%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWW473+2 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n012.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 09:10:18 AM UTC 2026
% Result : Theorem 17.95s 6.95s
% Output : Refutation 19.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 913
% Syntax : Number of formulae : 1828 ( 530 unt; 0 typ; 0 def)
% Number of atoms : 4925 (1118 equ; 0 cnn)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 24748 ( 442 ~; 123 |; 627 &;21209 @)
% ( 137 <=>;2210 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 281 ( 279 usr; 61 con; 0-2 aty)
% Number of variables : 4234 ( 0 ^;4092 !; 142 ?;4234 :)
% 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(hAPP_nat_nat_decl,type,
hAPP_nat_nat: $i > $i > $i ).
thf(plus_plus_nat_decl,type,
plus_plus_nat: $i > $i ).
thf(suc_decl,type,
suc: $i ).
thf(one_one_nat_decl,type,
one_one_nat: $i ).
thf(is_fun1661590463l_bool_decl,type,
is_fun1661590463l_bool: $i > $o ).
thf(hAPP_n850744903l_bool_decl,type,
hAPP_n850744903l_bool: $i > $i > $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(bot_bot_fun_a_bool_decl,type,
bot_bot_fun_a_bool: $i ).
thf(hAPP_f1637334154l_bool_decl,type,
hAPP_f1637334154l_bool: $i > $i > $i ).
thf(finite2012431853t_bool_decl,type,
finite2012431853t_bool: $i ).
thf(hAPP_f1772781669l_bool_decl,type,
hAPP_f1772781669l_bool: $i > $i > $i ).
thf(ord_le1454342156l_bool_decl,type,
ord_le1454342156l_bool: $i ).
thf(image_2129980159t_bool_decl,type,
image_2129980159t_bool: $i > $i > $i ).
thf(is_fun_pname_bool_decl,type,
is_fun_pname_bool: $i > $o ).
thf(hAPP_f1664156314l_bool_decl,type,
hAPP_f1664156314l_bool: $i > $i > $i ).
thf(hAPP_f434788991l_bool_decl,type,
hAPP_f434788991l_bool: $i > $i > $i ).
thf(ord_le313189616e_bool_decl,type,
ord_le313189616e_bool: $i ).
thf(finite_finite_pname_decl,type,
finite_finite_pname: $i ).
thf(hAPP_nat_bool_decl,type,
hAPP_nat_bool: $i > $i > $i ).
thf(hAPP_n1699378549t_bool_decl,type,
hAPP_n1699378549t_bool: $i > $i > $i ).
thf(ord_less_nat_decl,type,
ord_less_nat: $i ).
thf(cOMBK_bool_nat_decl,type,
cOMBK_bool_nat: $i > $i ).
thf(hAPP_f54304608l_bool_decl,type,
hAPP_f54304608l_bool: $i > $i > $i ).
thf(cOMBK_1994329625t_bool_decl,type,
cOMBK_1994329625t_bool: $i > $i ).
thf(hAPP_p338031245l_bool_decl,type,
hAPP_p338031245l_bool: $i > $i > $i ).
thf(member_pname_decl,type,
member_pname: $i ).
thf(hAPP_n215258509l_bool_decl,type,
hAPP_n215258509l_bool: $i > $i > $i ).
thf(member_nat_decl,type,
member_nat: $i ).
thf(hAPP_pname_nat_decl,type,
hAPP_pname_nat: $i > $i > $i ).
thf(image_pname_nat_decl,type,
image_pname_nat: $i > $i > $i ).
thf(bot_bot_bool_decl,type,
bot_bot_bool: $i ).
thf(cOMBS_350070575l_bool_decl,type,
cOMBS_350070575l_bool: $i > $i > $i ).
thf(bot_bo844097828e_bool_decl,type,
bot_bo844097828e_bool: $i ).
thf(insert_nat_decl,type,
insert_nat: $i > $i > $i ).
thf(bot_bot_fun_nat_bool_decl,type,
bot_bot_fun_nat_bool: $i ).
thf(image_47868345e_bool_decl,type,
image_47868345e_bool: $i > $i > $i ).
thf(ord_less_eq_nat_decl,type,
ord_less_eq_nat: $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(cOMBS_1187019125l_bool_decl,type,
cOMBS_1187019125l_bool: $i > $i > $i ).
thf(cOMBB_444170502t_bool_decl,type,
cOMBB_444170502t_bool: $i > $i > $i ).
thf(fdisj_decl,type,
fdisj: $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_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(wt_decl,type,
wt: $i > $i ).
thf(is_fun949378684l_bool_decl,type,
is_fun949378684l_bool: $i > $o ).
thf(cOMBB_2140588453a_bool_decl,type,
cOMBB_2140588453a_bool: $i > $i > $i ).
thf(finite_finite_nat_decl,type,
finite_finite_nat: $i ).
thf(collect_nat_decl,type,
collect_nat: $i > $i ).
thf(cOMBS_nat_bool_bool_decl,type,
cOMBS_nat_bool_bool: $i > $i > $i ).
thf(cOMBB_1015721476ol_nat_decl,type,
cOMBB_1015721476ol_nat: $i > $i > $i ).
thf(fconj_decl,type,
fconj: $i ).
thf(cOMBC_nat_nat_bool_decl,type,
cOMBC_nat_nat_bool: $i > $i ).
thf(hAPP_f389811538l_bool_decl,type,
hAPP_f389811538l_bool: $i > $i > $i ).
thf(hAPP_bool_bool_decl,type,
hAPP_bool_bool: $i > $i > $i ).
thf(hAPP_b589554111l_bool_decl,type,
hAPP_b589554111l_bool: $i > $i > $i ).
thf(ord_less_eq_bool_decl,type,
ord_less_eq_bool: $i ).
thf(hAPP_pname_bool_decl,type,
hAPP_pname_bool: $i > $i > $i ).
thf(bot_bot_nat_decl,type,
bot_bot_nat: $i ).
thf(zero_zero_nat_decl,type,
zero_zero_nat: $i ).
thf(collect_a_decl,type,
collect_a: $i > $i ).
thf(cOMBK_bool_a_decl,type,
cOMBK_bool_a: $i > $i ).
thf(fFalse_decl,type,
fFalse: $i ).
thf(minus_minus_nat_decl,type,
minus_minus_nat: $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(ord_le1568362934t_bool_decl,type,
ord_le1568362934t_bool: $i ).
thf(is_pname_decl,type,
is_pname: $i > $o ).
thf(image_nat_pname_decl,type,
image_nat_pname: $i > $i > $i ).
thf(hAPP_nat_pname_decl,type,
hAPP_nat_pname: $i > $i > $i ).
thf(image_112932426a_bool_decl,type,
image_112932426a_bool: $i > $i > $i ).
thf(image_1283814551_pname_decl,type,
image_1283814551_pname: $i > $i > $i ).
thf(ord_le675606854l_bool_decl,type,
ord_le675606854l_bool: $i ).
thf(finite595471783e_bool_decl,type,
finite595471783e_bool: $i ).
thf(hAPP_a_a_decl,type,
hAPP_a_a: $i > $i > $i ).
thf(cOMBC_385542954t_bool_decl,type,
cOMBC_385542954t_bool: $i > $i ).
thf(hAPP_f800510211t_bool_decl,type,
hAPP_f800510211t_bool: $i > $i > $i ).
thf(cOMBB_647938656_pname_decl,type,
cOMBB_647938656_pname: $i > $i > $i ).
thf(image_fun_a_bool_nat_decl,type,
image_fun_a_bool_nat: $i > $i > $i ).
thf(hAPP_f621171935l_bool_decl,type,
hAPP_f621171935l_bool: $i > $i > $i ).
thf(hAPP_f1434722111l_bool_decl,type,
hAPP_f1434722111l_bool: $i > $i > $i ).
thf(ord_le1375614389l_bool_decl,type,
ord_le1375614389l_bool: $i ).
thf(finite347923420a_bool_decl,type,
finite347923420a_bool: $i ).
thf(image_1854862208_pname_decl,type,
image_1854862208_pname: $i > $i > $i ).
thf(collect_fun_a_bool_decl,type,
collect_fun_a_bool: $i > $i ).
thf(hAPP_p61793385e_bool_decl,type,
hAPP_p61793385e_bool: $i > $i > $i ).
thf(insert_pname_decl,type,
insert_pname: $i > $i > $i ).
thf(hAPP_f1748468828l_bool_decl,type,
hAPP_f1748468828l_bool: $i > $i > $i ).
thf(hAPP_n1006566506l_bool_decl,type,
hAPP_n1006566506l_bool: $i > $i > $i ).
thf(cOMBB_bool_bool_nat_decl,type,
cOMBB_bool_bool_nat: $i > $i > $i ).
thf(image_nat_fun_a_bool_decl,type,
image_nat_fun_a_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(hAPP_f921600141ol_nat_decl,type,
hAPP_f921600141ol_nat: $i > $i > $i ).
thf(finite_card_pname_decl,type,
finite_card_pname: $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(insert1325755072e_bool_decl,type,
insert1325755072e_bool: $i > $i > $i ).
thf(collec1974731493e_bool_decl,type,
collec1974731493e_bool: $i > $i ).
thf(cOMBB_2095475776e_bool_decl,type,
cOMBB_2095475776e_bool: $i > $i > $i ).
thf(cOMBC_1284144636l_bool_decl,type,
cOMBC_1284144636l_bool: $i > $i ).
thf(fequal533582459e_bool_decl,type,
fequal533582459e_bool: $i ).
thf(hAPP_f559147733l_bool_decl,type,
hAPP_f559147733l_bool: $i > $i > $i ).
thf(cOMBC_1988546018l_bool_decl,type,
cOMBC_1988546018l_bool: $i > $i ).
thf(member799430823e_bool_decl,type,
member799430823e_bool: $i ).
thf(hAPP_f2009550088ol_nat_decl,type,
hAPP_f2009550088ol_nat: $i > $i > $i ).
thf(finite1306199131a_bool_decl,type,
finite1306199131a_bool: $i ).
thf(insert_fun_a_bool_decl,type,
insert_fun_a_bool: $i > $i > $i ).
thf(hAPP_p1534023578a_bool_decl,type,
hAPP_p1534023578a_bool: $i > $i > $i ).
thf(cOMBC_a_pname_bool_decl,type,
cOMBC_a_pname_bool: $i > $i ).
thf(hAPP_a93125764e_bool_decl,type,
hAPP_a93125764e_bool: $i > $i > $i ).
thf(hAPP_f1549043526a_bool_decl,type,
hAPP_f1549043526a_bool: $i > $i > $i ).
thf(cOMBC_777206479l_bool_decl,type,
cOMBC_777206479l_bool: $i > $i ).
thf(hAPP_a1392362872l_bool_decl,type,
hAPP_a1392362872l_bool: $i > $i > $i ).
thf(hAPP_f1476298914l_bool_decl,type,
hAPP_f1476298914l_bool: $i > $i > $i ).
thf(undefined_a_decl,type,
undefined_a: $i > $i ).
thf(x_a_decl,type,
x_a: $i ).
thf(fequal_nat_decl,type,
fequal_nat: $i ).
thf(hAPP_f1794073134e_bool_decl,type,
hAPP_f1794073134e_bool: $i > $i > $i ).
thf(cOMBB_1693087065a_bool_decl,type,
cOMBB_1693087065a_bool: $i > $i > $i ).
thf(hAPP_f1128469712_pname_decl,type,
hAPP_f1128469712_pname: $i > $i > $i ).
thf(collect_pname_decl,type,
collect_pname: $i > $i ).
thf(cOMBC_1149511130e_bool_decl,type,
cOMBC_1149511130e_bool: $i > $i ).
thf(fequal_pname_decl,type,
fequal_pname: $i ).
thf(cOMBB_743407885bool_a_decl,type,
cOMBB_743407885bool_a: $i > $i > $i ).
thf(hAPP_a_fun_nat_bool_decl,type,
hAPP_a_fun_nat_bool: $i > $i > $i ).
thf(hAPP_f1051908748a_bool_decl,type,
hAPP_f1051908748a_bool: $i > $i > $i ).
thf(bot_bo1649642514l_bool_decl,type,
bot_bo1649642514l_bool: $i ).
thf(cOMBB_610033911bool_a_decl,type,
cOMBB_610033911bool_a: $i > $i > $i ).
thf(hAPP_a_pname_decl,type,
hAPP_a_pname: $i > $i > $i ).
thf(cOMBB_800536526ol_nat_decl,type,
cOMBB_800536526ol_nat: $i > $i > $i ).
thf(hAPP_f292226953l_bool_decl,type,
hAPP_f292226953l_bool: $i > $i > $i ).
thf(hAPP_a217006258l_bool_decl,type,
hAPP_a217006258l_bool: $i > $i > $i ).
thf(cOMBB_1137537805bool_a_decl,type,
cOMBB_1137537805bool_a: $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(cOMBC_nat_a_bool_decl,type,
cOMBC_nat_a_bool: $i > $i ).
thf(hAPP_nat_fun_a_bool_decl,type,
hAPP_nat_fun_a_bool: $i > $i > $i ).
thf(hAPP_f654413245e_bool_decl,type,
hAPP_f654413245e_bool: $i > $i > $i ).
thf(cOMBB_141086128t_bool_decl,type,
cOMBB_141086128t_bool: $i > $i > $i ).
thf(hAPP_f1291551745_pname_decl,type,
hAPP_f1291551745_pname: $i > $i > $i ).
thf(hAPP_f55526627ol_nat_decl,type,
hAPP_f55526627ol_nat: $i > $i > $i ).
thf(finite1340463720e_bool_decl,type,
finite1340463720e_bool: $i ).
thf(cOMBC_1666426608t_bool_decl,type,
cOMBC_1666426608t_bool: $i > $i ).
thf(hAPP_f1066163005t_bool_decl,type,
hAPP_f1066163005t_bool: $i > $i > $i ).
thf(image_1921560913_pname_decl,type,
image_1921560913_pname: $i > $i > $i ).
thf(cOMBC_595898202l_bool_decl,type,
cOMBC_595898202l_bool: $i > $i ).
thf(cOMBC_226598744l_bool_decl,type,
cOMBC_226598744l_bool: $i > $i ).
thf(cOMBS_568398431l_bool_decl,type,
cOMBS_568398431l_bool: $i > $i > $i ).
thf(image_fun_nat_bool_a_decl,type,
image_fun_nat_bool_a: $i > $i > $i ).
thf(hAPP_n1025906991e_bool_decl,type,
hAPP_n1025906991e_bool: $i > $i > $i ).
thf(cOMBB_1212655066ol_nat_decl,type,
cOMBB_1212655066ol_nat: $i > $i > $i ).
thf(hAPP_p130839763l_bool_decl,type,
hAPP_p130839763l_bool: $i > $i > $i ).
thf(cOMBC_615407716e_bool_decl,type,
cOMBC_615407716e_bool: $i > $i ).
thf(image_pname_pname_decl,type,
image_pname_pname: $i > $i > $i ).
thf(cOMBB_bool_bool_a_decl,type,
cOMBB_bool_bool_a: $i > $i > $i ).
thf(cOMBB_2026977092ol_nat_decl,type,
cOMBB_2026977092ol_nat: $i > $i > $i ).
thf(cOMBC_267053842l_bool_decl,type,
cOMBC_267053842l_bool: $i > $i ).
thf(cOMBB_307249310e_bool_decl,type,
cOMBB_307249310e_bool: $i > $i > $i ).
thf(image_1551609309ol_nat_decl,type,
image_1551609309ol_nat: $i > $i > $i ).
thf(image_26036933t_bool_decl,type,
image_26036933t_bool: $i > $i > $i ).
thf(cOMBC_331553030l_bool_decl,type,
cOMBC_331553030l_bool: $i > $i ).
thf(cOMBK_1857069011e_bool_decl,type,
cOMBK_1857069011e_bool: $i > $i ).
thf(fTrue_decl,type,
fTrue: $i ).
thf(image_nat_a_decl,type,
image_nat_a: $i > $i > $i ).
thf(hAPP_f2050579477a_bool_decl,type,
hAPP_f2050579477a_bool: $i > $i > $i ).
thf(fimplies_decl,type,
fimplies: $i ).
thf(fNot_decl,type,
fNot: $i ).
thf(cOMBC_pname_a_bool_decl,type,
cOMBC_pname_a_bool: $i > $i ).
thf(cOMBK_bool_pname_decl,type,
cOMBK_bool_pname: $i > $i ).
thf(hAPP_p1824510254l_bool_decl,type,
hAPP_p1824510254l_bool: $i > $i > $i ).
thf(hAPP_n1414589940l_bool_decl,type,
hAPP_n1414589940l_bool: $i > $i > $i ).
thf(cOMBB_675860798_pname_decl,type,
cOMBB_675860798_pname: $i > $i > $i ).
thf(hAPP_p393069232l_bool_decl,type,
hAPP_p393069232l_bool: $i > $i > $i ).
thf(image_876012084bool_a_decl,type,
image_876012084bool_a: $i > $i > $i ).
thf(mgt_decl,type,
mgt: $i > $i ).
thf(cOMBC_pname_nat_bool_decl,type,
cOMBC_pname_nat_bool: $i > $i ).
thf(hAPP_p1499970991t_bool_decl,type,
hAPP_p1499970991t_bool: $i > $i > $i ).
thf(hAPP_f1951378235l_bool_decl,type,
hAPP_f1951378235l_bool: $i > $i > $i ).
thf(cOMBB_408569982_pname_decl,type,
cOMBB_408569982_pname: $i > $i > $i ).
thf(cOMBC_a_nat_bool_decl,type,
cOMBC_a_nat_bool: $i > $i ).
thf(cOMBS_a_bool_bool_decl,type,
cOMBS_a_bool_bool: $i > $i > $i ).
thf(hAPP_f696928925ol_nat_decl,type,
hAPP_f696928925ol_nat: $i > $i > $i ).
thf(finite346522414t_bool_decl,type,
finite346522414t_bool: $i ).
thf(cOMBB_1896684278e_bool_decl,type,
cOMBB_1896684278e_bool: $i > $i > $i ).
thf(image_819518260e_bool_decl,type,
image_819518260e_bool: $i > $i > $i ).
thf(cOMBB_598082538e_bool_decl,type,
cOMBB_598082538e_bool: $i > $i > $i ).
thf(hAPP_f1297739591_pname_decl,type,
hAPP_f1297739591_pname: $i > $i > $i ).
thf(image_1655916159e_bool_decl,type,
image_1655916159e_bool: $i > $i > $i ).
thf(cOMBB_1321347587bool_a_decl,type,
cOMBB_1321347587bool_a: $i > $i > $i ).
thf(hAPP_a_nat_decl,type,
hAPP_a_nat: $i > $i > $i ).
thf(cOMBS_1035972772l_bool_decl,type,
cOMBS_1035972772l_bool: $i > $i > $i ).
thf(bot_bo1389914601l_bool_decl,type,
bot_bo1389914601l_bool: $i ).
thf(undefined_pname_decl,type,
undefined_pname: $i > $i ).
thf(pname_decl,type,
pname: $i ).
thf(image_a_pname_decl,type,
image_a_pname: $i > $i > $i ).
thf(hAPP_f937997336l_bool_decl,type,
hAPP_f937997336l_bool: $i > $i > $i ).
thf(cOMBK_324466864a_bool_decl,type,
cOMBK_324466864a_bool: $i > $i ).
thf(finite_finite_a_decl,type,
finite_finite_a: $i ).
thf(cOMBB_1250273980t_bool_decl,type,
cOMBB_1250273980t_bool: $i > $i > $i ).
thf(hAPP_nat_a_decl,type,
hAPP_nat_a: $i > $i > $i ).
thf(bot_bo1701429464l_bool_decl,type,
bot_bo1701429464l_bool: $i ).
thf(image_a_a_decl,type,
image_a_a: $i > $i > $i ).
thf(hAPP_f2117159681l_bool_decl,type,
hAPP_f2117159681l_bool: $i > $i > $i ).
thf(image_fun_a_bool_a_decl,type,
image_fun_a_bool_a: $i > $i > $i ).
thf(cOMBC_386238098l_bool_decl,type,
cOMBC_386238098l_bool: $i > $i ).
thf(cOMBC_nat_pname_bool_decl,type,
cOMBC_nat_pname_bool: $i > $i ).
thf(cOMBC_1004116266e_bool_decl,type,
cOMBC_1004116266e_bool: $i > $i ).
thf(p_decl,type,
p: $i > $i ).
thf(cOMBB_2117322052ol_nat_decl,type,
cOMBB_2117322052ol_nat: $i > $i > $i ).
thf(hAPP_a85458249l_bool_decl,type,
hAPP_a85458249l_bool: $i > $i > $i ).
thf(hAPP_pname_pname_decl,type,
hAPP_pname_pname: $i > $i > $i ).
thf(cOMBB_542850580_pname_decl,type,
cOMBB_542850580_pname: $i > $i > $i ).
thf(cOMBB_928955006_pname_decl,type,
cOMBB_928955006_pname: $i > $i > $i ).
thf(cOMBB_1885489796ol_nat_decl,type,
cOMBB_1885489796ol_nat: $i > $i > $i ).
thf(cOMBB_238756964t_bool_decl,type,
cOMBB_238756964t_bool: $i > $i > $i ).
thf(cOMBB_a_fun_a_bool_a_decl,type,
cOMBB_a_fun_a_bool_a: $i > $i > $i ).
thf(cOMBB_523834888_pname_decl,type,
cOMBB_523834888_pname: $i > $i > $i ).
thf(hAPP_f282463732t_bool_decl,type,
hAPP_f282463732t_bool: $i > $i > $i ).
thf(cOMBB_164527437a_bool_decl,type,
cOMBB_164527437a_bool: $i > $i > $i ).
thf(hAPP_fun_a_bool_nat_decl,type,
hAPP_fun_a_bool_nat: $i > $i > $i ).
thf(image_496248727ol_nat_decl,type,
image_496248727ol_nat: $i > $i > $i ).
thf(cOMBC_1834145417l_bool_decl,type,
cOMBC_1834145417l_bool: $i > $i ).
thf(hAPP_f556039215l_bool_decl,type,
hAPP_f556039215l_bool: $i > $i > $i ).
thf(image_a_fun_a_bool_decl,type,
image_a_fun_a_bool: $i > $i > $i ).
thf(image_nat_nat_decl,type,
image_nat_nat: $i > $i > $i ).
thf(member_a_decl,type,
member_a: $i ).
thf(image_a_nat_decl,type,
image_a_nat: $i > $i > $i ).
thf(fequal_a_decl,type,
fequal_a: $i ).
thf(cOMBK_a_pname_decl,type,
cOMBK_a_pname: $i > $i ).
thf(cOMBB_338059395a_bool_decl,type,
cOMBB_338059395a_bool: $i > $i > $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(finite1701474069l_bool_decl,type,
finite1701474069l_bool: $i ).
thf(collec1015864663l_bool_decl,type,
collec1015864663l_bool: $i > $i ).
thf(cOMBB_392435466_pname_decl,type,
cOMBB_392435466_pname: $i > $i > $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(finite_card_a_decl,type,
finite_card_a: $i ).
thf(na_decl,type,
na: $i ).
thf(hAPP_f285962445l_bool_decl,type,
hAPP_f285962445l_bool: $i > $i > $i ).
thf(cOMBC_1355376034l_bool_decl,type,
cOMBC_1355376034l_bool: $i > $i ).
thf(cOMBB_1823939024ol_nat_decl,type,
cOMBB_1823939024ol_nat: $i > $i > $i ).
thf(the_com_decl,type,
the_com: $i > $i ).
thf(body_decl,type,
body: $i > $i ).
thf(cOMBC_1928494297l_bool_decl,type,
cOMBC_1928494297l_bool: $i > $i ).
thf(hAPP_f198738859l_bool_decl,type,
hAPP_f198738859l_bool: $i > $i > $i ).
thf(cOMBB_472261505bool_a_decl,type,
cOMBB_472261505bool_a: $i > $i > $i ).
thf(cOMBB_1897541054_pname_decl,type,
cOMBB_1897541054_pname: $i > $i > $i ).
thf(cOMBC_619334683t_bool_decl,type,
cOMBC_619334683t_bool: $i > $i ).
thf(cOMBC_445755039l_bool_decl,type,
cOMBC_445755039l_bool: $i > $i ).
thf(finite1381704300l_bool_decl,type,
finite1381704300l_bool: $i ).
thf(collec707592106l_bool_decl,type,
collec707592106l_bool: $i > $i ).
thf(cOMBC_1738168533e_bool_decl,type,
cOMBC_1738168533e_bool: $i > $i ).
thf(image_a_fun_nat_bool_decl,type,
image_a_fun_nat_bool: $i > $i > $i ).
thf(nat_case_bool_decl,type,
nat_case_bool: $i > $i > $i ).
thf(finite786885583l_bool_decl,type,
finite786885583l_bool: $i ).
thf(collec1613912337l_bool_decl,type,
collec1613912337l_bool: $i > $i ).
thf(450,axiom,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1549043526a_bool ) @ is_fun_a_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_It__a_Mtc__HOL) ).
thf(2452,plain,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1549043526a_bool ) @ is_fun_a_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(288,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ plus_plus_nat @ hAPP_nat_nat ) )
= ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ plus_plus_nat @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_573_add__Suc__shift) ).
thf(1879,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ plus_plus_nat @ hAPP_nat_nat ) )
= ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ plus_plus_nat @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(157,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/sandbox/benchmark/theBenchmark.p',fact_186_lift__Suc__mono__le) ).
thf(1411,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)],[157]) ).
thf(41,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/sandbox/benchmark/theBenchmark.p',fact_216_equalityI) ).
thf(1024,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)],[41]) ).
thf(558,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( C @ ( A @ image_nat_a ) @ ( B @ ( A @ hAPP_nat_a ) @ insert_a ) )
= ( C @ ( A @ image_nat_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_342_insert__image) ).
thf(2889,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( C @ ( A @ image_nat_a ) @ ( B @ ( A @ hAPP_nat_a ) @ insert_a ) )
= ( C @ ( A @ image_nat_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(533,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/sandbox/benchmark/theBenchmark.p',fact_366_image__subsetI) ).
thf(2778,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)],[533]) ).
thf(837,axiom,
! [A: $i] :
~ ( bot_bot_fun_a_bool @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_406_empty__iff) ).
thf(4062,plain,
! [A: $i] :
~ ( bot_bot_fun_a_bool @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).
thf(864,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/sandbox/benchmark/theBenchmark.p',fact_271_set__eq__subset) ).
thf(4169,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)],[864]) ).
thf(772,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/sandbox/benchmark/theBenchmark.p',fact_66_card__insert__disjoint) ).
thf(3798,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)],[772]) ).
thf(688,axiom,
! [A: $i] :
( ( bot_bot_fun_a_bool
= ( A @ collect_a ) )
<=> ! [B: $i] :
( ( B @ is_a )
=> ~ ( B @ ( A @ hAPP_a_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_411_empty__Collect__eq) ).
thf(3434,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ is_a )
=> ~ ( B @ ( A @ hAPP_a_bool ) @ hBOOL ) )
=> ( bot_bot_fun_a_bool
= ( A @ collect_a ) ) )
& ( ( bot_bot_fun_a_bool
= ( A @ collect_a ) )
=> ! [B: $i] :
( ( B @ is_a )
=> ~ ( B @ ( A @ hAPP_a_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(455,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/sandbox/benchmark/theBenchmark.p',fact_55_card__insert__le) ).
