%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWW473+1 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:10:17 AM UTC 2026
% Result : Theorem 18.04s 5.40s
% Output : Refutation 19.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 445
% Syntax : Number of formulae : 892 ( 252 unt; 0 typ; 0 def)
% Number of atoms : 2060 ( 358 equ; 0 cnn)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 10632 ( 137 ~; 87 |; 168 &;9327 @)
% ( 42 <=>; 871 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 228 ( 226 usr; 56 con; 0-2 aty)
% Number of variables : 1918 ( 0 ^;1903 !; 15 ?;1918 :)
% Comments :
%------------------------------------------------------------------------------
thf(hBOOL_decl,type,
hBOOL: $i > $o ).
thf(hAPP_fun_a_bool_bool_decl,type,
hAPP_fun_a_bool_bool: $i > $i > $i ).
thf(hAPP_f1631501043l_bool_decl,type,
hAPP_f1631501043l_bool: $i > $i > $i ).
thf(ord_le1311769555a_bool_decl,type,
ord_le1311769555a_bool: $i ).
thf(insert_a_decl,type,
insert_a: $i > $i > $i ).
thf(hAPP_pname_a_decl,type,
hAPP_pname_a: $i > $i > $i ).
thf(mgt_call_decl,type,
mgt_call: $i ).
thf(pn_decl,type,
pn: $i ).
thf(g_decl,type,
g: $i ).
thf(image_pname_a_decl,type,
image_pname_a: $i > $i > $i ).
thf(u_decl,type,
u: $i ).
thf(is_fun949378684l_bool_decl,type,
is_fun949378684l_bool: $i > $o ).
thf(image_nat_fun_a_bool_decl,type,
image_nat_fun_a_bool: $i > $i > $i ).
thf(is_fun1661590463l_bool_decl,type,
is_fun1661590463l_bool: $i > $o ).
thf(finite_finite_pname_decl,type,
finite_finite_pname: $i ).
thf(is_fun_a_bool_decl,type,
is_fun_a_bool: $i > $o ).
thf(is_a_decl,type,
is_a: $i > $o ).
thf(is_bool_decl,type,
is_bool: $i > $o ).
thf(hAPP_a_bool_decl,type,
hAPP_a_bool: $i > $i > $i ).
thf(hAPP_f595608956l_bool_decl,type,
hAPP_f595608956l_bool: $i > $i > $i ).
thf(hAPP_nat_fun_a_bool_decl,type,
hAPP_nat_fun_a_bool: $i > $i > $i ).
thf(collect_nat_decl,type,
collect_nat: $i > $i ).
thf(hAPP_bool_bool_decl,type,
hAPP_bool_bool: $i > $i > $i ).
thf(hAPP_f559147733l_bool_decl,type,
hAPP_f559147733l_bool: $i > $i > $i ).
thf(hAPP_f937997336l_bool_decl,type,
hAPP_f937997336l_bool: $i > $i > $i ).
thf(hAPP_f760187903l_bool_decl,type,
hAPP_f760187903l_bool: $i > $i > $i ).
thf(cOMBC_1269652216l_bool_decl,type,
cOMBC_1269652216l_bool: $i > $i ).
thf(is_fun_pname_bool_decl,type,
is_fun_pname_bool: $i > $o ).
thf(image_1921560913_pname_decl,type,
image_1921560913_pname: $i > $i > $i ).
thf(image_47868345e_bool_decl,type,
image_47868345e_bool: $i > $i > $i ).
thf(hAPP_f1935102916l_bool_decl,type,
hAPP_f1935102916l_bool: $i > $i > $i ).
thf(hAPP_f510955609l_bool_decl,type,
hAPP_f510955609l_bool: $i > $i > $i ).
thf(cOMBC_7971162l_bool_decl,type,
cOMBC_7971162l_bool: $i > $i ).
thf(hAPP_nat_nat_decl,type,
hAPP_nat_nat: $i > $i > $i ).
thf(minus_minus_nat_decl,type,
minus_minus_nat: $i > $i ).
thf(suc_decl,type,
suc: $i ).
thf(hAPP_f1748468828l_bool_decl,type,
hAPP_f1748468828l_bool: $i > $i > $i ).
thf(cOMBB_444170502t_bool_decl,type,
cOMBB_444170502t_bool: $i > $i > $i ).
thf(hAPP_b589554111l_bool_decl,type,
hAPP_b589554111l_bool: $i > $i > $i ).
thf(hAPP_f54304608l_bool_decl,type,
hAPP_f54304608l_bool: $i > $i > $i ).
thf(image_a_a_decl,type,
image_a_a: $i > $i > $i ).
thf(cOMBS_1187019125l_bool_decl,type,
cOMBS_1187019125l_bool: $i > $i > $i ).
thf(hAPP_nat_bool_decl,type,
hAPP_nat_bool: $i > $i > $i ).
thf(cOMBS_nat_bool_bool_decl,type,
cOMBS_nat_bool_bool: $i > $i > $i ).
thf(hAPP_n1006566506l_bool_decl,type,
hAPP_n1006566506l_bool: $i > $i > $i ).
thf(hAPP_pname_bool_decl,type,
hAPP_pname_bool: $i > $i > $i ).
thf(cOMBB_647938656_pname_decl,type,
cOMBB_647938656_pname: $i > $i > $i ).
thf(cOMBB_bool_bool_nat_decl,type,
cOMBB_bool_bool_nat: $i > $i > $i ).
thf(insert1325755072e_bool_decl,type,
insert1325755072e_bool: $i > $i > $i ).
thf(collect_fun_a_bool_decl,type,
collect_fun_a_bool: $i > $i ).
thf(hAPP_f621171935l_bool_decl,type,
hAPP_f621171935l_bool: $i > $i > $i ).
thf(hAPP_f759274231e_bool_decl,type,
hAPP_f759274231e_bool: $i > $i > $i ).
thf(cOMBC_1058051404l_bool_decl,type,
cOMBC_1058051404l_bool: $i > $i ).
thf(hAPP_f1664156314l_bool_decl,type,
hAPP_f1664156314l_bool: $i > $i > $i ).
thf(hAPP_p338031245l_bool_decl,type,
hAPP_p338031245l_bool: $i > $i > $i ).
thf(image_1655916159e_bool_decl,type,
image_1655916159e_bool: $i > $i > $i ).
thf(hAPP_a85458249l_bool_decl,type,
hAPP_a85458249l_bool: $i > $i > $i ).
thf(image_1604018183_pname_decl,type,
image_1604018183_pname: $i > $i > $i ).
thf(image_1283814551_pname_decl,type,
image_1283814551_pname: $i > $i > $i ).
thf(hAPP_f1476298914l_bool_decl,type,
hAPP_f1476298914l_bool: $i > $i > $i ).
thf(cOMBB_2095475776e_bool_decl,type,
cOMBB_2095475776e_bool: $i > $i > $i ).
thf(cOMBS_1035972772l_bool_decl,type,
cOMBS_1035972772l_bool: $i > $i > $i ).
thf(undefined_a_decl,type,
undefined_a: $i > $i ).
thf(x_a_decl,type,
x_a: $i ).
thf(insert_nat_decl,type,
insert_nat: $i > $i > $i ).
thf(insert_fun_nat_bool_decl,type,
insert_fun_nat_bool: $i > $i > $i ).
thf(collect_fun_nat_bool_decl,type,
collect_fun_nat_bool: $i > $i ).
thf(fimplies_decl,type,
fimplies: $i ).
thf(cOMBB_238756964t_bool_decl,type,
cOMBB_238756964t_bool: $i > $i > $i ).
thf(fNot_decl,type,
fNot: $i ).
thf(hAPP_f103356543l_bool_decl,type,
hAPP_f103356543l_bool: $i > $i > $i ).
thf(cOMBC_1693257480l_bool_decl,type,
cOMBC_1693257480l_bool: $i > $i ).
thf(fequal_fun_nat_bool_decl,type,
fequal_fun_nat_bool: $i ).
thf(hAPP_a93125764e_bool_decl,type,
hAPP_a93125764e_bool: $i > $i > $i ).
thf(hAPP_a_fun_a_bool_decl,type,
hAPP_a_fun_a_bool: $i > $i > $i ).
thf(cOMBC_a_a_bool_decl,type,
cOMBC_a_a_bool: $i > $i ).
thf(hAPP_a_fun_bool_bool_decl,type,
hAPP_a_fun_bool_bool: $i > $i > $i ).
thf(cOMBB_1972296269bool_a_decl,type,
cOMBB_1972296269bool_a: $i > $i > $i ).
thf(cOMBB_bool_bool_a_decl,type,
cOMBB_bool_bool_a: $i > $i > $i ).
thf(fdisj_decl,type,
fdisj: $i ).
thf(hAPP_f1246832597l_bool_decl,type,
hAPP_f1246832597l_bool: $i > $i > $i ).
thf(cOMBC_1245412066l_bool_decl,type,
cOMBC_1245412066l_bool: $i > $i ).
thf(member_fun_nat_bool_decl,type,
member_fun_nat_bool: $i ).
thf(hAPP_f1637334154l_bool_decl,type,
hAPP_f1637334154l_bool: $i > $i > $i ).
thf(hAPP_f1772781669l_bool_decl,type,
hAPP_f1772781669l_bool: $i > $i > $i ).
thf(cOMBC_595898202l_bool_decl,type,
cOMBC_595898202l_bool: $i > $i ).
thf(image_nat_pname_decl,type,
image_nat_pname: $i > $i > $i ).
thf(insert_pname_decl,type,
insert_pname: $i > $i > $i ).
thf(collect_pname_decl,type,
collect_pname: $i > $i ).
thf(cOMBS_568398431l_bool_decl,type,
cOMBS_568398431l_bool: $i > $i > $i ).
thf(cOMBB_675860798_pname_decl,type,
cOMBB_675860798_pname: $i > $i > $i ).
thf(hAPP_p61793385e_bool_decl,type,
hAPP_p61793385e_bool: $i > $i > $i ).
thf(cOMBC_1149511130e_bool_decl,type,
cOMBC_1149511130e_bool: $i > $i ).
thf(fequal_pname_decl,type,
fequal_pname: $i ).
thf(image_fun_a_bool_a_decl,type,
image_fun_a_bool_a: $i > $i > $i ).
thf(collec1974731493e_bool_decl,type,
collec1974731493e_bool: $i > $i ).
thf(cOMBS_350070575l_bool_decl,type,
cOMBS_350070575l_bool: $i > $i > $i ).
thf(cOMBB_307249310e_bool_decl,type,
cOMBB_307249310e_bool: $i > $i > $i ).
thf(hAPP_f434788991l_bool_decl,type,
hAPP_f434788991l_bool: $i > $i > $i ).
thf(cOMBC_1284144636l_bool_decl,type,
cOMBC_1284144636l_bool: $i > $i ).
thf(fequal533582459e_bool_decl,type,
fequal533582459e_bool: $i ).
thf(image_349102846bool_a_decl,type,
image_349102846bool_a: $i > $i > $i ).
thf(image_pname_pname_decl,type,
image_pname_pname: $i > $i > $i ).
thf(cOMBB_1015721476ol_nat_decl,type,
cOMBB_1015721476ol_nat: $i > $i > $i ).
thf(hAPP_n1699378549t_bool_decl,type,
hAPP_n1699378549t_bool: $i > $i > $i ).
thf(cOMBC_nat_nat_bool_decl,type,
cOMBC_nat_nat_bool: $i > $i ).
thf(fequal_nat_decl,type,
fequal_nat: $i ).
thf(hAPP_f800510211t_bool_decl,type,
hAPP_f800510211t_bool: $i > $i > $i ).
thf(cOMBC_226598744l_bool_decl,type,
cOMBC_226598744l_bool: $i > $i ).
thf(member_nat_decl,type,
member_nat: $i ).
thf(hAPP_f1434722111l_bool_decl,type,
hAPP_f1434722111l_bool: $i > $i > $i ).
thf(cOMBC_331553030l_bool_decl,type,
cOMBC_331553030l_bool: $i > $i ).
thf(cOMBC_1988546018l_bool_decl,type,
cOMBC_1988546018l_bool: $i > $i ).
thf(member799430823e_bool_decl,type,
member799430823e_bool: $i ).
thf(image_fun_nat_bool_a_decl,type,
image_fun_nat_bool_a: $i > $i > $i ).
thf(is_pname_decl,type,
is_pname: $i > $o ).
thf(cOMBC_pname_a_bool_decl,type,
cOMBC_pname_a_bool: $i > $i ).
thf(hAPP_p1534023578a_bool_decl,type,
hAPP_p1534023578a_bool: $i > $i > $i ).
thf(hAPP_p393069232l_bool_decl,type,
hAPP_p393069232l_bool: $i > $i > $i ).
thf(member_pname_decl,type,
member_pname: $i ).
thf(hAPP_n1025906991e_bool_decl,type,
hAPP_n1025906991e_bool: $i > $i > $i ).
thf(image_112932426a_bool_decl,type,
image_112932426a_bool: $i > $i > $i ).
thf(image_1705983821_pname_decl,type,
image_1705983821_pname: $i > $i > $i ).
thf(image_573985017bool_a_decl,type,
image_573985017bool_a: $i > $i > $i ).
thf(image_nat_a_decl,type,
image_nat_a: $i > $i > $i ).
thf(hAPP_f1951378235l_bool_decl,type,
hAPP_f1951378235l_bool: $i > $i > $i ).
thf(hAPP_f389811538l_bool_decl,type,
hAPP_f389811538l_bool: $i > $i > $i ).
thf(insert_fun_a_bool_decl,type,
insert_fun_a_bool: $i > $i > $i ).
thf(hAPP_f556039215l_bool_decl,type,
hAPP_f556039215l_bool: $i > $i > $i ).
thf(cOMBS_a_bool_bool_decl,type,
cOMBS_a_bool_bool: $i > $i > $i ).
thf(undefined_pname_decl,type,
undefined_pname: $i > $i ).
thf(pname_decl,type,
pname: $i ).
thf(hAPP_f2117159681l_bool_decl,type,
hAPP_f2117159681l_bool: $i > $i > $i ).
thf(image_526090948bool_a_decl,type,
image_526090948bool_a: $i > $i > $i ).
thf(finite_finite_a_decl,type,
finite_finite_a: $i ).
thf(hAPP_f1759205631l_bool_decl,type,
hAPP_f1759205631l_bool: $i > $i > $i ).
thf(cOMBC_336095980l_bool_decl,type,
cOMBC_336095980l_bool: $i > $i ).
thf(image_990671762_pname_decl,type,
image_990671762_pname: $i > $i > $i ).
thf(hAPP_f292226953l_bool_decl,type,
hAPP_f292226953l_bool: $i > $i > $i ).
thf(hAPP_f1050622307l_bool_decl,type,
hAPP_f1050622307l_bool: $i > $i > $i ).
thf(cOMBC_636888218l_bool_decl,type,
cOMBC_636888218l_bool: $i > $i ).
thf(collect_a_decl,type,
collect_a: $i > $i ).
thf(cOMBB_2140588453a_bool_decl,type,
cOMBB_2140588453a_bool: $i > $i > $i ).
thf(hAPP_f22106695ol_nat_decl,type,
hAPP_f22106695ol_nat: $i > $i > $i ).
thf(finite_card_nat_decl,type,
finite_card_nat: $i ).
thf(ord_less_eq_nat_decl,type,
ord_less_eq_nat: $i ).
thf(hAPP_f1363661463l_bool_decl,type,
hAPP_f1363661463l_bool: $i > $i > $i ).
thf(image_a_pname_decl,type,
image_a_pname: $i > $i > $i ).
thf(hAPP_f1295398978l_bool_decl,type,
hAPP_f1295398978l_bool: $i > $i > $i ).
thf(image_1854862208_pname_decl,type,
image_1854862208_pname: $i > $i > $i ).
thf(p_decl,type,
p: $i > $i ).
thf(image_876012084bool_a_decl,type,
image_876012084bool_a: $i > $i > $i ).
thf(hAPP_n215258509l_bool_decl,type,
hAPP_n215258509l_bool: $i > $i > $i ).
thf(hAPP_f2050579477a_bool_decl,type,
hAPP_f2050579477a_bool: $i > $i > $i ).
thf(finite786885583l_bool_decl,type,
finite786885583l_bool: $i ).
thf(image_1642285373l_bool_decl,type,
image_1642285373l_bool: $i > $i > $i ).
thf(finite_finite_nat_decl,type,
finite_finite_nat: $i ).
thf(ord_le1568362934t_bool_decl,type,
ord_le1568362934t_bool: $i ).
thf(finite347923420a_bool_decl,type,
finite347923420a_bool: $i ).
thf(cOMBB_338059395a_bool_decl,type,
cOMBB_338059395a_bool: $i > $i > $i ).
thf(fconj_decl,type,
fconj: $i ).
thf(ord_le313189616e_bool_decl,type,
ord_le313189616e_bool: $i ).
thf(hAPP_f921600141ol_nat_decl,type,
hAPP_f921600141ol_nat: $i > $i > $i ).
thf(finite_card_pname_decl,type,
finite_card_pname: $i ).
thf(hAPP_fun_a_bool_nat_decl,type,
hAPP_fun_a_bool_nat: $i > $i > $i ).
thf(finite_card_a_decl,type,
finite_card_a: $i ).
thf(finite1381704300l_bool_decl,type,
finite1381704300l_bool: $i ).
thf(image_pname_nat_decl,type,
image_pname_nat: $i > $i > $i ).
thf(ord_le1375614389l_bool_decl,type,
ord_le1375614389l_bool: $i ).
thf(finite2012431853t_bool_decl,type,
finite2012431853t_bool: $i ).
thf(collec707592106l_bool_decl,type,
collec707592106l_bool: $i > $i ).
thf(na_decl,type,
na: $i ).
thf(member_a_decl,type,
member_a: $i ).
thf(cOMBC_1355376034l_bool_decl,type,
cOMBC_1355376034l_bool: $i > $i ).
thf(hAPP_f98387925ol_nat_decl,type,
hAPP_f98387925ol_nat: $i > $i > $i ).
thf(finite269641166l_bool_decl,type,
finite269641166l_bool: $i ).
thf(fequal_a_decl,type,
fequal_a: $i ).
thf(hAPP_f2009550088ol_nat_decl,type,
hAPP_f2009550088ol_nat: $i > $i > $i ).
thf(finite1306199131a_bool_decl,type,
finite1306199131a_bool: $i ).
thf(hAPP_f696928925ol_nat_decl,type,
hAPP_f696928925ol_nat: $i > $i > $i ).
thf(finite346522414t_bool_decl,type,
finite346522414t_bool: $i ).
thf(hAPP_f198738859l_bool_decl,type,
hAPP_f198738859l_bool: $i > $i > $i ).
thf(image_fun_a_bool_nat_decl,type,
image_fun_a_bool_nat: $i > $i > $i ).
thf(finite595471783e_bool_decl,type,
finite595471783e_bool: $i ).
thf(finite1491191519l_bool_decl,type,
finite1491191519l_bool: $i ).
thf(collec792590109l_bool_decl,type,
collec792590109l_bool: $i > $i ).
thf(ord_le1375671464l_bool_decl,type,
ord_le1375671464l_bool: $i ).
thf(cOMBC_1732670874l_bool_decl,type,
cOMBC_1732670874l_bool: $i > $i ).
thf(fequal_fun_a_bool_decl,type,
fequal_fun_a_bool: $i ).
thf(cOMBC_1880041174l_bool_decl,type,
cOMBC_1880041174l_bool: $i > $i ).
thf(member_fun_a_bool_decl,type,
member_fun_a_bool: $i ).
thf(hAPP_f285962445l_bool_decl,type,
hAPP_f285962445l_bool: $i > $i > $i ).
thf(ord_le675606854l_bool_decl,type,
ord_le675606854l_bool: $i ).
