf(4063,plain,
! [SV1101: $i,SV1063: $i,SV383: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ ( insert_pname @ SV1063 @ SV1101 ) ) )
= $true )
| ( ( SV383 = SV1063 )
= $false )
| ( ( is_pname @ SV383 )
= $false )
| ( ( is_pname @ SV1063 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4043]) ).
thf(4064,plain,
! [SV1064: $i,SV1099: $i,SV383: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ SV1099 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV383 ) @ ( insert_pname @ SV1064 @ SV1099 ) ) )
= $true )
| ( ( is_pname @ SV383 )
= $false )
| ( ( is_pname @ SV1064 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4044]) ).
thf(4065,plain,
! [SV1068: $i,SV1087: $i,SV386: $i] :
( ( ( SV386 = SV1087 )
= $false )
| ( ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV386 @ SV1068 ) @ SV1087 ) )
= $true )
| ( ( is_a @ SV386 )
= $false )
| ( ( is_a @ SV1087 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4047]) ).
thf(4066,plain,
! [SV386: $i,SV1088: $i,SV1069: $i] :
( ( ( hBOOL @ ( hAPP_a_bool @ SV1069 @ SV1088 ) )
= $false )
| ( ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV386 @ SV1069 ) @ SV1088 ) )
= $true )
| ( ( is_a @ SV386 )
= $false )
| ( ( is_a @ SV1088 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4048]) ).
thf(4067,plain,
! [SV364: $i,SV1006: $i,SV1036: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( sK10_AA @ SV1036 @ SV1006 @ SV364 ) ) @ SV1036 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV364 ) @ ( image_pname_a @ SV1006 @ SV1036 ) ) )
= $false )
| ( ( is_fun_a_bool @ SV364 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4052]) ).
thf(4068,plain,
! [SV364: $i,SV1006: $i,SV1036: $i] :
( ( ( is_fun_pname_bool @ ( sK10_AA @ SV1036 @ SV1006 @ SV364 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV364 ) @ ( image_pname_a @ SV1006 @ SV1036 ) ) )
= $false )
| ( ( is_fun_a_bool @ SV364 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4053]) ).
thf(4069,plain,
! [SV369: $i,SV1016: $i,SV1050: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( sK11_X_1 @ SV1050 @ SV1016 @ SV369 ) ) @ SV1050 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV369 ) @ ( image_pname_a @ SV1016 @ SV1050 ) ) )
= $false )
| ( ( is_a @ SV369 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4059]) ).
thf(4070,plain,
! [SV369: $i,SV1016: $i,SV1050: $i] :
( ( ( is_pname @ ( sK11_X_1 @ SV1050 @ SV1016 @ SV369 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV369 ) @ ( image_pname_a @ SV1016 @ SV1050 ) ) )
= $false )
| ( ( is_a @ SV369 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4060]) ).
thf(4071,plain,
! [SV372: $i,SV722: $i,SV813: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( sK17_C_2 @ SV813 @ SV722 @ SV372 ) ) @ SV722 ) )
| ~ ( is_fun_pname_bool @ ( sK17_C_2 @ SV813 @ SV722 @ SV372 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV813 ) @ ( image_pname_a @ SV372 @ SV722 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV813 ) )
= $false )
| ( ( is_fun_a_bool @ SV813 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4061]) ).
thf(4072,plain,
! [SV372: $i,SV722: $i,SV813: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( sK17_C_2 @ SV813 @ SV722 @ SV372 ) ) @ SV722 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV813 ) @ ( image_pname_a @ SV372 @ SV722 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV813 ) )
= $false )
| ( ( is_fun_a_bool @ SV813 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4071]) ).
thf(4073,plain,
! [SV372: $i,SV722: $i,SV813: $i] :
( ( ( ~ ( is_fun_pname_bool @ ( sK17_C_2 @ SV813 @ SV722 @ SV372 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV813 ) @ ( image_pname_a @ SV372 @ SV722 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV813 ) )
= $false )
| ( ( is_fun_a_bool @ SV813 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4071]) ).
thf(4074,plain,
! [SV372: $i,SV722: $i,SV813: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( sK17_C_2 @ SV813 @ SV722 @ SV372 ) ) @ SV722 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV813 ) @ ( image_pname_a @ SV372 @ SV722 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV813 ) )
= $false )
| ( ( is_fun_a_bool @ SV813 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4072]) ).
thf(4075,plain,
! [SV372: $i,SV722: $i,SV813: $i] :
( ( ( is_fun_pname_bool @ ( sK17_C_2 @ SV813 @ SV722 @ SV372 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV813 ) @ ( image_pname_a @ SV372 @ SV722 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV813 ) )
= $false )
| ( ( is_fun_a_bool @ SV813 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4073]) ).