thf(2463,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)],[455]) ).
thf(275,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( C @ plus_plus_nat @ hAPP_nat_nat ) @ ( A @ ( B @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_620_add__less__mono1) ).
thf(1840,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( C @ plus_plus_nat @ hAPP_nat_nat ) @ ( A @ ( B @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(60,axiom,
! [A: $i,B: $i] :
( ( ( B @ is_fun_pname_bool )
& ( A @ is_pname ) )
=> ( B @ ( A @ insert_pname ) @ is_fun_pname_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oinsert_000tc__Com__Opname) ).
thf(1083,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)],[60]) ).
thf(825,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ image_a_nat ) @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ~ ! [D: $i] :
( ( D @ is_a )
=> ( ( A
= ( D @ ( B @ hAPP_a_nat ) ) )
=> ~ ( C @ ( D @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_355_imageE) ).
thf(4015,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ image_a_nat ) @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ~ ! [D: $i] :
( ( D @ is_a )
=> ( ( A
= ( D @ ( B @ hAPP_a_nat ) ) )
=> ~ ( C @ ( D @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).
thf(416,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ minus_minus_nat @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) )
= ( A @ ( B @ plus_plus_nat @ hAPP_nat_nat ) @ ( C @ ( suc @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_608_diff__Suc__diff__eq2) ).
thf(2331,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ minus_minus_nat @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) )
= ( A @ ( B @ plus_plus_nat @ hAPP_nat_nat ) @ ( C @ ( suc @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(633,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/sandbox/benchmark/theBenchmark.p',fact_98_finite__insert) ).
thf(3172,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)],[633]) ).
thf(381,axiom,
! [A: $i,B: $i] :
( ( B @ is_a )
=> ( B @ ( A @ hAPP_a85458249l_bool ) @ is_fun949378684l_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000t__a_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J) ).
thf(2199,plain,
! [A: $i,B: $i] :
( ( B @ is_a )
=> ( B @ ( A @ hAPP_a85458249l_bool ) @ is_fun949378684l_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(229,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
<=> ! [C: $i] :
( ( C @ is_pname )
=> ( C @ ( B @ hAPP_pname_bool ) @ ( C @ ( A @ hAPP_pname_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_374_le__fun__def) ).
thf(1665,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( C @ is_pname )
=> ( C @ ( B @ hAPP_pname_bool ) @ ( C @ ( A @ hAPP_pname_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) )
=> ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ! [C: $i] :
( ( C @ is_pname )
=> ( C @ ( B @ hAPP_pname_bool ) @ ( C @ ( A @ hAPP_pname_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(543,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 )
=> ? [C: $i] :
( ~ ( C @ ( A @ hAPP_nat_fun_a_bool ) @ ( A @ ( fequal_fun_a_bool @ cOMBB_1823939024ol_nat ) @ cOMBC_1928494297l_bool @ hAPP_f282463732t_bool ) @ ( B @ ( member_nat @ cOMBC_226598744l_bool @ hAPP_f800510211t_bool ) @ ( fconj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_pigeonhole__infinite) ).
thf(2822,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 )
=> ? [C: $i] :
( ~ ( C @ ( A @ hAPP_nat_fun_a_bool ) @ ( A @ ( fequal_fun_a_bool @ cOMBB_1823939024ol_nat ) @ cOMBC_1928494297l_bool @ hAPP_f282463732t_bool ) @ ( B @ ( member_nat @ cOMBC_226598744l_bool @ hAPP_f800510211t_bool ) @ ( fconj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(785,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/sandbox/benchmark/theBenchmark.p',fact_22_finite__imageI) ).
thf(3873,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)],[785]) ).
thf(866,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 )
=> ? [C: $i] :
( ~ ( C @ ( A @ hAPP_pname_nat ) @ ( A @ ( fequal_nat @ cOMBB_523834888_pname ) @ cOMBC_pname_nat_bool @ hAPP_n1025906991e_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/sandbox/benchmark/theBenchmark.p',fact_195_pigeonhole__infinite) ).
thf(4188,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 )
=> ? [C: $i] :
( ~ ( C @ ( A @ hAPP_pname_nat ) @ ( A @ ( fequal_nat @ cOMBB_523834888_pname ) @ cOMBC_pname_nat_bool @ hAPP_n1025906991e_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)],[866]) ).
thf(82,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun_pname_bool )
=> ( B @ ( A @ cOMBB_647938656_pname ) @ is_fun_pname_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname) ).
thf(1168,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)],[82]) ).
thf(669,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/sandbox/benchmark/theBenchmark.p',fact_94_finite__Collect__disjI) ).
thf(3345,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)],[669]) ).
thf(601,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/sandbox/benchmark/theBenchmark.p',fact_225_insertE) ).
thf(3053,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)],[601]) ).
thf(847,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ hAPP_a_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_a @ hAPP_a_fun_a_bool ) @ ( fconj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a )
= bot_bot_fun_a_bool ) )
& ( ( B @ ( A @ hAPP_a_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_a @ hAPP_a_fun_a_bool ) @ ( fconj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a )
= ( bot_bot_fun_a_bool @ ( B @ insert_a ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_478_Collect__conv__if2) ).
thf(4101,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ hAPP_a_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_a @ hAPP_a_fun_a_bool ) @ ( fconj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a )
= bot_bot_fun_a_bool ) )
& ( ( B @ ( A @ hAPP_a_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_a @ hAPP_a_fun_a_bool ) @ ( fconj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a )
= ( bot_bot_fun_a_bool @ ( B @ insert_a ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).
thf(589,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( C @ ( A @ image_a_nat ) @ ( B @ ( A @ image_a_nat ) @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_349_image__mono) ).
thf(3008,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( C @ ( A @ image_a_nat ) @ ( B @ ( A @ image_a_nat ) @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(362,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/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__O) ).
thf(2131,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)],[362]) ).
thf(172,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_pname_nat ) @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ image_pname_nat ) ) )
& ( 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/sandbox/benchmark/theBenchmark.p',fact_174_finite__subset__image) ).
thf(1454,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_pname_nat ) @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ image_pname_nat ) ) )
& ( 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)],[172]) ).
thf(742,axiom,
! [A: $i,B: $i] :
( ( bot_bot_fun_a_bool @ ( A @ body @ the_com @ mgt @ insert_a ) @ ( B @ ( A @ ( mgt_call @ hAPP_pname_a ) @ insert_a ) @ p @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( bot_bot_fun_a_bool @ ( A @ ( mgt_call @ hAPP_pname_a ) @ insert_a ) @ ( B @ p @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_562_assms_I2_J) ).
thf(3666,plain,
! [A: $i,B: $i] :
( ( bot_bot_fun_a_bool @ ( A @ body @ the_com @ mgt @ insert_a ) @ ( B @ ( A @ ( mgt_call @ hAPP_pname_a ) @ insert_a ) @ p @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( bot_bot_fun_a_bool @ ( A @ ( mgt_call @ hAPP_pname_a ) @ insert_a ) @ ( B @ p @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).
thf(240,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_pname_nat_bool @ hAPP_n1025906991e_bool ) @ hAPP_pname_bool ) )
= ( B @ ( C @ ( A @ hAPP_p1499970991t_bool ) @ hAPP_nat_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Nat__Onat_000tc__HOL__Obool_U) ).
thf(1729,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_pname_nat_bool @ hAPP_n1025906991e_bool ) @ hAPP_pname_bool ) )
= ( B @ ( C @ ( A @ hAPP_p1499970991t_bool ) @ hAPP_nat_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(128,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ image_pname_nat ) @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ~ ! [D: $i] :
( ( D @ is_pname )
=> ( ( A
= ( D @ ( B @ hAPP_pname_nat ) ) )
=> ~ ( C @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_354_imageE) ).
thf(1315,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ image_pname_nat ) @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ~ ! [D: $i] :
( ( D @ is_pname )
=> ( ( A
= ( D @ ( B @ hAPP_pname_nat ) ) )
=> ~ ( C @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(535,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( bot_bo1389914601l_bool @ ( A @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ! [C: $i,D: $i] :
( ( ( D @ is_fun949378684l_bool )
& ( C @ is_fun_a_bool ) )
=> ( ( D @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ~ ( D @ ( C @ ( member_fun_a_bool @ hAPP_f285962445l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( D @ ( A @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( D @ ( C @ insert_fun_a_bool ) @ ( A @ hAPP_f621171935l_bool ) @ hBOOL ) ) ) ) )
=> ( B @ ( A @ hAPP_f621171935l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_565_finite__induct) ).
thf(2787,plain,
! [A: $i,B: $i] :
( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( bot_bo1389914601l_bool @ ( A @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ! [C: $i,D: $i] :
( ( ( D @ is_fun949378684l_bool )
& ( C @ is_fun_a_bool ) )
=> ( ( D @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ~ ( D @ ( C @ ( member_fun_a_bool @ hAPP_f285962445l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( D @ ( A @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( D @ ( C @ insert_fun_a_bool ) @ ( A @ hAPP_f621171935l_bool ) @ hBOOL ) ) ) ) )
=> ( B @ ( A @ hAPP_f621171935l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(21,axiom,
bot_bot_bool @ is_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Orderings_Obot__class_Obot_000tc__HOL__Obool) ).
thf(977,plain,
bot_bot_bool @ is_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(96,axiom,
! [A: $i] :
( ( A @ is_bool )
=> ( A @ cOMBK_bool_a @ is_fun_a_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_COMBK_000tc__HOL__Obool_000t__a) ).
thf(1211,plain,
! [A: $i] :
( ( A @ is_bool )
=> ( A @ cOMBK_bool_a @ is_fun_a_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(580,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/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000t__a_T) ).
thf(2976,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)],[580]) ).
thf(906,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_a_fun_nat_bool ) @ ( C @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ image_a_fun_nat_bool ) ) )
& ( D @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( D @ is_fun_a_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_finite__subset__image) ).
thf(4339,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_a_fun_nat_bool ) @ ( C @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ image_a_fun_nat_bool ) ) )
& ( D @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( D @ is_fun_a_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).
thf(289,axiom,
pname @ undefined_pname @ is_pname,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_HOL_Oundefined_000tc__Com__Opname) ).
thf(1882,plain,
pname @ undefined_pname @ is_pname,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(472,axiom,
! [A: $i,B: $i] :
( ( B @ hBOOL )
| ~ ( A @ hBOOL )
| ~ ( B @ ( A @ ( fimplies @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_3_1_U) ).
thf(2527,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)],[472]) ).
thf(153,axiom,
! [A: $i,B: $i] : ( B @ ( A @ image_fun_nat_bool_a ) @ is_fun_a_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000t__a) ).
thf(1401,plain,
! [A: $i,B: $i] : ( B @ ( A @ image_fun_nat_bool_a ) @ is_fun_a_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(612,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/sandbox/benchmark/theBenchmark.p',fact_321_subset__insertI) ).
thf(3098,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)],[612]) ).
thf(259,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ? [C: $i] :
( B
= ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_673_less__imp__Suc__add) ).
thf(1793,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ? [C: $i] :
( B
= ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(125,axiom,
! [A: $i] :
( A
!= ( A @ ( suc @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_n__not__Suc__n) ).
thf(1305,plain,
! [A: $i] :
( A
!= ( A @ ( suc @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(167,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/sandbox/benchmark/theBenchmark.p',fact_29_card__image__le) ).
thf(1437,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)],[167]) ).
thf(607,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun_pname_bool )
=> ( ( ( B != bot_bo844097828e_bool )
=> ( ( B @ ( A @ cOMBK_a_pname @ image_pname_a ) )
= ( bot_bot_fun_a_bool @ ( A @ insert_a ) ) ) )
& ( ( B = bot_bo844097828e_bool )
=> ( ( B @ ( A @ cOMBK_a_pname @ image_pname_a ) )
= bot_bot_fun_a_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_498_image__constant__conv) ).
thf(3072,plain,
! [A: $i,B: $i] :
( ( B @ is_fun_pname_bool )
=> ( ( ( B != bot_bo844097828e_bool )
=> ( ( B @ ( A @ cOMBK_a_pname @ image_pname_a ) )
= ( bot_bot_fun_a_bool @ ( A @ insert_a ) ) ) )
& ( ( B = bot_bo844097828e_bool )
=> ( ( B @ ( A @ cOMBK_a_pname @ image_pname_a ) )
= bot_bot_fun_a_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(32,axiom,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f389811538l_bool ) @ is_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__) ).
thf(1005,plain,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f389811538l_bool ) @ is_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(386,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( C @ plus_plus_nat @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_615_termination__basic__simps_I1_J) ).
thf(2210,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( C @ plus_plus_nat @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(570,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C = A )
=> ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_527_ord__le__eq__trans) ).
thf(2940,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C = A )
=> ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(210,axiom,
fTrue @ is_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_fTrue) ).
thf(1596,plain,
fTrue @ is_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(191,axiom,
! [A: $i,B: $i] :
( ( A @ is_bool )
=> ( ( B @ ( A @ cOMBK_1857069011e_bool @ hAPP_f1664156314l_bool ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obo) ).
thf(1522,plain,
! [A: $i,B: $i] :
( ( A @ is_bool )
=> ( ( B @ ( A @ cOMBK_1857069011e_bool @ hAPP_f1664156314l_bool ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(765,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_47868345e_bool ) @ ( A @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( A @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_finite__surj) ).
thf(3762,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_47868345e_bool ) @ ( 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)],[765]) ).
thf(161,axiom,
! [A: $i] :
( ( A @ ( suc @ hAPP_nat_nat ) )
!= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_693_nat_Osimps_I3_J) ).
thf(1422,plain,
! [A: $i] :
( ( A @ ( suc @ hAPP_nat_nat ) )
!= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(809,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_112932426a_bool ) @ ( A @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( A @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_finite__surj) ).
thf(3959,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_112932426a_bool ) @ ( 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)],[809]) ).
thf(510,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( bot_bo1649642514l_bool @ ( A @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ! [C: $i,D: $i] :
( ( ( D @ is_fun1661590463l_bool )
& ( C @ is_fun_pname_bool ) )
=> ( ( D @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ~ ( D @ ( C @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( D @ ( A @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( D @ ( C @ insert1325755072e_bool ) @ ( A @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ) ) )
=> ( B @ ( A @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_564_finite__induct) ).
thf(2671,plain,
! [A: $i,B: $i] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( bot_bo1649642514l_bool @ ( A @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ! [C: $i,D: $i] :
( ( ( D @ is_fun1661590463l_bool )
& ( C @ is_fun_pname_bool ) )
=> ( ( D @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ~ ( D @ ( C @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( D @ ( A @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( D @ ( C @ insert1325755072e_bool ) @ ( A @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ) ) )
=> ( B @ ( A @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(324,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun_pname_bool )
=> ( B @ ( A @ hAPP_f1297739591_pname ) @ is_pname ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__Opname) ).
thf(2014,plain,
! [A: $i,B: $i] :
( ( B @ is_fun_pname_bool )
=> ( B @ ( A @ hAPP_f1297739591_pname ) @ is_pname ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(547,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_fun_nat_bool_a ) @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ image_fun_nat_bool_a ) ) )
& ( D @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_finite__subset__image) ).
thf(2837,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_fun_nat_bool_a ) @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ image_fun_nat_bool_a ) ) )
& ( D @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(74,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( B @ ( C @ plus_plus_nat @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_604_le__diff__conv) ).
thf(1142,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ plus_plus_nat @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( C @ ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( C @ plus_plus_nat @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(699,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( fdisj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
| ~ ( B @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_1_1_U) ).
thf(3498,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)],[699]) ).
thf(433,axiom,
! [A: $i,B: $i] :
( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ plus_plus_nat @ hAPP_nat_nat ) )
= ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_571_add__Suc__right) ).
thf(2380,plain,
! [A: $i,B: $i] :
( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ plus_plus_nat @ hAPP_nat_nat ) )
= ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(84,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/sandbox/benchmark/theBenchmark.p',fact_234_insert__compr) ).
thf(1173,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)],[84]) ).
thf(182,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun_a_bool )
=> ( B @ ( A @ hAPP_f1794073134e_bool ) @ is_fun_pname_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__Com__Opname_Mtc__H) ).
thf(1486,plain,
! [A: $i,B: $i] :
( ( B @ is_fun_a_bool )
=> ( B @ ( A @ hAPP_f1794073134e_bool ) @ is_fun_pname_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(600,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ insert_a ) )
!= bot_bot_fun_a_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_460_insert__not__empty) ).
thf(3049,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ insert_a ) )
!= bot_bot_fun_a_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(492,axiom,
! [A: $i] :
( ( A @ ( fequal_fun_a_bool @ cOMBC_1732670874l_bool @ hAPP_f1631501043l_bool ) @ collect_fun_a_bool )
= ( bot_bo1389914601l_bool @ ( A @ insert_fun_a_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_487_singleton__conv) ).
thf(2607,plain,
! [A: $i] :
( ( A @ ( fequal_fun_a_bool @ cOMBC_1732670874l_bool @ hAPP_f1631501043l_bool ) @ collect_fun_a_bool )
= ( bot_bo1389914601l_bool @ ( A @ insert_fun_a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(248,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_408569982_pname ) @ hAPP_p338031245l_bool ) )
= ( C @ ( B @ hAPP_p61793385e_bool ) @ ( A @ hAPP_f434788991l_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_025) ).
thf(1756,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_408569982_pname ) @ hAPP_p338031245l_bool ) )
= ( C @ ( B @ hAPP_p61793385e_bool ) @ ( A @ hAPP_f434788991l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(599,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_a_fun_a_bool ) @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ? [C: $i] :
( ~ ( C @ ( A @ hAPP_a_fun_a_bool ) @ ( A @ ( fequal_fun_a_bool @ cOMBB_472261505bool_a ) @ cOMBC_1355376034l_bool @ hAPP_f2050579477a_bool ) @ ( B @ ( member_a @ cOMBC_1355376034l_bool @ hAPP_f2050579477a_bool ) @ ( fconj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( C @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( C @ is_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_pigeonhole__infinite) ).
thf(3044,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_a_fun_a_bool ) @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ? [C: $i] :
( ~ ( C @ ( A @ hAPP_a_fun_a_bool ) @ ( A @ ( fequal_fun_a_bool @ cOMBB_472261505bool_a ) @ cOMBC_1355376034l_bool @ hAPP_f2050579477a_bool ) @ ( B @ ( member_a @ cOMBC_1355376034l_bool @ hAPP_f2050579477a_bool ) @ ( fconj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( C @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( C @ is_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(378,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ minus_minus_nat @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( B @ ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_667_less__diff__conv) ).
thf(2184,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( B @ minus_minus_nat @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( C @ ( B @ minus_minus_nat @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(113,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun_pname_bool )
=> ( B @ ( A @ hAPP_f1051908748a_bool ) @ is_fun_a_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It__a_Mtc__H) ).
thf(1275,plain,
! [A: $i,B: $i] :
( ( B @ is_fun_pname_bool )
=> ( B @ ( A @ hAPP_f1051908748a_bool ) @ is_fun_a_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(131,axiom,
! [A: $i] : ( A @ ( ord_less_nat @ cOMBC_nat_nat_bool @ hAPP_n1699378549t_bool ) @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_614_finite__Collect__less__nat) ).
thf(1327,plain,
! [A: $i] : ( A @ ( ord_less_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)],[131]) ).
thf(453,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun_a_bool )
=> ( B @ ( A @ image_a_fun_a_bool ) @ is_fun949378684l_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
thf(2459,plain,
! [A: $i,B: $i] :
( ( B @ is_fun_a_bool )
=> ( B @ ( A @ image_a_fun_a_bool ) @ is_fun949378684l_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(663,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/sandbox/benchmark/theBenchmark.p',fact_331_insert__mono) ).
thf(3313,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)],[663]) ).
thf(782,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/sandbox/benchmark/theBenchmark.p',fact_551_order__eq__iff) ).
thf(3848,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)],[782]) ).
thf(186,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_26036933t_bool ) @ ( C @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ image_26036933t_bool ) ) )
& ( D @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_finite__subset__image) ).
thf(1497,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_26036933t_bool ) @ ( C @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ image_26036933t_bool ) ) )
& ( D @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(236,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/sandbox/benchmark/theBenchmark.p',fact_183_lift__Suc__mono__le) ).
thf(1705,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)],[236]) ).
thf(592,axiom,
! [A: $i,B: $i] :
( ( A = B )
| ~ ( B @ ( A @ ( fequal_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Nat__Onat_T) ).
thf(3017,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)],[592]) ).
thf(58,axiom,
! [A: $i] :
( ( A @ is_fun949378684l_bool )
=> ( ( A @ collect_fun_a_bool )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_Collect__def) ).
thf(1078,plain,
! [A: $i] :
( ( A @ is_fun949378684l_bool )
=> ( ( A @ collect_fun_a_bool )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(162,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( B @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_629_less__trans__Suc) ).
thf(1426,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( B @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(588,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( fequal_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
| ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Nat__Onat_T) ).
thf(3004,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)],[588]) ).
thf(672,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( A @ cOMBK_a_pname @ image_pname_a ) )
= ( bot_bot_fun_a_bool @ ( A @ insert_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_497_image__constant) ).
thf(3367,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( A @ cOMBK_a_pname @ image_pname_a ) )
= ( bot_bot_fun_a_bool @ ( A @ insert_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(285,axiom,
bot_bo1389914601l_bool @ is_fun949378684l_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Orderings_Obot__class_Obot_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc) ).
thf(1872,plain,
bot_bo1389914601l_bool @ is_fun949378684l_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(515,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/sandbox/benchmark/theBenchmark.p',fact_86_le__trans) ).
thf(2712,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)],[515]) ).
thf(730,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/sandbox/benchmark/theBenchmark.p',fact_283_set__rev__mp) ).
thf(3616,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)],[730]) ).
thf(103,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun1661590463l_bool )
=> ( B @ ( A @ image_1283814551_pname ) @ is_fun_pname_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__Opnam) ).
thf(1233,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)],[103]) ).
thf(882,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/sandbox/benchmark/theBenchmark.p',fact_302_image__iff) ).
thf(4247,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)],[882]) ).
thf(715,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( fimplies @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
| ~ ( B @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_2_1_U) ).
thf(3562,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)],[715]) ).
thf(485,axiom,
! [A: $i] :
~ ( bot_bot_fun_a_bool @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_385_emptyE) ).
thf(2580,plain,
! [A: $i] :
~ ( bot_bot_fun_a_bool @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(792,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/sandbox/benchmark/theBenchmark.p',fact_107_finite__subset) ).
thf(3895,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)],[792]) ).
thf(425,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_644_termination__basic__simps_I5_J) ).
thf(2360,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_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)],[425]) ).
thf(673,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ image_a_nat ) @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
<=> ? [D: $i] :
( ( A
= ( D @ ( B @ image_a_nat ) ) )
& ( C @ ( D @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( D @ is_fun_a_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_346_subset__image__iff) ).
thf(3370,plain,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i] :
( ( A
= ( D @ ( B @ image_a_nat ) ) )
& ( C @ ( D @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( D @ is_fun_a_bool ) )
=> ( C @ ( B @ image_a_nat ) @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
& ( ( C @ ( B @ image_a_nat ) @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ? [D: $i] :
( ( A
= ( D @ ( B @ image_a_nat ) ) )
& ( C @ ( D @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( D @ is_fun_a_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(273,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_pname_nat ) @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_finite__surj) ).
thf(1835,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_pname_nat ) @ ( 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)],[273]) ).
thf(704,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( ( A @ hBOOL )
<=> ( B @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_515_order__antisym) ).
thf(3513,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( ( ( B @ hBOOL )
=> ( A @ hBOOL ) )
& ( ( A @ hBOOL )
=> ( B @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(19,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/sandbox/benchmark/theBenchmark.p',fact_279_in__mono) ).
thf(973,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)],[19]) ).
thf(662,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_2129980159t_bool ) @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ? [C: $i] :
( ~ ( C @ ( A @ hAPP_p1499970991t_bool ) @ ( A @ ( fequal_fun_nat_bool @ cOMBB_928955006_pname ) @ cOMBC_267053842l_bool @ hAPP_f654413245e_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/sandbox/benchmark/theBenchmark.p',fact_203_pigeonhole__infinite) ).
thf(3308,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_2129980159t_bool ) @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ? [C: $i] :
( ~ ( C @ ( A @ hAPP_p1499970991t_bool ) @ ( A @ ( fequal_fun_nat_bool @ cOMBB_928955006_pname ) @ cOMBC_267053842l_bool @ hAPP_f654413245e_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)],[662]) ).
thf(111,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] : ( D @ ( suc @ hAPP_nat_nat ) @ ( C @ hAPP_nat_bool ) @ ( D @ ( C @ hAPP_nat_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( C @ hAPP_nat_bool ) @ ( A @ ( C @ hAPP_nat_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_lift__Suc__mono__le) ).
thf(1265,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] : ( D @ ( suc @ hAPP_nat_nat ) @ ( C @ hAPP_nat_bool ) @ ( D @ ( C @ hAPP_nat_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( C @ hAPP_nat_bool ) @ ( A @ ( C @ hAPP_nat_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(440,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/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_) ).
thf(2405,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)],[440]) ).
thf(421,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/sandbox/benchmark/theBenchmark.p',fact_240_insert__Collect) ).
thf(2348,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)],[421]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun949378684l_bool )
=> ( B @ ( A @ cOMBB_2140588453a_bool ) @ is_fun949378684l_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_It__a_Mtc__HOL__Obool) ).
thf(1001,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)],[30]) ).
thf(393,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) )
= zero_zero_nat )
<=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_685_diff__is__0__eq) ).
thf(2227,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) )
= zero_zero_nat ) )
& ( ( ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) )
= zero_zero_nat )
=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(149,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun_pname_bool )
=> ( B @ ( A @ cOMBS_568398431l_bool ) @ is_fun_pname_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool) ).
thf(1391,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)],[149]) ).
thf(204,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/sandbox/benchmark/theBenchmark.p',fact_241_insert__Collect) ).
thf(1576,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)],[204]) ).
thf(212,axiom,
! [A: $i,B: $i] :
( ( A @ is_bool )
=> ( ( B @ ( A @ cOMBK_bool_pname @ hAPP_pname_bool ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Com__Opname_U) ).
thf(1601,plain,
! [A: $i,B: $i] :
( ( A @ is_bool )
=> ( ( B @ ( A @ cOMBK_bool_pname @ hAPP_pname_bool ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(147,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun949378684l_bool )
=> ( B @ ( A @ hAPP_f621171935l_bool ) @ is_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J_000tc__) ).
thf(1386,plain,
! [A: $i,B: $i] :
( ( B @ is_fun949378684l_bool )
=> ( B @ ( A @ hAPP_f621171935l_bool ) @ is_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(829,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( fequal_pname @ hAPP_p61793385e_bool ) @ hAPP_pname_bool ) @ hBOOL )
| ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Com__Opname_T) ).
thf(4030,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)],[829]) ).
thf(178,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( D @ ( A @ plus_plus_nat @ hAPP_nat_nat ) )
= ( B @ ( C @ plus_plus_nat @ hAPP_nat_nat ) ) )
=> ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_618_less__add__eq__less) ).
thf(1475,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( D @ ( A @ plus_plus_nat @ hAPP_nat_nat ) )
= ( B @ ( C @ plus_plus_nat @ hAPP_nat_nat ) ) )
=> ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(775,axiom,
! [A: $i,B: $i] :
( ( ( B @ is_a )
& ( A @ is_a ) )
=> ( ( bot_bot_fun_a_bool @ ( B @ insert_a ) @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_457_singleton__iff) ).