thf(hAPP_f55526627ol_nat_decl,type,
hAPP_f55526627ol_nat: $i > $i > $i ).
thf(finite1340463720e_bool_decl,type,
finite1340463720e_bool: $i ).
thf(image_2129980159t_bool_decl,type,
image_2129980159t_bool: $i > $i > $i ).
thf(finite1701474069l_bool_decl,type,
finite1701474069l_bool: $i ).
thf(image_2089570637ol_nat_decl,type,
image_2089570637ol_nat: $i > $i > $i ).
thf(finite719726885l_bool_decl,type,
finite719726885l_bool: $i ).
thf(collec1874991203l_bool_decl,type,
collec1874991203l_bool: $i > $i ).
thf(ord_le65145710l_bool_decl,type,
ord_le65145710l_bool: $i ).
thf(image_1551609309ol_nat_decl,type,
image_1551609309ol_nat: $i > $i > $i ).
thf(ord_le1454342156l_bool_decl,type,
ord_le1454342156l_bool: $i ).
thf(image_1874789623l_bool_decl,type,
image_1874789623l_bool: $i > $i > $i ).
thf(collec1015864663l_bool_decl,type,
collec1015864663l_bool: $i > $i ).
thf(cOMBB_1897541054_pname_decl,type,
cOMBB_1897541054_pname: $i > $i > $i ).
thf(hAPP_f1690079119ol_nat_decl,type,
hAPP_f1690079119ol_nat: $i > $i > $i ).
thf(finite1352710292l_bool_decl,type,
finite1352710292l_bool: $i ).
thf(hAPP_f1253658590ol_nat_decl,type,
hAPP_f1253658590ol_nat: $i > $i > $i ).
thf(finite1659325229l_bool_decl,type,
finite1659325229l_bool: $i ).
thf(image_26036933t_bool_decl,type,
image_26036933t_bool: $i > $i > $i ).
thf(image_a_nat_decl,type,
image_a_nat: $i > $i > $i ).
thf(image_496248727ol_nat_decl,type,
image_496248727ol_nat: $i > $i > $i ).
thf(image_1420695166l_bool_decl,type,
image_1420695166l_bool: $i > $i > $i ).
thf(image_1154884483l_bool_decl,type,
image_1154884483l_bool: $i > $i > $i ).
thf(image_1208015684l_bool_decl,type,
image_1208015684l_bool: $i > $i > $i ).
thf(image_1802975832ol_nat_decl,type,
image_1802975832ol_nat: $i > $i > $i ).
thf(finite1343359508l_bool_decl,type,
finite1343359508l_bool: $i ).
thf(collec1635217238l_bool_decl,type,
collec1635217238l_bool: $i > $i ).
thf(ord_le967226251l_bool_decl,type,
ord_le967226251l_bool: $i ).
thf(insert1117693814l_bool_decl,type,
insert1117693814l_bool: $i > $i > $i ).
thf(insert1457093509l_bool_decl,type,
insert1457093509l_bool: $i > $i > $i ).
thf(collec1613912337l_bool_decl,type,
collec1613912337l_bool: $i > $i ).
thf(image_1607900221l_bool_decl,type,
image_1607900221l_bool: $i > $i > $i ).
thf(image_1079571347ol_nat_decl,type,
image_1079571347ol_nat: $i > $i > $i ).
thf(insert2003652156l_bool_decl,type,
insert2003652156l_bool: $i > $i > $i ).
thf(301,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_set__rev__mp) ).
thf(1337,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(399,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( C @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_in__mono) ).
thf(1633,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( C @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(441,axiom,
! [A: $i,B: $i] :
( ( ( A @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
| ( B @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) )
=> ( A @ ( B @ ( fconj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_finite__Collect__conjI) ).
thf(1767,plain,
! [A: $i,B: $i] :
( ( ( A @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
| ( B @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) )
=> ( A @ ( B @ ( fconj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(243,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( member_fun_nat_bool @ hAPP_f1951378235l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_fun_nat_bool ) @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) )
= ( B @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) @ ( suc @ hAPP_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_card__insert__disjoint) ).
thf(1105,plain,
! [A: $i,B: $i] :
( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( member_fun_nat_bool @ hAPP_f1951378235l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_fun_nat_bool ) @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) )
= ( B @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) @ ( suc @ hAPP_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(76,axiom,
! [A: $i,B: $i] :
( ( ( B @ is_fun949378684l_bool )
& ( A @ is_fun_a_bool ) )
=> ( B @ ( A @ insert_fun_a_bool ) @ is_fun949378684l_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_Oinsert_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
thf(628,plain,
! [A: $i,B: $i] :
( ( ( B @ is_fun949378684l_bool )
& ( A @ is_fun_a_bool ) )
=> ( B @ ( A @ insert_fun_a_bool ) @ is_fun949378684l_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(33,axiom,
x_a @ undefined_a @ is_a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_HOL_Oundefined_000t__a) ).
thf(518,plain,
x_a @ undefined_a @ is_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(292,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( fdisj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
| ~ ( B @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fdisj_1_1_U) ).
thf(1295,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( fdisj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
| ~ ( B @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(377,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( B @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) @ ( A @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_card__mono) ).
thf(1549,plain,
! [A: $i,B: $i] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( B @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) @ ( A @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(257,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
<=> ( A @ ( B @ hAPP_pname_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_mem__def) ).
thf(1158,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ hAPP_pname_bool ) @ hBOOL )
=> ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( B @ hAPP_pname_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(324,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( B @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) @ ( B @ ( A @ image_fun_nat_bool_a ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_card__image__le) ).
thf(1406,plain,
! [A: $i,B: $i] :
( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( B @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) @ ( B @ ( A @ image_fun_nat_bool_a ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(116,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun1661590463l_bool )
=> ( B @ ( A @ cOMBS_350070575l_bool ) @ is_fun1661590463l_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__Obool_000t) ).
thf(730,plain,
! [A: $i,B: $i] :
( ( B @ is_fun1661590463l_bool )
=> ( B @ ( A @ cOMBS_350070575l_bool ) @ is_fun1661590463l_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(331,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( A @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_rev__finite__subset) ).
thf(1422,plain,
! [A: $i,B: $i] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( A @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(233,axiom,
! [A: $i,B: $i] :
( ( ( A @ collect_a @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
| ( B @ collect_a @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
=> ( A @ ( B @ ( fconj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_finite__Collect__conjI) ).
thf(1073,plain,
! [A: $i,B: $i] :
( ( ( A @ collect_a @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
| ( B @ collect_a @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
=> ( A @ ( B @ ( fconj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(375,axiom,
! [A: $i,B: $i] :
( ( ( B @ is_fun_a_bool )
& ( A @ is_fun_a_bool ) )
=> ( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( B @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A = B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_card__seteq) ).
thf(1544,plain,
! [A: $i,B: $i] :
( ( ( B @ is_fun_a_bool )
& ( A @ is_fun_a_bool ) )
=> ( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( B @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(427,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_set__rev__mp) ).
thf(1728,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(70,axiom,
! [A: $i,B: $i] : ( B @ ( A @ image_573985017bool_a ) @ is_fun_a_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J_0) ).
thf(614,plain,
! [A: $i,B: $i] : ( B @ ( A @ image_573985017bool_a ) @ is_fun_a_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(63,axiom,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_n1025906991e_bool ) @ is_fun_pname_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).
thf(597,plain,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_n1025906991e_bool ) @ is_fun_pname_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(356,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( suc @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) )
= ( A @ ( B @ minus_minus_nat @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_Suc__diff__le) ).
thf(1486,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( suc @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) )
= ( A @ ( B @ minus_minus_nat @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(436,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( C @ ( A @ insert_nat ) @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_insertI2) ).
thf(1750,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( C @ ( A @ insert_nat ) @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(204,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_338059395a_bool ) @ hAPP_f198738859l_bool ) )
= ( C @ ( B @ hAPP_fun_a_bool_bool ) @ ( A @ hAPP_b589554111l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_008) ).
thf(977,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_338059395a_bool ) @ hAPP_f198738859l_bool ) )
= ( C @ ( B @ hAPP_fun_a_bool_bool ) @ ( A @ hAPP_b589554111l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(174,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_pname_a ) @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_finite__surj) ).
thf(878,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_pname_a ) @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun1661590463l_bool )
=> ( B @ ( A @ image_1283814551_pname ) @ is_fun_pname_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__Opnam) ).
thf(511,plain,
! [A: $i,B: $i] :
( ( B @ is_fun1661590463l_bool )
=> ( B @ ( A @ image_1283814551_pname ) @ is_fun_pname_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(417,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1607900221l_bool ) @ ( finite1701474069l_bool @ hAPP_f937997336l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_finite__imageI) ).
thf(1705,plain,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1607900221l_bool ) @ ( finite1701474069l_bool @ hAPP_f937997336l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(392,axiom,
! [A: $i,B: $i] :
( ( A = B )
=> ~ ( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ~ ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_equalityE) ).
thf(1608,plain,
! [A: $i,B: $i] :
( ( A = B )
=> ~ ( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ~ ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(251,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( fdisj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
<=> ( ( B @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( A @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_finite__Collect__disjI) ).
thf(1137,plain,
! [A: $i,B: $i] :
( ( ( ( B @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( A @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) )
=> ( B @ ( A @ ( fdisj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( fdisj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( A @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun949378684l_bool )
=> ( B @ ( A @ hAPP_f621171935l_bool ) @ is_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J_000tc__) ).
thf(500,plain,
! [A: $i,B: $i] :
( ( B @ is_fun949378684l_bool )
=> ( B @ ( A @ hAPP_f621171935l_bool ) @ is_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(111,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ insert_fun_nat_bool ) )
= ( B @ ( member_fun_nat_bool @ cOMBC_1245412066l_bool @ hAPP_f1246832597l_bool ) @ ( A @ ( fequal_fun_nat_bool @ cOMBC_1693257480l_bool @ hAPP_f103356543l_bool ) @ ( fdisj @ cOMBB_444170502t_bool ) @ cOMBS_1187019125l_bool ) @ collect_fun_nat_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_insert__compr__raw) ).
thf(715,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ insert_fun_nat_bool ) )
= ( B @ ( member_fun_nat_bool @ cOMBC_1245412066l_bool @ hAPP_f1246832597l_bool ) @ ( A @ ( fequal_fun_nat_bool @ cOMBC_1693257480l_bool @ hAPP_f103356543l_bool ) @ ( fdisj @ cOMBB_444170502t_bool ) @ cOMBS_1187019125l_bool ) @ collect_fun_nat_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(283,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1854862208_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_finite__imageI) ).
thf(1275,plain,
! [A: $i,B: $i] :
( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1854862208_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(104,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBS_350070575l_bool ) @ hAPP_f1664156314l_bool ) )
= ( C @ ( B @ hAPP_f1664156314l_bool ) @ ( C @ ( A @ hAPP_f1476298914l_bool ) @ hAPP_bool_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__O) ).
thf(698,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBS_350070575l_bool ) @ hAPP_f1664156314l_bool ) )
= ( C @ ( B @ hAPP_f1664156314l_bool ) @ ( C @ ( A @ hAPP_f1476298914l_bool ) @ hAPP_bool_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(183,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( A @ insert_a ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( B @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_card__insert__le) ).
thf(913,plain,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( A @ insert_a ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( B @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(307,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ insert_nat ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
<=> ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_finite__insert) ).
thf(1354,plain,
! [A: $i,B: $i] :
( ( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( A @ insert_nat ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ insert_nat ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(346,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun_a_bool )
=> ( B @ ( A @ hAPP_f1631501043l_bool ) @ is_fun949378684l_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__a_Mtc__HOL) ).
thf(1458,plain,
! [A: $i,B: $i] :
( ( B @ is_fun_a_bool )
=> ( B @ ( A @ hAPP_f1631501043l_bool ) @ is_fun949378684l_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(258,axiom,
! [A: $i] :
( ( A @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( A @ ( ord_le1454342156l_bool @ cOMBC_595898202l_bool @ hAPP_f1772781669l_bool ) @ collec1015864663l_bool @ ( finite1701474069l_bool @ hAPP_f937997336l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_finite__Collect__subsets) ).
thf(1164,plain,
! [A: $i] :
( ( A @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( A @ ( ord_le1454342156l_bool @ cOMBC_595898202l_bool @ hAPP_f1772781669l_bool ) @ collec1015864663l_bool @ ( finite1701474069l_bool @ hAPP_f937997336l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(142,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_set__mp) ).
thf(797,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(152,axiom,
! [A: $i] :
( ( A @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( A @ ( ord_le1375614389l_bool @ cOMBC_331553030l_bool @ hAPP_f1434722111l_bool ) @ collec707592106l_bool @ ( finite1381704300l_bool @ hAPP_f292226953l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_finite__Collect__subsets) ).
thf(829,plain,
! [A: $i] :
( ( A @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( A @ ( ord_le1375614389l_bool @ cOMBC_331553030l_bool @ hAPP_f1434722111l_bool ) @ collec707592106l_bool @ ( finite1381704300l_bool @ hAPP_f292226953l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(211,axiom,
! [A: $i,B: $i] :
( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_Suc__le__mono) ).
thf(1001,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(136,axiom,
! [A: $i,B: $i] :
( ( ( A @ collect_fun_a_bool @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
| ( B @ collect_fun_a_bool @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL ) )
=> ( A @ ( B @ ( fconj @ cOMBB_338059395a_bool ) @ cOMBS_1035972772l_bool ) @ collect_fun_a_bool @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_finite__Collect__conjI) ).
thf(782,plain,
! [A: $i,B: $i] :
( ( ( A @ collect_fun_a_bool @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
| ( B @ collect_fun_a_bool @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL ) )
=> ( A @ ( B @ ( fconj @ cOMBB_338059395a_bool ) @ cOMBS_1035972772l_bool ) @ collect_fun_a_bool @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(158,axiom,
! [A: $i,B: $i] : ( B @ ( A @ insert_nat ) @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_insertI1) ).
thf(841,plain,
! [A: $i,B: $i] : ( B @ ( A @ insert_nat ) @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(177,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B = A ) )
=> ( C @ ( A @ insert_nat ) @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_insertCI) ).
thf(885,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B = A ) )
=> ( C @ ( A @ insert_nat ) @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(425,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ image_pname_nat ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_finite__imageI) ).
thf(1724,plain,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ image_pname_nat ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(51,axiom,
! [A: $i] :
( ( A @ is_fun_pname_bool )
=> ( ( A @ collect_pname )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_Collect__def) ).
thf(565,plain,
! [A: $i] :
( ( A @ is_fun_pname_bool )
=> ( ( A @ collect_pname )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(369,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_pname ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) )
= ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( suc @ hAPP_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_card__insert__disjoint) ).
thf(1529,plain,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_pname ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) )
= ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( suc @ hAPP_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(275,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( C @ is_a )
=> ( ( B @ ( C @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( C @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) )
=> ( A @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_subsetI) ).
thf(1243,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( C @ is_a )
=> ( ( B @ ( C @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( C @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) )
=> ( A @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(250,axiom,
! [A: $i,B: $i] :
( ( ( B @ is_fun_pname_bool )
& ( A @ is_fun_pname_bool ) )
=> ( ( A = B )
<=> ( ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_set__eq__subset) ).
thf(1127,plain,
! [A: $i,B: $i] :
( ( ( B @ is_fun_pname_bool )
& ( A @ is_fun_pname_bool ) )
=> ( ( ( ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(395,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_1897541054_pname ) @ hAPP_p1534023578a_bool ) )
= ( C @ ( B @ hAPP_pname_a ) @ ( A @ hAPP_a_fun_a_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opna) ).
thf(1623,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_1897541054_pname ) @ hAPP_p1534023578a_bool ) )
= ( C @ ( B @ hAPP_pname_a ) @ ( A @ hAPP_a_fun_a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(355,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A @ ( B @ insert_nat ) @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
<=> ( A @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_subset__insert) ).
thf(1482,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( ( A @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( B @ insert_nat ) @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
& ( ( A @ ( B @ insert_nat ) @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(288,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( C @ ( A @ insert_a ) @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_insertI2) ).
thf(1287,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( C @ ( A @ insert_a ) @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(419,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( B @ ( A @ insert_fun_a_bool ) @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) @ ( B @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_card__insert__le) ).
thf(1709,plain,
! [A: $i,B: $i] :
( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( B @ ( A @ insert_fun_a_bool ) @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) @ ( B @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(53,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ insert_nat ) )
= ( B @ ( member_nat @ cOMBC_226598744l_bool @ hAPP_f800510211t_bool ) @ ( A @ ( fequal_nat @ cOMBC_nat_nat_bool @ hAPP_n1699378549t_bool ) @ ( fdisj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_insert__compr__raw) ).
thf(570,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ insert_nat ) )
= ( B @ ( member_nat @ cOMBC_226598744l_bool @ hAPP_f800510211t_bool ) @ ( A @ ( fequal_nat @ cOMBC_nat_nat_bool @ hAPP_n1699378549t_bool ) @ ( fdisj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(408,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_subsetD) ).
thf(1660,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(72,axiom,
! [A: $i,B: $i] : ( B @ ( A @ image_nat_a ) @ is_fun_a_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__Nat__Onat_000t__a) ).
thf(619,plain,
! [A: $i,B: $i] : ( B @ ( A @ image_nat_a ) @ is_fun_a_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(285,axiom,
! [A: $i,B: $i] :
( ( B @ hBOOL )
| ( A @ hBOOL )
| ~ ( B @ ( A @ ( fdisj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fdisj_3_1_U) ).
thf(1279,plain,
! [A: $i,B: $i] :
( ( B @ hBOOL )
| ( A @ hBOOL )
| ~ ( B @ ( A @ ( fdisj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(345,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_nat ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_insert__absorb) ).
thf(1455,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_nat ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(191,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( ~ ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_pname ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) )
= ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( suc @ hAPP_nat_nat ) ) ) )
& ( ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_pname ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) )
= ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_card__insert__if) ).
thf(934,plain,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( ~ ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_pname ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) )
= ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( suc @ hAPP_nat_nat ) ) ) )
& ( ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_pname ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) )
= ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(348,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1154884483l_bool ) @ ( finite1701474069l_bool @ hAPP_f937997336l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_finite__imageI) ).
thf(1462,plain,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1154884483l_bool ) @ ( finite1701474069l_bool @ hAPP_f937997336l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_595898202l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__H) ).
thf(542,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_595898202l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( B @ is_bool )
=> ( B @ ( A @ hAPP_bool_bool ) @ is_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool) ).
thf(460,plain,
! [A: $i,B: $i] :
( ( B @ is_bool )
=> ( B @ ( A @ hAPP_bool_bool ) @ is_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_bool_bool_a ) @ hAPP_a_bool ) )
= ( C @ ( B @ hAPP_a_bool ) @ ( A @ hAPP_bool_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000t__a_U) ).
thf(559,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_bool_bool_a ) @ hAPP_a_bool ) )
= ( C @ ( B @ hAPP_a_bool ) @ ( A @ hAPP_bool_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(80,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_675860798_pname ) @ hAPP_p393069232l_bool ) )
= ( C @ ( B @ hAPP_pname_bool ) @ ( A @ hAPP_b589554111l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_007) ).
thf(638,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_675860798_pname ) @ hAPP_p393069232l_bool ) )
= ( C @ ( B @ hAPP_pname_bool ) @ ( A @ hAPP_b589554111l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(253,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1874789623l_bool ) @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_finite__imageI) ).
thf(1147,plain,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1874789623l_bool ) @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(385,axiom,
! [A: $i] :
( ( A @ ( finite1381704300l_bool @ hAPP_f292226953l_bool ) @ hBOOL )
=> ( A @ ( ord_le967226251l_bool @ cOMBC_636888218l_bool @ hAPP_f1050622307l_bool ) @ collec1635217238l_bool @ ( finite1343359508l_bool @ hAPP_f1363661463l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_finite__Collect__subsets) ).