thf(4076,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[764,4075,4074,4070,4069,4068,4067,4066,4065,4064,4063,4062,4058,4057,4056,4055,4054,4051,4050,4049,4046,4045,4040,4039,4032,4031,4026,4025,4022,4017,4013,4012,4007,4004,4001,4000,3997,3996,3983,3982,3981,3961,3960,3959,3958,3957,3956,3945,3944,3938,3937,3936,3935,3934,3933,3932,3921,3920,3907,3904,3899,3898,3897,3896,3895,3893,3887,3886,3883,3879,3878,3874,3873,3872,3871,3868,3865,3864,3861,3860,3859,3841,3840,3839,3838,3835,3834,3833,3832,3827,3825,3822,3820,3817,3816,3811,3809,3806,3796,3789,3788,3785,3780,3779,3777,3774,3770,3766,3760,3755,3754,3751,3750,3744,3737,3734,3684,3682,3674,3672,3670,3669,3664,3648,3647,3646,3641,3640,3621,3614,3611,3610,3609,3608,3607,3602,3601,3596,3595,3594,3583,3582,3572,3571,3569,3568,3564,3563,3547,3546,3542,3538,3537,3536,3533,3532,3527,3526,3522,3521,3495,3494,3493,3492,3485,3484,3480,3479,3472,3471,3470,3469,3455,3454,3453,3452,3451,3450,3449,3448,3442,3441,3440,3439,3438,3437,3436,3435,3434,3433,3432,3431,3428,3427,3426,3422,3421,3420,3419,3418,3417,3416,3401,3354,3336,3314,3254,3253,3239,3238,3235,3229,3221,3220,3219,3218,3217,3216,3215,3214,3213,3212,3211,3210,3208,3201,3200,3199,3198,3197,3196,3195,3194,3193,3192,3191,3190,3189,3188,3041,3039,3038,3037,3036,3035,3034,3033,3032,3030,3015,3014,3013,2997,2996,2994,2979,2978,2977,2976,2975,2974,2825,2823,2822,2821,2819,2817,2816,2815,2812,2810,2809,2808,2807,2805,2804,2781,2780,2779,2778,2777,2776,2773,2752,2750,2748,2735,2732,2731,2724,2723,2722,2721,2720,2719,2706,2705,2704,2703,2702,2701,2700,2699,2698,2697,2696,2695,2694,2693,2692,2691,2690,2689,2688,2687,2686,2685,2684,2683,2682,2681,2680,2679,2678,2677,2676,2675,2674,2673,2672,2671,2670,2669,2668,2667,2666,2665,2664,2663,2662,2661,2660,2659,2658,2657,2656,2655,2654,2653,2652,2651,2650,2649,2648,2647,2646,2645,2644,2643,2642,2641,2640,2639,2638,2637,2636,2635,2634,2633,2632,2631,2630,2629,2628,2627,2626,2624,2623,2618,2617,2616,2615,2614,2613,2612,2611,2610,2609,2608,2607,2606,2605,2604,2603,2602,2600,2598,2597,2596,2594,2465,2464,2463,2462,2461,2460,2459,2458,2457,2456,2455,2454,2453,2452,2451,2450,2449,2448,2447,2446,2445,2444,2443,2442,2441,2440,2439,2438,2437,2436,2435,2434,2433,2432,2427,2426,2425,2422,2413,2402,2393,2392,2391,2366,2365,2364,2344,2328,2327,2227,2226,2225,2224,2223,2222,2221,2220,2219,2217,2190,2189,2188,2187,2005,1993,1992,1991,1990,1989,1988,1987,1986,1985,1952,1951,1950,1949,1948,1947,1946,1945,1944,1943,1942,1941,1940,1939,1938,1937,1936,1935,1919,1914,1912,1891,1890,1782,1781,1780,1779,1778,1777,1776,1771,1767,1766,1755,1754,1753,1752,1751,1750,1749,1748,1743,1742,1741,1740,1719,1645,1583,1582,1581,1580,1558,1555,1535,1534,1533,1466,1458,1457,1290,797,796,795,794,793,792,791,781,780,779,778,777,776,775,774]) ).
thf(4077,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[4076]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SWW473+1 : TPTP v8.1.0. Released v5.3.0.
% 0.11/0.14 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.35 % Computer : n018.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sun Jun 5 02:10:03 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.20/0.52 ..........
% 0.62/0.79
% 0.62/0.79 No.of.Axioms: 448
% 0.62/0.79
% 0.62/0.79 Length.of.Defs: 0
% 0.62/0.79
% 0.62/0.79 Contains.Choice.Funs: false
% 0.74/0.94 .......................
% 0.77/1.01 (rf:2,axioms:114,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:450,loop_count:0,foatp_calls:0,translation:fof_full)..............................................................eprover: CPU time limit exceeded, terminating
% 75.22/75.45 ........eprover: CPU time limit exceeded, terminating
% 149.85/150.21 ignored arguments false
% 150.06/150.39 ..........
% 150.36/150.63 (rf:0,axioms:448,ps:0,u:1,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:false,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:450,loop_count:0,foatp_calls:0,translation:fof_full)............................................................................................................................................................................................................................................................
% 156.64/156.95
% 156.64/156.95 ********************************
% 156.64/156.95 * All subproblems solved! *
% 156.64/156.95 ********************************
% 156.64/156.95 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:448,ps:0,u:1,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:false,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:36,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:4076,loop_count:0,foatp_calls:1,translation:fof_full)
% 161.21/161.51
% 161.21/161.51 %**** Beginning of derivation protocol ****
% 161.21/161.51 % SZS output start CNFRefutation
% See solution above
% 161.21/161.53
% 161.21/161.53 %**** End of derivation protocol ****
% 161.21/161.53 %**** no. of clauses in derivation: 4077 ****
% 161.21/161.53 %**** clause counter: 4076 ****
% 161.21/161.53
% 161.21/161.53 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:448,ps:0,u:1,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:false,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:36,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:4076,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------