thf(3809,plain,
! [A: $i,B: $i] :
( ( ( B @ is_a )
& ( A @ is_a ) )
=> ( ( ( A = B )
=> ( bot_bot_fun_a_bool @ ( B @ insert_a ) @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
& ( ( bot_bot_fun_a_bool @ ( B @ insert_a ) @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).
thf(141,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/sandbox/benchmark/theBenchmark.p',fact_58_card__insert__le) ).
thf(1366,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)],[141]) ).
thf(901,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_fun_a_bool @ cOMBC_1732670874l_bool @ hAPP_f1631501043l_bool ) @ ( fconj @ cOMBB_338059395a_bool ) @ cOMBS_1035972772l_bool ) @ collect_fun_a_bool )
= bot_bo1389914601l_bool ) )
& ( ( B @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_fun_a_bool @ cOMBC_1732670874l_bool @ hAPP_f1631501043l_bool ) @ ( fconj @ cOMBB_338059395a_bool ) @ cOMBS_1035972772l_bool ) @ collect_fun_a_bool )
= ( bot_bo1389914601l_bool @ ( B @ insert_fun_a_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_475_Collect__conv__if) ).
thf(4322,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_fun_a_bool @ cOMBC_1732670874l_bool @ hAPP_f1631501043l_bool ) @ ( fconj @ cOMBB_338059395a_bool ) @ cOMBS_1035972772l_bool ) @ collect_fun_a_bool )
= bot_bo1389914601l_bool ) )
& ( ( B @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_fun_a_bool @ cOMBC_1732670874l_bool @ hAPP_f1631501043l_bool ) @ ( fconj @ cOMBB_338059395a_bool ) @ cOMBS_1035972772l_bool ) @ collect_fun_a_bool )
= ( bot_bo1389914601l_bool @ ( B @ insert_fun_a_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).
thf(542,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/sandbox/benchmark/theBenchmark.p',fact_68_card__insert__disjoint) ).
thf(2819,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)],[542]) ).
thf(860,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 )
=> ? [C: $i] :
( ~ ( C @ ( A @ hAPP_pname_pname ) @ ( A @ ( fequal_pname @ cOMBB_542850580_pname ) @ cOMBC_1149511130e_bool @ hAPP_p61793385e_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/sandbox/benchmark/theBenchmark.p',fact_189_pigeonhole__infinite) ).
thf(4156,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 )
=> ? [C: $i] :
( ~ ( C @ ( A @ hAPP_pname_pname ) @ ( A @ ( fequal_pname @ cOMBB_542850580_pname ) @ cOMBC_1149511130e_bool @ hAPP_p61793385e_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)],[860]) ).
thf(263,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/sandbox/benchmark/theBenchmark.p',fact_123_diff__Suc__Suc) ).
thf(1803,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)],[263]) ).
thf(218,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/sandbox/benchmark/theBenchmark.p',fact_317_insert__compr__raw) ).
thf(1623,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)],[218]) ).
thf(109,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/sandbox/benchmark/theBenchmark.p',fact_122_Suc__diff__diff) ).
thf(1254,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)],[109]) ).
thf(747,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/sandbox/benchmark/theBenchmark.p',fact_265_insert__absorb) ).
thf(3689,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)],[747]) ).
thf(697,axiom,
bot_bo1389914601l_bool @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_388_finite_OemptyI) ).
thf(3495,plain,
bot_bo1389914601l_bool @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(875,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/sandbox/benchmark/theBenchmark.p',fact_312_rev__image__eqI) ).
thf(4224,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)],[875]) ).
thf(778,axiom,
! [A: $i] :
( ( bot_bot_bool @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
<=> ( ( A @ hBOOL )
<=> ( bot_bot_bool @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_437_bot__unique) ).
thf(3821,plain,
! [A: $i] :
( ( ( ( ( bot_bot_bool @ hBOOL )
=> ( A @ hBOOL ) )
& ( ( A @ hBOOL )
=> ( bot_bot_bool @ hBOOL ) ) )
=> ( bot_bot_bool @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) )
& ( ( bot_bot_bool @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( ( ( bot_bot_bool @ hBOOL )
=> ( A @ hBOOL ) )
& ( ( A @ hBOOL )
=> ( bot_bot_bool @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).
thf(728,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( C @ hAPP_a_bool ) @ ( A @ ( B @ hAPP_a_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_379_le__funD) ).
thf(3612,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( C @ hAPP_a_bool ) @ ( A @ ( B @ hAPP_a_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).
thf(402,axiom,
( bot_bo1649642514l_bool
= ( fFalse @ cOMBK_1857069011e_bool @ collec1974731493e_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_421_empty__def) ).
thf(2274,plain,
( bot_bo1649642514l_bool
= ( fFalse @ cOMBK_1857069011e_bool @ collec1974731493e_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(768,axiom,
! [A: $i] :
( ( ( A @ collect_a )
= bot_bot_fun_a_bool )
<=> ! [B: $i] :
( ( B @ is_a )
=> ~ ( B @ ( A @ hAPP_a_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_402_Collect__empty__eq) ).
thf(3776,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ is_a )
=> ~ ( B @ ( A @ hAPP_a_bool ) @ hBOOL ) )
=> ( ( A @ collect_a )
= bot_bot_fun_a_bool ) )
& ( ( ( A @ collect_a )
= bot_bot_fun_a_bool )
=> ! [B: $i] :
( ( B @ is_a )
=> ~ ( B @ ( A @ hAPP_a_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).
thf(827,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B = A )
=> ( C @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_524_xt1_I4_J) ).
thf(4023,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B = A )
=> ( C @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).
thf(561,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( fdisj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
| ~ ( B @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_2_1_U) ).
thf(2897,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)],[561]) ).
thf(777,axiom,
u @ ( pn @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_4) ).
thf(3820,plain,
u @ ( pn @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).
thf(505,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/sandbox/benchmark/theBenchmark.p',conj_3) ).
thf(2654,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)],[505]) ).
thf(220,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/sandbox/benchmark/theBenchmark.p',fact_64_card__insert__if) ).
thf(1628,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)],[220]) ).
thf(50,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/sandbox/benchmark/theBenchmark.p',fact_285_set__mp) ).
thf(1055,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)],[50]) ).
thf(641,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/sandbox/benchmark/theBenchmark.p',fact_20_finite__imageI) ).
thf(3204,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)],[641]) ).
thf(490,axiom,
! [A: $i,B: $i] : ( A @ ( B @ insert_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_319_subset__insertI) ).
thf(2603,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)],[490]) ).
thf(415,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/sandbox/benchmark/theBenchmark.p',fact_243_insert__Collect) ).
thf(2328,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)],[415]) ).
thf(566,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ is_fun_pname_bool )
=> ( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_a_pname ) @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ image_a_pname ) ) )
& ( D @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( D @ is_fun_a_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_finite__subset__image) ).
thf(2916,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ is_fun_pname_bool )
=> ( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_a_pname ) @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ image_a_pname ) ) )
& ( D @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( D @ is_fun_a_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(164,axiom,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1637334154l_bool ) @ is_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HOL__Obool_) ).
thf(1430,plain,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1637334154l_bool ) @ is_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(737,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_a_nat ) @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ image_a_nat ) ) )
& ( D @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( D @ is_fun_a_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_finite__subset__image) ).
thf(3644,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_a_nat ) @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ image_a_nat ) ) )
& ( D @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( D @ is_fun_a_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).
thf(227,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/sandbox/benchmark/theBenchmark.p',fact_40_card__image__le) ).
thf(1660,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)],[227]) ).
thf(122,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_613_Suc__mono) ).
thf(1298,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(839,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/sandbox/benchmark/theBenchmark.p',fact_511_order__trans) ).
thf(4070,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)],[839]) ).
thf(509,axiom,
! [A: $i,B: $i] :
( ( A @ is_bool )
=> ( ( B @ ( A @ cOMBK_324466864a_bool @ hAPP_fun_a_bool_bool ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_It__a_Mtc__HOL__Obool_J_U) ).
thf(2667,plain,
! [A: $i,B: $i] :
( ( A @ is_bool )
=> ( ( B @ ( A @ cOMBK_324466864a_bool @ hAPP_fun_a_bool_bool ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(282,axiom,
! [A: $i] :
( ( A @ ( fequal_pname @ hAPP_p61793385e_bool ) @ collect_pname )
= ( bot_bo844097828e_bool @ ( A @ insert_pname ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_489_singleton__conv2) ).
thf(1860,plain,
! [A: $i] :
( ( A @ ( fequal_pname @ hAPP_p61793385e_bool ) @ collect_pname )
= ( bot_bo844097828e_bool @ ( A @ insert_pname ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(389,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_632_less__antisym) ).
thf(2217,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( ( B @ is_a )
& ( A @ is_fun_a_bool ) )
=> ( B @ ( A @ hAPP_a_bool ) @ is_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000t__a_000tc__HOL__Obool) ).
thf(949,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)],[11]) ).
thf(525,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/sandbox/benchmark/theBenchmark.p',fact_307_imageI) ).
thf(2745,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)],[525]) ).
thf(424,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( B @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_674_bounded__nat__set__is__finite) ).
thf(2356,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( B @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(262,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/sandbox/benchmark/theBenchmark.p',fact_116_le__SucE) ).
thf(1800,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)],[262]) ).
thf(911,axiom,
! [A: $i,B: $i] :
( ( A = B )
=> ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_272_equalityD1) ).
thf(4358,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)],[911]) ).
thf(865,axiom,
! [A: $i] :
( ( A @ is_fun_a_bool )
=> ( ? [B: $i] :
( ( A @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ is_a ) )
<=> ( A != bot_bot_fun_a_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_415_ex__in__conv) ).
thf(4179,plain,
! [A: $i] :
( ( A @ is_fun_a_bool )
=> ( ( ( A != bot_bot_fun_a_bool )
=> ? [B: $i] :
( ( A @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ is_a ) ) )
& ( ? [B: $i] :
( ( A @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ is_a ) )
=> ( A != bot_bot_fun_a_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_621_trans__less__add2) ).
thf(1013,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(185,axiom,
! [A: $i,B: $i] :
( ( ( bot_bot_fun_nat_bool @ ( A @ insert_nat ) )
= ( bot_bot_fun_nat_bool @ ( B @ insert_nat ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_447_singleton__inject) ).
thf(1494,plain,
! [A: $i,B: $i] :
( ( ( bot_bot_fun_nat_bool @ ( A @ insert_nat ) )
= ( bot_bot_fun_nat_bool @ ( B @ insert_nat ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(67,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/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Nat__Onat_U) ).
thf(1100,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)],[67]) ).
thf(278,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ is_fun1661590463l_bool )
=> ( ( C @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_1655916159e_bool ) @ ( C @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ image_1655916159e_bool ) ) )
& ( D @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_finite__subset__image) ).
thf(1847,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ is_fun1661590463l_bool )
=> ( ( C @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_1655916159e_bool ) @ ( C @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ image_1655916159e_bool ) ) )
& ( D @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(197,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/sandbox/benchmark/theBenchmark.p',fact_117_le__SucI) ).
thf(1545,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)],[197]) ).
thf(445,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun_a_bool )
=> ( B @ ( A @ hAPP_f1128469712_pname ) @ is_pname ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opname) ).
thf(2420,plain,
! [A: $i,B: $i] :
( ( B @ is_fun_a_bool )
=> ( B @ ( A @ hAPP_f1128469712_pname ) @ is_pname ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(705,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/sandbox/benchmark/theBenchmark.p',fact_257_insert__ident) ).
thf(3517,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)],[705]) ).
thf(818,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/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T) ).
thf(3998,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)],[818]) ).
thf(292,axiom,
! [A: $i] :
( ( A @ is_fun_pname_bool )
=> ( ? [B: $i] :
( ( A @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ is_pname ) )
<=> ( A != bot_bo844097828e_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_414_ex__in__conv) ).
thf(1892,plain,
! [A: $i] :
( ( A @ is_fun_pname_bool )
=> ( ( ( A != bot_bo844097828e_bool )
=> ? [B: $i] :
( ( A @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ is_pname ) ) )
& ( ? [B: $i] :
( ( A @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ is_pname ) )
=> ( A != bot_bo844097828e_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(693,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/sandbox/benchmark/theBenchmark.p',fact_24_finite_OinsertI) ).
thf(3463,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)],[693]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( ( B @ is_fun_pname_bool )
& ( A @ is_fun1661590463l_bool ) )
=> ( B @ ( A @ hAPP_f1664156314l_bool ) @ is_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__Obool) ).
thf(969,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)],[17]) ).
thf(430,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/sandbox/benchmark/theBenchmark.p',fact_278_in__mono) ).
thf(2373,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)],[430]) ).
thf(203,axiom,
! [A: $i,B: $i] :
( bot_bot_fun_nat_bool
!= ( B @ ( A @ insert_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_462_empty__not__insert) ).
thf(1572,plain,
! [A: $i,B: $i] :
( bot_bot_fun_nat_bool
!= ( B @ ( A @ insert_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(855,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/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opna) ).
thf(4141,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)],[855]) ).
thf(521,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/sandbox/benchmark/theBenchmark.p',fact_327_subset__insert) ).
thf(2730,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)],[521]) ).
thf(726,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/sandbox/benchmark/theBenchmark.p',fact_260_insertI2) ).
thf(3602,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)],[726]) ).
thf(714,axiom,
! [A: $i,B: $i] :
( ( B @ wt @ hBOOL )
=> ( ! [C: $i] :
( ( C @ is_pname )
=> ( ( u @ ( C @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( bot_bot_fun_a_bool @ ( C @ ( mgt_call @ hAPP_pname_a ) @ insert_a ) @ ( A @ p @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) )
=> ( bot_bot_fun_a_bool @ ( B @ mgt @ insert_a ) @ ( A @ p @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_373_assms_I3_J) ).
thf(3557,plain,
! [A: $i,B: $i] :
( ( B @ wt @ hBOOL )
=> ( ! [C: $i] :
( ( C @ is_pname )
=> ( ( u @ ( C @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( bot_bot_fun_a_bool @ ( C @ ( mgt_call @ hAPP_pname_a ) @ insert_a ) @ ( A @ p @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) )
=> ( bot_bot_fun_a_bool @ ( B @ mgt @ insert_a ) @ ( A @ p @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(287,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/sandbox/benchmark/theBenchmark.p',fact_325_subset__insert) ).
thf(1875,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)],[287]) ).
thf(255,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/sandbox/benchmark/theBenchmark.p',fact_120_not__less__eq__eq) ).
thf(1778,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)],[255]) ).
thf(549,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_a_a ) @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ image_a_a ) ) )
& ( D @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( D @ is_fun_a_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_finite__subset__image) ).
thf(2852,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_a_a ) @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ image_a_a ) ) )
& ( D @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( D @ is_fun_a_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(649,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_876012084bool_a ) @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ image_876012084bool_a ) ) )
& ( D @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
& ( D @ is_fun1661590463l_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_finite__subset__image) ).
thf(3231,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_876012084bool_a ) @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ image_876012084bool_a ) ) )
& ( D @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
& ( D @ is_fun1661590463l_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(175,axiom,
! [A: $i,B: $i] : ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_585_le__add1) ).
thf(1465,plain,
! [A: $i,B: $i] : ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(706,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/sandbox/benchmark/theBenchmark.p',fact_356_imageE) ).
thf(3524,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)],[706]) ).
thf(790,axiom,
! [A: $i] : ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_699_less__eq__nat_Osimps_I1_J) ).
thf(3887,plain,
! [A: $i] : ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).
thf(803,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/sandbox/benchmark/theBenchmark.p',fact_218_equalityI) ).
thf(3934,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)],[803]) ).
thf(840,axiom,
! [A: $i] :
( ( ( A @ collect_nat )
= bot_bot_fun_nat_bool )
<=> ! [B: $i] :
~ ( B @ ( A @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_403_Collect__empty__eq) ).
thf(4072,plain,
! [A: $i] :
( ( ! [B: $i] :
~ ( B @ ( A @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ collect_nat )
= bot_bot_fun_nat_bool ) )
& ( ( ( A @ collect_nat )
= bot_bot_fun_nat_bool )
=> ! [B: $i] :
~ ( B @ ( A @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).
thf(677,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/sandbox/benchmark/theBenchmark.p',fact_235_insert__compr) ).
thf(3393,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)],[677]) ).
thf(757,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/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Com__Opname_T) ).
thf(3724,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)],[757]) ).
thf(819,axiom,
bot_bo1701429464l_bool @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_386_finite_OemptyI) ).
thf(4001,plain,
bot_bo1701429464l_bool @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).
thf(504,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_nat_nat ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ? [C: $i] :
( ~ ( C @ ( A @ hAPP_nat_nat ) @ ( A @ ( fequal_nat @ cOMBB_800536526ol_nat ) @ cOMBC_nat_nat_bool @ hAPP_n1699378549t_bool ) @ ( B @ ( member_nat @ cOMBC_226598744l_bool @ hAPP_f800510211t_bool ) @ ( fconj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_pigeonhole__infinite) ).
thf(2650,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_nat_nat ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ? [C: $i] :
( ~ ( C @ ( A @ hAPP_nat_nat ) @ ( A @ ( fequal_nat @ cOMBB_800536526ol_nat ) @ cOMBC_nat_nat_bool @ hAPP_n1699378549t_bool ) @ ( B @ ( member_nat @ cOMBC_226598744l_bool @ hAPP_f800510211t_bool ) @ ( fconj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(160,axiom,
! [A: $i,B: $i] :
( bot_bo844097828e_bool
!= ( B @ ( A @ insert_pname ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_461_empty__not__insert) ).
thf(1418,plain,
! [A: $i,B: $i] :
( bot_bo844097828e_bool
!= ( B @ ( A @ insert_pname ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(73,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
<=> ! [C: $i] : ( C @ ( B @ hAPP_nat_bool ) @ ( C @ ( A @ hAPP_nat_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_375_le__fun__def) ).
thf(1136,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] : ( C @ ( B @ hAPP_nat_bool ) @ ( C @ ( A @ hAPP_nat_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ! [C: $i] : ( C @ ( B @ hAPP_nat_bool ) @ ( C @ ( A @ hAPP_nat_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(281,axiom,
! [A: $i,B: $i] :
( ( B @ is_a )
=> ( B @ ( A @ hAPP_a93125764e_bool ) @ is_fun_pname_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000t__a_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).
thf(1858,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)],[281]) ).
thf(76,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/sandbox/benchmark/theBenchmark.p',fact_45_card__mono) ).
thf(1151,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)],[76]) ).
thf(332,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ is_fun1661590463l_bool )
=> ( ( C @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_47868345e_bool ) @ ( C @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ image_47868345e_bool ) ) )
& ( 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/sandbox/benchmark/theBenchmark.p',fact_171_finite__subset__image) ).
thf(2034,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ is_fun1661590463l_bool )
=> ( ( C @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_47868345e_bool ) @ ( C @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ image_47868345e_bool ) ) )
& ( 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)],[332]) ).
thf(308,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/sandbox/benchmark/theBenchmark.p',fact_282_set__rev__mp) ).
thf(1960,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)],[308]) ).
thf(116,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/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_013) ).
thf(1283,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)],[116]) ).
thf(48,axiom,
! [A: $i,B: $i] : ( B @ ( A @ image_nat_pname ) @ is_fun_pname_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__Com__Opname) ).
thf(1051,plain,
! [A: $i,B: $i] : ( B @ ( A @ image_nat_pname ) @ is_fun_pname_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(376,axiom,
! [A: $i] :
( zero_zero_nat
!= ( A @ ( suc @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_692_Zero__neq__Suc) ).
thf(2178,plain,
! [A: $i] :
( zero_zero_nat
!= ( A @ ( suc @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(391,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_928955006_pname ) @ hAPP_p130839763l_bool ) )
= ( C @ ( B @ hAPP_p1499970991t_bool ) @ ( A @ hAPP_f103356543l_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__022) ).
thf(2222,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_928955006_pname ) @ hAPP_p130839763l_bool ) )
= ( C @ ( B @ hAPP_p1499970991t_bool ) @ ( A @ hAPP_f103356543l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(870,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_510_order__trans) ).
thf(4205,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).
thf(159,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_615407716e_bool @ hAPP_p130839763l_bool ) @ hAPP_f54304608l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f654413245e_bool ) @ hAPP_pname_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Com__Opn) ).
thf(1415,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_615407716e_bool @ hAPP_p130839763l_bool ) @ hAPP_f54304608l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f654413245e_bool ) @ hAPP_pname_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(893,axiom,
! [A: $i,B: $i] :
( ( A = B )
=> ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_276_equalityD2) ).
thf(4297,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)],[893]) ).
thf(458,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/sandbox/benchmark/theBenchmark.p',fact_70_card__insert__disjoint) ).
thf(2469,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)],[458]) ).
thf(815,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/sandbox/benchmark/theBenchmark.p',fact_11_finite__imageI) ).
thf(3986,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)],[815]) ).
thf(428,axiom,
! [A: $i] :
( ( A @ ( suc @ hAPP_nat_nat ) )
!= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_691_Suc__neq__Zero) ).
thf(2367,plain,
! [A: $i] :
( ( A @ ( suc @ hAPP_nat_nat ) )
!= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(494,axiom,
! [A: $i] :
( ( bot_bo1389914601l_bool
= ( A @ collect_fun_a_bool ) )
<=> ! [B: $i] :
( ( B @ is_fun_a_bool )
=> ~ ( B @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_410_empty__Collect__eq) ).
thf(2618,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ is_fun_a_bool )
=> ~ ( B @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
=> ( bot_bo1389914601l_bool
= ( A @ collect_fun_a_bool ) ) )
& ( ( bot_bo1389914601l_bool
= ( A @ collect_fun_a_bool ) )
=> ! [B: $i] :
( ( B @ is_fun_a_bool )
=> ~ ( B @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(462,axiom,
~ ( fFalse @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
thf(2483,plain,
~ ( fFalse @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(192,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( C @ hAPP_pname_bool ) @ ( A @ ( B @ hAPP_pname_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_380_le__funE) ).
thf(1526,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( C @ hAPP_pname_bool ) @ ( A @ ( B @ hAPP_pname_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(155,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/sandbox/benchmark/theBenchmark.p',fact_78_Suc__diff__le) ).
thf(1405,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)],[155]) ).
thf(92,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( C @ minus_minus_nat @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) @ ( A @ minus_minus_nat @ hAPP_nat_nat ) )
= ( C @ ( suc @ hAPP_nat_nat ) @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_609_diff__Suc__diff__eq1) ).
thf(1201,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( C @ minus_minus_nat @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) @ ( A @ minus_minus_nat @ hAPP_nat_nat ) )
= ( C @ ( suc @ hAPP_nat_nat ) @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(872,axiom,
! [A: $i] :
( ( A @ is_fun_a_bool )
=> ( ( bot_bot_fun_a_bool @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
<=> ( A = bot_bot_fun_a_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_466_subset__empty) ).
thf(4211,plain,
! [A: $i] :
( ( A @ is_fun_a_bool )
=> ( ( ( A = bot_bot_fun_a_bool )
=> ( bot_bot_fun_a_bool @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
& ( ( bot_bot_fun_a_bool @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A = bot_bot_fun_a_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).
thf(518,axiom,
! [A: $i,B: $i,C: $i] :
( ( B = C )
=> ( ( C @ ( A @ ( 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/sandbox/benchmark/theBenchmark.p',fact_531_xt1_I3_J) ).
thf(2718,plain,
! [A: $i,B: $i,C: $i] :
( ( B = C )
=> ( ( C @ ( A @ ( 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)],[518]) ).
thf(487,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ is_fun_pname_bool )
=> ( ( C @ ( B @ image_a_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
<=> ? [D: $i] :
( ( A
= ( D @ ( B @ image_a_pname ) ) )
& ( C @ ( D @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( D @ is_fun_a_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_345_subset__image__iff) ).
thf(2586,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ is_fun_pname_bool )
=> ( ( ? [D: $i] :
( ( A
= ( D @ ( B @ image_a_pname ) ) )
& ( C @ ( D @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( D @ is_fun_a_bool ) )
=> ( C @ ( B @ image_a_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
& ( ( C @ ( B @ image_a_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ? [D: $i] :
( ( A
= ( D @ ( B @ image_a_pname ) ) )
& ( C @ ( D @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( D @ is_fun_a_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(468,axiom,
! [A: $i] :
~ ( zero_zero_nat @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_678_less__zeroE) ).
thf(2508,plain,
! [A: $i] :
~ ( zero_zero_nat @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(24,axiom,
! [A: $i] :
( ( A @ is_fun_pname_bool )
=> ( ( bot_bo844097828e_bool @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
<=> ( A = bot_bo844097828e_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_465_subset__empty) ).
thf(981,plain,
! [A: $i] :
( ( A @ is_fun_pname_bool )
=> ( ( ( A = bot_bo844097828e_bool )
=> ( bot_bo844097828e_bool @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
& ( ( bot_bo844097828e_bool @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A = bot_bo844097828e_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(877,axiom,
! [A: $i] :
~ ( A @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_648_less__irrefl__nat) ).
thf(4230,plain,
! [A: $i] :
~ ( A @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).
thf(145,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_633_not__less__less__Suc__eq) ).
thf(1377,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( A = B )
=> ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(551,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/sandbox/benchmark/theBenchmark.p',conj_2) ).
thf(2861,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)],[551]) ).
thf(98,axiom,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_nat_pname ) @ is_pname ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__Com__Opname) ).
thf(1215,plain,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_nat_pname ) @ is_pname ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(379,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( 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 @ ( D @ plus_plus_nat @ hAPP_nat_nat ) @ ( A @ ( C @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_591_add__le__mono) ).
thf(2190,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( 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 @ ( D @ plus_plus_nat @ hAPP_nat_nat ) @ ( A @ ( C @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(685,axiom,
! [A: $i] :
~ ( bot_bo844097828e_bool @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_384_emptyE) ).
thf(3421,plain,
! [A: $i] :
~ ( bot_bo844097828e_bool @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(471,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B
= ( D @ ( C @ hAPP_a_nat ) ) )
=> ( ( A @ ( D @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( C @ image_a_nat ) @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_image__eqI) ).
thf(2523,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B
= ( D @ ( C @ hAPP_a_nat ) ) )
=> ( ( A @ ( D @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( C @ image_a_nat ) @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(260,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( C @ plus_plus_nat @ hAPP_nat_nat ) @ ( A @ ( B @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_590_add__le__mono1) ).
thf(1796,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( C @ plus_plus_nat @ hAPP_nat_nat ) @ ( A @ ( B @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(70,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/sandbox/benchmark/theBenchmark.p',fact_124_le__diff__iff) ).
thf(1119,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)],[70]) ).
thf(429,axiom,
! [A: $i,B: $i] : ( A @ ( B @ plus_plus_nat @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_656_less__add__Suc2) ).
thf(2371,plain,
! [A: $i,B: $i] : ( A @ ( B @ plus_plus_nat @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(581,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( ( B @ hBOOL )
<=> ( A @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_505_xt1_I5_J) ).
thf(2979,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( ( ( A @ hBOOL )
=> ( B @ hBOOL ) )
& ( ( B @ hBOOL )
=> ( A @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(671,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/sandbox/benchmark/theBenchmark.p',fact_288_mem__def) ).
thf(3361,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)],[671]) ).
thf(807,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( fconj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
| ~ ( A @ hBOOL )
| ~ ( B @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
thf(3955,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)],[807]) ).
thf(540,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/sandbox/benchmark/theBenchmark.p',fact_95_finite__Collect__disjI) ).