thf(1572,plain,
! [A: $i] :
( ( A @ ( finite1381704300l_bool @ hAPP_f292226953l_bool ) @ hBOOL )
=> ( A @ ( ord_le967226251l_bool @ cOMBC_636888218l_bool @ hAPP_f1050622307l_bool ) @ collec1635217238l_bool @ ( finite1343359508l_bool @ hAPP_f1363661463l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(214,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( B @ ( A @ image_fun_a_bool_a ) @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_finite__imageI) ).
thf(1013,plain,
! [A: $i,B: $i] :
( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( B @ ( A @ image_fun_a_bool_a ) @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(320,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_le__SucI) ).
thf(1398,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(245,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
| ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_nat__le__linear) ).
thf(1115,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
| ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(443,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( B @ ( A @ insert1325755072e_bool ) @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) @ ( B @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_card__insert__le) ).
thf(1773,plain,
! [A: $i,B: $i] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( B @ ( A @ insert1325755072e_bool ) @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) @ ( B @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(3,axiom,
! [A: $i,B: $i] : ( B @ ( A @ image_nat_fun_a_bool ) @ is_fun949378684l_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
thf(448,plain,
! [A: $i,B: $i] : ( B @ ( A @ image_nat_fun_a_bool ) @ is_fun949378684l_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(359,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ insert_pname ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_card__insert__le) ).
thf(1494,plain,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ insert_pname ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(294,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun_pname_bool )
=> ( B @ ( A @ image_pname_a ) @ is_fun_a_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__Com__Opname_000t__a) ).
thf(1302,plain,
! [A: $i,B: $i] :
( ( B @ is_fun_pname_bool )
=> ( B @ ( A @ image_pname_a ) @ is_fun_a_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(343,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ ( B @ ( C @ minus_minus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) )
= ( A @ ( C @ minus_minus_nat @ hAPP_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_Nat_Odiff__diff__eq) ).
thf(1450,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ ( B @ ( C @ minus_minus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) )
= ( A @ ( C @ minus_minus_nat @ hAPP_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBS_568398431l_bool ) @ hAPP_pname_bool ) )
= ( C @ ( B @ hAPP_pname_bool ) @ ( C @ ( A @ hAPP_p393069232l_bool ) @ hAPP_bool_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool_U) ).
thf(591,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBS_568398431l_bool ) @ hAPP_pname_bool ) )
= ( C @ ( B @ hAPP_pname_bool ) @ ( C @ ( A @ hAPP_p393069232l_bool ) @ hAPP_bool_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(223,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( A @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_card__mono) ).
thf(1040,plain,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( A @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(83,axiom,
! [A: $i,B: $i] :
( ( ( B @ is_fun_pname_bool )
& ( A @ is_fun1661590463l_bool ) )
=> ( B @ ( A @ hAPP_f1664156314l_bool ) @ is_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__Obool) ).
thf(646,plain,
! [A: $i,B: $i] :
( ( ( B @ is_fun_pname_bool )
& ( A @ is_fun1661590463l_bool ) )
=> ( B @ ( A @ hAPP_f1664156314l_bool ) @ is_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBS_nat_bool_bool ) @ hAPP_nat_bool ) )
= ( C @ ( B @ hAPP_nat_bool ) @ ( C @ ( A @ hAPP_n1006566506l_bool ) @ hAPP_bool_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__HOL__Obool_000tc__HOL__Obool_U) ).
thf(485,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBS_nat_bool_bool ) @ hAPP_nat_bool ) )
= ( C @ ( B @ hAPP_nat_bool ) @ ( C @ ( A @ hAPP_n1006566506l_bool ) @ hAPP_bool_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(387,axiom,
! [A: $i,B: $i] :
( ( ( B @ is_fun_a_bool )
& ( A @ is_fun_a_bool ) )
=> ( ( A = B )
| ~ ( B @ ( A @ ( fequal_fun_a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__fun_It__a_Mtc__HOL__Obool_J_T) ).
thf(1581,plain,
! [A: $i,B: $i] :
( ( ( B @ is_fun_a_bool )
& ( A @ is_fun_a_bool ) )
=> ( ( A = B )
| ~ ( B @ ( A @ ( fequal_fun_a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun_a_bool )
=> ( B @ ( A @ image_a_a ) @ is_fun_a_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000t__a_000t__a) ).
thf(480,plain,
! [A: $i,B: $i] :
( ( B @ is_fun_a_bool )
=> ( B @ ( A @ image_a_a ) @ is_fun_a_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(357,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1705983821_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_finite__imageI) ).
thf(1489,plain,
! [A: $i,B: $i] :
( ( B @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1705983821_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(328,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( A @ image_pname_a ) @ ( B @ ( A @ image_pname_a ) @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_image__mono) ).
thf(1415,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( A @ image_pname_a ) @ ( B @ ( A @ image_pname_a ) @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(228,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ is_fun_a_bool )
=> ( ( C @ ( B @ image_pname_a ) @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
<=> ? [D: $i] :
( ( A
= ( D @ ( B @ image_pname_a ) ) )
& ( C @ ( D @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( D @ is_fun_pname_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_subset__image__iff) ).
thf(1051,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ is_fun_a_bool )
=> ( ( ? [D: $i] :
( ( A
= ( D @ ( B @ image_pname_a ) ) )
& ( C @ ( D @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( D @ is_fun_pname_bool ) )
=> ( C @ ( B @ image_pname_a ) @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
& ( ( C @ ( B @ image_pname_a ) @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ? [D: $i] :
( ( A
= ( D @ ( B @ image_pname_a ) ) )
& ( C @ ( D @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( D @ is_fun_pname_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(150,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_le__trans) ).
thf(821,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(311,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_1880041174l_bool @ hAPP_f2117159681l_bool ) @ hAPP_fun_a_bool_bool ) )
= ( B @ ( C @ ( A @ hAPP_f285962445l_bool ) @ hAPP_f621171935l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__) ).
thf(1377,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_1880041174l_bool @ hAPP_f2117159681l_bool ) @ hAPP_fun_a_bool_bool ) )
= ( B @ ( C @ ( A @ hAPP_f285962445l_bool ) @ hAPP_f621171935l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(270,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ insert_a ) @ ( A @ insert_a ) )
= ( B @ ( A @ insert_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_insert__absorb2) ).
thf(1215,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ insert_a ) @ ( A @ insert_a ) )
= ( B @ ( A @ insert_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(101,axiom,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1363661463l_bool ) @ is_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HO) ).
thf(692,plain,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1363661463l_bool ) @ is_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(118,axiom,
! [A: $i] :
( ( A @ is_fun1661590463l_bool )
=> ( ( A @ collec1974731493e_bool )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_Collect__def) ).
thf(734,plain,
! [A: $i] :
( ( A @ is_fun1661590463l_bool )
=> ( ( A @ collec1974731493e_bool )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(342,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_le__antisym) ).
thf(1447,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(169,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( A @ insert_nat ) @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( B @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_card__insert__le) ).
thf(866,plain,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( A @ insert_nat ) @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( B @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(6,axiom,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f595608956l_bool ) @ is_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Oboo) ).
thf(453,plain,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f595608956l_bool ) @ is_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(318,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( B @ ( A @ image_47868345e_bool ) @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_card__image__le) ).
thf(1394,plain,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( B @ ( A @ image_47868345e_bool ) @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(87,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun949378684l_bool )
=> ( B @ ( A @ hAPP_f2117159681l_bool ) @ is_fun949378684l_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J_000tc___004) ).
thf(660,plain,
! [A: $i,B: $i] :
( ( B @ is_fun949378684l_bool )
=> ( B @ ( A @ hAPP_f2117159681l_bool ) @ is_fun949378684l_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(390,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( A @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_finite__subset) ).
thf(1600,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( A @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(367,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( fconj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
| ~ ( A @ hBOOL )
| ~ ( B @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
thf(1521,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( fconj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
| ~ ( A @ hBOOL )
| ~ ( B @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( B @ is_a )
=> ( B @ ( A @ hAPP_a85458249l_bool ) @ is_fun949378684l_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000t__a_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J) ).
thf(507,plain,
! [A: $i,B: $i] :
( ( B @ is_a )
=> ( B @ ( A @ hAPP_a85458249l_bool ) @ is_fun949378684l_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(37,axiom,
! [A: $i] :
( A
!= ( A @ ( suc @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_n__not__Suc__n) ).
thf(527,plain,
! [A: $i] :
( A
!= ( A @ ( suc @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(383,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
<=> ( A @ ( B @ hAPP_a_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_mem__def) ).
thf(1564,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ hAPP_a_bool ) @ hBOOL )
=> ( B @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( B @ hAPP_a_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(305,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( fdisj @ cOMBB_444170502t_bool ) @ cOMBS_1187019125l_bool ) @ collect_fun_nat_bool @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
<=> ( ( B @ collect_fun_nat_bool @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
& ( A @ collect_fun_nat_bool @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_finite__Collect__disjI) ).
thf(1345,plain,
! [A: $i,B: $i] :
( ( ( ( B @ collect_fun_nat_bool @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
& ( A @ collect_fun_nat_bool @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL ) )
=> ( B @ ( A @ ( fdisj @ cOMBB_444170502t_bool ) @ cOMBS_1187019125l_bool ) @ collect_fun_nat_bool @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( fdisj @ cOMBB_444170502t_bool ) @ cOMBS_1187019125l_bool ) @ collect_fun_nat_bool @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ collect_fun_nat_bool @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
& ( A @ collect_fun_nat_bool @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(208,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( fdisj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
<=> ( ( B @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
& ( A @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_finite__Collect__disjI) ).
thf(988,plain,
! [A: $i,B: $i] :
( ( ( ( B @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
& ( A @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) )
=> ( B @ ( A @ ( fdisj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( fdisj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
& ( A @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(266,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ image_pname_a ) @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_finite__imageI) ).
thf(1206,plain,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ image_pname_a ) @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(187,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( C @ ( A @ insert_nat ) @ ( B @ ( A @ insert_nat ) @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_insert__mono) ).
thf(920,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( C @ ( A @ insert_nat ) @ ( B @ ( A @ insert_nat ) @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(193,axiom,
! [A: $i] : ( A @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_order__refl) ).
thf(942,plain,
! [A: $i] : ( A @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(95,axiom,
! [A: $i,B: $i] :
( ( B @ is_pname )
=> ( B @ ( A @ hAPP_p338031245l_bool ) @ is_fun1661590463l_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obo) ).
thf(678,plain,
! [A: $i,B: $i] :
( ( B @ is_pname )
=> ( B @ ( A @ hAPP_p338031245l_bool ) @ is_fun1661590463l_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(337,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( B @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) @ ( B @ ( A @ image_1551609309ol_nat ) @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_card__image__le) ).
thf(1438,plain,
! [A: $i,B: $i] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( B @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) @ ( B @ ( A @ image_1551609309ol_nat ) @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(265,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( fdisj @ cOMBB_338059395a_bool ) @ cOMBS_1035972772l_bool ) @ collect_fun_a_bool @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
<=> ( ( B @ collect_fun_a_bool @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
& ( A @ collect_fun_a_bool @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_finite__Collect__disjI) ).
thf(1199,plain,
! [A: $i,B: $i] :
( ( ( ( B @ collect_fun_a_bool @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
& ( A @ collect_fun_a_bool @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL ) )
=> ( B @ ( A @ ( fdisj @ cOMBB_338059395a_bool ) @ cOMBS_1035972772l_bool ) @ collect_fun_a_bool @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( fdisj @ cOMBB_338059395a_bool ) @ cOMBS_1035972772l_bool ) @ collect_fun_a_bool @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ collect_fun_a_bool @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
& ( A @ collect_fun_a_bool @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(147,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( A @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_finite__subset) ).
thf(810,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( A @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(351,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_set__rev__mp) ).
thf(1470,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_1972296269bool_a ) @ hAPP_a_fun_bool_bool ) )
= ( C @ ( B @ hAPP_a_bool ) @ ( A @ hAPP_b589554111l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo) ).
thf(534,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_1972296269bool_a ) @ hAPP_a_fun_bool_bool ) )
= ( C @ ( B @ hAPP_a_bool ) @ ( A @ hAPP_b589554111l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(430,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( B @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) @ ( B @ ( A @ image_496248727ol_nat ) @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_card__image__le) ).
thf(1736,plain,
! [A: $i,B: $i] :
( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( B @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) @ ( B @ ( A @ image_496248727ol_nat ) @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(255,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( C @ ( A @ insert_nat ) @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_subset__insertI2) ).
thf(1153,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( C @ ( A @ insert_nat ) @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(128,axiom,
! [A: $i] :
( ( A @ is_fun1661590463l_bool )
=> ( A @ collec1974731493e_bool @ is_fun1661590463l_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_OCollect_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).
thf(761,plain,
! [A: $i] :
( ( A @ is_fun1661590463l_bool )
=> ( A @ collec1974731493e_bool @ is_fun1661590463l_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(226,axiom,
! [A: $i] :
( ( A @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( ord_le1311769555a_bool @ cOMBC_1732670874l_bool @ hAPP_f1631501043l_bool ) @ collect_fun_a_bool @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_finite__Collect__subsets) ).
thf(1047,plain,
! [A: $i] :
( ( A @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( ord_le1311769555a_bool @ cOMBC_1732670874l_bool @ hAPP_f1631501043l_bool ) @ collect_fun_a_bool @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(428,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite1701474069l_bool @ hAPP_f937997336l_bool ) @ hBOOL )
=> ( B @ ( A @ insert2003652156l_bool ) @ ( finite1701474069l_bool @ hAPP_f937997336l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_finite_OinsertI) ).
thf(1730,plain,
! [A: $i,B: $i] :
( ( B @ ( finite1701474069l_bool @ hAPP_f937997336l_bool ) @ hBOOL )
=> ( B @ ( A @ insert2003652156l_bool ) @ ( finite1701474069l_bool @ hAPP_f937997336l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(304,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( fimplies @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
| ~ ( B @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fimplies_2_1_U) ).
thf(1343,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( fimplies @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
| ~ ( B @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(224,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_2140588453a_bool ) @ hAPP_fun_a_bool_bool ) )
= ( C @ ( B @ hAPP_fun_a_bool_bool ) @ ( A @ hAPP_bool_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_It__a_Mtc__H) ).
thf(1042,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_2140588453a_bool ) @ hAPP_fun_a_bool_bool ) )
= ( C @ ( B @ hAPP_fun_a_bool_bool ) @ ( A @ hAPP_bool_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(362,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( A @ insert_nat ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_finite_OinsertI) ).
thf(1502,plain,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( A @ insert_nat ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(77,axiom,
! [A: $i,B: $i] :
( ( B @ is_pname )
=> ( B @ ( A @ hAPP_p1534023578a_bool ) @ is_fun_a_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Com__Opname_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
thf(630,plain,
! [A: $i,B: $i] :
( ( B @ is_pname )
=> ( B @ ( A @ hAPP_p1534023578a_bool ) @ is_fun_a_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(149,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B = A ) )
=> ( C @ ( A @ insert_pname ) @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_insertCI) ).
thf(815,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B = A ) )
=> ( C @ ( A @ insert_pname ) @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(382,axiom,
! [A: $i,B: $i] :
( ( A = B )
=> ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_equalityD1) ).
thf(1560,plain,
! [A: $i,B: $i] :
( ( A = B )
=> ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(199,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ insert_fun_a_bool ) )
= ( B @ ( member_fun_a_bool @ cOMBC_1880041174l_bool @ hAPP_f2117159681l_bool ) @ ( A @ ( fequal_fun_a_bool @ cOMBC_1732670874l_bool @ hAPP_f1631501043l_bool ) @ ( fdisj @ cOMBB_338059395a_bool ) @ cOMBS_1035972772l_bool ) @ collect_fun_a_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_insert__compr) ).
thf(957,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ insert_fun_a_bool ) )
= ( B @ ( member_fun_a_bool @ cOMBC_1880041174l_bool @ hAPP_f2117159681l_bool ) @ ( A @ ( fequal_fun_a_bool @ cOMBC_1732670874l_bool @ hAPP_f1631501043l_bool ) @ ( fdisj @ cOMBB_338059395a_bool ) @ cOMBS_1035972772l_bool ) @ collect_fun_a_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(179,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( B @ p @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_assms_I1_J) ).
thf(894,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( B @ p @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(218,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
<=> ( A @ ( B @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_mem__def) ).
thf(1021,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( B @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(134,axiom,
! [A: $i] : ( A @ ( ord_less_eq_nat @ cOMBC_nat_nat_bool @ hAPP_n1699378549t_bool ) @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_finite__Collect__le__nat) ).
thf(778,plain,
! [A: $i] : ( A @ ( ord_less_eq_nat @ cOMBC_nat_nat_bool @ hAPP_n1699378549t_bool ) @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(248,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( A @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_rev__finite__subset) ).
thf(1123,plain,
! [A: $i,B: $i] :
( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( A @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(167,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL )
=> ( B @ ( finite269641166l_bool @ hAPP_f98387925ol_nat ) @ ( B @ ( A @ image_349102846bool_a ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_card__image__le) ).
thf(862,plain,
! [A: $i,B: $i] :
( ( B @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL )
=> ( B @ ( finite269641166l_bool @ hAPP_f98387925ol_nat ) @ ( B @ ( A @ image_349102846bool_a ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(384,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( B @ ( A @ image_fun_a_bool_nat ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_finite__imageI) ).
thf(1570,plain,
! [A: $i,B: $i] :
( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( B @ ( A @ image_fun_a_bool_nat ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(260,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( B @ ( A @ insert_fun_a_bool ) @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_finite_OinsertI) ).
thf(1174,plain,
! [A: $i,B: $i] :
( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( B @ ( A @ insert_fun_a_bool ) @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(412,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ insert_a ) @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
<=> ( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( C @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_insert__subset) ).
thf(1676,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( C @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
=> ( C @ ( B @ ( A @ insert_a ) @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
& ( ( C @ ( B @ ( A @ insert_a ) @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( C @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(138,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] : ( D @ ( suc @ hAPP_nat_nat ) @ ( C @ hAPP_n1025906991e_bool ) @ ( D @ ( C @ hAPP_n1025906991e_bool ) @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( C @ hAPP_n1025906991e_bool ) @ ( A @ ( C @ hAPP_n1025906991e_bool ) @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_lift__Suc__mono__le) ).
thf(788,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] : ( D @ ( suc @ hAPP_nat_nat ) @ ( C @ hAPP_n1025906991e_bool ) @ ( D @ ( C @ hAPP_n1025906991e_bool ) @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( C @ hAPP_n1025906991e_bool ) @ ( A @ ( C @ hAPP_n1025906991e_bool ) @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(309,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( fequal533582459e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
| ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T) ).
thf(1370,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( fequal533582459e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(161,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_1355376034l_bool @ hAPP_f2050579477a_bool ) @ hAPP_a_bool ) )
= ( B @ ( C @ ( A @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Oboo) ).
thf(847,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_1355376034l_bool @ hAPP_f2050579477a_bool ) @ hAPP_a_bool ) )
= ( B @ ( C @ ( A @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(379,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite1381704300l_bool @ hAPP_f292226953l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1802975832ol_nat ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_finite__imageI) ).
thf(1555,plain,
! [A: $i,B: $i] :
( ( B @ ( finite1381704300l_bool @ hAPP_f292226953l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1802975832ol_nat ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(90,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ insert_nat ) )
= ( B @ ( member_nat @ cOMBC_226598744l_bool @ hAPP_f800510211t_bool ) @ ( A @ ( fequal_nat @ cOMBC_nat_nat_bool @ hAPP_n1699378549t_bool ) @ ( fdisj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_insert__compr) ).
thf(665,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ insert_nat ) )
= ( B @ ( member_nat @ cOMBC_226598744l_bool @ hAPP_f800510211t_bool ) @ ( A @ ( fequal_nat @ cOMBC_nat_nat_bool @ hAPP_n1699378549t_bool ) @ ( fdisj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(414,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( C @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_in__mono) ).
thf(1687,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( C @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( B @ collect_fun_nat_bool @ ( A @ insert_fun_nat_bool ) )
= ( B @ ( A @ ( fequal_fun_nat_bool @ cOMBC_1693257480l_bool @ hAPP_f103356543l_bool ) @ ( fNot @ cOMBB_238756964t_bool ) @ ( fimplies @ cOMBB_444170502t_bool ) @ cOMBS_1187019125l_bool ) @ collect_fun_nat_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_insert__Collect) ).
thf(522,plain,
! [A: $i,B: $i] :
( ( B @ collect_fun_nat_bool @ ( A @ insert_fun_nat_bool ) )
= ( B @ ( A @ ( fequal_fun_nat_bool @ cOMBC_1693257480l_bool @ hAPP_f103356543l_bool ) @ ( fNot @ cOMBB_238756964t_bool ) @ ( fimplies @ cOMBB_444170502t_bool ) @ cOMBS_1187019125l_bool ) @ collect_fun_nat_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(219,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( A @ image_pname_a ) @ ( B @ ( A @ hAPP_pname_a ) @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_imageI) ).
thf(1027,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( A @ image_pname_a ) @ ( B @ ( A @ hAPP_pname_a ) @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(97,axiom,
! [A: $i] :
( ( A @ is_fun_a_bool )
=> ( A @ collect_a @ is_fun_a_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_OCollect_000t__a) ).
thf(682,plain,
! [A: $i] :
( ( A @ is_fun_a_bool )
=> ( A @ collect_a @ is_fun_a_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(286,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ insert_a ) @ ( A @ insert_a ) )
= ( C @ ( A @ insert_a ) @ ( B @ insert_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_insert__commute) ).
thf(1281,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ insert_a ) @ ( A @ insert_a ) )
= ( C @ ( A @ insert_a ) @ ( B @ insert_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(317,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( C @ minus_minus_nat @ hAPP_nat_nat ) @ ( A @ ( B @ minus_minus_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_diff__le__mono) ).
thf(1392,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( C @ minus_minus_nat @ hAPP_nat_nat ) @ ( A @ ( B @ minus_minus_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(432,axiom,
! [A: $i,B: $i] :
( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A
= ( B @ ( suc @ hAPP_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_le__SucE) ).
thf(1740,plain,
! [A: $i,B: $i] :
( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A
= ( B @ ( suc @ hAPP_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(203,axiom,
! [A: $i,B: $i] :
( ( ( B @ is_a )
& ( A @ is_a ) )
=> ( ( A = B )
| ~ ( B @ ( A @ ( fequal_a @ hAPP_a_fun_a_bool ) @ hAPP_a_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000t__a_T) ).
thf(974,plain,
! [A: $i,B: $i] :
( ( ( B @ is_a )
& ( A @ is_a ) )
=> ( ( A = B )
| ~ ( B @ ( A @ ( fequal_a @ hAPP_a_fun_a_bool ) @ hAPP_a_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(185,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( A @ image_a_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_finite__imageI) ).
thf(916,plain,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( A @ image_a_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(12,axiom,
! [A: $i,B: $i] : ( B @ ( A @ image_1921560913_pname ) @ is_fun_pname_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Com__Opname) ).
thf(467,plain,
! [A: $i,B: $i] : ( B @ ( A @ image_1921560913_pname ) @ is_fun_pname_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(221,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ insert_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
<=> ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_finite__insert) ).
thf(1032,plain,
! [A: $i,B: $i] :
( ( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ insert_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ insert_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(391,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ insert_fun_a_bool ) @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
<=> ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_finite__insert) ).
thf(1602,plain,
! [A: $i,B: $i] :
( ( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( B @ ( A @ insert_fun_a_bool ) @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ insert_fun_a_bool ) @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(268,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( B @ ( A @ image_fun_nat_bool_a ) @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_finite__imageI) ).
thf(1210,plain,
! [A: $i,B: $i] :
( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( B @ ( A @ image_fun_nat_bool_a ) @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(406,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1921560913_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_finite__imageI) ).
thf(1656,plain,
! [A: $i,B: $i] :
( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1921560913_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(290,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite1381704300l_bool @ hAPP_f292226953l_bool ) @ hBOOL )
=> ( B @ ( finite1659325229l_bool @ hAPP_f1253658590ol_nat ) @ ( B @ ( A @ image_573985017bool_a ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_card__image__le) ).
thf(1291,plain,
! [A: $i,B: $i] :
( ( B @ ( finite1381704300l_bool @ hAPP_f292226953l_bool ) @ hBOOL )
=> ( B @ ( finite1659325229l_bool @ hAPP_f1253658590ol_nat ) @ ( B @ ( A @ image_573985017bool_a ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(109,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun_a_bool )
=> ( B @ ( A @ cOMBS_a_bool_bool ) @ is_fun_a_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_COMBS_000t__a_000tc__HOL__Obool_000tc__HOL__Obool) ).
thf(710,plain,
! [A: $i,B: $i] :
( ( B @ is_fun_a_bool )
=> ( B @ ( A @ cOMBS_a_bool_bool ) @ is_fun_a_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(322,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] : ( D @ ( suc @ hAPP_nat_nat ) @ ( C @ hAPP_n1699378549t_bool ) @ ( D @ ( C @ hAPP_n1699378549t_bool ) @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( C @ hAPP_n1699378549t_bool ) @ ( A @ ( C @ hAPP_n1699378549t_bool ) @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_lift__Suc__mono__le) ).
thf(1402,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] : ( D @ ( suc @ hAPP_nat_nat ) @ ( C @ hAPP_n1699378549t_bool ) @ ( D @ ( C @ hAPP_n1699378549t_bool ) @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( C @ hAPP_n1699378549t_bool ) @ ( A @ ( C @ hAPP_n1699378549t_bool ) @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(308,axiom,
! [A: $i,B: $i] :
( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( ( A
= ( B @ ( suc @ hAPP_nat_nat ) ) )
| ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_le__Suc__eq) ).
thf(1360,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( B @ ( suc @ hAPP_nat_nat ) ) )
| ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A
= ( B @ ( suc @ hAPP_nat_nat ) ) )
| ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(374,axiom,
! [A: $i,B: $i] :
( ( ( B @ is_fun_pname_bool )
& ( A @ is_fun_pname_bool ) )
=> ( ( A = B )
| ~ ( B @ ( A @ ( fequal533582459e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T) ).
thf(1541,plain,
! [A: $i,B: $i] :
( ( ( B @ is_fun_pname_bool )
& ( A @ is_fun_pname_bool ) )
=> ( ( A = B )
| ~ ( B @ ( A @ ( fequal533582459e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(172,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( B @ ( A @ image_112932426a_bool ) @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_card__image__le) ).
thf(874,plain,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( B @ ( A @ image_112932426a_bool ) @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(281,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_rev__finite__subset) ).
thf(1270,plain,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(195,axiom,
! [A: $i] : ( A @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_subset__refl) ).
thf(948,plain,
! [A: $i] : ( A @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(231,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ is_fun_pname_bool )
& ( A @ is_fun_pname_bool ) )
=> ( ~ ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ~ ( A @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( ( C @ ( B @ insert_pname ) )
= ( A @ ( B @ insert_pname ) ) )
<=> ( C = A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_insert__ident) ).
thf(1064,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ is_fun_pname_bool )
& ( A @ is_fun_pname_bool ) )
=> ( ~ ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ~ ( A @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( ( C = A )
=> ( ( C @ ( B @ insert_pname ) )
= ( A @ ( B @ insert_pname ) ) ) )
& ( ( ( C @ ( B @ insert_pname ) )
= ( A @ ( B @ insert_pname ) ) )
=> ( C = A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(114,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun1661590463l_bool )
=> ( B @ ( A @ image_876012084bool_a ) @ is_fun_a_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000t__a) ).
thf(725,plain,
! [A: $i,B: $i] :
( ( B @ is_fun1661590463l_bool )
=> ( B @ ( A @ image_876012084bool_a ) @ is_fun_a_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(205,axiom,
! [A: $i,B: $i] :
( ( ( B @ is_fun1661590463l_bool )
& ( A @ is_fun1661590463l_bool ) )
=> ( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( A @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) @ ( B @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A = B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_card__seteq) ).
thf(980,plain,
! [A: $i,B: $i] :
( ( ( B @ is_fun1661590463l_bool )
& ( A @ is_fun1661590463l_bool ) )
=> ( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( A @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) @ ( B @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(410,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_diff__le__self) ).
thf(1672,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(423,axiom,
! [A: $i,B: $i] :
( ( B @ hBOOL )
| ~ ( B @ ( A @ ( fconj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
thf(1719,plain,
! [A: $i,B: $i] :
( ( B @ hBOOL )
| ~ ( B @ ( A @ ( fconj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(68,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun_pname_bool )
=> ( B @ ( A @ image_112932426a_bool ) @ is_fun949378684l_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__Com__Opname_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
thf(610,plain,
! [A: $i,B: $i] :
( ( B @ is_fun_pname_bool )
=> ( B @ ( A @ image_112932426a_bool ) @ is_fun949378684l_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(165,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( A @ image_nat_a ) @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_finite__imageI) ).
thf(857,plain,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( A @ image_nat_a ) @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ insert_nat ) @ ( A @ insert_nat ) )
= ( B @ ( A @ insert_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_insert__absorb2) ).
thf(519,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ insert_nat ) @ ( A @ insert_nat ) )
= ( B @ ( A @ insert_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(56,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_331553030l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool) ).
thf(578,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_331553030l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(371,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( A @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_card__mono) ).
thf(1534,plain,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( A @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(216,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_finite__subset) ).
thf(1017,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_7971162l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_) ).
thf(471,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_7971162l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(413,axiom,
! [A: $i,B: $i] :
( ( A = B )
=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_eq__imp__le) ).
thf(1683,plain,
! [A: $i,B: $i] :
( ( A = B )
=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(236,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( A @ insert_pname ) @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_subset__insertI2) ).
thf(1082,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( A @ insert_pname ) @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_647938656_pname ) @ hAPP_pname_bool ) )
= ( C @ ( B @ hAPP_pname_bool ) @ ( A @ hAPP_bool_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname_U) ).
thf(488,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_647938656_pname ) @ hAPP_pname_bool ) )
= ( C @ ( B @ hAPP_pname_bool ) @ ( A @ hAPP_bool_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(47,axiom,
! [A: $i,B: $i] :
( ( B @ collec1974731493e_bool @ ( A @ insert1325755072e_bool ) )
= ( B @ ( A @ ( fequal533582459e_bool @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ ( fNot @ cOMBB_307249310e_bool ) @ ( fimplies @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_insert__Collect) ).
thf(554,plain,
! [A: $i,B: $i] :
( ( B @ collec1974731493e_bool @ ( A @ insert1325755072e_bool ) )
= ( B @ ( A @ ( fequal533582459e_bool @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ ( fNot @ cOMBB_307249310e_bool ) @ ( fimplies @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(40,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun_a_bool )
=> ( B @ ( A @ cOMBB_bool_bool_a ) @ is_fun_a_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000t__a) ).
thf(537,plain,
! [A: $i,B: $i] :
( ( B @ is_fun_a_bool )
=> ( B @ ( A @ cOMBB_bool_bool_a ) @ is_fun_a_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(99,axiom,
! [A: $i] :
( ( A @ ( ord_less_eq_nat @ cOMBC_nat_nat_bool @ hAPP_n1699378549t_bool ) @ collect_nat @ ( finite_card_nat @ hAPP_f22106695ol_nat ) )
= ( A @ ( suc @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_card__Collect__le__nat) ).
thf(686,plain,
! [A: $i] :
( ( A @ ( ord_less_eq_nat @ cOMBC_nat_nat_bool @ hAPP_n1699378549t_bool ) @ collect_nat @ ( finite_card_nat @ hAPP_f22106695ol_nat ) )
= ( A @ ( suc @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(332,axiom,
! [A: $i,B: $i] :
( ( ( B @ is_pname )
& ( A @ is_pname ) )
=> ( ( A = B )
| ~ ( B @ ( A @ ( fequal_pname @ hAPP_p61793385e_bool ) @ hAPP_pname_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Com__Opname_T) ).
thf(1424,plain,
! [A: $i,B: $i] :
( ( ( B @ is_pname )
& ( A @ is_pname ) )
=> ( ( A = B )
| ~ ( B @ ( A @ ( fequal_pname @ hAPP_p61793385e_bool ) @ hAPP_pname_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(388,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B = A ) )
=> ( C @ ( A @ insert_a ) @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_insertCI) ).
thf(1584,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B = A ) )
=> ( C @ ( A @ insert_a ) @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(107,axiom,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f292226953l_bool ) @ is_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_) ).
thf(706,plain,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f292226953l_bool ) @ is_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(256,axiom,
! [A: $i,B: $i] :
( ( A @ hBOOL )
| ~ ( B @ ( A @ ( fconj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
thf(1155,plain,
! [A: $i,B: $i] :
( ( A @ hBOOL )
| ~ ( B @ ( A @ ( fconj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(44,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun_pname_bool )
=> ( B @ ( A @ cOMBB_647938656_pname ) @ is_fun_pname_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname) ).
thf(547,plain,
! [A: $i,B: $i] :
( ( B @ is_fun_pname_bool )
=> ( B @ ( A @ cOMBB_647938656_pname ) @ is_fun_pname_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(156,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( C @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_set__mp) ).
thf(837,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( C @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(240,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( A @ image_nat_fun_a_bool ) @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_finite__imageI) ).
thf(1099,plain,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( A @ image_nat_fun_a_bool ) @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(105,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ insert1325755072e_bool ) )
= ( B @ ( member799430823e_bool @ cOMBC_1988546018l_bool @ hAPP_f559147733l_bool ) @ ( A @ ( fequal533582459e_bool @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ ( fdisj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_insert__compr__raw) ).
thf(701,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ insert1325755072e_bool ) )
= ( B @ ( member799430823e_bool @ cOMBC_1988546018l_bool @ hAPP_f559147733l_bool ) @ ( A @ ( fequal533582459e_bool @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ ( fdisj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(353,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( B @ ( A @ image_a_nat ) @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_card__image__le) ).
thf(1478,plain,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( B @ ( A @ image_a_nat ) @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(293,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( D @ is_pname )
=> ( ( C @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( D @ ( A @ hAPP_pname_a ) @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) )
=> ( B @ ( C @ ( A @ image_pname_a ) @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_image__subsetI) ).
thf(1297,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( D @ is_pname )
=> ( ( C @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( D @ ( A @ hAPP_pname_a ) @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) )
=> ( B @ ( C @ ( A @ image_pname_a ) @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(313,axiom,
! [A: $i] : ( A @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_le__refl) ).
thf(1382,plain,
! [A: $i] : ( A @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(279,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_rev__finite__subset) ).
thf(1266,plain,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(264,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ insert_nat ) @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
<=> ( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
& ( C @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_insert__subset) ).
thf(1192,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
& ( C @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
=> ( C @ ( B @ ( A @ insert_nat ) @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
& ( ( C @ ( B @ ( A @ insert_nat ) @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
& ( C @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ collect_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_Collect__def) ).
thf(457,plain,
! [A: $i] :
( ( A @ collect_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(182,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( B @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) @ ( B @ ( A @ image_fun_a_bool_nat ) @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_card__image__le) ).
thf(911,plain,
! [A: $i,B: $i] :
( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( B @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) @ ( B @ ( A @ image_fun_a_bool_nat ) @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(113,axiom,
! [A: $i] :
( ( A @ ( suc @ hAPP_nat_nat ) )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_Suc__n__not__n) ).
thf(721,plain,
! [A: $i] :
( ( A @ ( suc @ hAPP_nat_nat ) )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(334,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ insert_nat ) @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A != B )
=> ( C @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_insertE) ).
thf(1429,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ insert_nat ) @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A != B )
=> ( C @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(336,axiom,
! [A: $i,B: $i] :
( ( A = B )
=> ( A @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_equalityD2) ).
thf(1434,plain,
! [A: $i,B: $i] :
( ( A = B )
=> ( A @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(297,axiom,
! [A: $i] : ( A @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_order__refl) ).
thf(1318,plain,
! [A: $i] : ( A @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(140,axiom,
! [A: $i,B: $i] :
( ( ( B @ is_fun_a_bool )
& ( A @ is_fun_a_bool ) )
=> ( ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_equalityI) ).
thf(792,plain,
! [A: $i,B: $i] :
( ( ( B @ is_fun_a_bool )
& ( A @ is_fun_a_bool ) )
=> ( ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(446,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( A @ ( B @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_not__less__eq__eq) ).
thf(1779,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ~ ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ~ ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( B @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(145,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_nat ) @ ( finite_card_nat @ hAPP_f22106695ol_nat ) )
= ( B @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( suc @ hAPP_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_card__insert__disjoint) ).
thf(805,plain,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_nat ) @ ( finite_card_nat @ hAPP_f22106695ol_nat ) )
= ( B @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( suc @ hAPP_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(416,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ is_pname )
& ( A @ is_pname ) )
=> ( ( C @ ( B @ insert_pname ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
<=> ( ( C @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_insert__iff) ).
thf(1695,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ is_pname )
& ( A @ is_pname ) )
=> ( ( ( ( C @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
| ( A = B ) )
=> ( C @ ( B @ insert_pname ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
& ( ( C @ ( B @ insert_pname ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
| ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(130,axiom,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_nat_bool ) @ is_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool) ).
thf(765,plain,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_nat_bool ) @ is_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(232,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite1701474069l_bool @ hAPP_f937997336l_bool ) @ hBOOL )
=> ( B @ ( A @ image_2089570637ol_nat ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_finite__imageI) ).
thf(1071,plain,
! [A: $i,B: $i] :
( ( B @ ( finite1701474069l_bool @ hAPP_f937997336l_bool ) @ hBOOL )
=> ( B @ ( A @ image_2089570637ol_nat ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(365,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ insert_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_finite_OinsertI) ).
thf(1515,plain,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ insert_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(393,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( C @ is_pname )
=> ( ( B @ ( C @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( C @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) )
=> ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_subsetI) ).
thf(1616,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( C @ is_pname )
=> ( ( B @ ( C @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( C @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) )
=> ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(59,axiom,
! [A: $i,B: $i] :
( ( B @ is_pname )
=> ( B @ ( A @ hAPP_p61793385e_bool ) @ is_fun_pname_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).
thf(586,plain,
! [A: $i,B: $i] :
( ( B @ is_pname )
=> ( B @ ( A @ hAPP_p61793385e_bool ) @ is_fun_pname_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(429,axiom,
! [A: $i,B: $i] :
( ( A = B )
=> ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_equalityD2) ).
thf(1732,plain,
! [A: $i,B: $i] :
( ( A = B )
=> ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(189,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( ~ ( B @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_a ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) )
= ( B @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( suc @ hAPP_nat_nat ) ) ) )
& ( ( B @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_a ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) )
= ( B @ ( finite_card_a @ hAPP_fun_a_bool_nat ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_card__insert__if) ).
thf(926,plain,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( ~ ( B @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_a ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) )
= ( B @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( suc @ hAPP_nat_nat ) ) ) )
& ( ( B @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_a ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) )
= ( B @ ( finite_card_a @ hAPP_fun_a_bool_nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(198,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( B @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
=> ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_subsetI) ).
thf(953,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( B @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
=> ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(263,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ insert_pname ) @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
<=> ( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( C @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_insert__subset) ).
thf(1185,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( C @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
=> ( C @ ( B @ ( A @ insert_pname ) @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
& ( ( C @ ( B @ ( A @ insert_pname ) @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( C @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(88,axiom,
! [A: $i,B: $i] : ( B @ ( A @ image_526090948bool_a ) @ is_fun_a_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HOL__) ).