thf(2809,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)],[540]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( bot_bot_fun_nat_bool @ ( B @ insert_nat ) @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_449_singletonE) ).
thf(988,plain,
! [A: $i,B: $i] :
( ( bot_bot_fun_nat_bool @ ( B @ insert_nat ) @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(405,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/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It) ).
thf(2286,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)],[405]) ).
thf(831,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
<=> ( ( B @ hBOOL )
<=> ( A @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_540_order__antisym__conv) ).
thf(4038,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( ( ( ( ( A @ hBOOL )
=> ( B @ hBOOL ) )
& ( ( B @ hBOOL )
=> ( A @ hBOOL ) ) )
=> ( A @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) )
& ( ( A @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( ( ( A @ hBOOL )
=> ( B @ hBOOL ) )
& ( ( B @ hBOOL )
=> ( A @ hBOOL ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).
thf(437,axiom,
! [A: $i] :
( zero_zero_nat
!= ( A @ ( suc @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_696_Zero__not__Suc) ).
thf(2392,plain,
! [A: $i] :
( zero_zero_nat
!= ( A @ ( suc @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(795,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( C @ ( A @ image_a_pname ) @ ( B @ ( A @ hAPP_a_pname ) @ insert_pname ) )
= ( C @ ( A @ image_a_pname ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_340_insert__image) ).
thf(3906,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( C @ ( A @ image_a_pname ) @ ( B @ ( A @ hAPP_a_pname ) @ insert_pname ) )
= ( C @ ( A @ image_a_pname ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).
thf(703,axiom,
! [A: $i] :
~ ( bot_bot_fun_nat_bool @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_383_emptyE) ).
thf(3510,plain,
! [A: $i] :
~ ( bot_bot_fun_nat_bool @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(838,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/sandbox/benchmark/theBenchmark.p',fact_359_subsetI) ).
thf(4065,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)],[838]) ).
thf(283,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ is_fun_pname_bool )
=> ( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_1854862208_pname ) @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ image_1854862208_pname ) ) )
& ( D @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
& ( D @ is_fun949378684l_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_finite__subset__image) ).
thf(1863,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ is_fun_pname_bool )
=> ( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_1854862208_pname ) @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ image_1854862208_pname ) ) )
& ( D @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
& ( D @ is_fun949378684l_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(575,axiom,
! [A: $i] :
( ( A @ is_fun_a_bool )
=> ( ( bot_bot_fun_a_bool @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
<=> ( A = bot_bot_fun_a_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_439_bot__unique) ).
thf(2954,plain,
! [A: $i] :
( ( A @ is_fun_a_bool )
=> ( ( ( A = bot_bot_fun_a_bool )
=> ( bot_bot_fun_a_bool @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
& ( ( bot_bot_fun_a_bool @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A = bot_bot_fun_a_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(383,axiom,
! [A: $i,B: $i] :
( ( B @ is_pname )
=> ( B @ ( A @ hAPP_pname_pname ) @ is_pname ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Com__Opname_000tc__Com__Opname) ).
thf(2204,plain,
! [A: $i,B: $i] :
( ( B @ is_pname )
=> ( B @ ( A @ hAPP_pname_pname ) @ is_pname ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(77,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ insert_pname ) @ ( A @ insert_pname ) )
= ( B @ ( A @ insert_pname ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_insert__absorb2) ).
thf(1153,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ insert_pname ) @ ( A @ insert_pname ) )
= ( B @ ( A @ insert_pname ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(357,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/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_004) ).
thf(2118,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)],[357]) ).
thf(336,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/sandbox/benchmark/theBenchmark.p',fact_316_insert__compr__raw) ).
thf(2047,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)],[336]) ).
thf(523,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/sandbox/benchmark/theBenchmark.p',fact_111_rev__finite__subset) ).
thf(2737,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)],[523]) ).
thf(500,axiom,
! [A: $i] : ( A @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_369_order__refl) ).
thf(2641,plain,
! [A: $i] : ( A @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(713,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/sandbox/benchmark/theBenchmark.p',fact_324_insert__subset) ).
thf(3550,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)],[713]) ).
thf(684,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_1738168533e_bool @ hAPP_p1824510254l_bool ) @ hAPP_fun_a_bool_bool ) )
= ( B @ ( C @ ( A @ hAPP_f1794073134e_bool ) @ hAPP_pname_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opname_000tc) ).
thf(3418,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_1738168533e_bool @ hAPP_p1824510254l_bool ) @ hAPP_fun_a_bool_bool ) )
= ( B @ ( C @ ( A @ hAPP_f1794073134e_bool ) @ hAPP_pname_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(323,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/sandbox/benchmark/theBenchmark.p',fact_90_diff__commute) ).
thf(2011,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)],[323]) ).
thf(611,axiom,
u @ is_fun_pname_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_U) ).
thf(3097,plain,
u @ is_fun_pname_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(483,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/sandbox/benchmark/theBenchmark.p',fact_106_finite__subset) ).
thf(2574,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)],[483]) ).
thf(755,axiom,
! [A: $i] : ( A @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_le__refl) ).
thf(3720,plain,
! [A: $i] : ( A @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).
thf(814,axiom,
! [A: $i] : ( A @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_subset__refl) ).
thf(3984,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)],[814]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) )
= ( B @ ( C @ plus_plus_nat @ hAPP_nat_nat ) ) )
<=> ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_574_nat__add__right__cancel) ).
thf(925,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A = C )
=> ( ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) )
= ( B @ ( C @ plus_plus_nat @ hAPP_nat_nat ) ) ) )
& ( ( ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) )
= ( B @ ( C @ plus_plus_nat @ hAPP_nat_nat ) ) )
=> ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(707,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/sandbox/benchmark/theBenchmark.p',fact_10_finite__imageI) ).
thf(3531,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)],[707]) ).
thf(734,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_649_less__not__refl2) ).
thf(3635,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).
thf(427,axiom,
! [A: $i,B: $i] :
( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_628_less__SucE) ).
thf(2364,plain,
! [A: $i,B: $i] :
( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(372,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( suc @ hAPP_nat_nat ) )
= ( B @ ( suc @ hAPP_nat_nat ) ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_nat_Oinject) ).
thf(2164,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)],[372]) ).
thf(349,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_386238098l_bool @ hAPP_f1066163005t_bool ) @ hAPP_nat_bool ) )
= ( B @ ( C @ ( A @ hAPP_n850744903l_bool ) @ hAPP_f1664156314l_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Oboo) ).
thf(2083,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_386238098l_bool @ hAPP_f1066163005t_bool ) @ hAPP_nat_bool ) )
= ( B @ ( C @ ( A @ hAPP_n850744903l_bool ) @ hAPP_f1664156314l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(55,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_less_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_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_642_diff__less__mono2) ).
thf(1067,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_less_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_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(896,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/sandbox/benchmark/theBenchmark.p',fact_15_finite__imageI) ).
thf(4312,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)],[896]) ).
thf(507,axiom,
! [A: $i,B: $i] :
( ( A = B )
=> ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_549_order__eq__refl) ).
thf(2660,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)],[507]) ).
thf(564,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/sandbox/benchmark/theBenchmark.p',fact_8_finite__imageI) ).
thf(2905,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)],[564]) ).
thf(597,axiom,
! [A: $i,B: $i] :
( ( A = B )
=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_548_order__eq__refl) ).
thf(3037,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)],[597]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_385542954t_bool @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f800510211t_bool ) @ hAPP_nat_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Nat__Ona) ).
thf(1057,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_385542954t_bool @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f800510211t_bool ) @ hAPP_nat_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(80,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/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob) ).
thf(1163,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)],[80]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_2129980159t_bool ) @ ( C @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ image_2129980159t_bool ) ) )
& ( 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/sandbox/benchmark/theBenchmark.p',fact_170_finite__subset__image) ).
thf(952,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_2129980159t_bool ) @ ( C @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ image_2129980159t_bool ) ) )
& ( 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)],[13]) ).
thf(488,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( D @ is_a )
=> ( ( C @ ( D @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( D @ ( A @ hAPP_a_nat ) @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) )
=> ( B @ ( C @ ( A @ image_a_nat ) @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_362_image__subsetI) ).
thf(2596,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( D @ is_a )
=> ( ( C @ ( D @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( D @ ( A @ hAPP_a_nat ) @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) )
=> ( B @ ( C @ ( A @ image_a_nat ) @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(71,axiom,
! [A: $i] :
( ( A @ ( A @ minus_minus_nat @ hAPP_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_688_diff__self__eq__0) ).
thf(1123,plain,
! [A: $i] :
( ( A @ ( A @ minus_minus_nat @ hAPP_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(246,axiom,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f654413245e_bool ) @ is_fun_pname_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__Com__Opna) ).
thf(1751,plain,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f654413245e_bool ) @ is_fun_pname_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(623,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/sandbox/benchmark/theBenchmark.p',fact_52_card__seteq) ).
thf(3134,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)],[623]) ).
thf(290,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/sandbox/benchmark/theBenchmark.p',fact_63_card__insert__if) ).
thf(1883,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)],[290]) ).
thf(489,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/sandbox/benchmark/theBenchmark.p',fact_7_finite__imageI) ).
thf(2601,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)],[489]) ).
thf(447,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/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oinsert_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
thf(2428,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)],[447]) ).
thf(135,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_nat_a_bool @ hAPP_a_fun_nat_bool ) @ hAPP_nat_bool ) )
= ( B @ ( C @ ( A @ hAPP_nat_fun_a_bool ) @ hAPP_a_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000t__a_000tc__HOL__Obool_U) ).
thf(1343,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_nat_a_bool @ hAPP_a_fun_nat_bool ) @ hAPP_nat_bool ) )
= ( B @ ( C @ ( A @ hAPP_nat_fun_a_bool ) @ hAPP_a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(538,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/sandbox/benchmark/theBenchmark.p',fact_104_finite__subset) ).
thf(2805,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)],[538]) ).
thf(99,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/sandbox/benchmark/theBenchmark.p',fact_322_insert__subset) ).
thf(1217,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)],[99]) ).
thf(368,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/sandbox/benchmark/theBenchmark.p',fact_119_le__Suc__eq) ).
thf(2147,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)],[368]) ).
thf(763,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( C @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_500_xt1_I6_J) ).
thf(3752,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( C @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).
thf(852,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 )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_508_xt1_I5_J) ).
thf(4128,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 )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).
thf(776,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/sandbox/benchmark/theBenchmark.p',fact_227_insertE) ).
thf(3816,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)],[776]) ).
thf(216,axiom,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_n1414589940l_bool ) @ is_fun949378684l_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL) ).
thf(1619,plain,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_n1414589940l_bool ) @ is_fun949378684l_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(331,axiom,
! [A: $i,B: $i] :
( ( B @ is_a )
=> ( B @ ( A @ hAPP_a_pname ) @ is_pname ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000t__a_000tc__Com__Opname) ).
thf(2032,plain,
! [A: $i,B: $i] :
( ( B @ is_a )
=> ( B @ ( A @ hAPP_a_pname ) @ is_pname ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(584,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 )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_543_order__antisym__conv) ).
thf(2986,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( B = A )
=> ( A @ ( 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 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(438,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_496248727ol_nat ) @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ image_496248727ol_nat ) ) )
& ( D @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_finite__subset__image) ).
thf(2396,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_496248727ol_nat ) @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ image_496248727ol_nat ) ) )
& ( D @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(745,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_a_fun_nat_bool ) @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ? [C: $i] :
( ~ ( C @ ( A @ hAPP_a_fun_nat_bool ) @ ( A @ ( fequal_fun_nat_bool @ cOMBB_743407885bool_a ) @ cOMBC_777206479l_bool @ hAPP_f1549043526a_bool ) @ ( B @ ( member_a @ cOMBC_1355376034l_bool @ hAPP_f2050579477a_bool ) @ ( fconj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( C @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( C @ is_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_pigeonhole__infinite) ).
thf(3682,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_a_fun_nat_bool ) @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ? [C: $i] :
( ~ ( C @ ( A @ hAPP_a_fun_nat_bool ) @ ( A @ ( fequal_fun_nat_bool @ cOMBB_743407885bool_a ) @ cOMBC_777206479l_bool @ hAPP_f1549043526a_bool ) @ ( B @ ( member_a @ cOMBC_1355376034l_bool @ hAPP_f2050579477a_bool ) @ ( fconj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( C @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( C @ is_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).
thf(826,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( C @ hAPP_a_bool ) @ ( A @ ( B @ hAPP_a_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_382_le__funE) ).
thf(4021,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( C @ hAPP_a_bool ) @ ( A @ ( B @ hAPP_a_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).
thf(105,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( suc @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_663_le__less__Suc__eq) ).
thf(1238,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( B = A )
=> ( A @ ( suc @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( A @ ( suc @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(791,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/sandbox/benchmark/theBenchmark.p',fact_99_finite__insert) ).
thf(3889,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)],[791]) ).
thf(528,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/sandbox/benchmark/theBenchmark.p',fact_19_finite__imageI) ).
thf(2758,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)],[528]) ).
thf(297,axiom,
! [A: $i,B: $i] :
~ ( A @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_625_not__add__less1) ).
thf(1920,plain,
! [A: $i,B: $i] :
~ ( A @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(544,axiom,
! [A: $i] :
( ( A @ ( bot_bo844097828e_bool @ hAPP_pname_bool ) @ hBOOL )
<=> ( bot_bot_bool @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_425_bot__fun__def) ).
thf(2826,plain,
! [A: $i] :
( ( ( bot_bot_bool @ hBOOL )
=> ( A @ ( bot_bo844097828e_bool @ hAPP_pname_bool ) @ hBOOL ) )
& ( ( A @ ( bot_bo844097828e_bool @ hAPP_pname_bool ) @ hBOOL )
=> ( bot_bot_bool @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(86,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_a_pname_bool @ hAPP_p1534023578a_bool ) @ hAPP_a_bool ) )
= ( B @ ( C @ ( A @ hAPP_a93125764e_bool ) @ hAPP_pname_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000t__a_000tc__Com__Opname_000tc__HOL__Obool_U) ).
thf(1178,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_a_pname_bool @ hAPP_p1534023578a_bool ) @ hAPP_a_bool ) )
= ( B @ ( C @ ( A @ hAPP_a93125764e_bool ) @ hAPP_pname_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(304,axiom,
! [A: $i] :
( ( A @ is_bool )
=> ( A @ cOMBK_324466864a_bool @ is_fun949378684l_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_COMBK_000tc__HOL__Obool_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
thf(1951,plain,
! [A: $i] :
( ( A @ is_bool )
=> ( A @ cOMBK_324466864a_bool @ is_fun949378684l_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(711,axiom,
! [A: $i,B: $i] : ( A @ ( B @ insert_nat ) @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_320_subset__insertI) ).
thf(3546,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)],[711]) ).
thf(257,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_a_nat_bool @ hAPP_nat_fun_a_bool ) @ hAPP_a_bool ) )
= ( B @ ( C @ ( A @ hAPP_a_fun_nat_bool ) @ hAPP_nat_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000t__a_000tc__Nat__Onat_000tc__HOL__Obool_U) ).
thf(1787,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_a_nat_bool @ hAPP_nat_fun_a_bool ) @ hAPP_a_bool ) )
= ( B @ ( C @ ( A @ hAPP_a_fun_nat_bool ) @ hAPP_nat_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ is_pname )
=> ( ( C @ ( B @ image_nat_pname ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ~ ! [D: $i] :
( ( A
= ( D @ ( B @ hAPP_nat_pname ) ) )
=> ~ ( C @ ( D @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_352_imageE) ).
thf(1027,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ is_pname )
=> ( ( C @ ( B @ image_nat_pname ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ~ ! [D: $i] :
( ( A
= ( D @ ( B @ hAPP_nat_pname ) ) )
=> ~ ( C @ ( D @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(475,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( C @ ( A @ image_a_nat ) @ ( B @ ( A @ hAPP_a_nat ) @ insert_nat ) )
= ( C @ ( A @ image_a_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_341_insert__image) ).
thf(2547,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( C @ ( A @ image_a_nat ) @ ( B @ ( A @ hAPP_a_nat ) @ insert_nat ) )
= ( C @ ( A @ image_a_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(758,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/sandbox/benchmark/theBenchmark.p',fact_514_order__trans) ).
thf(3727,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)],[758]) ).
thf(221,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/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool_U) ).
thf(1634,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)],[221]) ).
thf(802,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/sandbox/benchmark/theBenchmark.p',fact_318_insert__compr__raw) ).
thf(3931,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)],[802]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) )
= ( A @ ( B @ plus_plus_nat @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_578_nat__add__commute) ).
thf(916,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) )
= ( A @ ( B @ plus_plus_nat @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(892,axiom,
! [A: $i,B: $i] :
( ( ( B @ is_fun_a_bool )
& ( A @ is_a ) )
=> ( B @ ( A @ insert_a ) @ is_fun_a_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oinsert_000t__a) ).
thf(4295,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)],[892]) ).
thf(274,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_598082538e_bool ) @ hAPP_f759274231e_bool ) )
= ( C @ ( B @ hAPP_f1297739591_pname ) @ ( A @ hAPP_p61793385e_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_017) ).
thf(1837,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_598082538e_bool ) @ hAPP_f759274231e_bool ) )
= ( C @ ( B @ hAPP_f1297739591_pname ) @ ( A @ hAPP_p61793385e_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(731,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( 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/sandbox/benchmark/theBenchmark.p',fact_553_order__eq__iff) ).
thf(3618,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 ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( 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)],[731]) ).
thf(679,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B
= ( D @ ( C @ hAPP_nat_a ) ) )
=> ( ( A @ ( D @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( C @ image_nat_a ) @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_image__eqI) ).
thf(3403,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B
= ( D @ ( C @ hAPP_nat_a ) ) )
=> ( ( A @ ( D @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( C @ image_nat_a ) @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(639,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/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_010) ).
thf(3198,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)],[639]) ).
thf(660,axiom,
! [A: $i] :
( ( bot_bot_fun_nat_bool @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
<=> ( A = bot_bot_fun_nat_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_464_subset__empty) ).
thf(3297,plain,
! [A: $i] :
( ( ( A = bot_bot_fun_nat_bool )
=> ( bot_bot_fun_nat_bool @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
& ( ( bot_bot_fun_nat_bool @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A = bot_bot_fun_nat_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(624,axiom,
! [A: $i] :
( ( A @ ( fNot @ hAPP_bool_bool ) @ hBOOL )
| ( A @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_2_1_U) ).
thf(3137,plain,
! [A: $i] :
( ( A @ ( fNot @ hAPP_bool_bool ) @ hBOOL )
| ( A @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(121,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( C @ plus_plus_nat @ hAPP_nat_nat ) @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_610_termination__basic__simps_I3_J) ).
thf(1296,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( C @ plus_plus_nat @ hAPP_nat_nat ) @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(787,axiom,
! [A: $i,B: $i,C: $i] :
( ( B = C )
=> ( ( C @ ( A @ ( 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/sandbox/benchmark/theBenchmark.p',fact_532_xt1_I3_J) ).
thf(3877,plain,
! [A: $i,B: $i,C: $i] :
( ( B = C )
=> ( ( C @ ( A @ ( 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)],[787]) ).
thf(95,axiom,
x_a @ undefined_a @ is_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_HOL_Oundefined_000t__a) ).
thf(1210,plain,
x_a @ undefined_a @ is_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(225,axiom,
! [A: $i] :
( ( A @ is_fun_pname_bool )
=> ( A @ collect_pname @ is_fun_pname_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_OCollect_000tc__Com__Opname) ).
thf(1656,plain,
! [A: $i] :
( ( A @ is_fun_pname_bool )
=> ( A @ collect_pname @ is_fun_pname_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(594,axiom,
! [A: $i,B: $i] :
( ( A = B )
=> ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_equalityD1) ).
thf(3028,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)],[594]) ).
thf(420,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/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Nat__On) ).
thf(2345,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)],[420]) ).
thf(800,axiom,
! [A: $i,B: $i] :
( ( B @ is_pname )
=> ( B @ ( A @ hAPP_pname_a ) @ is_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Com__Opname_000t__a) ).
thf(3926,plain,
! [A: $i,B: $i] :
( ( B @ is_pname )
=> ( B @ ( A @ hAPP_pname_a ) @ is_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).
thf(119,axiom,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f292226953l_bool ) @ is_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_) ).
thf(1291,plain,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f292226953l_bool ) @ is_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(841,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A
= ( C @ ( B @ hAPP_nat_a ) ) )
=> ( D @ ( B @ image_nat_a ) @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_rev__image__eqI) ).
thf(4080,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A
= ( C @ ( B @ hAPP_nat_a ) ) )
=> ( D @ ( B @ image_nat_a ) @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).
thf(689,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/sandbox/benchmark/theBenchmark.p',fact_297_subset__trans) ).
thf(3445,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)],[689]) ).
thf(828,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ insert_nat ) @ ( A @ image_nat_a ) )
= ( C @ ( A @ image_nat_a ) @ ( B @ ( A @ hAPP_nat_a ) @ insert_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_336_image__insert) ).
thf(4027,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ insert_nat ) @ ( A @ image_nat_a ) )
= ( C @ ( A @ image_nat_a ) @ ( B @ ( A @ hAPP_nat_a ) @ insert_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).
thf(898,axiom,
! [A: $i,B: $i] :
( ( B @ hBOOL )
| ~ ( B @ ( A @ ( fconj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
thf(4316,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)],[898]) ).
thf(760,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( C @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( bot_bo1701429464l_bool @ ( A @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ! [D: $i,E: $i] :
( ( E @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( D @ ( member_fun_nat_bool @ hAPP_f1951378235l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ~ ( E @ ( D @ ( member_fun_nat_bool @ hAPP_f1951378235l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( E @ ( A @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( E @ ( D @ insert_fun_nat_bool ) @ ( A @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ) ) )
=> ( C @ ( A @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_559_finite__subset__induct) ).
thf(3731,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( C @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( bot_bo1701429464l_bool @ ( A @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ! [D: $i,E: $i] :
( ( E @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( D @ ( member_fun_nat_bool @ hAPP_f1951378235l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ~ ( E @ ( D @ ( member_fun_nat_bool @ hAPP_f1951378235l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( E @ ( A @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( E @ ( D @ insert_fun_nat_bool ) @ ( A @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ) ) )
=> ( C @ ( A @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).
thf(139,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_1666426608t_bool @ hAPP_n850744903l_bool ) @ hAPP_f1664156314l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f1066163005t_bool ) @ hAPP_nat_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Nat__O) ).
thf(1360,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_1666426608t_bool @ hAPP_n850744903l_bool ) @ hAPP_f1664156314l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f1066163005t_bool ) @ hAPP_nat_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(315,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_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_660_Suc__le__eq) ).
thf(1983,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(432,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_523834888_pname ) @ hAPP_p1499970991t_bool ) )
= ( C @ ( B @ hAPP_pname_nat ) @ ( A @ hAPP_n1699378549t_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__005) ).
thf(2377,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_523834888_pname ) @ hAPP_p1499970991t_bool ) )
= ( C @ ( B @ hAPP_pname_nat ) @ ( A @ hAPP_n1699378549t_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(560,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/sandbox/benchmark/theBenchmark.p',fact_35_card__image__le) ).
thf(2895,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)],[560]) ).
thf(54,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/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname_U) ).
thf(1064,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)],[54]) ).
thf(207,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/sandbox/benchmark/theBenchmark.p',fact_517_order__antisym) ).
thf(1587,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)],[207]) ).
thf(513,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/sandbox/benchmark/theBenchmark.p',fact_270_set__eq__subset) ).
thf(2694,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)],[513]) ).
thf(797,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( fequal_a @ hAPP_a_fun_a_bool ) @ hAPP_a_bool ) @ hBOOL )
| ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000t__a_T) ).
thf(3916,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)],[797]) ).
thf(615,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B = A )
=> ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_523_xt1_I4_J) ).
thf(3105,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B = A )
=> ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(751,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/sandbox/benchmark/theBenchmark.p',fact_36_card__image__le) ).
thf(3699,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)],[751]) ).
thf(465,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/sandbox/benchmark/theBenchmark.p',fact_103_finite__subset) ).
thf(2498,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)],[465]) ).
thf(796,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/sandbox/benchmark/theBenchmark.p',fact_93_finite__Collect__disjI) ).
thf(3909,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)],[796]) ).
thf(195,axiom,
! [A: $i,B: $i] : ( B @ ( A @ image_nat_a ) @ is_fun_a_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__Nat__Onat_000t__a) ).
thf(1541,plain,
! [A: $i,B: $i] : ( B @ ( A @ image_nat_a ) @ is_fun_a_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(369,axiom,
! [A: $i] :
( ( A @ is_fun_a_bool )
=> ( A @ p @ is_fun949378684l_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_P) ).
thf(2157,plain,
! [A: $i] :
( ( A @ is_fun_a_bool )
=> ( A @ p @ is_fun949378684l_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(356,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_nat_pname_bool @ hAPP_p1499970991t_bool ) @ hAPP_nat_bool ) )
= ( B @ ( C @ ( A @ hAPP_n1025906991e_bool ) @ hAPP_pname_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Com__Opname_000tc__HOL__Obool_U) ).
thf(2115,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_nat_pname_bool @ hAPP_p1499970991t_bool ) @ hAPP_nat_bool ) )
= ( B @ ( C @ ( A @ hAPP_n1025906991e_bool ) @ hAPP_pname_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(354,axiom,
! [A: $i,B: $i] :
( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_659_less__Suc__eq__le) ).
thf(2100,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_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_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)],[354]) ).
thf(683,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( D @ is_a )
=> ( ( C @ ( D @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( D @ ( A @ hAPP_a_pname ) @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) )
=> ( B @ ( C @ ( A @ image_a_pname ) @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_363_image__subsetI) ).
thf(3413,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( D @ is_a )
=> ( ( C @ ( D @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( D @ ( A @ hAPP_a_pname ) @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) )
=> ( B @ ( C @ ( A @ image_a_pname ) @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(253,axiom,
! [A: $i] :
( ( A @ is_fun_pname_bool )
=> ( ( bot_bo844097828e_bool @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A = bot_bo844097828e_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_431_le__bot) ).
thf(1772,plain,
! [A: $i] :
( ( A @ is_fun_pname_bool )
=> ( ( bot_bo844097828e_bool @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A = bot_bo844097828e_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(572,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/sandbox/benchmark/theBenchmark.p',fact_17_finite__imageI) ).
thf(2946,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)],[572]) ).
thf(38,axiom,
! [A: $i,B: $i] : ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_655_less__add__Suc1) ).
thf(1017,plain,
! [A: $i,B: $i] : ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(305,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/sandbox/benchmark/theBenchmark.p',fact_357_subsetI) ).
thf(1953,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)],[305]) ).
thf(512,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( C @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( bot_bo1649642514l_bool @ ( A @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ! [D: $i,E: $i] :
( ( ( E @ is_fun1661590463l_bool )
& ( D @ is_fun_pname_bool ) )
=> ( ( E @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( D @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ~ ( E @ ( D @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( E @ ( A @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( E @ ( D @ insert1325755072e_bool ) @ ( A @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ) ) ) )
=> ( C @ ( A @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_560_finite__subset__induct) ).
thf(2685,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( C @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( bot_bo1649642514l_bool @ ( A @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ! [D: $i,E: $i] :
( ( ( E @ is_fun1661590463l_bool )
& ( D @ is_fun_pname_bool ) )
=> ( ( E @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( D @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ~ ( E @ ( D @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( E @ ( A @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( E @ ( D @ insert1325755072e_bool ) @ ( A @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ) ) ) )
=> ( C @ ( A @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(311,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/sandbox/benchmark/theBenchmark.p',fact_48_card__seteq) ).
thf(1970,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)],[311]) ).
thf(101,axiom,
! [A: $i] :
( ( A @ ( fequal_nat @ hAPP_n1699378549t_bool ) @ collect_nat )
= ( bot_bot_fun_nat_bool @ ( A @ insert_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_488_singleton__conv2) ).
thf(1227,plain,
! [A: $i] :
( ( A @ ( fequal_nat @ hAPP_n1699378549t_bool ) @ collect_nat )
= ( bot_bot_fun_nat_bool @ ( A @ insert_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(833,axiom,
g @ is_fun_a_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_G) ).
thf(4048,plain,
g @ is_fun_a_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).
thf(280,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun949378684l_bool )
=> ( B @ ( A @ cOMBS_1035972772l_bool ) @ is_fun949378684l_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_COMBS_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000tc__HOL__Obo) ).
thf(1856,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)],[280]) ).
thf(65,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/sandbox/benchmark/theBenchmark.p',fact_130_diff__le__self) ).
thf(1096,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)],[65]) ).
thf(614,axiom,
! [A: $i] :
~ ( bot_bot_fun_nat_bool @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_404_empty__iff) ).
thf(3102,plain,
! [A: $i] :
~ ( bot_bot_fun_nat_bool @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(878,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/sandbox/benchmark/theBenchmark.p',fact_76_finite__Collect__conjI) ).
thf(4233,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)],[878]) ).
thf(733,axiom,
! [A: $i] :
~ ( A @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_645_less__not__refl) ).
thf(3632,plain,
! [A: $i] :
~ ( A @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(845,axiom,
! [A: $i,B: $i,C: $i] :
( ( B = C )
=> ( ( 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/sandbox/benchmark/theBenchmark.p',fact_537_ord__eq__le__trans) ).
thf(4095,plain,
! [A: $i,B: $i,C: $i] :
( ( B = C )
=> ( ( 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)],[845]) ).
thf(499,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ insert_a ) @ ( A @ image_a_pname ) )
= ( C @ ( A @ image_a_pname ) @ ( B @ ( A @ hAPP_a_pname ) @ insert_pname ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_334_image__insert) ).
thf(2638,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ insert_a ) @ ( A @ image_a_pname ) )
= ( C @ ( A @ image_a_pname ) @ ( B @ ( A @ hAPP_a_pname ) @ insert_pname ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(848,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/sandbox/benchmark/theBenchmark.p',fact_513_order__trans) ).
thf(4109,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)],[848]) ).
thf(151,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_nat_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_finite__surj) ).
thf(1397,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_nat_pname ) @ ( 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)],[151]) ).
thf(885,axiom,
bot_bo1649642514l_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_387_finite_OemptyI) ).
thf(4263,plain,
bot_bo1649642514l_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).
thf(900,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( C @ ( A @ image_a_pname ) @ ( B @ ( A @ image_a_pname ) @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_348_image__mono) ).
thf(4320,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( C @ ( A @ image_a_pname ) @ ( B @ ( A @ image_a_pname ) @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).
thf(894,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/sandbox/benchmark/theBenchmark.p',fact_72_finite__Collect__conjI) ).
thf(4301,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)],[894]) ).
thf(302,axiom,
! [A: $i] :
( ( A @ ( zero_zero_nat @ minus_minus_nat @ hAPP_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_690_diff__0__eq__0) ).
thf(1942,plain,
! [A: $i] :
( ( A @ ( zero_zero_nat @ minus_minus_nat @ hAPP_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(413,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun1661590463l_bool )
=> ( B @ ( A @ hAPP_f1935102916l_bool ) @ is_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo) ).
thf(2323,plain,
! [A: $i,B: $i] :
( ( B @ is_fun1661590463l_bool )
=> ( B @ ( A @ hAPP_f1935102916l_bool ) @ is_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ plus_plus_nat @ hAPP_nat_nat ) )
= ( C @ ( B @ plus_plus_nat @ hAPP_nat_nat ) @ ( A @ plus_plus_nat @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_576_nat__add__assoc) ).
thf(933,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ plus_plus_nat @ hAPP_nat_nat ) )
= ( C @ ( B @ plus_plus_nat @ hAPP_nat_nat ) @ ( A @ plus_plus_nat @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(754,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 ) @ ( fFalse @ nat_case_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_570_less__eq__nat_Osimps_I2_J) ).
thf(3714,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ ( fFalse @ nat_case_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( 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 ) @ ( fFalse @ nat_case_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).
thf(348,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/sandbox/benchmark/theBenchmark.p',fact_239_insert__Collect) ).
thf(2080,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)],[348]) ).
thf(276,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( C @ hAPP_nat_bool ) @ ( A @ ( B @ hAPP_nat_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_381_le__funE) ).
thf(1842,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( C @ hAPP_nat_bool ) @ ( A @ ( B @ hAPP_nat_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(206,axiom,
! [A: $i,B: $i] :
( ( ( B @ is_pname )
& ( A @ is_pname ) )
=> ( ( bot_bo844097828e_bool @ ( B @ insert_pname ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_450_singletonE) ).
thf(1584,plain,
! [A: $i,B: $i] :
( ( ( B @ is_pname )
& ( A @ is_pname ) )
=> ( ( bot_bo844097828e_bool @ ( B @ insert_pname ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(595,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/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_It__a_Mtc__H) ).
thf(3032,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)],[595]) ).
thf(373,axiom,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_nat_bool ) @ is_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool) ).
thf(2172,plain,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_nat_bool ) @ is_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(459,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ ( B @ minus_minus_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_643_less__imp__diff__less) ).
thf(2472,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ ( B @ minus_minus_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(719,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/sandbox/benchmark/theBenchmark.p',fact_343_insert__image) ).
thf(3573,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)],[719]) ).
thf(834,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( C @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_501_xt1_I6_J) ).
thf(4049,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( C @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).
thf(132,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( C @ ( D @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( D @ ( A @ hAPP_nat_pname ) @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
=> ( B @ ( C @ ( A @ image_nat_pname ) @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_364_image__subsetI) ).
thf(1329,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( C @ ( D @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( D @ ( A @ hAPP_nat_pname ) @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
=> ( B @ ( C @ ( A @ image_nat_pname ) @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(79,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 )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_507_xt1_I5_J) ).
thf(1160,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 )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(626,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal533582459e_bool @ hAPP_f434788991l_bool ) @ ( fconj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool )
= bot_bo1649642514l_bool ) )
& ( ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal533582459e_bool @ hAPP_f434788991l_bool ) @ ( fconj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool )
= ( bot_bo1649642514l_bool @ ( B @ insert1325755072e_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_480_Collect__conv__if2) ).
thf(3141,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal533582459e_bool @ hAPP_f434788991l_bool ) @ ( fconj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool )
= bot_bo1649642514l_bool ) )
& ( ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal533582459e_bool @ hAPP_f434788991l_bool ) @ ( fconj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool )
= ( bot_bo1649642514l_bool @ ( B @ insert1325755072e_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(680,axiom,
! [A: $i,B: $i] :
( ( B @ hBOOL )
| ( A @ hBOOL )
| ~ ( B @ ( A @ ( fdisj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_3_1_U) ).
thf(3407,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)],[680]) ).
thf(480,axiom,
! [A: $i] :
( ( A @ ( fequal_a @ hAPP_a_fun_a_bool ) @ collect_a )
= ( bot_bot_fun_a_bool @ ( A @ insert_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_490_singleton__conv2) ).
thf(2561,plain,
! [A: $i] :
( ( A @ ( fequal_a @ hAPP_a_fun_a_bool ) @ collect_a )
= ( bot_bot_fun_a_bool @ ( A @ insert_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(644,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/sandbox/benchmark/theBenchmark.p',fact_27_finite_OinsertI) ).
thf(3210,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)],[644]) ).
thf(863,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/sandbox/benchmark/theBenchmark.p',fact_59_card__insert__le) ).
thf(4167,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)],[863]) ).
thf(173,axiom,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_n1025906991e_bool ) @ is_fun_pname_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).
thf(1461,plain,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_n1025906991e_bool ) @ is_fun_pname_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(409,axiom,
! [A: $i] :
( ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) )
= ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_670_less__eq__Suc__le__raw) ).
thf(2312,plain,
! [A: $i] :
( ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) )
= ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(590,axiom,
! [A: $i] :
( ( bot_bot_fun_nat_bool @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A = bot_bot_fun_nat_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_433_le__bot) ).
thf(3010,plain,
! [A: $i] :
( ( bot_bot_fun_nat_bool @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A = bot_bot_fun_nat_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(477,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_nat ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_insert__absorb) ).
thf(2551,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)],[477]) ).
thf(94,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/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_016) ).
thf(1207,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)],[94]) ).
thf(291,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( A @ ( B @ minus_minus_nat @ hAPP_nat_nat ) @ plus_plus_nat @ hAPP_nat_nat ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_599_le__add__diff__inverse2) ).
thf(1889,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( A @ ( B @ minus_minus_nat @ hAPP_nat_nat ) @ plus_plus_nat @ hAPP_nat_nat ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(223,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( ( A != B )
& ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_641_nat__less__le) ).
thf(1644,plain,
! [A: $i,B: $i] :
( ( ( ( A != B )
& ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A != B )
& ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(651,axiom,
! [A: $i] : ( A @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_371_order__refl) ).
thf(3242,plain,
! [A: $i] : ( A @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(130,axiom,
! [A: $i] :
( ( A @ ( ord_less_nat @ cOMBC_nat_nat_bool @ hAPP_n1699378549t_bool ) @ collect_nat @ ( finite_card_nat @ hAPP_f22106695ol_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_653_card__Collect__less__nat) ).
thf(1324,plain,
! [A: $i] :
( ( A @ ( ord_less_nat @ cOMBC_nat_nat_bool @ hAPP_n1699378549t_bool ) @ collect_nat @ ( finite_card_nat @ hAPP_f22106695ol_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(171,axiom,
! [A: $i] :
( ( A @ collect_fun_nat_bool )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_292_Collect__def) ).
thf(1451,plain,
! [A: $i] :
( ( A @ collect_fun_nat_bool )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(769,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/sandbox/benchmark/theBenchmark.p',fact_518_order__antisym) ).
thf(3787,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)],[769]) ).
thf(464,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( C @ ( A @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( ( ( B = C )
=> ( B @ ( C @ ( A @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( ( ( B @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( C @ ( A @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( B @ ( C @ ( A @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_651_nat__less__cases) ).
thf(2487,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( C @ ( A @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( ( ( B = C )
=> ( B @ ( C @ ( A @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( ( ( B @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( C @ ( A @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( B @ ( C @ ( A @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(271,axiom,
! [A: $i,B: $i] : ( A @ ( B @ plus_plus_nat @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_584_le__add2) ).
thf(1831,plain,
! [A: $i,B: $i] : ( A @ ( B @ plus_plus_nat @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(767,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_nat_a ) @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ image_nat_a ) ) )
& ( D @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_finite__subset__image) ).
thf(3770,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_nat_a ) @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ image_nat_a ) ) )
& ( D @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).
thf(397,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) )
= ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) )
<=> ( ( ( B
= ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) )
& ( A = zero_zero_nat ) )
| ( ( B = zero_zero_nat )
& ( A
= ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_681_add__is__1) ).
thf(2243,plain,
! [A: $i,B: $i] :
( ( ( ( ( B
= ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) )
& ( A = zero_zero_nat ) )
| ( ( B = zero_zero_nat )
& ( A
= ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) ) ) )
=> ( ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) )
= ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) ) )
& ( ( ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) )
= ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) )
=> ( ( ( B
= ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) )
& ( A = zero_zero_nat ) )
| ( ( B = zero_zero_nat )
& ( A
= ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(804,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/sandbox/benchmark/theBenchmark.p',fact_244_insert__Collect) ).
thf(3937,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)],[804]) ).
thf(619,axiom,
! [A: $i] :
( ( bot_bot_nat @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( A = bot_bot_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_440_bot__unique) ).
thf(3115,plain,
! [A: $i] :
( ( ( A = bot_bot_nat )
=> ( bot_bot_nat @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( bot_bot_nat @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A = bot_bot_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(667,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/sandbox/benchmark/theBenchmark.p',fact_92_finite__Collect__disjI) ).
thf(3333,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)],[667]) ).
thf(884,axiom,
! [A: $i,B: $i] :
( bot_bot_fun_a_bool
!= ( B @ ( A @ insert_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_463_empty__not__insert) ).
thf(4259,plain,
! [A: $i,B: $i] :
( bot_bot_fun_a_bool
!= ( B @ ( A @ insert_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).
thf(798,axiom,
! [A: $i,B: $i] :
( ( A = B )
=> ( A @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_equalityD2) ).
thf(3920,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)],[798]) ).
thf(365,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun_pname_bool )
=> ( B @ ( A @ hAPP_f434788991l_bool ) @ is_fun1661590463l_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc) ).
thf(2140,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)],[365]) ).
thf(179,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_267053842l_bool @ hAPP_f654413245e_bool ) @ hAPP_pname_bool ) )
= ( B @ ( C @ ( A @ hAPP_p130839763l_bool ) @ hAPP_f54304608l_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Oboo) ).
thf(1478,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_267053842l_bool @ hAPP_f654413245e_bool ) @ hAPP_pname_bool ) )
= ( B @ ( C @ ( A @ hAPP_p130839763l_bool ) @ hAPP_f54304608l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(470,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_26036933t_bool ) @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ? [C: $i] :
( ~ ( C @ ( A @ hAPP_n1699378549t_bool ) @ ( A @ ( fequal_fun_nat_bool @ cOMBB_2026977092ol_nat ) @ cOMBC_226598744l_bool @ hAPP_f800510211t_bool ) @ ( B @ ( member_nat @ cOMBC_226598744l_bool @ hAPP_f800510211t_bool ) @ ( fconj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_pigeonhole__infinite) ).
thf(2519,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_26036933t_bool ) @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ? [C: $i] :
( ~ ( C @ ( A @ hAPP_n1699378549t_bool ) @ ( A @ ( fequal_fun_nat_bool @ cOMBB_2026977092ol_nat ) @ cOMBC_226598744l_bool @ hAPP_f800510211t_bool ) @ ( B @ ( member_nat @ cOMBC_226598744l_bool @ hAPP_f800510211t_bool ) @ ( fconj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(474,axiom,
! [A: $i] :
( ( ( A @ collect_pname )
= bot_bo844097828e_bool )
<=> ! [B: $i] :
( ( B @ is_pname )
=> ~ ( B @ ( A @ hAPP_pname_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_398_Collect__empty__eq) ).
thf(2536,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ is_pname )
=> ~ ( B @ ( A @ hAPP_pname_bool ) @ hBOOL ) )
=> ( ( A @ collect_pname )
= bot_bo844097828e_bool ) )
& ( ( ( A @ collect_pname )
= bot_bo844097828e_bool )
=> ! [B: $i] :
( ( B @ is_pname )
=> ~ ( B @ ( A @ hAPP_pname_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(709,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/sandbox/benchmark/theBenchmark.p',fact_110_rev__finite__subset) ).
thf(3541,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)],[709]) ).
thf(456,axiom,
! [A: $i,B: $i] :
( ( B @ is_a )
=> ( B @ ( A @ hAPP_a_fun_a_bool ) @ is_fun_a_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
thf(2465,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)],[456]) ).
thf(52,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/sandbox/benchmark/theBenchmark.p',fact_6_finite__Collect__subsets) ).
thf(1060,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)],[52]) ).
thf(879,axiom,
! [A: $i] : ( A @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_367_order__refl) ).
thf(4237,plain,
! [A: $i] : ( A @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).
thf(676,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/sandbox/benchmark/theBenchmark.p',fact_238_insert__compr) ).
thf(3390,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)],[676]) ).
thf(647,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/sandbox/benchmark/theBenchmark.p',fact_37_card__image__le) ).
thf(3222,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)],[647]) ).
thf(321,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) )
= ( B @ ( C @ minus_minus_nat @ hAPP_nat_nat ) @ ( A @ plus_plus_nat @ hAPP_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_597_diff__add__assoc) ).
thf(2006,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) )
= ( B @ ( C @ minus_minus_nat @ hAPP_nat_nat ) @ ( A @ plus_plus_nat @ hAPP_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(681,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( C @ ( A @ image_a_nat ) @ ( B @ ( A @ hAPP_a_nat ) @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_304_imageI) ).
thf(3409,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( C @ ( A @ image_a_nat ) @ ( B @ ( A @ hAPP_a_nat ) @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(552,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_nat_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/sandbox/benchmark/theBenchmark.p',fact_140_finite__surj) ).
thf(2862,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_nat_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)],[552]) ).
thf(748,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/sandbox/benchmark/theBenchmark.p',fact_38_card__image__le) ).
thf(3692,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)],[748]) ).
thf(338,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/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Com__Opname_000tc__HOL__Obool_U) ).
thf(2052,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)],[338]) ).
thf(616,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/sandbox/benchmark/theBenchmark.p',fact_329_subset__insertI2) ).
thf(3109,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)],[616]) ).
thf(313,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun_a_bool )
=> ( B @ ( A @ cOMBS_a_bool_bool ) @ is_fun_a_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_COMBS_000t__a_000tc__HOL__Obool_000tc__HOL__Obool) ).
thf(1979,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)],[313]) ).
thf(631,axiom,
! [A: $i,B: $i] :
( ( ( B @ hBOOL )
<=> ( A @ hBOOL ) )
=> ( A @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_545_order__eq__refl) ).
thf(3162,plain,
! [A: $i,B: $i] :
( ( ( ( A @ hBOOL )
=> ( B @ hBOOL ) )
& ( ( B @ hBOOL )
=> ( A @ hBOOL ) ) )
=> ( A @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(640,axiom,
! [A: $i,B: $i] :
( ( A @ hBOOL )
| ~ ( B @ ( A @ ( fconj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
thf(3201,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)],[640]) ).
thf(249,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/sandbox/benchmark/theBenchmark.p',fact_228_zero__induct__lemma) ).
thf(1759,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)],[249]) ).
thf(150,axiom,
! [A: $i] :
( ( A @ ( suc @ hAPP_nat_nat ) )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_Suc__n__not__n) ).
thf(1393,plain,
! [A: $i] :
( ( A @ ( suc @ hAPP_nat_nat ) )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(862,axiom,
! [A: $i,B: $i] :
( ( B = bot_bot_fun_nat_bool )
=> ~ ( B @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_395_equals0D) ).
thf(4163,plain,
! [A: $i,B: $i] :
( ( B = bot_bot_fun_nat_bool )
=> ~ ( B @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).
thf(133,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_nat @ hAPP_n1699378549t_bool ) @ ( fconj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat )
= bot_bot_fun_nat_bool ) )
& ( ( B @ ( A @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_nat @ hAPP_n1699378549t_bool ) @ ( fconj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat )
= ( bot_bot_fun_nat_bool @ ( B @ insert_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_476_Collect__conv__if2) ).
thf(1333,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_nat @ hAPP_n1699378549t_bool ) @ ( fconj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat )
= bot_bot_fun_nat_bool ) )
& ( ( B @ ( A @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_nat @ hAPP_n1699378549t_bool ) @ ( fconj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat )
= ( bot_bot_fun_nat_bool @ ( B @ insert_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(568,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/sandbox/benchmark/theBenchmark.p',fact_251_insert__iff) ).
thf(2926,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)],[568]) ).
thf(267,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/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_007) ).
thf(1814,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)],[267]) ).
thf(385,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( C @ hAPP_nat_bool ) @ ( A @ ( B @ hAPP_nat_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_378_le__funD) ).
thf(2208,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( C @ hAPP_nat_bool ) @ ( A @ ( B @ hAPP_nat_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(557,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( ( ( C @ hBOOL )
<=> ( A @ hBOOL ) )
=> ( A @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_525_ord__le__eq__trans) ).
thf(2883,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( ( ( ( A @ hBOOL )
=> ( C @ hBOOL ) )
& ( ( C @ hBOOL )
=> ( A @ hBOOL ) ) )
=> ( A @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(201,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/sandbox/benchmark/theBenchmark.p',fact_264_insert__absorb) ).
thf(1563,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)],[201]) ).
thf(83,axiom,
! [A: $i] :
( ( zero_zero_nat @ ( A @ minus_minus_nat @ hAPP_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_689_minus__nat_Odiff__0) ).
thf(1170,plain,
! [A: $i] :
( ( zero_zero_nat @ ( A @ minus_minus_nat @ hAPP_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(439,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_1834145417l_bool @ hAPP_f1051908748a_bool ) @ hAPP_a_bool ) )
= ( B @ ( C @ ( A @ hAPP_a217006258l_bool ) @ hAPP_f1664156314l_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000t__a_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc) ).
thf(2402,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_1834145417l_bool @ hAPP_f1051908748a_bool ) @ hAPP_a_bool ) )
= ( B @ ( C @ ( A @ hAPP_a217006258l_bool ) @ hAPP_f1664156314l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(735,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/sandbox/benchmark/theBenchmark.p',fact_105_finite__subset) ).
thf(3639,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)],[735]) ).
thf(473,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/sandbox/benchmark/theBenchmark.p',fact_91_finite__Collect__disjI) ).
thf(2529,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)],[473]) ).
thf(241,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_623_nat__add__left__cancel__less) ).
thf(1732,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(774,axiom,
! [A: $i] : ( A @ ( bot_bo844097828e_bool @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_392_empty__subsetI) ).
thf(3807,plain,
! [A: $i] : ( A @ ( bot_bo844097828e_bool @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(858,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/sandbox/benchmark/theBenchmark.p',fact_39_card__image__le) ).
thf(4148,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)],[858]) ).
thf(497,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/sandbox/benchmark/theBenchmark.p',fact_88_nat__le__linear) ).
thf(2634,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)],[497]) ).
thf(527,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ is_fun_a_bool )
=> ( ( C @ ( B @ image_nat_a ) @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
<=> ? [D: $i] :
( ( A
= ( D @ ( B @ image_nat_a ) ) )
& ( C @ ( D @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_344_subset__image__iff) ).
thf(2749,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ is_fun_a_bool )
=> ( ( ? [D: $i] :
( ( A
= ( D @ ( B @ image_nat_a ) ) )
& ( C @ ( D @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
=> ( C @ ( B @ image_nat_a ) @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
& ( ( C @ ( B @ image_nat_a ) @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ? [D: $i] :
( ( A
= ( D @ ( B @ image_nat_a ) ) )
& ( C @ ( D @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(166,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( suc @ hAPP_nat_nat ) )
= ( B @ ( suc @ hAPP_nat_nat ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_Suc__inject) ).
thf(1434,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)],[166]) ).
thf(317,axiom,
! [A: $i] :
( ( A @ ( fequal_fun_nat_bool @ cOMBC_1693257480l_bool @ hAPP_f103356543l_bool ) @ collect_fun_nat_bool )
= ( bot_bo1701429464l_bool @ ( A @ insert_fun_nat_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_485_singleton__conv) ).
thf(1991,plain,
! [A: $i] :
( ( A @ ( fequal_fun_nat_bool @ cOMBC_1693257480l_bool @ hAPP_f103356543l_bool ) @ collect_fun_nat_bool )
= ( bot_bo1701429464l_bool @ ( A @ insert_fun_nat_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(779,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/sandbox/benchmark/theBenchmark.p',fact_516_order__antisym) ).
thf(3834,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)],[779]) ).
thf(530,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ insert_a ) @ ( A @ insert_a ) )
= ( B @ ( A @ insert_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_insert__absorb2) ).
thf(2761,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ insert_a ) @ ( A @ insert_a ) )
= ( B @ ( A @ insert_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(868,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_fun_nat_bool @ hAPP_f103356543l_bool ) @ ( fconj @ cOMBB_444170502t_bool ) @ cOMBS_1187019125l_bool ) @ collect_fun_nat_bool )
= bot_bo1701429464l_bool ) )
& ( ( B @ ( A @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_fun_nat_bool @ hAPP_f103356543l_bool ) @ ( fconj @ cOMBB_444170502t_bool ) @ cOMBS_1187019125l_bool ) @ collect_fun_nat_bool )
= ( bot_bo1701429464l_bool @ ( B @ insert_fun_nat_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_479_Collect__conv__if2) ).
thf(4195,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_fun_nat_bool @ hAPP_f103356543l_bool ) @ ( fconj @ cOMBB_444170502t_bool ) @ cOMBS_1187019125l_bool ) @ collect_fun_nat_bool )
= bot_bo1701429464l_bool ) )
& ( ( B @ ( A @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_fun_nat_bool @ hAPP_f103356543l_bool ) @ ( fconj @ cOMBB_444170502t_bool ) @ cOMBS_1187019125l_bool ) @ collect_fun_nat_bool )
= ( bot_bo1701429464l_bool @ ( B @ insert_fun_nat_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).
thf(334,axiom,
! [A: $i,B: $i] :
( ( B @ is_a )
=> ( B @ ( A @ hAPP_a217006258l_bool ) @ is_fun1661590463l_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000t__a_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__H) ).
thf(2043,plain,
! [A: $i,B: $i] :
( ( B @ is_a )
=> ( B @ ( A @ hAPP_a217006258l_bool ) @ is_fun1661590463l_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(723,axiom,
! [A: $i] :
( ( bot_bo844097828e_bool @ ( A @ image_pname_a ) )
= bot_bot_fun_a_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_468_image__empty) ).
thf(3587,plain,
! [A: $i] :
( ( bot_bo844097828e_bool @ ( A @ image_pname_a ) )
= bot_bot_fun_a_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(340,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ plus_plus_nat @ hAPP_nat_nat ) )
= ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_572_add__Suc) ).
thf(2057,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ plus_plus_nat @ hAPP_nat_nat ) )
= ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(239,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( bot_bot_fun_nat_bool @ ( B @ insert_nat ) @ ( A @ insert_nat ) )
= ( bot_bot_fun_nat_bool @ ( D @ insert_nat ) @ ( C @ insert_nat ) ) )
<=> ( ( ( B = C )
& ( A = D ) )
| ( ( B = D )
& ( A = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_453_doubleton__eq__iff) ).
thf(1712,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( ( B = C )
& ( A = D ) )
| ( ( B = D )
& ( A = C ) ) )
=> ( ( bot_bot_fun_nat_bool @ ( B @ insert_nat ) @ ( A @ insert_nat ) )
= ( bot_bot_fun_nat_bool @ ( D @ insert_nat ) @ ( C @ insert_nat ) ) ) )
& ( ( ( bot_bot_fun_nat_bool @ ( B @ insert_nat ) @ ( A @ insert_nat ) )
= ( bot_bot_fun_nat_bool @ ( D @ insert_nat ) @ ( C @ insert_nat ) ) )
=> ( ( ( B = C )
& ( A = D ) )
| ( ( B = D )
& ( A = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(725,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/sandbox/benchmark/theBenchmark.p',fact_347_subset__image__iff) ).
thf(3592,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)],[725]) ).
thf(577,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( fequal_fun_nat_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
| ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T) ).
thf(2963,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)],[577]) ).
thf(117,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_800536526ol_nat ) @ hAPP_n1699378549t_bool ) )
= ( C @ ( B @ hAPP_nat_nat ) @ ( A @ hAPP_n1699378549t_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__003) ).