thf(662,plain,
! [A: $i,B: $i] : ( B @ ( A @ image_526090948bool_a ) @ is_fun_a_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(112,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ insert_nat ) @ ( A @ insert_nat ) )
= ( C @ ( A @ insert_nat ) @ ( B @ insert_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_insert__commute) ).
thf(718,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ insert_nat ) @ ( A @ insert_nat ) )
= ( C @ ( A @ insert_nat ) @ ( B @ insert_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(405,axiom,
! [A: $i,B: $i] :
( ( A = B )
=> ~ ( ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ~ ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_equalityE) ).
thf(1648,plain,
! [A: $i,B: $i] :
( ( A = B )
=> ~ ( ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ~ ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(124,axiom,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f54304608l_bool ) @ is_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obool) ).
thf(750,plain,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f54304608l_bool ) @ is_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(439,axiom,
! [A: $i,B: $i] : ( B @ ( A @ insert_a ) @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_insertI1) ).
thf(1764,plain,
! [A: $i,B: $i] : ( B @ ( A @ insert_a ) @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(242,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1551609309ol_nat ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_finite__imageI) ).
thf(1103,plain,
! [A: $i,B: $i] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1551609309ol_nat ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(122,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( suc @ hAPP_nat_nat ) )
= ( B @ ( suc @ hAPP_nat_nat ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_Suc__inject) ).
thf(745,plain,
! [A: $i,B: $i] :
( ( ( A @ ( suc @ hAPP_nat_nat ) )
= ( B @ ( suc @ hAPP_nat_nat ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(54,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun_pname_bool )
=> ( B @ ( A @ cOMBS_568398431l_bool ) @ is_fun_pname_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool) ).
thf(573,plain,
! [A: $i,B: $i] :
( ( B @ is_fun_pname_bool )
=> ( B @ ( A @ cOMBS_568398431l_bool ) @ is_fun_pname_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(100,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_1149511130e_bool @ hAPP_p61793385e_bool ) @ hAPP_pname_bool ) )
= ( B @ ( C @ ( A @ hAPP_p61793385e_bool ) @ hAPP_pname_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Com__Opname_000tc__HOL__Obool_U) ).
thf(689,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_1149511130e_bool @ hAPP_p61793385e_bool ) @ hAPP_pname_bool ) )
= ( B @ ( C @ ( A @ hAPP_p61793385e_bool ) @ hAPP_pname_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(310,axiom,
! [A: $i,B: $i] :
( ( B @ collect_fun_a_bool @ ( A @ insert_fun_a_bool ) )
= ( B @ ( A @ ( fequal_fun_a_bool @ cOMBC_1732670874l_bool @ hAPP_f1631501043l_bool ) @ ( fNot @ cOMBB_2140588453a_bool ) @ ( fimplies @ cOMBB_338059395a_bool ) @ cOMBS_1035972772l_bool ) @ collect_fun_a_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_insert__Collect) ).
thf(1374,plain,
! [A: $i,B: $i] :
( ( B @ collect_fun_a_bool @ ( A @ insert_fun_a_bool ) )
= ( B @ ( A @ ( fequal_fun_a_bool @ cOMBC_1732670874l_bool @ hAPP_f1631501043l_bool ) @ ( fNot @ cOMBB_2140588453a_bool ) @ ( fimplies @ cOMBB_338059395a_bool ) @ cOMBS_1035972772l_bool ) @ collect_fun_a_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(398,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( A @ insert_a ) @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_finite_OinsertI) ).
thf(1631,plain,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( A @ insert_a ) @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(65,axiom,
! [A: $i] :
( ( A @ collect_fun_nat_bool )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_Collect__def) ).
thf(601,plain,
! [A: $i] :
( ( A @ collect_fun_nat_bool )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_2095475776e_bool ) @ hAPP_f1476298914l_bool ) )
= ( C @ ( B @ hAPP_f1664156314l_bool ) @ ( A @ hAPP_b589554111l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_010) ).
thf(513,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_2095475776e_bool ) @ hAPP_f1476298914l_bool ) )
= ( C @ ( B @ hAPP_f1664156314l_bool ) @ ( A @ hAPP_b589554111l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(438,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ insert_nat ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( ( C @ ( B @ hAPP_nat_bool ) @ hBOOL )
| ( A = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_insert__code) ).
thf(1754,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( B @ hAPP_nat_bool ) @ hBOOL )
| ( A = C ) )
=> ( C @ ( B @ ( A @ insert_nat ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( C @ ( B @ ( A @ insert_nat ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( C @ ( B @ hAPP_nat_bool ) @ hBOOL )
| ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(58,axiom,
! [A: $i,B: $i] : ( B @ ( A @ image_fun_nat_bool_a ) @ is_fun_a_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000t__a) ).
thf(584,plain,
! [A: $i,B: $i] : ( B @ ( A @ image_fun_nat_bool_a ) @ is_fun_a_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(50,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( suc @ hAPP_nat_nat ) @ ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) )
= ( C @ ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_Suc__diff__diff) ).
thf(562,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( suc @ hAPP_nat_nat ) @ ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) )
= ( C @ ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(117,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun_pname_bool )
=> ( B @ ( A @ hAPP_f759274231e_bool ) @ is_fun_pname_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_Itc__Com__Op) ).
thf(732,plain,
! [A: $i,B: $i] :
( ( B @ is_fun_pname_bool )
=> ( B @ ( A @ hAPP_f759274231e_bool ) @ is_fun_pname_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(437,axiom,
! [A: $i] : ( A @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_subset__refl) ).
thf(1752,plain,
! [A: $i] : ( A @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(315,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_finite__subset) ).
thf(1388,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(121,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun1661590463l_bool )
=> ( B @ ( A @ cOMBB_307249310e_bool ) @ is_fun1661590463l_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc_) ).
thf(743,plain,
! [A: $i,B: $i] :
( ( B @ is_fun1661590463l_bool )
=> ( B @ ( A @ cOMBB_307249310e_bool ) @ is_fun1661590463l_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(212,axiom,
! [A: $i,B: $i] :
( ( ( B @ is_fun_a_bool )
& ( A @ is_fun949378684l_bool ) )
=> ( B @ ( A @ hAPP_fun_a_bool_bool ) @ is_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool) ).
thf(1007,plain,
! [A: $i,B: $i] :
( ( ( B @ is_fun_a_bool )
& ( A @ is_fun949378684l_bool ) )
=> ( B @ ( A @ hAPP_fun_a_bool_bool ) @ is_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(102,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun_a_bool )
=> ( B @ ( A @ image_a_pname ) @ is_fun_pname_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000t__a_000tc__Com__Opname) ).
thf(694,plain,
! [A: $i,B: $i] :
( ( B @ is_fun_a_bool )
=> ( B @ ( A @ image_a_pname ) @ is_fun_pname_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(159,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( A @ image_nat_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_finite__imageI) ).
thf(843,plain,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( A @ image_nat_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(249,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1655916159e_bool ) @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_finite__imageI) ).
thf(1125,plain,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1655916159e_bool ) @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(273,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ is_a )
& ( A @ is_a ) )
=> ( ( C @ ( B @ insert_a ) @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
<=> ( ( C @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_insert__iff) ).
thf(1226,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ is_a )
& ( A @ is_a ) )
=> ( ( ( ( C @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
| ( A = B ) )
=> ( C @ ( B @ insert_a ) @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
& ( ( C @ ( B @ insert_a ) @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( C @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
| ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(43,axiom,
! [A: $i,B: $i] : ( B @ ( A @ image_nat_pname ) @ is_fun_pname_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__Com__Opname) ).
thf(545,plain,
! [A: $i,B: $i] : ( B @ ( A @ image_nat_pname ) @ is_fun_pname_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(81,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBS_a_bool_bool ) @ hAPP_a_bool ) )
= ( C @ ( B @ hAPP_a_bool ) @ ( C @ ( A @ hAPP_a_fun_bool_bool ) @ hAPP_bool_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000t__a_000tc__HOL__Obool_000tc__HOL__Obool_U) ).
thf(641,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBS_a_bool_bool ) @ hAPP_a_bool ) )
= ( C @ ( B @ hAPP_a_bool ) @ ( C @ ( A @ hAPP_a_fun_bool_bool ) @ hAPP_bool_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(418,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1079571347ol_nat ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_finite__imageI) ).
thf(1707,plain,
! [A: $i,B: $i] :
( ( B @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1079571347ol_nat ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(24,axiom,
! [A: $i] :
( ( A @ is_fun949378684l_bool )
=> ( A @ collect_fun_a_bool @ is_fun949378684l_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_OCollect_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
thf(498,plain,
! [A: $i] :
( ( A @ is_fun949378684l_bool )
=> ( A @ collect_fun_a_bool @ is_fun949378684l_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(400,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( A @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_rev__finite__subset) ).
thf(1635,plain,
! [A: $i,B: $i] :
( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( A @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(299,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_1732670874l_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) )
= ( B @ ( C @ ( A @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_It__a_Mtc__HO) ).
thf(1332,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_1732670874l_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) )
= ( B @ ( C @ ( A @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(239,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( fdisj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
<=> ( ( B @ collect_a @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( A @ collect_a @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_finite__Collect__disjI) ).
thf(1092,plain,
! [A: $i,B: $i] :
( ( ( ( B @ collect_a @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( A @ collect_a @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
=> ( B @ ( A @ ( fdisj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( fdisj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ collect_a @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( A @ collect_a @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(238,axiom,
! [A: $i] :
( ( A @ ( finite1701474069l_bool @ hAPP_f937997336l_bool ) @ hBOOL )
=> ( A @ ( ord_le65145710l_bool @ cOMBC_1269652216l_bool @ hAPP_f760187903l_bool ) @ collec1874991203l_bool @ ( finite719726885l_bool @ hAPP_f1295398978l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_finite__Collect__subsets) ).
thf(1090,plain,
! [A: $i] :
( ( A @ ( finite1701474069l_bool @ hAPP_f937997336l_bool ) @ hBOOL )
=> ( A @ ( ord_le65145710l_bool @ cOMBC_1269652216l_bool @ hAPP_f760187903l_bool ) @ collec1874991203l_bool @ ( finite719726885l_bool @ hAPP_f1295398978l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(349,axiom,
! [A: $i,B: $i] :
( ( ( A @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
| ( B @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) )
=> ( A @ ( B @ ( fconj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_finite__Collect__conjI) ).
thf(1464,plain,
! [A: $i,B: $i] :
( ( ( A @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
| ( B @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) )
=> ( A @ ( B @ ( fconj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(272,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite1701474069l_bool @ hAPP_f937997336l_bool ) @ hBOOL )
=> ( B @ ( finite1352710292l_bool @ hAPP_f1690079119ol_nat ) @ ( B @ ( A @ image_526090948bool_a ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_card__image__le) ).
thf(1224,plain,
! [A: $i,B: $i] :
( ( B @ ( finite1701474069l_bool @ hAPP_f937997336l_bool ) @ hBOOL )
=> ( B @ ( finite1352710292l_bool @ hAPP_f1690079119ol_nat ) @ ( B @ ( A @ image_526090948bool_a ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(278,axiom,
! [A: $i,B: $i] :
( ( A = B )
=> ~ ( ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ~ ( A @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_equalityE) ).
thf(1258,plain,
! [A: $i,B: $i] :
( ( A = B )
=> ~ ( ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ~ ( A @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(106,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun949378684l_bool )
=> ( B @ ( A @ image_1854862208_pname ) @ is_fun_pname_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opname) ).
thf(704,plain,
! [A: $i,B: $i] :
( ( B @ is_fun949378684l_bool )
=> ( B @ ( A @ image_1854862208_pname ) @ is_fun_pname_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(66,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_1015721476ol_nat ) @ hAPP_n1006566506l_bool ) )
= ( C @ ( B @ hAPP_nat_bool ) @ ( A @ hAPP_b589554111l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_006) ).
thf(604,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_1015721476ol_nat ) @ hAPP_n1006566506l_bool ) )
= ( C @ ( B @ hAPP_nat_bool ) @ ( A @ hAPP_b589554111l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(153,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( B @ ( A @ insert_fun_nat_bool ) @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_finite_OinsertI) ).
thf(831,plain,
! [A: $i,B: $i] :
( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( B @ ( A @ insert_fun_nat_bool ) @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(325,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( B @ ( A @ image_496248727ol_nat ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_finite__imageI) ).
thf(1408,plain,
! [A: $i,B: $i] :
( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( B @ ( A @ image_496248727ol_nat ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(246,axiom,
! [A: $i,B: $i] :
( ( ( B @ is_fun_pname_bool )
& ( A @ is_fun_pname_bool ) )
=> ( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A = B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_card__seteq) ).
thf(1117,plain,
! [A: $i,B: $i] :
( ( ( B @ is_fun_pname_bool )
& ( A @ is_fun_pname_bool ) )
=> ( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(386,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ is_a )
=> ( ( C @ ( B @ image_pname_a ) @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ~ ! [D: $i] :
( ( D @ is_pname )
=> ( ( A
= ( D @ ( B @ hAPP_pname_a ) ) )
=> ~ ( C @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_imageE) ).
thf(1574,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ is_a )
=> ( ( C @ ( B @ image_pname_a ) @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ~ ! [D: $i] :
( ( D @ is_pname )
=> ( ( A
= ( D @ ( B @ hAPP_pname_a ) ) )
=> ~ ( C @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( ( B @ is_a )
& ( A @ is_fun_a_bool ) )
=> ( B @ ( A @ hAPP_a_bool ) @ is_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000t__a_000tc__HOL__Obool) ).
thf(451,plain,
! [A: $i,B: $i] :
( ( ( B @ is_a )
& ( A @ is_fun_a_bool ) )
=> ( B @ ( A @ hAPP_a_bool ) @ is_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(252,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ insert_a ) )
= ( B @ ( member_a @ cOMBC_1355376034l_bool @ hAPP_f2050579477a_bool ) @ ( A @ ( fequal_a @ cOMBC_a_a_bool @ hAPP_a_fun_a_bool ) @ ( fdisj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_insert__compr) ).
thf(1144,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ insert_a ) )
= ( B @ ( member_a @ cOMBC_1355376034l_bool @ hAPP_f2050579477a_bool ) @ ( A @ ( fequal_a @ cOMBC_a_a_bool @ hAPP_a_fun_a_bool ) @ ( fdisj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(71,axiom,
! [A: $i,B: $i] :
( ( B @ collect_nat @ ( A @ insert_nat ) )
= ( B @ ( A @ ( fequal_nat @ cOMBC_nat_nat_bool @ hAPP_n1699378549t_bool ) @ ( fNot @ cOMBB_bool_bool_nat ) @ ( fimplies @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_insert__Collect) ).
thf(616,plain,
! [A: $i,B: $i] :
( ( B @ collect_nat @ ( A @ insert_nat ) )
= ( B @ ( A @ ( fequal_nat @ cOMBC_nat_nat_bool @ hAPP_n1699378549t_bool ) @ ( fNot @ cOMBB_bool_bool_nat ) @ ( fimplies @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(64,axiom,
! [A: $i] :
( ( A @ is_fun_pname_bool )
=> ( A @ collect_pname @ is_fun_pname_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_OCollect_000tc__Com__Opname) ).
thf(599,plain,
! [A: $i] :
( ( A @ is_fun_pname_bool )
=> ( A @ collect_pname @ is_fun_pname_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(442,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( B @ ( A @ image_pname_pname ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_card__image__le) ).
thf(1771,plain,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( B @ ( A @ image_pname_pname ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(119,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_1693257480l_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc_) ).
thf(737,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_1693257480l_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(29,axiom,
! [A: $i,B: $i] : ( B @ ( A @ image_1604018183_pname ) @ is_fun_pname_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HOL___003) ).
thf(509,plain,
! [A: $i,B: $i] : ( B @ ( A @ image_1604018183_pname ) @ is_fun_pname_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(175,axiom,
! [A: $i,B: $i] :
( ( ( B @ is_fun_pname_bool )
& ( A @ is_fun_pname_bool ) )
=> ( ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_equalityI) ).
thf(880,plain,
! [A: $i,B: $i] :
( ( ( B @ is_fun_pname_bool )
& ( A @ is_fun_pname_bool ) )
=> ( ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(85,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) )
= ( B @ ( C @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_diff__commute) ).
thf(649,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) )
= ( B @ ( C @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_444170502t_bool ) @ hAPP_f1748468828l_bool ) )
= ( C @ ( B @ hAPP_f54304608l_bool ) @ ( A @ hAPP_b589554111l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_009) ).
thf(477,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_444170502t_bool ) @ hAPP_f1748468828l_bool ) )
= ( C @ ( B @ hAPP_f54304608l_bool ) @ ( A @ hAPP_b589554111l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(62,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ insert_pname ) )
= ( B @ ( member_pname @ cOMBC_1058051404l_bool @ hAPP_f759274231e_bool ) @ ( A @ ( fequal_pname @ cOMBC_1149511130e_bool @ hAPP_p61793385e_bool ) @ ( fdisj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_insert__compr__raw) ).
thf(594,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ insert_pname ) )
= ( B @ ( member_pname @ cOMBC_1058051404l_bool @ hAPP_f759274231e_bool ) @ ( A @ ( fequal_pname @ cOMBC_1149511130e_bool @ hAPP_p61793385e_bool ) @ ( fdisj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(143,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ hAPP_nat_bool ) @ hBOOL )
=> ( ! [D: $i] :
( ( D @ ( suc @ hAPP_nat_nat ) @ ( B @ hAPP_nat_bool ) @ hBOOL )
=> ( D @ ( B @ hAPP_nat_bool ) @ hBOOL ) )
=> ( A @ ( C @ minus_minus_nat @ hAPP_nat_nat ) @ ( B @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_zero__induct__lemma) ).
thf(799,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ hAPP_nat_bool ) @ hBOOL )
=> ( ! [D: $i] :
( ( D @ ( suc @ hAPP_nat_nat ) @ ( B @ hAPP_nat_bool ) @ hBOOL )
=> ( D @ ( B @ hAPP_nat_bool ) @ hBOOL ) )
=> ( A @ ( C @ minus_minus_nat @ hAPP_nat_nat ) @ ( B @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(73,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_1245412066l_bool @ hAPP_f1246832597l_bool ) @ hAPP_f54304608l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f1951378235l_bool ) @ hAPP_f1637334154l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__011) ).
thf(621,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_1245412066l_bool @ hAPP_f1246832597l_bool ) @ hAPP_f54304608l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f1951378235l_bool ) @ hAPP_f1637334154l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(220,axiom,
! [A: $i,B: $i] :
( ( A = B )
| ~ ( B @ ( A @ ( fequal_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Nat__Onat_T) ).
thf(1029,plain,
! [A: $i,B: $i] :
( ( A = B )
| ~ ( B @ ( A @ ( fequal_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( ( B @ is_fun1661590463l_bool )
& ( A @ is_fun_pname_bool ) )
=> ( B @ ( A @ insert1325755072e_bool ) @ is_fun1661590463l_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_Oinsert_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).
thf(494,plain,
! [A: $i,B: $i] :
( ( ( B @ is_fun1661590463l_bool )
& ( A @ is_fun_pname_bool ) )
=> ( B @ ( A @ insert1325755072e_bool ) @ is_fun1661590463l_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(235,axiom,
! [A: $i] : ( A @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_subset__refl) ).
thf(1080,plain,
! [A: $i] : ( A @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(127,axiom,
! [A: $i] :
( ( A @ is_fun949378684l_bool )
=> ( ( A @ collect_fun_a_bool )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_Collect__def) ).
thf(758,plain,
! [A: $i] :
( ( A @ is_fun949378684l_bool )
=> ( ( A @ collect_fun_a_bool )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(302,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ image_112932426a_bool ) @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_finite__imageI) ).
thf(1339,plain,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ image_112932426a_bool ) @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(380,axiom,
g @ is_fun_a_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_v_G) ).