thf(1286,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_800536526ol_nat ) @ hAPP_n1699378549t_bool ) )
= ( C @ ( B @ hAPP_nat_nat ) @ ( A @ hAPP_n1699378549t_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) )
= ( C @ ( B @ plus_plus_nat @ hAPP_nat_nat ) @ ( A @ minus_minus_nat @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_581_diff__diff__left) ).
thf(1035,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) )
= ( C @ ( B @ plus_plus_nat @ hAPP_nat_nat ) @ ( A @ minus_minus_nat @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(441,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( C @ minus_minus_nat @ hAPP_nat_nat ) @ ( A @ minus_minus_nat @ hAPP_nat_nat ) )
= ( C @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_605_diff__diff__right) ).
thf(2408,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( C @ minus_minus_nat @ hAPP_nat_nat ) @ ( A @ minus_minus_nat @ hAPP_nat_nat ) )
= ( C @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(637,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/sandbox/benchmark/theBenchmark.p',fact_328_subset__insertI2) ).
thf(3190,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)],[637]) ).
thf(502,axiom,
! [A: $i] : ( A @ ( bot_bo844097828e_bool @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_441_bot__least) ).
thf(2645,plain,
! [A: $i] : ( A @ ( bot_bo844097828e_bool @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(586,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 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_499_linorder__le__cases) ).
thf(2995,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 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(821,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/sandbox/benchmark/theBenchmark.p',fact_512_order__trans) ).
thf(4004,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)],[821]) ).
thf(319,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_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_652_finite__nat__set__iff__bounded) ).
thf(1996,plain,
! [A: $i] :
( ( ? [B: $i] :
! [C: $i] :
( ( A @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( C @ ( ord_less_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_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(744,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 )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_544_order__antisym__conv) ).
thf(3675,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 )
=> ( ( ( B = A )
=> ( A @ ( B @ ( 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 )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).
thf(295,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/sandbox/benchmark/theBenchmark.p',fact_252_insert__iff) ).
thf(1906,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)],[295]) ).
thf(569,axiom,
! [A: $i,B: $i,C: $i] :
( ( B = C )
=> ( ( 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/sandbox/benchmark/theBenchmark.p',fact_536_ord__eq__le__trans) ).
thf(2936,plain,
! [A: $i,B: $i,C: $i] :
( ( B = C )
=> ( ( 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)],[569]) ).
thf(741,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/sandbox/benchmark/theBenchmark.p',fact_97_finite__insert) ).
thf(3660,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)],[741]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( A @ is_bool )
=> ( ( B @ ( A @ cOMBK_1994329625t_bool @ hAPP_f54304608l_bool ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool) ).
thf(965,plain,
! [A: $i,B: $i] :
( ( A @ is_bool )
=> ( ( B @ ( A @ cOMBK_1994329625t_bool @ hAPP_f54304608l_bool ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(853,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_fun_a_bool_a ) @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ image_fun_a_bool_a ) ) )
& ( D @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
& ( D @ is_fun949378684l_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_finite__subset__image) ).
thf(4131,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_fun_a_bool_a ) @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ image_fun_a_bool_a ) ) )
& ( D @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
& ( D @ is_fun949378684l_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).
thf(375,axiom,
( bot_bo844097828e_bool
= ( fFalse @ cOMBK_bool_pname @ collect_pname ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_419_empty__def) ).
thf(2176,plain,
( bot_bo844097828e_bool
= ( fFalse @ cOMBK_bool_pname @ collect_pname ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(68,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/sandbox/benchmark/theBenchmark.p',fact_552_order__eq__iff) ).
thf(1103,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)],[68]) ).
thf(517,axiom,
u @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2717,plain,
u @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(696,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 )
=> ? [C: $i] :
( ~ ( C @ ( A @ hAPP_nat_a ) @ ( A @ ( fequal_a @ cOMBB_1885489796ol_nat ) @ cOMBC_nat_a_bool @ hAPP_a_fun_nat_bool ) @ ( B @ ( member_nat @ cOMBC_226598744l_bool @ hAPP_f800510211t_bool ) @ ( fconj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_pigeonhole__infinite) ).
thf(3491,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 )
=> ? [C: $i] :
( ~ ( C @ ( A @ hAPP_nat_a ) @ ( A @ ( fequal_a @ cOMBB_1885489796ol_nat ) @ cOMBC_nat_a_bool @ hAPP_a_fun_nat_bool ) @ ( B @ ( member_nat @ cOMBC_226598744l_bool @ hAPP_f800510211t_bool ) @ ( fconj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(655,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_a_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/sandbox/benchmark/theBenchmark.p',fact_131_finite__surj) ).
thf(3262,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_a_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)],[655]) ).
thf(659,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/sandbox/benchmark/theBenchmark.p',fact_256_insert__code) ).
thf(3289,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)],[659]) ).
thf(771,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( ( ( B @ hBOOL )
<=> ( A @ hBOOL ) )
=> ( C @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_520_xt1_I4_J) ).
thf(3792,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( ( ( ( A @ hBOOL )
=> ( B @ hBOOL ) )
& ( ( B @ hBOOL )
=> ( A @ hBOOL ) ) )
=> ( C @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).
thf(617,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_26036933t_bool ) @ ( A @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( A @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_finite__surj) ).
thf(3111,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_26036933t_bool ) @ ( 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)],[617]) ).
thf(750,axiom,
! [A: $i,B: $i] :
( ( ( B @ is_a )
& ( A @ is_a ) )
=> ( ( ( bot_bot_fun_a_bool @ ( A @ insert_a ) )
= ( bot_bot_fun_a_bool @ ( B @ insert_a ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_448_singleton__inject) ).
thf(3696,plain,
! [A: $i,B: $i] :
( ( ( B @ is_a )
& ( A @ is_a ) )
=> ( ( ( bot_bot_fun_a_bool @ ( A @ insert_a ) )
= ( bot_bot_fun_a_bool @ ( B @ insert_a ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).
thf(144,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/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__H) ).
thf(1374,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)],[144]) ).
thf(678,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ is_fun1661590463l_bool )
=> ( ( C @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_819518260e_bool ) @ ( C @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ image_819518260e_bool ) ) )
& ( D @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( D @ is_fun_a_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_finite__subset__image) ).
thf(3396,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ is_fun1661590463l_bool )
=> ( ( C @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_819518260e_bool ) @ ( C @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ image_819518260e_bool ) ) )
& ( D @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( D @ is_fun_a_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(358,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_1004116266e_bool @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f759274231e_bool ) @ hAPP_pname_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__O) ).
thf(2121,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_1004116266e_bool @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f759274231e_bool ) @ hAPP_pname_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(394,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ plus_plus_nat @ hAPP_nat_nat ) @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) )
= ( C @ ( A @ minus_minus_nat @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_583_diff__cancel2) ).
thf(2235,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ plus_plus_nat @ hAPP_nat_nat ) @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) )
= ( C @ ( A @ minus_minus_nat @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(367,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/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__HOL__Obool_U) ).
thf(2144,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)],[367]) ).
thf(108,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_743407885bool_a ) @ hAPP_a1392362872l_bool ) )
= ( C @ ( B @ hAPP_a_fun_nat_bool ) @ ( A @ hAPP_f103356543l_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc_) ).
thf(1251,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_743407885bool_a ) @ hAPP_a1392362872l_bool ) )
= ( C @ ( B @ hAPP_a_fun_nat_bool ) @ ( A @ hAPP_f103356543l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(443,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ insert_nat ) )
!= bot_bot_fun_nat_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_459_insert__not__empty) ).
thf(2413,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ insert_nat ) )
!= bot_bot_fun_nat_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(608,axiom,
! [A: $i] : ( A @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_subset__refl) ).
thf(3079,plain,
! [A: $i] : ( A @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(245,axiom,
! [A: $i] :
( zero_zero_nat
!= ( A @ ( suc @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_695_nat_Osimps_I2_J) ).
thf(1747,plain,
! [A: $i] :
( zero_zero_nat
!= ( A @ ( suc @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(761,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/sandbox/benchmark/theBenchmark.p',fact_255_insert__code) ).
thf(3738,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)],[761]) ).
thf(329,axiom,
! [A: $i] :
( ( A @ is_fun_a_bool )
=> ( A @ collect_a @ is_fun_a_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_OCollect_000t__a) ).
thf(2028,plain,
! [A: $i] :
( ( A @ is_fun_a_bool )
=> ( A @ collect_a @ is_fun_a_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(522,axiom,
! [A: $i] :
( ( A @ ( fequal_a @ cOMBC_a_a_bool @ hAPP_a_fun_a_bool ) @ collect_a )
= ( bot_bot_fun_a_bool @ ( A @ insert_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_484_singleton__conv) ).
thf(2734,plain,
! [A: $i] :
( ( A @ ( fequal_a @ cOMBC_a_a_bool @ hAPP_a_fun_a_bool ) @ collect_a )
= ( bot_bot_fun_a_bool @ ( A @ insert_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(629,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/sandbox/benchmark/theBenchmark.p',fact_16_finite__imageI) ).
thf(3158,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)],[629]) ).
thf(398,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_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_664_Suc__le__lessD) ).
thf(2260,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_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(856,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/sandbox/benchmark/theBenchmark.p',fact_25_finite_OinsertI) ).
thf(4144,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)],[856]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( A @ image_pname_nat ) @ ( B @ ( A @ hAPP_pname_nat ) @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_303_imageI) ).
thf(975,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( A @ image_pname_nat ) @ ( B @ ( A @ hAPP_pname_nat ) @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(272,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun_a_bool )
=> ( B @ ( A @ image_819518260e_bool ) @ is_fun1661590463l_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000t__a_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).
thf(1833,plain,
! [A: $i,B: $i] :
( ( B @ is_fun_a_bool )
=> ( B @ ( A @ image_819518260e_bool ) @ is_fun1661590463l_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(606,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/sandbox/benchmark/theBenchmark.p',fact_14_finite__imageI) ).
thf(3070,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)],[606]) ).
thf(296,axiom,
! [A: $i,B: $i] :
( ( A @ is_fun_pname_bool )
=> ( ( bot_bo844097828e_bool @ ( B @ insert_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A
= ( bot_bo844097828e_bool @ ( B @ insert_pname ) ) )
| ( A = bot_bo844097828e_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_495_subset__singletonD) ).
thf(1916,plain,
! [A: $i,B: $i] :
( ( A @ is_fun_pname_bool )
=> ( ( bot_bo844097828e_bool @ ( B @ insert_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A
= ( bot_bo844097828e_bool @ ( B @ insert_pname ) ) )
| ( A = bot_bo844097828e_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(550,axiom,
! [A: $i] : ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_679_le0) ).
thf(2859,plain,
! [A: $i] : ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(256,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/sandbox/benchmark/theBenchmark.p',fact_80_card__Collect__le__nat) ).
thf(1784,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)],[256]) ).
thf(325,axiom,
( bot_bo1389914601l_bool
= ( fFalse @ cOMBK_324466864a_bool @ collect_fun_a_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_422_empty__def) ).
thf(2016,plain,
( bot_bo1389914601l_bool
= ( fFalse @ cOMBK_324466864a_bool @ collect_fun_a_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(148,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/sandbox/benchmark/theBenchmark.p',fact_236_insert__compr) ).
thf(1388,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)],[148]) ).
thf(794,axiom,
! [A: $i] :
( ( A @ ( bot_bo844097828e_bool @ hAPP_pname_bool ) @ hBOOL )
<=> ( bot_bot_bool @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_428_bot__apply) ).
thf(3900,plain,
! [A: $i] :
( ( ( bot_bot_bool @ hBOOL )
=> ( A @ ( bot_bo844097828e_bool @ hAPP_pname_bool ) @ hBOOL ) )
& ( ( A @ ( bot_bo844097828e_bool @ hAPP_pname_bool ) @ hBOOL )
=> ( bot_bot_bool @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(154,axiom,
! [A: $i,B: $i] :
( ! [C: $i] : ( C @ ( B @ hAPP_nat_nat ) @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_less_eq_nat @ cOMBB_800536526ol_nat ) @ cOMBC_nat_nat_bool @ hAPP_n1699378549t_bool ) @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_566_finite__less__ub) ).
thf(1403,plain,
! [A: $i,B: $i] :
( ! [C: $i] : ( C @ ( B @ hAPP_nat_nat ) @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_less_eq_nat @ cOMBB_800536526ol_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)],[154]) ).
thf(727,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/sandbox/benchmark/theBenchmark.p',fact_299_equalityE) ).
thf(3604,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)],[727]) ).
thf(310,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( C @ ( A @ hAPP_nat_bool ) @ hBOOL )
=> ( ! [D: $i] :
( ( C @ ( D @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( D @ ( suc @ hAPP_nat_nat ) @ ( A @ hAPP_nat_bool ) @ hBOOL )
=> ( D @ ( A @ hAPP_nat_bool ) @ hBOOL ) ) )
=> ( B @ ( A @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_672_inc__induct) ).
thf(1965,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( C @ ( A @ hAPP_nat_bool ) @ hBOOL )
=> ( ! [D: $i] :
( ( C @ ( D @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( D @ ( suc @ hAPP_nat_nat ) @ ( A @ hAPP_nat_bool ) @ hBOOL )
=> ( D @ ( A @ hAPP_nat_bool ) @ hBOOL ) ) )
=> ( B @ ( A @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(190,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_627_Suc__lessD) ).
thf(1520,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(183,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_1551609309ol_nat ) @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_finite__surj) ).
thf(1488,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_1551609309ol_nat ) @ ( 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)],[183]) ).
thf(363,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B
= ( D @ ( C @ hAPP_pname_nat ) ) )
=> ( ( A @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( C @ image_pname_nat ) @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_image__eqI) ).
thf(2134,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B
= ( D @ ( C @ hAPP_pname_nat ) ) )
=> ( ( A @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( C @ image_pname_nat ) @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(579,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/sandbox/benchmark/theBenchmark.p',fact_65_card__insert__if) ).
thf(2970,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)],[579]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( C @ hAPP_pname_bool ) @ ( A @ ( B @ hAPP_pname_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_377_le__funD) ).
thf(1007,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( C @ hAPP_pname_bool ) @ ( A @ ( B @ hAPP_pname_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(665,axiom,
! [A: $i] :
( ( bot_bo844097828e_bool
= ( A @ collect_pname ) )
<=> ! [B: $i] :
( ( B @ is_pname )
=> ~ ( B @ ( A @ hAPP_pname_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_407_empty__Collect__eq) ).
thf(3319,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ is_pname )
=> ~ ( B @ ( A @ hAPP_pname_bool ) @ hBOOL ) )
=> ( bot_bo844097828e_bool
= ( A @ collect_pname ) ) )
& ( ( bot_bo844097828e_bool
= ( A @ collect_pname ) )
=> ! [B: $i] :
( ( B @ is_pname )
=> ~ ( B @ ( A @ hAPP_pname_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(392,axiom,
! [A: $i,B: $i] : ( B @ ( A @ image_1655916159e_bool ) @ is_fun1661590463l_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).
thf(2225,plain,
! [A: $i,B: $i] : ( B @ ( A @ image_1655916159e_bool ) @ is_fun1661590463l_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(701,axiom,
! [A: $i,B: $i] : ( B @ ( A @ insert_pname ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_insertI1) ).
thf(3504,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)],[701]) ).
thf(609,axiom,
! [A: $i] :
( ( ( A @ collec1974731493e_bool )
= bot_bo1649642514l_bool )
<=> ! [B: $i] :
( ( B @ is_fun_pname_bool )
=> ~ ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_400_Collect__empty__eq) ).
thf(3081,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ is_fun_pname_bool )
=> ~ ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL ) )
=> ( ( A @ collec1974731493e_bool )
= bot_bo1649642514l_bool ) )
& ( ( ( A @ collec1974731493e_bool )
= bot_bo1649642514l_bool )
=> ! [B: $i] :
( ( B @ is_fun_pname_bool )
=> ~ ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(299,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/sandbox/benchmark/theBenchmark.p',fact_226_insertE) ).
thf(1929,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)],[299]) ).
thf(235,axiom,
! [A: $i] :
( ( A @ ( suc @ hAPP_nat_nat ) )
!= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_694_Suc__not__Zero) ).
thf(1701,plain,
! [A: $i] :
( ( A @ ( suc @ hAPP_nat_nat ) )
!= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(724,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_fun_a_bool_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/sandbox/benchmark/theBenchmark.p',fact_134_finite__surj) ).
thf(3590,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_fun_a_bool_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)],[724]) ).
thf(163,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_611_termination__basic__simps_I4_J) ).
thf(1428,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(187,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/sandbox/benchmark/theBenchmark.p',fact_118_Suc__le__mono) ).
thf(1503,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)],[187]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ ( suc @ hAPP_nat_nat ) )
= ( one_one_nat @ ( A @ plus_plus_nat @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_606_Suc__eq__plus1) ).
thf(936,plain,
! [A: $i] :
( ( A @ ( suc @ hAPP_nat_nat ) )
= ( one_one_nat @ ( A @ plus_plus_nat @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(390,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( D @ plus_plus_nat @ hAPP_nat_nat ) @ ( A @ ( C @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_619_add__less__mono) ).
thf(2220,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( D @ plus_plus_nat @ hAPP_nat_nat ) @ ( A @ ( C @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(237,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/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Op) ).
thf(1707,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)],[237]) ).
thf(127,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/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo) ).
thf(1312,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)],[127]) ).
thf(668,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_1283814551_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ? [C: $i] :
( ~ ( C @ ( A @ hAPP_f1297739591_pname ) @ ( A @ ( fequal_pname @ cOMBB_598082538e_bool ) @ cOMBC_1004116266e_bool @ hAPP_p338031245l_bool ) @ ( B @ ( member799430823e_bool @ cOMBC_1988546018l_bool @ hAPP_f559147733l_bool ) @ ( fconj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
& ( B @ ( C @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
& ( C @ is_fun_pname_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_pigeonhole__infinite) ).
thf(3340,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_1283814551_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ? [C: $i] :
( ~ ( C @ ( A @ hAPP_f1297739591_pname ) @ ( A @ ( fequal_pname @ cOMBB_598082538e_bool ) @ cOMBC_1004116266e_bool @ hAPP_p338031245l_bool ) @ ( B @ ( member799430823e_bool @ cOMBC_1988546018l_bool @ hAPP_f559147733l_bool ) @ ( fconj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
& ( B @ ( C @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
& ( C @ is_fun_pname_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(620,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/sandbox/benchmark/theBenchmark.p',fact_210_pigeonhole__infinite) ).
thf(3123,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)],[620]) ).
thf(339,axiom,
! [A: $i] : ( A @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_612_lessI) ).
thf(2055,plain,
! [A: $i] : ( A @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(514,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/sandbox/benchmark/theBenchmark.p',fact_62_card__insert__if) ).
thf(2706,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)],[514]) ).
thf(63,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/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__HOL__Obool_000tc__HOL__Obool_U) ).
thf(1090,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)],[63]) ).
thf(717,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/sandbox/benchmark/theBenchmark.p',fact_298_subset__trans) ).
thf(3568,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)],[717]) ).
thf(738,axiom,
! [A: $i,B: $i] :
( ( A = B )
=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_eq__imp__le) ).
thf(3651,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)],[738]) ).
thf(846,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/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool) ).
thf(4099,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)],[846]) ).
thf(666,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 )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_509_xt1_I5_J) ).
thf(3330,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 )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(643,axiom,
! [A: $i] : ( A @ ( bot_bot_fun_nat_bool @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_443_bot__least) ).
thf(3208,plain,
! [A: $i] : ( A @ ( bot_bot_fun_nat_bool @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(873,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A
= ( C @ ( B @ hAPP_a_nat ) ) )
=> ( D @ ( B @ image_a_nat ) @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_309_rev__image__eqI) ).
thf(4218,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A
= ( C @ ( B @ hAPP_a_nat ) ) )
=> ( D @ ( B @ image_a_nat ) @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).
thf(452,axiom,
! [A: $i] :
( ( A @ is_fun1661590463l_bool )
=> ( A @ collec1974731493e_bool @ is_fun1661590463l_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_OCollect_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).
thf(2457,plain,
! [A: $i] :
( ( A @ is_fun1661590463l_bool )
=> ( A @ collec1974731493e_bool @ is_fun1661590463l_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ plus_plus_nat @ hAPP_nat_nat ) @ ( A @ plus_plus_nat @ hAPP_nat_nat ) )
= ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( B @ plus_plus_nat @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_577_nat__add__left__commute) ).
thf(919,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ plus_plus_nat @ hAPP_nat_nat ) @ ( A @ plus_plus_nat @ hAPP_nat_nat ) )
= ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( B @ plus_plus_nat @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(736,axiom,
! [A: $i] :
( ( A @ is_fun_a_bool )
=> ( ( bot_bot_fun_a_bool @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A = bot_bot_fun_a_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_434_le__bot) ).
thf(3641,plain,
! [A: $i] :
( ( A @ is_fun_a_bool )
=> ( ( bot_bot_fun_a_bool @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A = bot_bot_fun_a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(460,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/sandbox/benchmark/theBenchmark.p',fact_323_insert__subset) ).
thf(2474,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)],[460]) ).
thf(10,axiom,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_n850744903l_bool ) @ is_fun1661590463l_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool) ).
thf(947,plain,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_n850744903l_bool ) @ is_fun1661590463l_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(881,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/sandbox/benchmark/theBenchmark.p',fact_332_insert__mono) ).
thf(4245,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)],[881]) ).
thf(100,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ plus_plus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) )
= ( A @ ( B @ ( C @ minus_minus_nat @ hAPP_nat_nat ) @ plus_plus_nat @ hAPP_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_595_diff__add__assoc2) ).
thf(1224,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ plus_plus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) )
= ( A @ ( B @ ( C @ minus_minus_nat @ hAPP_nat_nat ) @ plus_plus_nat @ hAPP_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun1661590463l_bool )
=> ( B @ ( A @ cOMBS_350070575l_bool ) @ is_fun1661590463l_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__Obool_000t) ).
thf(979,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)],[23]) ).
thf(91,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/sandbox/benchmark/theBenchmark.p',fact_258_insert__ident) ).
thf(1194,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)],[91]) ).
thf(347,axiom,
fFalse @ is_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_fFalse) ).
thf(2079,plain,
fFalse @ is_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(670,axiom,
! [A: $i] :
( ( A @ is_fun_a_bool )
=> ( ! [B: $i] :
( ( B @ is_a )
=> ~ ( A @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
<=> ( A = bot_bot_fun_a_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_418_all__not__in__conv) ).
thf(3352,plain,
! [A: $i] :
( ( A @ is_fun_a_bool )
=> ( ( ( A = bot_bot_fun_a_bool )
=> ! [B: $i] :
( ( B @ is_a )
=> ~ ( A @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) )
& ( ! [B: $i] :
( ( B @ is_a )
=> ~ ( A @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
=> ( A = bot_bot_fun_a_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(913,axiom,
! [A: $i] :
( ( bot_bot_nat @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A = bot_bot_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_435_le__bot) ).
thf(4369,plain,
! [A: $i] :
( ( bot_bot_nat @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A = bot_bot_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[913]) ).
thf(766,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ hBOOL )
<=> ( B @ hBOOL ) )
=> ( ( B @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( C @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_530_xt1_I3_J) ).
thf(3764,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( B @ hBOOL )
=> ( C @ hBOOL ) )
& ( ( C @ hBOOL )
=> ( B @ hBOOL ) ) )
=> ( ( B @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( C @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).
thf(808,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/sandbox/benchmark/theBenchmark.p',fact_12_finite__imageI) ).
thf(3957,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)],[808]) ).
thf(137,axiom,
! [A: $i] :
( ( A @ is_fun_pname_bool )
=> ( ! [B: $i] :
( ( B @ is_pname )
=> ~ ( A @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
<=> ( A = bot_bo844097828e_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_417_all__not__in__conv) ).
thf(1349,plain,
! [A: $i] :
( ( A @ is_fun_pname_bool )
=> ( ( ( A = bot_bo844097828e_bool )
=> ! [B: $i] :
( ( B @ is_pname )
=> ~ ( A @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) )
& ( ! [B: $i] :
( ( B @ is_pname )
=> ~ ( A @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
=> ( A = bot_bo844097828e_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(700,axiom,
! [A: $i,B: $i] :
( ( A = B )
=> ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_547_order__eq__refl) ).
thf(3500,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)],[700]) ).
thf(630,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun_pname_bool )
=> ( B @ ( A @ image_pname_a ) @ is_fun_a_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__Com__Opname_000t__a) ).
thf(3160,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)],[630]) ).
thf(905,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/sandbox/benchmark/theBenchmark.p',fact_2_finite__Collect__subsets) ).
thf(4337,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)],[905]) ).
thf(511,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/sandbox/benchmark/theBenchmark.p',fact_224_insertCI) ).
thf(2679,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)],[511]) ).
thf(876,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/sandbox/benchmark/theBenchmark.p',fact_46_card__mono) ).
thf(4228,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)],[876]) ).
thf(817,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/sandbox/benchmark/theBenchmark.p',fact_261_insertI2) ).
thf(3996,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)],[817]) ).
thf(279,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_1321347587bool_a ) @ hAPP_a_fun_nat_bool ) )
= ( C @ ( B @ hAPP_a_nat ) @ ( A @ hAPP_n1699378549t_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_) ).
thf(1853,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_1321347587bool_a ) @ hAPP_a_fun_nat_bool ) )
= ( C @ ( B @ hAPP_a_nat ) @ ( A @ hAPP_n1699378549t_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(156,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_1212655066ol_nat ) @ hAPP_n1025906991e_bool ) )
= ( C @ ( B @ hAPP_nat_pname ) @ ( A @ hAPP_p61793385e_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_006) ).
thf(1408,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_1212655066ol_nat ) @ hAPP_n1025906991e_bool ) )
= ( C @ ( B @ hAPP_nat_pname ) @ ( A @ hAPP_p61793385e_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(650,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/sandbox/benchmark/theBenchmark.p',fact_75_finite__Collect__conjI) ).
thf(3238,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)],[650]) ).
thf(388,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_542850580_pname ) @ hAPP_p61793385e_bool ) )
= ( C @ ( B @ hAPP_pname_pname ) @ ( A @ hAPP_p61793385e_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_008) ).
thf(2214,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_542850580_pname ) @ hAPP_p61793385e_bool ) )
= ( C @ ( B @ hAPP_pname_pname ) @ ( A @ hAPP_p61793385e_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(434,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_164527437a_bool ) @ hAPP_f282463732t_bool ) )
= ( C @ ( B @ hAPP_fun_a_bool_nat ) @ ( A @ hAPP_n1699378549t_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__009) ).
thf(2383,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_164527437a_bool ) @ hAPP_f282463732t_bool ) )
= ( C @ ( B @ hAPP_fun_a_bool_nat ) @ ( A @ hAPP_n1699378549t_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(446,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( A @ ( suc @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_636_not__less__eq) ).
thf(2422,plain,
! [A: $i,B: $i] :
( ( ( A @ ( suc @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( suc @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(895,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/sandbox/benchmark/theBenchmark.p',fact_181_finite__subset__image) ).
thf(4305,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)],[895]) ).
thf(264,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/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000t__a_000tc__HOL__Obool_000tc__HOL__Obool_U) ).
thf(1806,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)],[264]) ).
thf(35,axiom,
( bot_bot_fun_a_bool
= ( fFalse @ cOMBK_bool_a @ collect_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_423_empty__def) ).
thf(1011,plain,
( bot_bot_fun_a_bool
= ( fFalse @ cOMBK_bool_a @ collect_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(28,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/sandbox/benchmark/theBenchmark.p',fact_313_insert__compr__raw) ).
thf(996,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)],[28]) ).
thf(300,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/sandbox/benchmark/theBenchmark.p',fact_126_eq__diff__iff) ).
thf(1933,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)],[300]) ).
thf(605,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B = A )
=> ( C @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_521_xt1_I4_J) ).
thf(3066,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B = A )
=> ( C @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(233,axiom,
! [A: $i,B: $i] :
( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ minus_minus_nat @ hAPP_nat_nat ) )
= ( B @ ( one_one_nat @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_568_diff__Suc__eq__diff__pred) ).
thf(1690,plain,
! [A: $i,B: $i] :
( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ minus_minus_nat @ hAPP_nat_nat ) )
= ( B @ ( one_one_nat @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(635,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ hBOOL )
<=> ( B @ hBOOL ) )
=> ( ( A @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( A @ ( C @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_535_ord__eq__le__trans) ).
thf(3182,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( B @ hBOOL )
=> ( C @ hBOOL ) )
& ( ( C @ hBOOL )
=> ( B @ hBOOL ) ) )
=> ( ( A @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( A @ ( C @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(554,axiom,
! [A: $i,B: $i] :
( ( A @ is_fun_a_bool )
=> ( ( bot_bot_fun_a_bool @ ( B @ insert_a ) @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A
= ( bot_bot_fun_a_bool @ ( B @ insert_a ) ) )
| ( A = bot_bot_fun_a_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_496_subset__singletonD) ).
thf(2871,plain,
! [A: $i,B: $i] :
( ( A @ is_fun_a_bool )
=> ( ( bot_bot_fun_a_bool @ ( B @ insert_a ) @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A
= ( bot_bot_fun_a_bool @ ( B @ insert_a ) ) )
| ( A = bot_bot_fun_a_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(168,axiom,
! [A: $i,B: $i] :
( ( ( B @ is_pname )
& ( A @ is_pname ) )
=> ( ( ( bot_bo844097828e_bool @ ( A @ insert_pname ) )
= ( bot_bo844097828e_bool @ ( B @ insert_pname ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_446_singleton__inject) ).
thf(1439,plain,
! [A: $i,B: $i] :
( ( ( B @ is_pname )
& ( A @ is_pname ) )
=> ( ( ( bot_bo844097828e_bool @ ( A @ insert_pname ) )
= ( bot_bo844097828e_bool @ ( B @ insert_pname ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(691,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_819518260e_bool ) @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ? [C: $i] :
( ~ ( C @ ( A @ hAPP_a93125764e_bool ) @ ( A @ ( fequal533582459e_bool @ cOMBB_1137537805bool_a ) @ cOMBC_1834145417l_bool @ hAPP_f1051908748a_bool ) @ ( B @ ( member_a @ cOMBC_1355376034l_bool @ hAPP_f2050579477a_bool ) @ ( fconj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( C @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( C @ is_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_pigeonhole__infinite) ).
thf(3456,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_819518260e_bool ) @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ? [C: $i] :
( ~ ( C @ ( A @ hAPP_a93125764e_bool ) @ ( A @ ( fequal533582459e_bool @ cOMBB_1137537805bool_a ) @ cOMBC_1834145417l_bool @ hAPP_f1051908748a_bool ) @ ( B @ ( member_a @ cOMBC_1355376034l_bool @ hAPP_f2050579477a_bool ) @ ( fconj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( C @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( C @ is_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(869,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/sandbox/benchmark/theBenchmark.p',fact_262_insertI2) ).
thf(4203,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)],[869]) ).
thf(377,axiom,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1291551745_pname ) @ is_pname ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Com__Opname) ).
thf(2182,plain,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1291551745_pname ) @ is_pname ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(401,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 )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_542_order__antisym__conv) ).
thf(2267,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 )
=> ( ( ( B = A )
=> ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
& ( ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(886,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/sandbox/benchmark/theBenchmark.p',fact_71_card__insert__disjoint) ).
thf(4264,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)],[886]) ).
thf(889,axiom,
! [A: $i,B: $i] :
( ( A = B )
=> ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_275_equalityD2) ).
thf(4277,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)],[889]) ).
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/sandbox/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(915,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(120,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_1137537805bool_a ) @ hAPP_a217006258l_bool ) )
= ( C @ ( B @ hAPP_a93125764e_bool ) @ ( A @ hAPP_f434788991l_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It) ).
thf(1293,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_1137537805bool_a ) @ hAPP_a217006258l_bool ) )
= ( C @ ( B @ hAPP_a93125764e_bool ) @ ( A @ hAPP_f434788991l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(454,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/sandbox/benchmark/theBenchmark.p',fact_115_Suc__leD) ).
thf(2461,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)],[454]) ).
thf(269,axiom,
! [A: $i,B: $i] :
( ( ( B @ is_pname )
& ( A @ is_pname ) )
=> ( ( bot_bo844097828e_bool @ ( B @ insert_pname ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_456_singleton__iff) ).
thf(1820,plain,
! [A: $i,B: $i] :
( ( ( B @ is_pname )
& ( A @ is_pname ) )
=> ( ( ( A = B )
=> ( bot_bo844097828e_bool @ ( B @ insert_pname ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
& ( ( bot_bo844097828e_bool @ ( B @ insert_pname ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(232,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun_pname_bool )
=> ( B @ ( A @ hAPP_f759274231e_bool ) @ is_fun_pname_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_Itc__Com__Op) ).
thf(1688,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)],[232]) ).
thf(328,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) )
= zero_zero_nat )
=> ( ( ( A @ ( B @ minus_minus_nat @ hAPP_nat_nat ) )
= zero_zero_nat )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_687_diffs0__imp__equal) ).
thf(2025,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) )
= zero_zero_nat )
=> ( ( ( A @ ( B @ minus_minus_nat @ hAPP_nat_nat ) )
= zero_zero_nat )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(496,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/sandbox/benchmark/theBenchmark.p',fact_23_finite_OinsertI) ).
thf(2632,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)],[496]) ).
thf(491,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/sandbox/benchmark/theBenchmark.p',fact_1_finite__Collect__subsets) ).
thf(2605,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)],[491]) ).
thf(493,axiom,
! [A: $i] :
( ( zero_zero_nat @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_698_le__0__eq) ).
thf(2610,plain,
! [A: $i] :
( ( ( A = zero_zero_nat )
=> ( zero_zero_nat @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( zero_zero_nat @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(200,axiom,
! [A: $i,B: $i] :
( ( ( A = B )
| ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_637_less__or__eq__imp__le) ).
thf(1557,plain,
! [A: $i,B: $i] :
( ( ( A = B )
| ( B @ ( A @ ( ord_less_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)],[200]) ).
thf(823,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/sandbox/benchmark/theBenchmark.p',fact_77_finite__Collect__conjI) ).
thf(4009,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)],[823]) ).
thf(361,axiom,
! [A: $i] :
( ( A @ is_bool )
=> ( A @ cOMBK_bool_pname @ is_fun_pname_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_COMBK_000tc__HOL__Obool_000tc__Com__Opname) ).
thf(2129,plain,
! [A: $i] :
( ( A @ is_bool )
=> ( A @ cOMBK_bool_pname @ is_fun_pname_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(743,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun_pname_bool )
=> ( ( bot_bot_fun_a_bool
= ( B @ ( A @ image_pname_a ) ) )
<=> ( B = bot_bo844097828e_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_469_empty__is__image) ).
thf(3668,plain,
! [A: $i,B: $i] :
( ( B @ is_fun_pname_bool )
=> ( ( ( B = bot_bo844097828e_bool )
=> ( bot_bot_fun_a_bool
= ( B @ ( A @ image_pname_a ) ) ) )
& ( ( bot_bot_fun_a_bool
= ( B @ ( A @ image_pname_a ) ) )
=> ( B = bot_bo844097828e_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(903,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( A @ image_pname_nat ) @ ( B @ ( A @ hAPP_pname_nat ) @ insert_nat ) )
= ( C @ ( A @ image_pname_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_339_insert__image) ).
thf(4332,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( A @ image_pname_nat ) @ ( B @ ( A @ hAPP_pname_nat ) @ insert_nat ) )
= ( C @ ( A @ image_pname_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).
thf(638,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/sandbox/benchmark/theBenchmark.p',fact_100_finite__insert) ).
thf(3192,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)],[638]) ).
thf(567,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/sandbox/benchmark/theBenchmark.p',fact_217_equalityI) ).
thf(2923,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)],[567]) ).
thf(729,axiom,
! [A: $i] : ( A @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_368_order__refl) ).
thf(3614,plain,
! [A: $i] : ( A @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(406,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_pname ) @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) )
=> ( B @ ( C @ ( A @ image_pname_pname ) @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_361_image__subsetI) ).
thf(2289,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_pname ) @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) )
=> ( B @ ( C @ ( A @ image_pname_pname ) @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(503,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/sandbox/benchmark/theBenchmark.p',fact_315_insert__compr__raw) ).
thf(2647,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)],[503]) ).
thf(40,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/sandbox/benchmark/theBenchmark.p',fact_184_lift__Suc__mono__le) ).
thf(1022,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)],[40]) ).
thf(508,axiom,
! [A: $i,B: $i] :
( ( ( B @ is_a )
& ( A @ is_a ) )
=> ( ( bot_bot_fun_a_bool @ ( B @ insert_a ) @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_451_singletonE) ).
thf(2664,plain,
! [A: $i,B: $i] :
( ( ( B @ is_a )
& ( A @ is_a ) )
=> ( ( bot_bot_fun_a_bool @ ( B @ insert_a ) @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(520,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_1551609309ol_nat ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ? [C: $i] :
( ~ ( C @ ( A @ hAPP_f921600141ol_nat ) @ ( A @ ( fequal_nat @ cOMBB_1896684278e_bool ) @ cOMBC_1666426608t_bool @ hAPP_n850744903l_bool ) @ ( B @ ( member799430823e_bool @ cOMBC_1988546018l_bool @ hAPP_f559147733l_bool ) @ ( fconj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
& ( B @ ( C @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
& ( C @ is_fun_pname_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_pigeonhole__infinite) ).
thf(2725,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_1551609309ol_nat ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ? [C: $i] :
( ~ ( C @ ( A @ hAPP_f921600141ol_nat ) @ ( A @ ( fequal_nat @ cOMBB_1896684278e_bool ) @ cOMBC_1666426608t_bool @ hAPP_n850744903l_bool ) @ ( B @ ( member799430823e_bool @ cOMBC_1988546018l_bool @ hAPP_f559147733l_bool ) @ ( fconj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
& ( B @ ( C @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
& ( C @ is_fun_pname_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(193,axiom,
! [A: $i] :
( ( A @ is_bool )
=> ( ( A = fFalse )
| ( A = fTrue ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
thf(1528,plain,
! [A: $i] :
( ( A @ is_bool )
=> ( ( A = fFalse )
| ( A = fTrue ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(350,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_592_add__leD2) ).
thf(2086,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(746,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun_a_bool )
=> ( B @ ( A @ hAPP_f1631501043l_bool ) @ is_fun949378684l_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__a_Mtc__HOL) ).
thf(3687,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)],[746]) ).
thf(85,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/sandbox/benchmark/theBenchmark.p',fact_56_card__insert__le) ).
thf(1176,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)],[85]) ).
thf(254,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/sandbox/benchmark/theBenchmark.p',fact_50_card__seteq) ).
thf(1775,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)],[254]) ).
thf(327,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/sandbox/benchmark/theBenchmark.p',fact_125_Nat_Odiff__diff__eq) ).
thf(2022,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)],[327]) ).
thf(753,axiom,
! [A: $i] :
( ( bot_bot_fun_nat_bool @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
<=> ( A = bot_bot_fun_nat_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_438_bot__unique) ).
thf(3706,plain,
! [A: $i] :
( ( ( A = bot_bot_fun_nat_bool )
=> ( bot_bot_fun_nat_bool @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
& ( ( bot_bot_fun_nat_bool @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A = bot_bot_fun_nat_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).
thf(578,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ insert_a ) @ ( A @ image_a_nat ) )
= ( C @ ( A @ image_a_nat ) @ ( B @ ( A @ hAPP_a_nat ) @ insert_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_335_image__insert) ).
thf(2967,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ insert_a ) @ ( A @ image_a_nat ) )
= ( C @ ( A @ image_a_nat ) @ ( B @ ( A @ hAPP_a_nat ) @ insert_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(634,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_496248727ol_nat ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ? [C: $i] :
( ~ ( C @ ( A @ hAPP_f22106695ol_nat ) @ ( A @ ( fequal_nat @ cOMBB_1250273980t_bool ) @ cOMBC_385542954t_bool @ hAPP_n215258509l_bool ) @ ( B @ ( member_fun_nat_bool @ cOMBC_1245412066l_bool @ hAPP_f1246832597l_bool ) @ ( fconj @ cOMBB_444170502t_bool ) @ cOMBS_1187019125l_bool ) @ collect_fun_nat_bool @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
& ( B @ ( C @ ( member_fun_nat_bool @ hAPP_f1951378235l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_pigeonhole__infinite) ).
thf(3178,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_496248727ol_nat ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ? [C: $i] :
( ~ ( C @ ( A @ hAPP_f22106695ol_nat ) @ ( A @ ( fequal_nat @ cOMBB_1250273980t_bool ) @ cOMBC_385542954t_bool @ hAPP_n215258509l_bool ) @ ( B @ ( member_fun_nat_bool @ cOMBC_1245412066l_bool @ hAPP_f1246832597l_bool ) @ ( fconj @ cOMBB_444170502t_bool ) @ cOMBS_1187019125l_bool ) @ collect_fun_nat_bool @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
& ( B @ ( C @ ( member_fun_nat_bool @ hAPP_f1951378235l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ ( suc @ hAPP_nat_nat ) )
= ( A @ ( one_one_nat @ plus_plus_nat @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_607_Suc__eq__plus1__left) ).
thf(922,plain,
! [A: $i] :
( ( A @ ( suc @ hAPP_nat_nat ) )
= ( A @ ( one_one_nat @ plus_plus_nat @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(344,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun949378684l_bool )
=> ( B @ ( A @ image_fun_a_bool_a ) @ is_fun_a_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_It__a_Mtc__HOL__Obool_J_000t__a) ).
thf(2069,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)],[344]) ).
thf(532,axiom,
! [A: $i] :
( ( ( A @ collect_fun_nat_bool )
= bot_bo1701429464l_bool )
<=> ! [B: $i] :
~ ( B @ ( A @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_399_Collect__empty__eq) ).
thf(2770,plain,
! [A: $i] :
( ( ! [B: $i] :
~ ( B @ ( A @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A @ collect_fun_nat_bool )
= bot_bo1701429464l_bool ) )
& ( ( ( A @ collect_fun_nat_bool )
= bot_bo1701429464l_bool )
=> ! [B: $i] :
~ ( B @ ( A @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(346,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ~ ( ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ~ ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_594_add__leE) ).
thf(2075,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ~ ( ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ~ ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(387,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/sandbox/benchmark/theBenchmark.p',fact_54_card__insert__le) ).
thf(2212,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)],[387]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_616_termination__basic__simps_I2_J) ).
thf(959,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(97,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/sandbox/benchmark/theBenchmark.p',fact_219_subsetD) ).
thf(1213,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)],[97]) ).
thf(546,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/sandbox/benchmark/theBenchmark.p',fact_0_assms_I1_J) ).
thf(2835,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)],[546]) ).
thf(476,axiom,
bot_bot_fun_a_bool @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_389_finite_OemptyI) ).
thf(2550,plain,
bot_bot_fun_a_bool @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(106,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 ) @ ( A @ plus_plus_nat @ hAPP_nat_nat ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_602_le__add__diff__inverse) ).
thf(1245,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 ) @ ( A @ plus_plus_nat @ hAPP_nat_nat ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(461,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_nat_nat ) @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_finite__surj) ).
thf(2481,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_nat_nat ) @ ( 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)],[461]) ).
thf(843,axiom,
! [A: $i] :
( ( bot_bot_bool @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( ( A @ hBOOL )
<=> ( bot_bot_bool @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_432_le__bot) ).
thf(4085,plain,
! [A: $i] :
( ( bot_bot_bool @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( ( ( bot_bot_bool @ hBOOL )
=> ( A @ hBOOL ) )
& ( ( A @ hBOOL )
=> ( bot_bot_bool @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).
thf(912,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/sandbox/benchmark/theBenchmark.p',fact_96_finite__Collect__disjI) ).
thf(4362,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)],[912]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( 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_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_668_diff__less__mono) ).
thf(1015,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( 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_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(806,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_fun_nat_bool_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/sandbox/benchmark/theBenchmark.p',fact_132_finite__surj) ).
thf(3953,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_fun_nat_bool_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)],[806]) ).
thf(69,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ is_fun949378684l_bool )
=> ( ( C @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_nat_fun_a_bool ) @ ( C @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ image_nat_fun_a_bool ) ) )
& ( D @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_finite__subset__image) ).
thf(1113,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ is_fun949378684l_bool )
=> ( ( C @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_nat_fun_a_bool ) @ ( C @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ image_nat_fun_a_bool ) ) )
& ( D @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(537,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ hAPP_pname_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_pname @ hAPP_p61793385e_bool ) @ ( fconj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname )
= bot_bo844097828e_bool ) )
& ( ( B @ ( A @ hAPP_pname_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_pname @ hAPP_p61793385e_bool ) @ ( fconj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname )
= ( bot_bo844097828e_bool @ ( B @ insert_pname ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_477_Collect__conv__if2) ).
thf(2797,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ hAPP_pname_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_pname @ hAPP_p61793385e_bool ) @ ( fconj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname )
= bot_bo844097828e_bool ) )
& ( ( B @ ( A @ hAPP_pname_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_pname @ hAPP_p61793385e_bool ) @ ( fconj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname )
= ( bot_bo844097828e_bool @ ( B @ insert_pname ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(583,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_1655916159e_bool ) @ ( A @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( A @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_finite__surj) ).
thf(2984,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_1655916159e_bool ) @ ( 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)],[583]) ).
thf(312,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ is_fun_pname_bool )
=> ( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_1921560913_pname ) @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ image_1921560913_pname ) ) )
& ( D @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_finite__subset__image) ).
thf(1973,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ is_fun_pname_bool )
=> ( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_1921560913_pname ) @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ image_1921560913_pname ) ) )
& ( D @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(467,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/sandbox/benchmark/theBenchmark.p',fact_333_insert__mono) ).
thf(2506,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)],[467]) ).
thf(674,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_fun_nat_bool @ cOMBC_1693257480l_bool @ hAPP_f103356543l_bool ) @ ( fconj @ cOMBB_444170502t_bool ) @ cOMBS_1187019125l_bool ) @ collect_fun_nat_bool )
= bot_bo1701429464l_bool ) )
& ( ( B @ ( A @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_fun_nat_bool @ cOMBC_1693257480l_bool @ hAPP_f103356543l_bool ) @ ( fconj @ cOMBB_444170502t_bool ) @ cOMBS_1187019125l_bool ) @ collect_fun_nat_bool )
= ( bot_bo1701429464l_bool @ ( B @ insert_fun_nat_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_473_Collect__conv__if) ).
thf(3380,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_fun_nat_bool @ cOMBC_1693257480l_bool @ hAPP_f103356543l_bool ) @ ( fconj @ cOMBB_444170502t_bool ) @ cOMBS_1187019125l_bool ) @ collect_fun_nat_bool )
= bot_bo1701429464l_bool ) )
& ( ( B @ ( A @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_fun_nat_bool @ cOMBC_1693257480l_bool @ hAPP_f103356543l_bool ) @ ( fconj @ cOMBB_444170502t_bool ) @ cOMBS_1187019125l_bool ) @ collect_fun_nat_bool )
= ( bot_bo1701429464l_bool @ ( B @ insert_fun_nat_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(842,axiom,
bot_bo844097828e_bool @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_390_finite_OemptyI) ).
thf(4084,plain,
bot_bo844097828e_bool @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).
thf(219,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/sandbox/benchmark/theBenchmark.p',fact_129_diff__le__mono2) ).
thf(1626,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)],[219]) ).
thf(871,axiom,
! [A: $i,B: $i] :
( ( B = bot_bo844097828e_bool )
=> ~ ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_396_equals0D) ).
thf(4207,plain,
! [A: $i,B: $i] :
( ( B = bot_bo844097828e_bool )
=> ~ ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).
thf(396,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/sandbox/benchmark/theBenchmark.p',fact_326_subset__insert) ).
thf(2239,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)],[396]) ).
thf(541,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_1928494297l_bool @ hAPP_f282463732t_bool ) @ hAPP_nat_bool ) )
= ( B @ ( C @ ( A @ hAPP_n1414589940l_bool ) @ hAPP_fun_a_bool_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__) ).
thf(2816,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_1928494297l_bool @ hAPP_f282463732t_bool ) @ hAPP_nat_bool ) )
= ( B @ ( C @ ( A @ hAPP_n1414589940l_bool ) @ hAPP_fun_a_bool_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(265,axiom,
! [A: $i] :
( ( A @ collect_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_Collect__def) ).
thf(1809,plain,
! [A: $i] :
( ( A @ collect_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(228,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/sandbox/benchmark/theBenchmark.p',fact_49_card__seteq) ).
thf(1662,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)],[228]) ).
thf(81,axiom,
! [A: $i] :
( ( A @ is_fun949378684l_bool )
=> ( A @ collect_fun_a_bool @ is_fun949378684l_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_OCollect_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
thf(1166,plain,
! [A: $i] :
( ( A @ is_fun949378684l_bool )
=> ( A @ collect_fun_a_bool @ is_fun949378684l_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(720,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_1655916159e_bool ) @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ? [C: $i] :
( ~ ( C @ ( A @ hAPP_n1025906991e_bool ) @ ( A @ ( fequal533582459e_bool @ cOMBB_2117322052ol_nat ) @ cOMBC_386238098l_bool @ hAPP_f1066163005t_bool ) @ ( B @ ( member_nat @ cOMBC_226598744l_bool @ hAPP_f800510211t_bool ) @ ( fconj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_pigeonhole__infinite) ).
thf(3576,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_1655916159e_bool ) @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ? [C: $i] :
( ~ ( C @ ( A @ hAPP_n1025906991e_bool ) @ ( A @ ( fequal533582459e_bool @ cOMBB_2117322052ol_nat ) @ cOMBC_386238098l_bool @ hAPP_f1066163005t_bool ) @ ( B @ ( member_nat @ cOMBC_226598744l_bool @ hAPP_f800510211t_bool ) @ ( fconj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).
thf(176,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_nat ) @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) )
=> ( B @ ( C @ ( A @ image_pname_nat ) @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_360_image__subsetI) ).
thf(1467,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_nat ) @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) )
=> ( B @ ( C @ ( A @ image_pname_nat ) @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(188,axiom,
! [A: $i,B: $i] :
( ( bot_bot_fun_nat_bool @ ( B @ insert_nat ) @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_455_singleton__iff) ).
thf(1509,plain,
! [A: $i,B: $i] :
( ( ( A = B )
=> ( bot_bot_fun_nat_bool @ ( B @ insert_nat ) @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
& ( ( bot_bot_fun_nat_bool @ ( B @ insert_nat ) @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) )
= ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) ) )
<=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_575_nat__add__left__cancel) ).
thf(939,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B = C )
=> ( ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) )
= ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) ) ) )
& ( ( ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) )
= ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(177,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_2026977092ol_nat ) @ hAPP_n215258509l_bool ) )
= ( C @ ( B @ hAPP_n1699378549t_bool ) @ ( A @ hAPP_f103356543l_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__020) ).
thf(1472,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_2026977092ol_nat ) @ hAPP_n215258509l_bool ) )
= ( C @ ( B @ hAPP_n1699378549t_bool ) @ ( A @ hAPP_f103356543l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(481,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
<=> ! [C: $i] :
( ( C @ is_a )
=> ( C @ ( B @ hAPP_a_bool ) @ ( C @ ( A @ hAPP_a_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_376_le__fun__def) ).
thf(2564,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( C @ is_a )
=> ( C @ ( B @ hAPP_a_bool ) @ ( C @ ( A @ hAPP_a_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) )
=> ( B @ ( A @ ( 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 )
=> ! [C: $i] :
( ( C @ is_a )
=> ( C @ ( B @ hAPP_a_bool ) @ ( C @ ( A @ hAPP_a_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(909,axiom,
pn @ is_pname,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_pn) ).
thf(4355,plain,
pn @ is_pname,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).
thf(562,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_1921560913_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ? [C: $i] :
( ~ ( C @ ( A @ hAPP_f1291551745_pname ) @ ( A @ ( fequal_pname @ cOMBB_141086128t_bool ) @ cOMBC_615407716e_bool @ hAPP_p130839763l_bool ) @ ( B @ ( member_fun_nat_bool @ cOMBC_1245412066l_bool @ hAPP_f1246832597l_bool ) @ ( fconj @ cOMBB_444170502t_bool ) @ cOMBS_1187019125l_bool ) @ collect_fun_nat_bool @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
& ( B @ ( C @ ( member_fun_nat_bool @ hAPP_f1951378235l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_pigeonhole__infinite) ).
thf(2899,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_1921560913_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ? [C: $i] :
( ~ ( C @ ( A @ hAPP_f1291551745_pname ) @ ( A @ ( fequal_pname @ cOMBB_141086128t_bool ) @ cOMBC_615407716e_bool @ hAPP_p130839763l_bool ) @ ( B @ ( member_fun_nat_bool @ cOMBC_1245412066l_bool @ hAPP_f1246832597l_bool ) @ ( fconj @ cOMBB_444170502t_bool ) @ cOMBS_1187019125l_bool ) @ collect_fun_nat_bool @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
& ( B @ ( C @ ( member_fun_nat_bool @ hAPP_f1951378235l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(87,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_777206479l_bool @ hAPP_f1549043526a_bool ) @ hAPP_a_bool ) )
= ( B @ ( C @ ( A @ hAPP_a1392362872l_bool ) @ hAPP_f54304608l_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000t__a_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__) ).
thf(1181,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_777206479l_bool @ hAPP_f1549043526a_bool ) @ hAPP_a_bool ) )
= ( B @ ( C @ ( A @ hAPP_a1392362872l_bool ) @ hAPP_f54304608l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(47,axiom,
! [A: $i,B: $i] :
( ( B @ is_a )
=> ( B @ ( A @ hAPP_a_a ) @ is_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000t__a_000t__a) ).
thf(1049,plain,
! [A: $i,B: $i] :
( ( B @ is_a )
=> ( B @ ( A @ hAPP_a_a ) @ is_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(158,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/sandbox/benchmark/theBenchmark.p',fact_5_finite__Collect__subsets) ).
thf(1413,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)],[158]) ).
thf(57,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_1854862208_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_finite__surj) ).
thf(1076,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_1854862208_pname ) @ ( 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)],[57]) ).
thf(788,axiom,
! [A: $i,B: $i,C: $i] :
( ( B = C )
=> ( ( C @ ( 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 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_533_xt1_I3_J) ).
thf(3881,plain,
! [A: $i,B: $i,C: $i] :
( ( B = C )
=> ( ( C @ ( 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 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).
thf(286,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/sandbox/benchmark/theBenchmark.p',fact_34_card__image__le) ).
thf(1873,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)],[286]) ).
thf(824,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( 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 )
=> ( C @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_504_xt1_I6_J) ).
thf(4013,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( 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 )
=> ( C @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).
thf(411,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( C @ plus_plus_nat @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_622_trans__less__add1) ).