thf(1557,plain,
g @ is_fun_a_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(46,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun949378684l_bool )
=> ( B @ ( A @ image_fun_a_bool_a ) @ is_fun_a_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_It__a_Mtc__HOL__Obool_J_000t__a) ).
thf(552,plain,
! [A: $i,B: $i] :
( ( B @ is_fun949378684l_bool )
=> ( B @ ( A @ image_fun_a_bool_a ) @ is_fun_a_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(254,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( B @ insert_pname ) @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
<=> ( A @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_subset__insert) ).
thf(1149,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( ( A @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( B @ insert_pname ) @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
& ( ( A @ ( B @ insert_pname ) @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(201,axiom,
! [A: $i,B: $i] :
( ( ( A @ collect_fun_nat_bool @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
| ( B @ collect_fun_nat_bool @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL ) )
=> ( A @ ( B @ ( fconj @ cOMBB_444170502t_bool ) @ cOMBS_1187019125l_bool ) @ collect_fun_nat_bool @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_finite__Collect__conjI) ).
thf(964,plain,
! [A: $i,B: $i] :
( ( ( A @ collect_fun_nat_bool @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
| ( B @ collect_fun_nat_bool @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL ) )
=> ( A @ ( B @ ( fconj @ cOMBB_444170502t_bool ) @ cOMBS_1187019125l_bool ) @ collect_fun_nat_bool @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(75,axiom,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f389811538l_bool ) @ is_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__) ).
thf(626,plain,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f389811538l_bool ) @ is_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(184,axiom,
u @ ( mgt_call @ image_pname_a ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( na @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).
thf(915,plain,
u @ ( mgt_call @ image_pname_a ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( na @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(132,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( fdisj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
<=> ( ( B @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( A @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_finite__Collect__disjI) ).
thf(769,plain,
! [A: $i,B: $i] :
( ( ( ( B @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( A @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) )
=> ( B @ ( A @ ( fdisj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( fdisj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( A @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(347,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1420695166l_bool ) @ ( finite1381704300l_bool @ hAPP_f292226953l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_finite__imageI) ).
thf(1460,plain,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1420695166l_bool ) @ ( finite1381704300l_bool @ hAPP_f292226953l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(291,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_rev__finite__subset) ).
thf(1293,plain,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(91,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_336095980l_bool @ hAPP_f1759205631l_bool ) @ hAPP_f389811538l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f1759205631l_bool ) @ hAPP_f389811538l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obo) ).
thf(668,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_336095980l_bool @ hAPP_f1759205631l_bool ) @ hAPP_f389811538l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f1759205631l_bool ) @ hAPP_f389811538l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun1661590463l_bool )
=> ( B @ ( A @ hAPP_f559147733l_bool ) @ is_fun1661590463l_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo_005) ).
thf(462,plain,
! [A: $i,B: $i] :
( ( B @ is_fun1661590463l_bool )
=> ( B @ ( A @ hAPP_f559147733l_bool ) @ is_fun1661590463l_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(190,axiom,
! [A: $i,B: $i] :
( ( ( B @ is_fun_a_bool )
& ( A @ is_a ) )
=> ( B @ ( A @ insert_a ) @ is_fun_a_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_Oinsert_000t__a) ).
thf(932,plain,
! [A: $i,B: $i] :
( ( ( B @ is_fun_a_bool )
& ( A @ is_a ) )
=> ( B @ ( A @ insert_a ) @ is_fun_a_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(229,axiom,
u @ is_fun_pname_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_v_U) ).
thf(1061,plain,
u @ is_fun_pname_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(206,axiom,
! [A: $i,B: $i] :
( ( B @ collect_a @ ( A @ insert_a ) )
= ( B @ ( A @ ( fequal_a @ cOMBC_a_a_bool @ hAPP_a_fun_a_bool ) @ ( fNot @ cOMBB_bool_bool_a ) @ ( fimplies @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_insert__Collect) ).
thf(983,plain,
! [A: $i,B: $i] :
( ( B @ collect_a @ ( A @ insert_a ) )
= ( B @ ( A @ ( fequal_a @ cOMBC_a_a_bool @ hAPP_a_fun_a_bool ) @ ( fNot @ cOMBB_bool_bool_a ) @ ( fimplies @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(319,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ image_2129980159t_bool ) @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_finite__imageI) ).
thf(1396,plain,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ image_2129980159t_bool ) @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(215,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] : ( D @ ( suc @ hAPP_nat_nat ) @ ( C @ hAPP_nat_nat ) @ ( D @ ( C @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( C @ hAPP_nat_nat ) @ ( A @ ( C @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_lift__Suc__mono__le) ).
thf(1015,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] : ( D @ ( suc @ hAPP_nat_nat ) @ ( C @ hAPP_nat_nat ) @ ( D @ ( C @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( C @ hAPP_nat_nat ) @ ( A @ ( C @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(261,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ is_pname )
& ( A @ is_pname ) )
=> ( ( C @ ( B @ insert_pname ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A != B )
=> ( C @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_insertE) ).
thf(1176,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ is_pname )
& ( A @ is_pname ) )
=> ( ( C @ ( B @ insert_pname ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A != B )
=> ( C @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(207,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( B @ ( A @ image_2129980159t_bool ) @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_card__image__le) ).
thf(986,plain,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( B @ ( A @ image_2129980159t_bool ) @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(444,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ ( C @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_diff__le__mono2) ).
thf(1775,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ ( C @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(360,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( fequal_a @ hAPP_a_fun_a_bool ) @ hAPP_a_bool ) @ hBOOL )
| ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000t__a_T) ).
thf(1496,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( fequal_a @ hAPP_a_fun_a_bool ) @ hAPP_a_bool ) @ hBOOL )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(163,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A
= ( C @ ( B @ hAPP_pname_a ) ) )
=> ( D @ ( B @ image_pname_a ) @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_rev__image__eqI) ).
thf(851,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A
= ( C @ ( B @ hAPP_pname_a ) ) )
=> ( D @ ( B @ image_pname_a ) @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(27,axiom,
! [A: $i,B: $i] : ( B @ ( A @ image_1655916159e_bool ) @ is_fun1661590463l_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).
thf(505,plain,
! [A: $i,B: $i] : ( B @ ( A @ image_1655916159e_bool ) @ is_fun1661590463l_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(188,axiom,
! [A: $i,B: $i] :
( ( ( A @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
| ( B @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) )
=> ( A @ ( B @ ( fconj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_finite__Collect__conjI) ).
thf(922,plain,
! [A: $i,B: $i] :
( ( ( A @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
| ( B @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) )
=> ( A @ ( B @ ( fconj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(341,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( B @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) @ ( A @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_card__mono) ).
thf(1445,plain,
! [A: $i,B: $i] :
( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( B @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) @ ( A @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(170,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun_pname_bool )
=> ( ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_pname ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_insert__absorb) ).
thf(868,plain,
! [A: $i,B: $i] :
( ( B @ is_fun_pname_bool )
=> ( ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_pname ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(135,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( C @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_set__mp) ).
thf(780,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( C @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(403,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( B @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_card__seteq) ).
thf(1643,plain,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( B @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(7,axiom,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_nat_fun_a_bool ) @ is_fun_a_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
thf(455,plain,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_nat_fun_a_bool ) @ is_fun_a_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(176,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( A @ image_a_a ) @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_finite__imageI) ).
thf(883,plain,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( A @ image_a_a ) @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(426,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ image_47868345e_bool ) @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_finite__imageI) ).
thf(1726,plain,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ image_47868345e_bool ) @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(277,axiom,
! [A: $i] :
( ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
<=> ? [B: $i] :
! [C: $i] :
( ( A @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_finite__nat__set__iff__bounded__le) ).
thf(1250,plain,
! [A: $i] :
( ( ? [B: $i] :
! [C: $i] :
( ( A @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) )
& ( ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ? [B: $i] :
! [C: $i] :
( ( A @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(396,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ? [C: $i] :
( B
= ( C @ ( suc @ hAPP_nat_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_Suc__le__D) ).
thf(1626,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ? [C: $i] :
( B
= ( C @ ( suc @ hAPP_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(94,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_636888218l_bool @ hAPP_f1050622307l_bool ) @ hAPP_f292226953l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f1050622307l_bool ) @ hAPP_f292226953l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__H) ).
thf(675,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_636888218l_bool @ hAPP_f1050622307l_bool ) @ hAPP_f292226953l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f1050622307l_bool ) @ hAPP_f292226953l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(409,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ insert_nat ) @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
<=> ( ( C @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_insert__iff) ).
thf(1662,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
| ( A = B ) )
=> ( C @ ( B @ insert_nat ) @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
& ( ( C @ ( B @ insert_nat ) @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( C @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(295,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ is_a )
=> ( ( C @ ( B @ image_pname_a ) @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
<=> ? [D: $i] :
( ( A
= ( D @ ( B @ hAPP_pname_a ) ) )
& ( C @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( D @ is_pname ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_image__iff) ).
thf(1304,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ is_a )
=> ( ( ? [D: $i] :
( ( A
= ( D @ ( B @ hAPP_pname_a ) ) )
& ( C @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( D @ is_pname ) )
=> ( C @ ( B @ image_pname_a ) @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
& ( ( C @ ( B @ image_pname_a ) @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ? [D: $i] :
( ( A
= ( D @ ( B @ hAPP_pname_a ) ) )
& ( C @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( D @ is_pname ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(259,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ is_a )
& ( A @ is_a ) )
=> ( ( C @ ( B @ ( A @ insert_a ) @ hAPP_a_bool ) @ hBOOL )
<=> ( ( C @ ( B @ hAPP_a_bool ) @ hBOOL )
| ( A = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_insert__code) ).
thf(1166,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ is_a )
& ( A @ is_a ) )
=> ( ( ( ( C @ ( B @ hAPP_a_bool ) @ hBOOL )
| ( A = C ) )
=> ( C @ ( B @ ( A @ insert_a ) @ hAPP_a_bool ) @ hBOOL ) )
& ( ( C @ ( B @ ( A @ insert_a ) @ hAPP_a_bool ) @ hBOOL )
=> ( ( C @ ( B @ hAPP_a_bool ) @ hBOOL )
| ( A = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(267,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( B @ ( A @ image_nat_pname ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_card__image__le) ).
thf(1208,plain,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( B @ ( A @ image_nat_pname ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(330,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( B @ ( A @ image_nat_fun_a_bool ) @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_card__image__le) ).
thf(1420,plain,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( B @ ( A @ image_nat_fun_a_bool ) @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(284,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( A @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_finite__subset) ).
thf(1277,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( A @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(84,axiom,
pname @ undefined_pname @ is_pname,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_HOL_Oundefined_000tc__Com__Opname) ).
thf(648,plain,
pname @ undefined_pname @ is_pname,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(148,axiom,
! [A: $i] :
~ ( A @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_Suc__n__not__le__n) ).
thf(812,plain,
! [A: $i] :
~ ( A @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun949378684l_bool )
=> ( B @ ( A @ cOMBS_1035972772l_bool ) @ is_fun949378684l_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_COMBS_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000tc__HOL__Obo) ).
thf(516,plain,
! [A: $i,B: $i] :
( ( B @ is_fun949378684l_bool )
=> ( B @ ( A @ cOMBS_1035972772l_bool ) @ is_fun949378684l_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(352,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( ~ ( B @ ( A @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert1325755072e_bool ) @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) )
= ( B @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) @ ( suc @ hAPP_nat_nat ) ) ) )
& ( ( B @ ( A @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert1325755072e_bool ) @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) )
= ( B @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_card__insert__if) ).
thf(1472,plain,
! [A: $i,B: $i] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( ~ ( B @ ( A @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert1325755072e_bool ) @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) )
= ( B @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) @ ( suc @ hAPP_nat_nat ) ) ) )
& ( ( B @ ( A @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert1325755072e_bool ) @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) )
= ( B @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(378,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( fequal_pname @ hAPP_p61793385e_bool ) @ hAPP_pname_bool ) @ hBOOL )
| ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Com__Opname_T) ).
thf(1551,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( fequal_pname @ hAPP_p61793385e_bool ) @ hAPP_pname_bool ) @ hBOOL )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(227,axiom,
! [A: $i] :
( ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( ord_le1568362934t_bool @ cOMBC_1693257480l_bool @ hAPP_f103356543l_bool ) @ collect_fun_nat_bool @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_finite__Collect__subsets) ).
thf(1049,plain,
! [A: $i] :
( ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( ord_le1568362934t_bool @ cOMBC_1693257480l_bool @ hAPP_f103356543l_bool ) @ collect_fun_nat_bool @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_a_a_bool @ hAPP_a_fun_a_bool ) @ hAPP_a_bool ) )
= ( B @ ( C @ ( A @ hAPP_a_fun_a_bool ) @ hAPP_a_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000t__a_000t__a_000tc__HOL__Obool_U) ).
thf(531,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_a_a_bool @ hAPP_a_fun_a_bool ) @ hAPP_a_bool ) )
= ( B @ ( C @ ( A @ hAPP_a_fun_a_bool ) @ hAPP_a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(194,axiom,
! [A: $i,B: $i] :
( ( A = B )
=> ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_equalityD1) ).
thf(944,plain,
! [A: $i,B: $i] :
( ( A = B )
=> ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(141,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite1381704300l_bool @ hAPP_f292226953l_bool ) @ hBOOL )
=> ( B @ ( A @ image_990671762_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_finite__imageI) ).
thf(795,plain,
! [A: $i,B: $i] :
( ( B @ ( finite1381704300l_bool @ hAPP_f292226953l_bool ) @ hBOOL )
=> ( B @ ( A @ image_990671762_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(96,axiom,
! [A: $i,B: $i] :
( ( ( B @ is_fun_pname_bool )
& ( A @ is_pname ) )
=> ( B @ ( A @ insert_pname ) @ is_fun_pname_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_Oinsert_000tc__Com__Opname) ).
thf(680,plain,
! [A: $i,B: $i] :
( ( ( B @ is_fun_pname_bool )
& ( A @ is_pname ) )
=> ( B @ ( A @ insert_pname ) @ is_fun_pname_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(202,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( ~ ( B @ ( A @ ( member_fun_a_bool @ hAPP_f285962445l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_fun_a_bool ) @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) )
= ( B @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) @ ( suc @ hAPP_nat_nat ) ) ) )
& ( ( B @ ( A @ ( member_fun_a_bool @ hAPP_f285962445l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_fun_a_bool ) @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) )
= ( B @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_card__insert__if) ).
thf(968,plain,
! [A: $i,B: $i] :
( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( ~ ( B @ ( A @ ( member_fun_a_bool @ hAPP_f285962445l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_fun_a_bool ) @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) )
= ( B @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) @ ( suc @ hAPP_nat_nat ) ) ) )
& ( ( B @ ( A @ ( member_fun_a_bool @ hAPP_f285962445l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_fun_a_bool ) @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) )
= ( B @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(151,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ insert_fun_nat_bool ) @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
<=> ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_finite__insert) ).
thf(823,plain,
! [A: $i,B: $i] :
( ( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( B @ ( A @ insert_fun_nat_bool ) @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ insert_fun_nat_bool ) @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( B @ is_a )
=> ( B @ ( A @ hAPP_a93125764e_bool ) @ is_fun_pname_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000t__a_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).
thf(525,plain,
! [A: $i,B: $i] :
( ( B @ is_a )
=> ( B @ ( A @ hAPP_a93125764e_bool ) @ is_fun_pname_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(164,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( A @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_card__mono) ).
thf(855,plain,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( A @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(376,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1208015684l_bool ) @ ( finite1381704300l_bool @ hAPP_f292226953l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_finite__imageI) ).
thf(1547,plain,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1208015684l_bool ) @ ( finite1381704300l_bool @ hAPP_f292226953l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(133,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1642285373l_bool ) @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_finite__imageI) ).
thf(776,plain,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1642285373l_bool ) @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(435,axiom,
! [A: $i,B: $i] : ( A @ ( B @ insert_a ) @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_subset__insertI) ).
thf(1748,plain,
! [A: $i,B: $i] : ( A @ ( B @ insert_a ) @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(110,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_nat_nat_bool @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) )
= ( B @ ( C @ ( A @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__HOL__Obool_U) ).
thf(712,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_nat_nat_bool @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) )
= ( B @ ( C @ ( A @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(48,axiom,
! [A: $i,B: $i] : ( B @ ( A @ image_349102846bool_a ) @ is_fun_a_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL) ).
thf(557,plain,
! [A: $i,B: $i] : ( B @ ( A @ image_349102846bool_a ) @ is_fun_a_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(433,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( B @ ( A @ image_876012084bool_a ) @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_finite__imageI) ).
thf(1743,plain,
! [A: $i,B: $i] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( B @ ( A @ image_876012084bool_a ) @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(321,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( A @ image_a_nat ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_finite__imageI) ).
thf(1400,plain,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( A @ image_a_nat ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(420,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_Suc__leD) ).
thf(1711,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(93,axiom,
! [A: $i,B: $i] : ( B @ ( A @ image_990671762_pname ) @ is_fun_pname_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J_0_001) ).
thf(673,plain,
! [A: $i,B: $i] : ( B @ ( A @ image_990671762_pname ) @ is_fun_pname_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(335,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( B @ ( A @ insert1325755072e_bool ) @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_finite_OinsertI) ).
thf(1432,plain,
! [A: $i,B: $i] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( B @ ( A @ insert1325755072e_bool ) @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(401,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( C @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_subsetD) ).
thf(1637,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( C @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(222,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite1701474069l_bool @ hAPP_f937997336l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1604018183_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_finite__imageI) ).
thf(1038,plain,
! [A: $i,B: $i] :
( ( B @ ( finite1701474069l_bool @ hAPP_f937997336l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1604018183_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_1058051404l_bool @ hAPP_f759274231e_bool ) @ hAPP_pname_bool ) )
= ( B @ ( C @ ( A @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob) ).
thf(502,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_1058051404l_bool @ hAPP_f759274231e_bool ) @ hAPP_pname_bool ) )
= ( B @ ( C @ ( A @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(407,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_subset__trans) ).
thf(1658,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(373,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun_a_bool )
=> ( ( B @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_a ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_insert__absorb) ).
thf(1538,plain,
! [A: $i,B: $i] :
( ( B @ is_fun_a_bool )
=> ( ( B @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_a ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(197,axiom,
! [A: $i] :
( ( A @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL )
=> ( A @ ( ord_le1375671464l_bool @ cOMBC_336095980l_bool @ hAPP_f1759205631l_bool ) @ collec792590109l_bool @ ( finite1491191519l_bool @ hAPP_f595608956l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_finite__Collect__subsets) ).
thf(951,plain,
! [A: $i] :
( ( A @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL )
=> ( A @ ( ord_le1375671464l_bool @ cOMBC_336095980l_bool @ hAPP_f1759205631l_bool ) @ collec792590109l_bool @ ( finite1491191519l_bool @ hAPP_f595608956l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(146,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( C @ ( A @ insert_a ) @ ( B @ ( A @ insert_a ) @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_insert__mono) ).
thf(808,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( C @ ( A @ insert_a ) @ ( B @ ( A @ insert_a ) @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(431,axiom,
! [A: $i,B: $i] : ( B @ ( A @ insert_pname ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_insertI1) ).
thf(1738,plain,
! [A: $i,B: $i] : ( B @ ( A @ insert_pname ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(271,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ insert_a ) @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
<=> ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_finite__insert) ).
thf(1218,plain,
! [A: $i,B: $i] :
( ( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( A @ insert_a ) @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
& ( ( B @ ( A @ insert_a ) @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(323,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( B @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) @ ( B @ ( A @ image_1283814551_pname ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_card__image__le) ).
thf(1404,plain,
! [A: $i,B: $i] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( B @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) @ ( B @ ( A @ image_1283814551_pname ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(440,axiom,
pn @ is_pname,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_v_pn) ).
thf(1766,plain,
pn @ is_pname,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(372,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1283814551_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_finite__imageI) ).
thf(1536,plain,
! [A: $i,B: $i] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1283814551_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(287,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( member_fun_a_bool @ hAPP_f285962445l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_fun_a_bool ) @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) )
= ( B @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) @ ( suc @ hAPP_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_card__insert__disjoint) ).
thf(1284,plain,
! [A: $i,B: $i] :
( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( member_fun_a_bool @ hAPP_f285962445l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_fun_a_bool ) @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) )
= ( B @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) @ ( suc @ hAPP_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(168,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( B @ ( A @ image_a_a ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_card__image__le) ).
thf(864,plain,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( B @ ( A @ image_a_a ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(333,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( A @ insert_pname ) @ ( B @ ( A @ insert_pname ) @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_insert__mono) ).
thf(1427,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( A @ insert_pname ) @ ( B @ ( A @ insert_pname ) @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(422,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_subset__trans) ).
thf(1717,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(173,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( B @ ( A @ insert_fun_nat_bool ) @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) @ ( B @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_card__insert__le) ).
thf(876,plain,
! [A: $i,B: $i] :
( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( B @ ( A @ insert_fun_nat_bool ) @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) @ ( B @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(166,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ insert_pname ) @ ( A @ image_pname_a ) )
= ( C @ ( A @ image_pname_a ) @ ( B @ ( A @ hAPP_pname_a ) @ insert_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_image__insert) ).
thf(859,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ insert_pname ) @ ( A @ image_pname_a ) )
= ( C @ ( A @ image_pname_a ) @ ( B @ ( A @ hAPP_pname_a ) @ insert_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(363,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B
= ( D @ ( C @ hAPP_pname_a ) ) )
=> ( ( A @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( C @ image_pname_a ) @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_image__eqI) ).
thf(1504,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B
= ( D @ ( C @ hAPP_pname_a ) ) )
=> ( ( A @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( C @ image_pname_a ) @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(115,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ insert_pname ) )
= ( B @ ( member_pname @ cOMBC_1058051404l_bool @ hAPP_f759274231e_bool ) @ ( A @ ( fequal_pname @ cOMBC_1149511130e_bool @ hAPP_p61793385e_bool ) @ ( fdisj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_insert__compr) ).
thf(727,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ insert_pname ) )
= ( B @ ( member_pname @ cOMBC_1058051404l_bool @ hAPP_f759274231e_bool ) @ ( A @ ( fequal_pname @ cOMBC_1149511130e_bool @ hAPP_p61793385e_bool ) @ ( fdisj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(282,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( A @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) @ ( B @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_card__seteq) ).
thf(1272,plain,
! [A: $i,B: $i] :
( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( A @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) @ ( B @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(69,axiom,
! [A: $i,B: $i] : ( B @ ( A @ image_1705983821_pname ) @ is_fun_pname_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL_002) ).
thf(612,plain,
! [A: $i,B: $i] : ( B @ ( A @ image_1705983821_pname ) @ is_fun_pname_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(160,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( A @ insert_pname ) @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_insertI2) ).
thf(845,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( A @ insert_pname ) @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(262,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_pname_a ) @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ? [C: $i] :
( ~ ( C @ ( A @ hAPP_pname_a ) @ ( A @ ( fequal_a @ cOMBB_1897541054_pname ) @ cOMBC_pname_a_bool @ hAPP_a93125764e_bool ) @ ( B @ ( member_pname @ cOMBC_1058051404l_bool @ hAPP_f759274231e_bool ) @ ( fconj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ ( C @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( C @ is_pname ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_pigeonhole__infinite) ).
thf(1180,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_pname_a ) @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ? [C: $i] :
( ~ ( C @ ( A @ hAPP_pname_a ) @ ( A @ ( fequal_a @ cOMBB_1897541054_pname ) @ cOMBC_pname_a_bool @ hAPP_a93125764e_bool ) @ ( B @ ( member_pname @ cOMBC_1058051404l_bool @ hAPP_f759274231e_bool ) @ ( fconj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ ( C @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( C @ is_pname ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ insert_fun_nat_bool ) )
= ( B @ ( member_fun_nat_bool @ cOMBC_1245412066l_bool @ hAPP_f1246832597l_bool ) @ ( A @ ( fequal_fun_nat_bool @ cOMBC_1693257480l_bool @ hAPP_f103356543l_bool ) @ ( fdisj @ cOMBB_444170502t_bool ) @ cOMBS_1187019125l_bool ) @ collect_fun_nat_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_insert__compr) ).
thf(539,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ insert_fun_nat_bool ) )
= ( B @ ( member_fun_nat_bool @ cOMBC_1245412066l_bool @ hAPP_f1246832597l_bool ) @ ( A @ ( fequal_fun_nat_bool @ cOMBC_1693257480l_bool @ hAPP_f103356543l_bool ) @ ( fdisj @ cOMBB_444170502t_bool ) @ cOMBS_1187019125l_bool ) @ collect_fun_nat_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBS_1187019125l_bool ) @ hAPP_f54304608l_bool ) )
= ( C @ ( B @ hAPP_f54304608l_bool ) @ ( C @ ( A @ hAPP_f1748468828l_bool ) @ hAPP_bool_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obo) ).
thf(482,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBS_1187019125l_bool ) @ hAPP_f54304608l_bool ) )
= ( C @ ( B @ hAPP_f54304608l_bool ) @ ( C @ ( A @ hAPP_f1748468828l_bool ) @ hAPP_bool_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(92,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun1661590463l_bool )
=> ( B @ ( A @ hAPP_f1935102916l_bool ) @ is_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo) ).
thf(671,plain,
! [A: $i,B: $i] :
( ( B @ is_fun1661590463l_bool )
=> ( B @ ( A @ hAPP_f1935102916l_bool ) @ is_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(181,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ is_pname )
& ( A @ is_pname ) )
=> ( ( C @ ( B @ ( A @ insert_pname ) @ hAPP_pname_bool ) @ hBOOL )
<=> ( ( C @ ( B @ hAPP_pname_bool ) @ hBOOL )
| ( A = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_insert__code) ).
thf(903,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ is_pname )
& ( A @ is_pname ) )
=> ( ( ( ( C @ ( B @ hAPP_pname_bool ) @ hBOOL )
| ( A = C ) )
=> ( C @ ( B @ ( A @ insert_pname ) @ hAPP_pname_bool ) @ hBOOL ) )
& ( ( C @ ( B @ ( A @ insert_pname ) @ hAPP_pname_bool ) @ hBOOL )
=> ( ( C @ ( B @ hAPP_pname_bool ) @ hBOOL )
| ( A = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(57,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ insert1325755072e_bool ) )
= ( B @ ( member799430823e_bool @ cOMBC_1988546018l_bool @ hAPP_f559147733l_bool ) @ ( A @ ( fequal533582459e_bool @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ ( fdisj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_insert__compr) ).
thf(581,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ insert1325755072e_bool ) )
= ( B @ ( member799430823e_bool @ cOMBC_1988546018l_bool @ hAPP_f559147733l_bool ) @ ( A @ ( fequal533582459e_bool @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ ( fdisj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(327,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_a ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) )
= ( B @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( suc @ hAPP_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_card__insert__disjoint) ).
thf(1412,plain,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_a ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) )
= ( B @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( suc @ hAPP_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(366,axiom,
! [A: $i,B: $i] :
( ( A = B )
=> ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_equalityD1) ).
thf(1517,plain,
! [A: $i,B: $i] :
( ( A = B )
=> ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(178,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBS_1035972772l_bool ) @ hAPP_fun_a_bool_bool ) )
= ( C @ ( B @ hAPP_fun_a_bool_bool ) @ ( C @ ( A @ hAPP_f198738859l_bool ) @ hAPP_bool_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000tc_) ).
thf(891,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBS_1035972772l_bool ) @ hAPP_fun_a_bool_bool ) )
= ( C @ ( B @ hAPP_fun_a_bool_bool ) @ ( C @ ( A @ hAPP_f198738859l_bool ) @ hAPP_bool_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(316,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( A @ image_26036933t_bool ) @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_finite__imageI) ).
thf(1390,plain,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( A @ image_26036933t_bool ) @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(244,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ~ ( A @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( ( C @ ( B @ insert_nat ) )
= ( A @ ( B @ insert_nat ) ) )
<=> ( C = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_insert__ident) ).
thf(1108,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ~ ( A @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( ( C = A )
=> ( ( C @ ( B @ insert_nat ) )
= ( A @ ( B @ insert_nat ) ) ) )
& ( ( ( C @ ( B @ insert_nat ) )
= ( A @ ( B @ insert_nat ) ) )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(4,axiom,
finite_finite_pname @ is_fun1661590463l_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Finite__Set_Ofinite_000tc__Com__Opname) ).
thf(450,plain,
finite_finite_pname @ is_fun1661590463l_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(237,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ insert1325755072e_bool ) @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
<=> ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_finite__insert) ).
thf(1084,plain,
! [A: $i,B: $i] :
( ( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( B @ ( A @ insert1325755072e_bool ) @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ insert1325755072e_bool ) @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(289,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( B @ ( A @ image_nat_a ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_card__image__le) ).
thf(1289,plain,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( B @ ( A @ image_nat_a ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(344,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ image_pname_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_finite__imageI) ).
thf(1453,plain,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ image_pname_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(389,axiom,
! [A: $i,B: $i] :
( ( ( B @ is_fun_a_bool )
& ( A @ is_fun_a_bool ) )
=> ( ( A = B )
<=> ( ( A @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_set__eq__subset) ).
thf(1590,plain,
! [A: $i,B: $i] :
( ( ( B @ is_fun_a_bool )
& ( A @ is_fun_a_bool ) )
=> ( ( ( ( A @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( A @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(404,axiom,
! [A: $i] :
( ( A @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( A @ ( ord_le675606854l_bool @ cOMBC_7971162l_bool @ hAPP_f510955609l_bool ) @ collec1613912337l_bool @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_finite__Collect__subsets) ).
thf(1646,plain,
! [A: $i] :
( ( A @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( A @ ( ord_le675606854l_bool @ cOMBC_7971162l_bool @ hAPP_f510955609l_bool ) @ collec1613912337l_bool @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(60,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_pname_a_bool @ hAPP_a93125764e_bool ) @ hAPP_pname_bool ) )
= ( B @ ( C @ ( A @ hAPP_p1534023578a_bool ) @ hAPP_a_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000t__a_000tc__HOL__Obool_U) ).
thf(588,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_pname_a_bool @ hAPP_a93125764e_bool ) @ hAPP_pname_bool ) )
= ( B @ ( C @ ( A @ hAPP_p1534023578a_bool ) @ hAPP_a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(424,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ insert_fun_a_bool ) )
= ( B @ ( member_fun_a_bool @ cOMBC_1880041174l_bool @ hAPP_f2117159681l_bool ) @ ( A @ ( fequal_fun_a_bool @ cOMBC_1732670874l_bool @ hAPP_f1631501043l_bool ) @ ( fdisj @ cOMBB_338059395a_bool ) @ cOMBS_1035972772l_bool ) @ collect_fun_a_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_insert__compr__raw) ).
thf(1721,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ insert_fun_a_bool ) )
= ( B @ ( member_fun_a_bool @ cOMBC_1880041174l_bool @ hAPP_f2117159681l_bool ) @ ( A @ ( fequal_fun_a_bool @ cOMBC_1732670874l_bool @ hAPP_f1631501043l_bool ) @ ( fdisj @ cOMBB_338059395a_bool ) @ cOMBS_1035972772l_bool ) @ collect_fun_a_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(241,axiom,
! [A: $i] :
( ( A @ ( fNot @ hAPP_bool_bool ) @ hBOOL )
| ( A @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fNot_2_1_U) ).
thf(1101,plain,
! [A: $i] :
( ( A @ ( fNot @ hAPP_bool_bool ) @ hBOOL )
| ( A @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(86,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( suc @ hAPP_nat_nat ) )
= ( B @ ( suc @ hAPP_nat_nat ) ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_nat_Oinject) ).
thf(652,plain,
! [A: $i,B: $i] :
( ( ( A = B )
=> ( ( A @ ( suc @ hAPP_nat_nat ) )
= ( B @ ( suc @ hAPP_nat_nat ) ) ) )
& ( ( ( A @ ( suc @ hAPP_nat_nat ) )
= ( B @ ( suc @ hAPP_nat_nat ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(397,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite1381704300l_bool @ hAPP_f292226953l_bool ) @ hBOOL )
=> ( B @ ( A @ insert1457093509l_bool ) @ ( finite1381704300l_bool @ hAPP_f292226953l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_finite_OinsertI) ).
thf(1629,plain,
! [A: $i,B: $i] :
( ( B @ ( finite1381704300l_bool @ hAPP_f292226953l_bool ) @ hBOOL )
=> ( B @ ( A @ insert1457093509l_bool ) @ ( finite1381704300l_bool @ hAPP_f292226953l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(434,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_equalityI) ).
thf(1745,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(78,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_1988546018l_bool @ hAPP_f559147733l_bool ) @ hAPP_f1664156314l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_012) ).
thf(632,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_1988546018l_bool @ hAPP_f559147733l_bool ) @ hAPP_f1664156314l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(368,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( ~ ( B @ ( A @ ( member_fun_nat_bool @ hAPP_f1951378235l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_fun_nat_bool ) @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) )
= ( B @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) @ ( suc @ hAPP_nat_nat ) ) ) )
& ( ( B @ ( A @ ( member_fun_nat_bool @ hAPP_f1951378235l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_fun_nat_bool ) @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) )
= ( B @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_card__insert__if) ).
thf(1523,plain,
! [A: $i,B: $i] :
( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( ~ ( B @ ( A @ ( member_fun_nat_bool @ hAPP_f1951378235l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_fun_nat_bool ) @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) )
= ( B @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) @ ( suc @ hAPP_nat_nat ) ) ) )
& ( ( B @ ( A @ ( member_fun_nat_bool @ hAPP_f1951378235l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_fun_nat_bool ) @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) )
= ( B @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(137,axiom,
! [A: $i,B: $i] :
( ( B @ hBOOL )
| ~ ( A @ hBOOL )
| ~ ( B @ ( A @ ( fimplies @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fimplies_3_1_U) ).
thf(786,plain,
! [A: $i,B: $i] :
( ( B @ hBOOL )
| ~ ( A @ hBOOL )
| ~ ( B @ ( A @ ( fimplies @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(303,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( C @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_subsetD) ).
thf(1341,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( C @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(180,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( B @ ( C @ minus_minus_nat @ hAPP_nat_nat ) )
= ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) ) )
<=> ( C = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_eq__diff__iff) ).
thf(896,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( C = A )
=> ( ( B @ ( C @ minus_minus_nat @ hAPP_nat_nat ) )
= ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) ) ) )
& ( ( ( B @ ( C @ minus_minus_nat @ hAPP_nat_nat ) )
= ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) ) )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(123,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun_pname_bool )
=> ( B @ ( A @ hAPP_f434788991l_bool ) @ is_fun1661590463l_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc) ).
thf(748,plain,
! [A: $i,B: $i] :
( ( B @ is_fun_pname_bool )
=> ( B @ ( A @ hAPP_f434788991l_bool ) @ is_fun1661590463l_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(411,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( B @ ( A @ image_26036933t_bool ) @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_card__image__le) ).
thf(1674,plain,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( B @ ( A @ image_26036933t_bool ) @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(402,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A @ ( B @ insert_a ) @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
<=> ( A @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_subset__insert) ).
thf(1639,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( ( A @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( B @ insert_a ) @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
& ( ( A @ ( B @ insert_a ) @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(230,axiom,
! [A: $i] :
( ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( ord_le313189616e_bool @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_finite__Collect__subsets) ).
thf(1062,plain,
! [A: $i] :
( ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( ord_le313189616e_bool @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(364,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ is_fun_a_bool )
=> ( ( C @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_pname_a ) @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ image_pname_a ) ) )
& ( D @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( D @ is_fun_pname_bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_finite__subset__image) ).
thf(1508,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ is_fun_a_bool )
=> ( ( C @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_pname_a ) @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ image_pname_a ) ) )
& ( D @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( D @ is_fun_pname_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(209,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( fequal_fun_nat_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
| ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T) ).
thf(995,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( fequal_fun_nat_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(381,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( B @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) @ ( B @ ( A @ image_876012084bool_a ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_card__image__le) ).
thf(1558,plain,
! [A: $i,B: $i] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( B @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) @ ( B @ ( A @ image_876012084bool_a ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(358,axiom,
! [A: $i,B: $i] :
( ( A = B )
| ~ ( B @ ( A @ ( fequal_fun_nat_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T) ).
thf(1491,plain,
! [A: $i,B: $i] :
( ( A = B )
| ~ ( B @ ( A @ ( fequal_fun_nat_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(415,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( ~ ( B @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_nat ) @ ( finite_card_nat @ hAPP_f22106695ol_nat ) )
= ( B @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( suc @ hAPP_nat_nat ) ) ) )
& ( ( B @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_nat ) @ ( finite_card_nat @ hAPP_f22106695ol_nat ) )
= ( B @ ( finite_card_nat @ hAPP_f22106695ol_nat ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_card__insert__if) ).
thf(1689,plain,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( ~ ( B @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_nat ) @ ( finite_card_nat @ hAPP_f22106695ol_nat ) )
= ( B @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( suc @ hAPP_nat_nat ) ) ) )
& ( ( B @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_nat ) @ ( finite_card_nat @ hAPP_f22106695ol_nat ) )
= ( B @ ( finite_card_nat @ hAPP_f22106695ol_nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(52,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun_pname_bool )
=> ( B @ ( A @ image_pname_pname ) @ is_fun_pname_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__Com__Opname_000tc__Com__Opname) ).
thf(568,plain,
! [A: $i,B: $i] :
( ( B @ is_fun_pname_bool )
=> ( B @ ( A @ image_pname_pname ) @ is_fun_pname_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(445,axiom,
! [A: $i] :
( ~ ( A @ hBOOL )
| ~ ( A @ ( fNot @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fNot_1_1_U) ).
thf(1777,plain,
! [A: $i] :
( ~ ( A @ hBOOL )
| ~ ( A @ ( fNot @ hAPP_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(338,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( fimplies @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
| ( B @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fimplies_1_1_U) ).
thf(1440,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( fimplies @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
| ( B @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(234,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( A @ image_pname_a ) @ ( B @ ( A @ hAPP_pname_a ) @ insert_a ) )
= ( C @ ( A @ image_pname_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_insert__image) ).
thf(1077,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( A @ image_pname_a ) @ ( B @ ( A @ hAPP_pname_a ) @ insert_a ) )
= ( C @ ( A @ image_pname_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(269,axiom,
! [A: $i,B: $i] :
( ( ( B @ is_fun949378684l_bool )
& ( A @ is_fun949378684l_bool ) )
=> ( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( A @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) @ ( B @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A = B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_card__seteq) ).
thf(1212,plain,
! [A: $i,B: $i] :
( ( ( B @ is_fun949378684l_bool )
& ( A @ is_fun949378684l_bool ) )
=> ( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( A @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) @ ( B @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(129,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun_a_bool )
=> ( B @ ( A @ hAPP_f2050579477a_bool ) @ is_fun_a_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
thf(763,plain,
! [A: $i,B: $i] :
( ( B @ is_fun_a_bool )
=> ( B @ ( A @ hAPP_f2050579477a_bool ) @ is_fun_a_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(98,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun949378684l_bool )
=> ( B @ ( A @ cOMBB_2140588453a_bool ) @ is_fun949378684l_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_It__a_Mtc__HOL__Obool) ).
thf(684,plain,
! [A: $i,B: $i] :
( ( B @ is_fun949378684l_bool )
=> ( B @ ( A @ cOMBB_2140588453a_bool ) @ is_fun949378684l_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(225,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( B @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) @ ( B @ ( A @ image_1854862208_pname ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_card__image__le) ).
thf(1045,plain,
! [A: $i,B: $i] :
( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( B @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) @ ( B @ ( A @ image_1854862208_pname ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(45,axiom,
! [A: $i,B: $i] :
( ( B @ collect_pname @ ( A @ insert_pname ) )
= ( B @ ( A @ ( fequal_pname @ cOMBC_1149511130e_bool @ hAPP_p61793385e_bool ) @ ( fNot @ cOMBB_647938656_pname ) @ ( fimplies @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_insert__Collect) ).
thf(549,plain,
! [A: $i,B: $i] :
( ( B @ collect_pname @ ( A @ insert_pname ) )
= ( B @ ( A @ ( fequal_pname @ cOMBC_1149511130e_bool @ hAPP_p61793385e_bool ) @ ( fNot @ cOMBB_647938656_pname ) @ ( fimplies @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(340,axiom,
u @ ( pn @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_4) ).
thf(1444,plain,
u @ ( pn @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(339,axiom,
! [A: $i] : ( A @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_order__refl) ).
thf(1442,plain,
! [A: $i] : ( A @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(210,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_in__mono) ).
thf(999,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(125,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_238756964t_bool ) @ hAPP_f54304608l_bool ) )
= ( C @ ( B @ hAPP_f54304608l_bool ) @ ( A @ hAPP_bool_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Nat__On) ).
thf(752,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_238756964t_bool ) @ hAPP_f54304608l_bool ) )
= ( C @ ( B @ hAPP_f54304608l_bool ) @ ( A @ hAPP_bool_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(1,conjecture,
u @ ( mgt_call @ image_pname_a ) @ ( g @ ( pn @ ( mgt_call @ hAPP_pname_a ) @ insert_a ) @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_6) ).
thf(2,negated_conjecture,
~ ( u @ ( mgt_call @ image_pname_a ) @ ( g @ ( pn @ ( mgt_call @ hAPP_pname_a ) @ insert_a ) @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(447,plain,
~ ( u @ ( mgt_call @ image_pname_a ) @ ( g @ ( pn @ ( mgt_call @ hAPP_pname_a ) @ insert_a ) @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(154,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( C @ ( A @ insert_a ) @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_subset__insertI2) ).
thf(833,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( C @ ( A @ insert_a ) @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(312,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( B @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) @ ( A @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_card__mono) ).
thf(1380,plain,
! [A: $i,B: $i] :
( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( B @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) @ ( A @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(354,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( B @ ( A @ image_pname_a ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_card__image__le) ).
thf(1480,plain,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( B @ ( A @ image_pname_a ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(196,axiom,
u @ ( mgt_call @ image_pname_a ) @ ( g @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
thf(950,plain,
u @ ( mgt_call @ image_pname_a ) @ ( g @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(155,axiom,
( ( g @ ( finite_card_a @ hAPP_fun_a_bool_nat ) )
= ( na @ ( suc @ hAPP_nat_nat ) @ ( u @ ( mgt_call @ image_pname_a ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ minus_minus_nat @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_3) ).
thf(835,plain,
( ( g @ ( finite_card_a @ hAPP_fun_a_bool_nat ) )
= ( na @ ( suc @ hAPP_nat_nat ) @ ( u @ ( mgt_call @ image_pname_a ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ minus_minus_nat @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(276,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] : ( D @ ( suc @ hAPP_nat_nat ) @ ( C @ hAPP_nat_fun_a_bool ) @ ( D @ ( C @ hAPP_nat_fun_a_bool ) @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( C @ hAPP_nat_fun_a_bool ) @ ( A @ ( C @ hAPP_nat_fun_a_bool ) @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_lift__Suc__mono__le) ).
thf(1248,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] : ( D @ ( suc @ hAPP_nat_nat ) @ ( C @ hAPP_nat_fun_a_bool ) @ ( D @ ( C @ hAPP_nat_fun_a_bool ) @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( C @ hAPP_nat_fun_a_bool ) @ ( A @ ( C @ hAPP_nat_fun_a_bool ) @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(139,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( B @ ( A @ image_a_pname ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_card__image__le) ).
thf(790,plain,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( B @ ( A @ image_a_pname ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(186,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( fdisj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
| ~ ( B @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fdisj_2_1_U) ).
thf(918,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( fdisj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
| ~ ( B @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(296,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( fequal_fun_a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
| ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__fun_It__a_Mtc__HOL__Obool_J_T) ).
thf(1314,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( fequal_fun_a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(300,axiom,
! [A: $i,B: $i] : ( A @ ( B @ insert_nat ) @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_subset__insertI) ).
thf(1335,plain,
! [A: $i,B: $i] : ( A @ ( B @ insert_nat ) @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(89,axiom,
finite_finite_a @ is_fun949378684l_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Finite__Set_Ofinite_000t__a) ).
thf(664,plain,
finite_finite_a @ is_fun949378684l_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(103,axiom,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1295398978l_bool ) @ is_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_) ).
thf(696,plain,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1295398978l_bool ) @ is_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( suc @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) )
= ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_diff__Suc__Suc) ).
thf(474,plain,
! [A: $i,B: $i] :
( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( suc @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) )
= ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(326,axiom,
~ ( g @ ( pn @ ( mgt_call @ hAPP_pname_a ) @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_5) ).
thf(1410,plain,
~ ( g @ ( pn @ ( mgt_call @ hAPP_pname_a ) @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(131,axiom,
! [A: $i,B: $i] :
( ( B @ is_a )
=> ( B @ ( A @ hAPP_a_fun_a_bool ) @ is_fun_a_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
thf(767,plain,
! [A: $i,B: $i] :
( ( B @ is_a )
=> ( B @ ( A @ hAPP_a_fun_a_bool ) @ is_fun_a_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(200,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ ( B @ ( C @ minus_minus_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( A @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_le__diff__iff) ).
thf(960,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( A @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ ( B @ ( C @ minus_minus_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ ( B @ ( C @ minus_minus_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(79,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ insert_pname ) @ ( A @ insert_pname ) )
= ( C @ ( A @ insert_pname ) @ ( B @ insert_pname ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_insert__commute) ).
thf(635,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ insert_pname ) @ ( A @ insert_pname ) )
= ( C @ ( A @ insert_pname ) @ ( B @ insert_pname ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(120,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It) ).
thf(740,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(274,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ is_fun_a_bool )
& ( A @ is_fun_a_bool ) )
=> ( ~ ( C @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ~ ( A @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( ( C @ ( B @ insert_a ) )
= ( A @ ( B @ insert_a ) ) )
<=> ( C = A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_insert__ident) ).
thf(1236,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ is_fun_a_bool )
& ( A @ is_fun_a_bool ) )
=> ( ~ ( C @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ~ ( A @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( ( C = A )
=> ( ( C @ ( B @ insert_a ) )
= ( A @ ( B @ insert_a ) ) ) )
& ( ( ( C @ ( B @ insert_a ) )
= ( A @ ( B @ insert_a ) ) )
=> ( C = A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(370,axiom,
! [A: $i,B: $i] : ( A @ ( B @ insert_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_subset__insertI) ).
thf(1532,plain,
! [A: $i,B: $i] : ( A @ ( B @ insert_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(314,axiom,
! [A: $i,B: $i] :
( ( A = B )
=> ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_equalityD2) ).
thf(1384,plain,
! [A: $i,B: $i] :
( ( A = B )
=> ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(217,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_finite__subset) ).
thf(1019,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(82,axiom,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1637334154l_bool ) @ is_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HOL__Obool_) ).
thf(644,plain,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1637334154l_bool ) @ is_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(361,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( B @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) @ ( B @ ( A @ image_fun_a_bool_a ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_card__image__le) ).
thf(1500,plain,
! [A: $i,B: $i] :
( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( B @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) @ ( B @ ( A @ image_fun_a_bool_a ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(171,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ insert_a ) )
= ( B @ ( member_a @ cOMBC_1355376034l_bool @ hAPP_f2050579477a_bool ) @ ( A @ ( fequal_a @ cOMBC_a_a_bool @ hAPP_a_fun_a_bool ) @ ( fdisj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_insert__compr__raw) ).
thf(871,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ insert_a ) )
= ( B @ ( member_a @ cOMBC_1355376034l_bool @ hAPP_f2050579477a_bool ) @ ( A @ ( fequal_a @ cOMBC_a_a_bool @ hAPP_a_fun_a_bool ) @ ( fdisj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(394,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL )
=> ( B @ ( A @ insert1117693814l_bool ) @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_finite_OinsertI) ).
thf(1621,plain,
! [A: $i,B: $i] :
( ( B @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL )
=> ( B @ ( A @ insert1117693814l_bool ) @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(247,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert1325755072e_bool ) @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) )
= ( B @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) @ ( suc @ hAPP_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_card__insert__disjoint) ).
thf(1120,plain,
! [A: $i,B: $i] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert1325755072e_bool ) @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) )
= ( B @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) @ ( suc @ hAPP_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(67,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_307249310e_bool ) @ hAPP_f1664156314l_bool ) )
= ( C @ ( B @ hAPP_f1664156314l_bool ) @ ( A @ hAPP_bool_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Op) ).
thf(607,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_307249310e_bool ) @ hAPP_f1664156314l_bool ) )
= ( C @ ( B @ hAPP_f1664156314l_bool ) @ ( A @ hAPP_bool_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(74,axiom,
! [A: $i,B: $i] :
( ( ( B @ is_pname )
& ( A @ is_fun_pname_bool ) )
=> ( B @ ( A @ hAPP_pname_bool ) @ is_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Com__Opname_000tc__HOL__Obool) ).
thf(624,plain,
! [A: $i,B: $i] :
( ( ( B @ is_pname )
& ( A @ is_fun_pname_bool ) )
=> ( B @ ( A @ hAPP_pname_bool ) @ is_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(157,axiom,
! [A: $i,B: $i] :
( ( B @ is_pname )
=> ( B @ ( A @ hAPP_pname_a ) @ is_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Com__Opname_000t__a) ).
thf(839,plain,
! [A: $i,B: $i] :
( ( B @ is_pname )
=> ( B @ ( A @ hAPP_pname_a ) @ is_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(306,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( B @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) @ ( B @ ( A @ image_1921560913_pname ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_card__image__le) ).
thf(1352,plain,
! [A: $i,B: $i] :
( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( B @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) @ ( B @ ( A @ image_1921560913_pname ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_1269652216l_bool @ hAPP_f760187903l_bool ) @ hAPP_f937997336l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f760187903l_bool ) @ hAPP_f937997336l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool) ).
thf(464,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_1269652216l_bool @ hAPP_f760187903l_bool ) @ hAPP_f937997336l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f760187903l_bool ) @ hAPP_f937997336l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(280,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_subset__trans) ).
thf(1268,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(55,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ insert_pname ) @ ( A @ insert_pname ) )
= ( B @ ( A @ insert_pname ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_insert__absorb2) ).
thf(575,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ insert_pname ) @ ( A @ insert_pname ) )
= ( B @ ( A @ insert_pname ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(162,axiom,
u @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(850,plain,
u @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(421,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ is_a )
& ( A @ is_a ) )
=> ( ( C @ ( B @ insert_a ) @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A != B )
=> ( C @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_insertE) ).
thf(1713,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ is_a )
& ( A @ is_a ) )
=> ( ( C @ ( B @ insert_a ) @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A != B )
=> ( C @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(144,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( B @ ( A @ image_pname_nat ) @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_card__image__le) ).
thf(803,plain,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( B @ ( A @ image_pname_nat ) @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(298,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_set__eq__subset) ).
thf(1320,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(213,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( fequal_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
| ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Nat__Onat_T) ).
thf(1009,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( fequal_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(126,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_226598744l_bool @ hAPP_f800510211t_bool ) @ hAPP_nat_bool ) )
= ( B @ ( C @ ( A @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_) ).
thf(755,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_226598744l_bool @ hAPP_f800510211t_bool ) @ hAPP_nat_bool ) )
= ( B @ ( C @ ( A @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_bool_bool_nat ) @ hAPP_nat_bool ) )
= ( C @ ( B @ hAPP_nat_bool ) @ ( A @ hAPP_bool_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Nat__Onat_U) ).
thf(491,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_bool_bool_nat ) @ hAPP_nat_bool ) )
= ( C @ ( B @ hAPP_nat_bool ) @ ( A @ hAPP_bool_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(350,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( B @ ( A @ image_1655916159e_bool ) @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_card__image__le) ).
thf(1468,plain,
! [A: $i,B: $i] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( B @ ( A @ image_1655916159e_bool ) @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(23,axiom,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f937997336l_bool ) @ is_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HO) ).
thf(496,plain,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f937997336l_bool ) @ is_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(108,axiom,
! [A: $i] :
( ( A @ is_fun_a_bool )
=> ( A @ p @ is_fun949378684l_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_v_P) ).
thf(708,plain,
! [A: $i] :
( ( A @ is_fun_a_bool )
=> ( A @ p @ is_fun949378684l_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(329,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ minus_minus_nat @ hAPP_nat_nat ) @ ( B @ minus_minus_nat @ hAPP_nat_nat ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_diff__diff__cancel) ).
thf(1417,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ minus_minus_nat @ hAPP_nat_nat ) @ ( B @ minus_minus_nat @ hAPP_nat_nat ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun_pname_bool )
=> ( B @ ( A @ image_47868345e_bool ) @ is_fun1661590463l_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_) ).
thf(469,plain,
! [A: $i,B: $i] :
( ( B @ is_fun_pname_bool )
=> ( B @ ( A @ image_47868345e_bool ) @ is_fun1661590463l_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(192,axiom,
! [A: $i] : ( A @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_order__refl) ).
thf(940,plain,
! [A: $i] : ( A @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(1803,plain,
$false,
inference(e,[status(thm)],[1337,1633,1767,1105,628,518,1295,1549,1158,1406,730,1422,1073,1544,1728,614,597,1486,1750,977,878,511,1705,1608,1137,500,715,1275,698,913,1354,1458,1164,797,829,1001,782,841,885,1724,565,1529,1243,1127,1623,1482,1287,1709,570,1660,619,1279,1455,934,1462,542,460,559,638,1147,1572,1013,1398,1115,1773,448,1494,1302,1450,591,1040,646,485,1581,480,1489,1415,1051,821,1377,1215,692,734,1447,866,453,1394,660,1600,1521,507,527,1564,1345,988,1206,920,942,678,1438,1199,810,1470,534,1736,1153,761,1047,1730,1343,1042,1502,630,815,1560,957,894,1021,778,1123,862,1570,1174,1676,788,1370,847,1555,665,1687,522,1027,682,1281,1392,1740,974,916,467,1032,1602,1210,1656,1291,710,1402,1360,1541,874,1270,948,1064,725,980,1672,1719,610,857,519,578,1534,1017,471,1683,1082,488,554,537,686,1424,1584,706,1155,547,837,1099,701,1478,1297,1382,1266,1192,457,911,721,1429,1434,1318,792,1779,805,1695,765,1071,1515,1616,586,1732,926,953,1185,662,718,1648,750,1764,1103,745,573,689,1374,1631,601,513,1754,584,562,732,1752,1388,743,1007,694,843,1125,1226,545,641,1707,498,1635,1332,1092,1090,1464,1224,1258,704,604,831,1408,1117,1574,451,1144,616,599,1771,737,509,880,649,477,594,799,621,1029,494,1080,758,1339,1557,552,1149,964,626,915,769,1460,1293,668,462,932,1061,983,1396,1015,1176,986,1775,1496,851,505,922,1445,868,780,1643,455,883,1726,1250,1626,675,1662,1304,1166,1208,1420,1277,648,812,516,1472,1551,1049,531,944,795,680,968,823,525,855,1547,776,1748,712,557,1743,1400,1711,673,1432,1637,1038,502,1658,1538,951,808,1738,1218,1404,1766,1536,1284,864,1427,1717,876,859,1504,727,1272,612,845,1180,539,482,671,903,581,1412,1517,891,1390,1108,450,1084,1289,1453,1590,1646,588,1721,1101,652,1629,1745,632,1523,786,1341,896,748,1674,1639,1062,1508,995,1558,1491,1689,568,1777,1440,1077,1212,763,684,1045,549,1444,1442,999,752,447,833,1380,1480,950,835,1248,790,918,1314,1335,664,696,474,1410,767,960,635,740,1236,1532,1384,1019,644,1500,871,1621,1120,607,624,839,1352,464,1268,575,850,1713,803,1320,1009,755,491,1468,496,708,1417,469,940]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW473+1 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.13/0.40 % Computer : n016.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sat Sep 26 16:06:16 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.86/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.94/1.37 % [INFO] Parsing done (370ms).
% 1.94/1.38 % [INFO] Running in sequential loop mode.
% 3.22/1.78 % [INFO] eprover registered as external prover.
% 3.22/1.79 % [INFO] Scanning for conjecture ...
% 3.70/1.99 % [INFO] Found a conjecture (or negated_conjecture) and 448 axioms. Running axiom selection ...
% 4.90/2.21 % [INFO] Axiom selection finished. Selected 444 axioms (removed 4 axioms).
% 6.11/2.55 % [INFO] Problem is first-order (TPTP FOF).
% 6.11/2.58 % [INFO] Type checking passed.
% 6.11/2.58 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 17.36/5.39 % External prover 'e' found a proof!
% 17.36/5.39 % [INFO] Killing All external provers ...
% 17.36/5.39 % Time passed: 4842ms (effective reasoning time: 4003ms)
% 17.36/5.39 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 17.36/5.40 % Axioms used in derivation (444): help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_It__a_Mtc__H, fact_248_subset__trans, gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_, fact_8_finite__Collect__subsets, fact_277_subset__insert, help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__011, fact_265_insert__compr__raw, help_fimplies_2_1_U, fact_24_finite__imageI, fact_87_card__seteq, fact_205_insert__absorb2, gsy_c_Set_Oimage_000tc__Com__Opname_000tc__Com__Opname, gsy_c_Set_Oimage_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J_0_001, gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obool, fact_11_finite__imageI, fact_197_insert__compr, help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool, gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc_, fact_269_subset__insertI, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_010, gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_Itc__Com__Op, help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It, fact_131_finite__Collect__disjI, fact_58_card__image__le, gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__, fact_43_finite__imageI, fact_97_card__insert__le, gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool, help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_, gsy_c_hAPP_000t__a_000tc__HOL__Obool, gsy_c_Set_Oimage_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_, help_fconj_3_1_U, fact_135_finite__insert, gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obo, fact_35_finite__imageI, fact_38_finite__imageI, fact_15_finite__imageI, gsy_c_Set_Oimage_000tc__Com__Opname_000t__a, fact_246_subset__trans, fact_52_finite_OinsertI, fact_274_insert__subset, gsy_c_Set_Oinsert_000tc__Com__Opname, gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_, help_fequal_1_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T, fact_29_finite__imageI, fact_226_subset__refl, gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo_005, fact_281_insert__mono, fact_250_equalityE, gsy_c_hAPP_000tc__Com__Opname_000tc__HOL__Obool, help_fequal_2_1_fequal_000tc__Nat__Onat_T, fact_25_finite__imageI, fact_32_finite__imageI, fact_142_finite__subset, fact_216_insert__ident, fact_118_card__Collect__le__nat, fact_243_set__mp, fact_175_pigeonhole__infinite, fact_200_insert__Collect, fact_145_finite__subset, fact_255_Collect__def, conj_3, fact_206_insert__absorb2, fact_80_card__mono, gsy_c_Finite__Set_Ofinite_000t__a, help_fequal_2_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T, gsy_c_Set_Oimage_000tc__Nat__Onat_000t__a, fact_221_insertI2, fact_264_insert__compr__raw, 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% 17.36/5.40 % No. of inferences in proof: 892
% 18.04/5.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4842 ms resp. 4003 ms w/o parsing
% 19.29/5.73 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 19.29/5.73 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------