thf(2318,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( C @ plus_plus_nat @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(642,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/sandbox/benchmark/theBenchmark.p',fact_18_finite__imageI) ).
thf(3206,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)],[642]) ).
thf(114,axiom,
! [A: $i] :
( ( A @ ( fequal533582459e_bool @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ collec1974731493e_bool )
= ( bot_bo1649642514l_bool @ ( A @ insert1325755072e_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_486_singleton__conv) ).
thf(1277,plain,
! [A: $i] :
( ( A @ ( fequal533582459e_bool @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ collec1974731493e_bool )
= ( bot_bo1649642514l_bool @ ( A @ insert1325755072e_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(359,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( A @ ( suc @ hAPP_nat_nat ) )
!= B )
=> ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_630_Suc__lessI) ).
thf(2124,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( A @ ( suc @ hAPP_nat_nat ) )
!= B )
=> ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(59,axiom,
! [A: $i,B: $i] :
( ( B @ is_pname )
=> ( B @ ( A @ hAPP_p61793385e_bool ) @ is_fun_pname_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).
thf(1081,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(495,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_392435466_pname ) @ hAPP_p1824510254l_bool ) )
= ( C @ ( B @ hAPP_p1534023578a_bool ) @ ( A @ hAPP_f1631501043l_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It___019) ).
thf(2629,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_392435466_pname ) @ hAPP_p1824510254l_bool ) )
= ( C @ ( B @ hAPP_p1534023578a_bool ) @ ( A @ hAPP_f1631501043l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(658,axiom,
! [A: $i] :
( ( ( A @ collect_fun_a_bool )
= bot_bo1389914601l_bool )
<=> ! [B: $i] :
( ( B @ is_fun_a_bool )
=> ~ ( B @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_401_Collect__empty__eq) ).
thf(3278,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ is_fun_a_bool )
=> ~ ( B @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
=> ( ( A @ collect_fun_a_bool )
= bot_bo1389914601l_bool ) )
& ( ( ( A @ collect_fun_a_bool )
= bot_bo1389914601l_bool )
=> ! [B: $i] :
( ( B @ is_fun_a_bool )
=> ~ ( B @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(307,axiom,
! [A: $i,B: $i] :
( ( B @ is_pname )
=> ( B @ ( A @ hAPP_p1534023578a_bool ) @ is_fun_a_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Com__Opname_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
thf(1958,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)],[307]) ).
thf(816,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_fun_a_bool @ hAPP_f1631501043l_bool ) @ ( fconj @ cOMBB_338059395a_bool ) @ cOMBS_1035972772l_bool ) @ collect_fun_a_bool )
= bot_bo1389914601l_bool ) )
& ( ( B @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_fun_a_bool @ hAPP_f1631501043l_bool ) @ ( fconj @ cOMBB_338059395a_bool ) @ cOMBS_1035972772l_bool ) @ collect_fun_a_bool )
= ( bot_bo1389914601l_bool @ ( B @ insert_fun_a_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_481_Collect__conv__if2) ).
thf(3988,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_fun_a_bool @ hAPP_f1631501043l_bool ) @ ( fconj @ cOMBB_338059395a_bool ) @ cOMBS_1035972772l_bool ) @ collect_fun_a_bool )
= bot_bo1389914601l_bool ) )
& ( ( B @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_fun_a_bool @ hAPP_f1631501043l_bool ) @ ( fconj @ cOMBB_338059395a_bool ) @ cOMBS_1035972772l_bool ) @ collect_fun_a_bool )
= ( bot_bo1389914601l_bool @ ( B @ insert_fun_a_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(198,axiom,
! [A: $i,B: $i] :
~ ( B @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_624_not__add__less2) ).
thf(1547,plain,
! [A: $i,B: $i] :
~ ( B @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(261,axiom,
! [A: $i] :
( ( A @ is_bool )
=> ( A @ cOMBK_1857069011e_bool @ is_fun1661590463l_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).
thf(1798,plain,
! [A: $i] :
( ( A @ is_bool )
=> ( A @ cOMBK_1857069011e_bool @ is_fun1661590463l_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(31,axiom,
! [A: $i,B: $i] : ( B @ ( ord_less_nat @ cOMBC_nat_nat_bool @ hAPP_n1699378549t_bool ) @ ( A @ ( fconj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_654_finite__M__bounded__by__nat) ).
thf(1003,plain,
! [A: $i,B: $i] : ( B @ ( ord_less_nat @ cOMBC_nat_nat_bool @ hAPP_n1699378549t_bool ) @ ( A @ ( 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)],[31]) ).
thf(664,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( C = A )
=> ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_526_ord__le__eq__trans) ).
thf(3315,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( C = A )
=> ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(341,axiom,
! [A: $i] :
( ( one_one_nat @ ( A @ ( suc @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_569_diff__Suc__1) ).
thf(2060,plain,
! [A: $i] :
( ( one_one_nat @ ( A @ ( suc @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(380,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( bot_bot_fun_nat_bool @ ( A @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ! [D: $i,E: $i] :
( ( E @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( D @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ~ ( E @ ( D @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( E @ ( A @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( E @ ( D @ insert_nat ) @ ( A @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ) )
=> ( C @ ( A @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_556_finite__subset__induct) ).
thf(2192,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( bot_bot_fun_nat_bool @ ( A @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ! [D: $i,E: $i] :
( ( E @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( D @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ~ ( E @ ( D @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( E @ ( A @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( E @ ( D @ insert_nat ) @ ( A @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ) )
=> ( C @ ( A @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(18,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/sandbox/benchmark/theBenchmark.p',fact_220_subsetD) ).
thf(971,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)],[18]) ).
thf(202,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ is_fun_pname_bool )
=> ( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_nat_pname ) @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ image_nat_pname ) ) )
& ( D @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_finite__subset__image) ).
thf(1566,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ is_fun_pname_bool )
=> ( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_nat_pname ) @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ image_nat_pname ) ) )
& ( D @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(142,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A
= ( C @ ( B @ hAPP_nat_pname ) ) )
=> ( D @ ( B @ image_nat_pname ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_310_rev__image__eqI) ).
thf(1368,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A
= ( C @ ( B @ hAPP_nat_pname ) ) )
=> ( D @ ( B @ image_nat_pname ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(194,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/sandbox/benchmark/theBenchmark.p',fact_269_set__eq__subset) ).
thf(1531,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)],[194]) ).
thf(66,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( C @ plus_plus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_603_le__add__diff) ).
thf(1098,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( C @ plus_plus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A != B )
=> ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_638_le__neq__implies__less) ).
thf(993,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A != B )
=> ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(431,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_631_less__SucI) ).
thf(2375,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(78,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B
= ( D @ ( C @ hAPP_nat_pname ) ) )
=> ( ( A @ ( D @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( C @ image_nat_pname ) @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_image__eqI) ).
thf(1156,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B
= ( D @ ( C @ hAPP_nat_pname ) ) )
=> ( ( A @ ( D @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( C @ image_nat_pname ) @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(213,axiom,
! [A: $i,B: $i] :
( ( B @ is_pname )
=> ( B @ ( A @ hAPP_p1824510254l_bool ) @ is_fun949378684l_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__H) ).
thf(1605,plain,
! [A: $i,B: $i] :
( ( B @ is_pname )
=> ( B @ ( A @ hAPP_p1824510254l_bool ) @ is_fun949378684l_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(764,axiom,
! [A: $i] :
( ( bot_bo1701429464l_bool
= ( A @ collect_fun_nat_bool ) )
<=> ! [B: $i] :
~ ( B @ ( A @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_408_empty__Collect__eq) ).
thf(3754,plain,
! [A: $i] :
( ( ! [B: $i] :
~ ( B @ ( A @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( bot_bo1701429464l_bool
= ( A @ collect_fun_nat_bool ) ) )
& ( ( bot_bo1701429464l_bool
= ( A @ collect_fun_nat_bool ) )
=> ! [B: $i] :
~ ( B @ ( A @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).
thf(247,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/sandbox/benchmark/theBenchmark.p',fact_69_card__insert__disjoint) ).
thf(1753,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)],[247]) ).
thf(112,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_nat @ cOMBC_nat_nat_bool @ hAPP_n1699378549t_bool ) @ ( fconj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat )
= bot_bot_fun_nat_bool ) )
& ( ( B @ ( A @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_nat @ cOMBC_nat_nat_bool @ hAPP_n1699378549t_bool ) @ ( fconj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat )
= ( bot_bot_fun_nat_bool @ ( B @ insert_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_470_Collect__conv__if) ).
thf(1267,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_nat @ cOMBC_nat_nat_bool @ hAPP_n1699378549t_bool ) @ ( fconj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat )
= bot_bot_fun_nat_bool ) )
& ( ( B @ ( A @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_nat @ cOMBC_nat_nat_bool @ hAPP_n1699378549t_bool ) @ ( fconj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat )
= ( bot_bot_fun_nat_bool @ ( B @ insert_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(603,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 )
=> ? [C: $i] :
( ~ ( C @ ( A @ hAPP_nat_pname ) @ ( A @ ( fequal_pname @ cOMBB_1212655066ol_nat ) @ cOMBC_nat_pname_bool @ hAPP_p1499970991t_bool ) @ ( B @ ( member_nat @ cOMBC_226598744l_bool @ hAPP_f800510211t_bool ) @ ( fconj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_pigeonhole__infinite) ).
thf(3058,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 )
=> ? [C: $i] :
( ~ ( C @ ( A @ hAPP_nat_pname ) @ ( A @ ( fequal_pname @ cOMBB_1212655066ol_nat ) @ cOMBC_nat_pname_bool @ hAPP_p1499970991t_bool ) @ ( B @ ( member_nat @ cOMBC_226598744l_bool @ hAPP_f800510211t_bool ) @ ( fconj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(435,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ insert_nat ) @ ( A @ insert_nat ) )
= ( B @ ( A @ insert_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_insert__absorb2) ).
thf(2386,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ insert_nat ) @ ( A @ insert_nat ) )
= ( B @ ( A @ insert_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(102,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_1693087065a_bool ) @ hAPP_f1794073134e_bool ) )
= ( C @ ( B @ hAPP_f1128469712_pname ) @ ( A @ hAPP_p61793385e_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_011) ).
thf(1230,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_1693087065a_bool ) @ hAPP_f1794073134e_bool ) )
= ( C @ ( B @ hAPP_f1128469712_pname ) @ ( A @ hAPP_p61793385e_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(181,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun1661590463l_bool )
=> ( B @ ( A @ cOMBB_307249310e_bool ) @ is_fun1661590463l_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc_) ).
thf(1484,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)],[181]) ).
thf(653,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/sandbox/benchmark/theBenchmark.p',fact_253_insert__iff) ).
thf(3246,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)],[653]) ).
thf(897,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_pname_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_finite__surj) ).
thf(4314,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_pname_pname ) @ ( 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)],[897]) ).
thf(907,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/sandbox/benchmark/theBenchmark.p',fact_215_image__eqI) ).
thf(4346,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)],[907]) ).
thf(353,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( B @ ( C @ minus_minus_nat @ hAPP_nat_nat ) )
= A )
<=> ( C
= ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_598_le__imp__diff__is__add) ).
thf(2092,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( C
= ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) ) )
=> ( ( B @ ( C @ minus_minus_nat @ hAPP_nat_nat ) )
= A ) )
& ( ( ( B @ ( C @ minus_minus_nat @ hAPP_nat_nat ) )
= A )
=> ( C
= ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(756,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/sandbox/benchmark/theBenchmark.p',fact_221_subsetD) ).
thf(3722,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)],[756]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ is_fun_pname_bool )
=> ( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_1283814551_pname ) @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ image_1283814551_pname ) ) )
& ( D @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
& ( D @ is_fun1661590463l_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_finite__subset__image) ).
thf(1038,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ is_fun_pname_bool )
=> ( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_1283814551_pname ) @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ image_1283814551_pname ) ) )
& ( D @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
& ( D @ is_fun1661590463l_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(874,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/sandbox/benchmark/theBenchmark.p',fact_154_finite__surj) ).
thf(4222,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)],[874]) ).
thf(695,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ is_a )
& ( C @ is_a )
& ( B @ is_a )
& ( A @ is_a ) )
=> ( ( ( bot_bot_fun_a_bool @ ( B @ insert_a ) @ ( A @ insert_a ) )
= ( bot_bot_fun_a_bool @ ( D @ insert_a ) @ ( C @ insert_a ) ) )
<=> ( ( ( B = C )
& ( A = D ) )
| ( ( B = D )
& ( A = C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_454_doubleton__eq__iff) ).
thf(3475,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ is_a )
& ( C @ is_a )
& ( B @ is_a )
& ( A @ is_a ) )
=> ( ( ( ( ( B = C )
& ( A = D ) )
| ( ( B = D )
& ( A = C ) ) )
=> ( ( bot_bot_fun_a_bool @ ( B @ insert_a ) @ ( A @ insert_a ) )
= ( bot_bot_fun_a_bool @ ( D @ insert_a ) @ ( C @ insert_a ) ) ) )
& ( ( ( bot_bot_fun_a_bool @ ( B @ insert_a ) @ ( A @ insert_a ) )
= ( bot_bot_fun_a_bool @ ( D @ insert_a ) @ ( C @ insert_a ) ) )
=> ( ( ( B = C )
& ( A = D ) )
| ( ( B = D )
& ( A = C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(250,axiom,
! [A: $i] :
( ( A @ is_fun1661590463l_bool )
=> ( ( A @ collec1974731493e_bool )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_Collect__def) ).
thf(1763,plain,
! [A: $i] :
( ( A @ is_fun1661590463l_bool )
=> ( ( A @ collec1974731493e_bool )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(293,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun_a_bool )
=> ( B @ ( A @ image_a_pname ) @ is_fun_pname_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000t__a_000tc__Com__Opname) ).
thf(1901,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)],[293]) ).
thf(716,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B = A )
=> ( C @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_522_xt1_I4_J) ).
thf(3564,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B = A )
=> ( C @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(205,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ~ ! [C: $i] :
( ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B
!= ( C @ ( suc @ hAPP_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_676_Suc__lessE) ).
thf(1579,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ~ ! [C: $i] :
( ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B
!= ( C @ ( suc @ hAPP_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(506,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( C = A )
=> ( A @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_529_ord__le__eq__trans) ).
thf(2656,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( C = A )
=> ( A @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(526,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/sandbox/benchmark/theBenchmark.p',fact_31_card__image__le) ).
thf(2747,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)],[526]) ).
thf(49,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_662_Suc__leI) ).
thf(1053,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(258,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/sandbox/benchmark/theBenchmark.p',fact_51_card__seteq) ).
thf(1790,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)],[258]) ).
thf(805,axiom,
! [A: $i,B: $i] :
( ( ( B @ hBOOL )
<=> ( A @ hBOOL ) )
<=> ( ( B @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
& ( A @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_550_order__eq__iff) ).
thf(3940,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
& ( A @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) )
=> ( ( ( A @ hBOOL )
=> ( B @ hBOOL ) )
& ( ( B @ hBOOL )
=> ( A @ hBOOL ) ) ) )
& ( ( ( ( A @ hBOOL )
=> ( B @ hBOOL ) )
& ( ( B @ hBOOL )
=> ( A @ hBOOL ) ) )
=> ( ( B @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
& ( A @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).
thf(451,axiom,
! [A: $i] :
( ( A @ ( fequal_fun_nat_bool @ hAPP_f103356543l_bool ) @ collect_fun_nat_bool )
= ( bot_bo1701429464l_bool @ ( A @ insert_fun_nat_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_491_singleton__conv2) ).
thf(2454,plain,
! [A: $i] :
( ( A @ ( fequal_fun_nat_bool @ hAPP_f103356543l_bool ) @ collect_fun_nat_bool )
= ( bot_bo1701429464l_bool @ ( A @ insert_fun_nat_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(661,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_445755039l_bool @ hAPP_f1794073134e_bool ) @ hAPP_pname_bool ) )
= ( B @ ( C @ ( A @ hAPP_p1824510254l_bool ) @ hAPP_fun_a_bool_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc) ).
thf(3305,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_445755039l_bool @ hAPP_f1794073134e_bool ) @ hAPP_pname_bool ) )
= ( B @ ( C @ ( A @ hAPP_p1824510254l_bool ) @ hAPP_fun_a_bool_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(165,axiom,
! [A: $i,B: $i] : ( B @ ( A @ image_1921560913_pname ) @ is_fun_pname_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Com__Opname) ).
thf(1432,plain,
! [A: $i,B: $i] : ( B @ ( A @ image_1921560913_pname ) @ is_fun_pname_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(789,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/sandbox/benchmark/theBenchmark.p',fact_185_lift__Suc__mono__le) ).
thf(3885,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)],[789]) ).
thf(123,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/sandbox/benchmark/theBenchmark.p',fact_229_Suc__le__D) ).
thf(1300,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)],[123]) ).
thf(222,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ is_fun_pname_bool )
=> ( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_pname_pname ) @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ image_pname_pname ) ) )
& ( 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/sandbox/benchmark/theBenchmark.p',fact_173_finite__subset__image) ).
thf(1637,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ is_fun_pname_bool )
=> ( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_pname_pname ) @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ image_pname_pname ) ) )
& ( 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)],[222]) ).
thf(90,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/sandbox/benchmark/theBenchmark.p',fact_287_mem__def) ).
thf(1188,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)],[90]) ).
thf(89,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_fun_a_bool_nat ) @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_finite__surj) ).
thf(1186,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_fun_a_bool_nat ) @ ( 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)],[89]) ).
thf(739,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/sandbox/benchmark/theBenchmark.p',fact_85_le__antisym) ).
thf(3655,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)],[739]) ).
thf(104,axiom,
! [A: $i] :
( ( A @ ( fequal_nat @ cOMBC_nat_nat_bool @ hAPP_n1699378549t_bool ) @ collect_nat )
= ( bot_bot_fun_nat_bool @ ( A @ insert_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_482_singleton__conv) ).
thf(1235,plain,
! [A: $i] :
( ( A @ ( fequal_nat @ cOMBC_nat_nat_bool @ hAPP_n1699378549t_bool ) @ collect_nat )
= ( bot_bot_fun_nat_bool @ ( A @ insert_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(403,axiom,
! [A: $i] :
( ( A @ is_fun_pname_bool )
=> ( ( bot_bo844097828e_bool @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
<=> ( A = bot_bo844097828e_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_436_bot__unique) ).
thf(2276,plain,
! [A: $i] :
( ( A @ is_fun_pname_bool )
=> ( ( ( A = bot_bo844097828e_bool )
=> ( bot_bo844097828e_bool @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
& ( ( bot_bo844097828e_bool @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A = bot_bo844097828e_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(773,axiom,
! [A: $i] :
( ( A @ ( bot_bot_fun_nat_bool @ hAPP_nat_bool ) @ hBOOL )
<=> ( bot_bot_bool @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_426_bot__fun__def) ).
thf(3801,plain,
! [A: $i] :
( ( ( bot_bot_bool @ hBOOL )
=> ( A @ ( bot_bot_fun_nat_bool @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( A @ ( bot_bot_fun_nat_bool @ hAPP_nat_bool ) @ hBOOL )
=> ( bot_bot_bool @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).
thf(61,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/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obo) ).
thf(1085,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)],[61]) ).
thf(226,axiom,
! [A: $i] : ( A @ mgt @ is_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_mgt) ).
thf(1658,plain,
! [A: $i] : ( A @ mgt @ is_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(12,axiom,
bot_bot_fun_a_bool @ is_fun_a_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Orderings_Obot__class_Obot_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
thf(951,plain,
bot_bot_fun_a_bool @ is_fun_a_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(563,axiom,
! [A: $i] : ( A @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_370_order__refl) ).
thf(2903,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)],[563]) ).
thf(242,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ insert_pname ) )
!= bot_bo844097828e_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_458_insert__not__empty) ).
thf(1738,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ insert_pname ) )
!= bot_bo844097828e_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(598,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_472261505bool_a ) @ hAPP_a85458249l_bool ) )
= ( C @ ( B @ hAPP_a_fun_a_bool ) @ ( A @ hAPP_f1631501043l_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__) ).
thf(3041,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_472261505bool_a ) @ hAPP_a85458249l_bool ) )
= ( C @ ( B @ hAPP_a_fun_a_bool ) @ ( A @ hAPP_f1631501043l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(138,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/sandbox/benchmark/theBenchmark.p',fact_43_card__mono) ).
thf(1358,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)],[138]) ).
thf(573,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 )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_506_xt1_I5_J) ).
thf(2948,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 )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(110,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/sandbox/benchmark/theBenchmark.p',fact_372_finite__nat__set__iff__bounded__le) ).
thf(1257,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)],[110]) ).
thf(314,axiom,
! [A: $i,B: $i] :
( ( ( B @ is_fun1661590463l_bool )
& ( A @ is_fun_pname_bool ) )
=> ( B @ ( A @ insert1325755072e_bool ) @ is_fun1661590463l_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oinsert_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).
thf(1981,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)],[314]) ).
thf(548,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( bot_bot_fun_a_bool @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ! [D: $i,E: $i] :
( ( ( E @ is_fun_a_bool )
& ( D @ is_a ) )
=> ( ( E @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( D @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ~ ( E @ ( D @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( E @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( E @ ( D @ insert_a ) @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ) ) )
=> ( C @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_558_finite__subset__induct) ).
thf(2843,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( bot_bot_fun_a_bool @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ! [D: $i,E: $i] :
( ( ( E @ is_fun_a_bool )
& ( D @ is_a ) )
=> ( ( E @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( D @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ~ ( E @ ( D @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( E @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( E @ ( D @ insert_a ) @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ) ) )
=> ( C @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(412,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_580_diff__add__inverse) ).
thf(2320,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(675,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/sandbox/benchmark/theBenchmark.p',fact_3_finite__Collect__subsets) ).
thf(3388,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)],[675]) ).
thf(519,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_1823939024ol_nat ) @ hAPP_n1414589940l_bool ) )
= ( C @ ( B @ hAPP_nat_fun_a_bool ) @ ( A @ hAPP_f1631501043l_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It___018) ).
thf(2722,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_1823939024ol_nat ) @ hAPP_n1414589940l_bool ) )
= ( C @ ( B @ hAPP_nat_fun_a_bool ) @ ( A @ hAPP_f1631501043l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(810,axiom,
! [A: $i,B: $i] :
( ( A = B )
=> ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_546_order__eq__refl) ).
thf(3961,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)],[810]) ).
thf(859,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_nat_nat ) @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ image_nat_nat ) ) )
& ( D @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_finite__subset__image) ).
thf(4150,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_nat_nat ) @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ image_nat_nat ) ) )
& ( D @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).
thf(883,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/sandbox/benchmark/theBenchmark.p',fact_109_rev__finite__subset) ).
thf(4257,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)],[883]) ).
thf(849,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/sandbox/benchmark/theBenchmark.p',fact_67_card__insert__disjoint) ).
thf(4111,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)],[849]) ).
thf(442,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_496248727ol_nat ) @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_finite__surj) ).
thf(2411,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_496248727ol_nat ) @ ( 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)],[442]) ).
thf(466,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ is_a )
=> ( ( C @ ( B @ image_nat_a ) @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ~ ! [D: $i] :
( ( A
= ( D @ ( B @ hAPP_nat_a ) ) )
=> ~ ( C @ ( D @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_353_imageE) ).
thf(2500,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ is_a )
=> ( ( C @ ( B @ image_nat_a ) @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ~ ! [D: $i] :
( ( A
= ( D @ ( B @ hAPP_nat_a ) ) )
=> ~ ( C @ ( D @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(196,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun_a_bool )
=> ( B @ ( A @ hAPP_f2050579477a_bool ) @ is_fun_a_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
thf(1543,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)],[196]) ).
thf(251,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/sandbox/benchmark/theBenchmark.p',fact_237_insert__compr) ).
thf(1766,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)],[251]) ).
thf(479,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( A @ image_pname_pname ) @ ( B @ ( A @ hAPP_pname_pname ) @ insert_pname ) )
= ( C @ ( A @ image_pname_pname ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_338_insert__image) ).
thf(2558,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( A @ image_pname_pname ) @ ( B @ ( A @ hAPP_pname_pname ) @ insert_pname ) )
= ( C @ ( A @ image_pname_pname ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(812,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/sandbox/benchmark/theBenchmark.p',fact_300_equalityE) ).
thf(3970,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)],[812]) ).
thf(832,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( C @ ( A @ image_nat_a ) @ ( B @ ( A @ hAPP_nat_a ) @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_306_imageI) ).
thf(4046,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( C @ ( A @ image_nat_a ) @ ( B @ ( A @ hAPP_nat_a ) @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).
thf(648,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun_pname_bool )
=> ( ( ( B @ ( A @ image_pname_a ) )
= bot_bot_fun_a_bool )
<=> ( B = bot_bo844097828e_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_467_image__is__empty) ).
thf(3224,plain,
! [A: $i,B: $i] :
( ( B @ is_fun_pname_bool )
=> ( ( ( B = bot_bo844097828e_bool )
=> ( ( B @ ( A @ image_pname_a ) )
= bot_bot_fun_a_bool ) )
& ( ( ( B @ ( A @ image_pname_a ) )
= bot_bot_fun_a_bool )
=> ( B = bot_bo844097828e_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(22,axiom,
finite_finite_pname @ is_fun1661590463l_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Finite__Set_Ofinite_000tc__Com__Opname) ).
thf(978,plain,
finite_finite_pname @ is_fun1661590463l_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(469,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/sandbox/benchmark/theBenchmark.p',fact_301_equalityE) ).
thf(2511,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)],[469]) ).
thf(887,axiom,
! [A: $i,B: $i,C: $i] :
( ( B = C )
=> ( ( C @ ( A @ ( 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/sandbox/benchmark/theBenchmark.p',fact_534_xt1_I3_J) ).
thf(4267,plain,
! [A: $i,B: $i,C: $i] :
( ( B = C )
=> ( ( C @ ( A @ ( 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)],[887]) ).
thf(330,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun_a_bool )
=> ( B @ ( A @ cOMBB_bool_bool_a ) @ is_fun_a_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000t__a) ).
thf(2030,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)],[330]) ).
thf(143,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_1921560913_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_finite__surj) ).
thf(1372,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_1921560913_pname ) @ ( 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)],[143]) ).
thf(654,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/sandbox/benchmark/theBenchmark.p',fact_60_card__insert__if) ).
thf(3256,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)],[654]) ).
thf(559,axiom,
! [A: $i] :
( ( A @ ( fequal_fun_a_bool @ hAPP_f1631501043l_bool ) @ collect_fun_a_bool )
= ( bot_bo1389914601l_bool @ ( A @ insert_fun_a_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_493_singleton__conv2) ).
thf(2892,plain,
! [A: $i] :
( ( A @ ( fequal_fun_a_bool @ hAPP_f1631501043l_bool ) @ collect_fun_a_bool )
= ( bot_bo1389914601l_bool @ ( A @ insert_fun_a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(539,axiom,
! [A: $i] : ( A @ ( bot_bot_nat @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_445_bot__least) ).
thf(2807,plain,
! [A: $i] : ( A @ ( bot_bot_nat @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(628,axiom,
! [A: $i,B: $i] : ( B @ ( A @ insert_a ) @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_insertI1) ).
thf(3156,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)],[628]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun_pname_bool )
=> ( B @ ( A @ image_47868345e_bool ) @ is_fun1661590463l_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_) ).
thf(991,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)],[26]) ).
thf(215,axiom,
! [A: $i,B: $i] : ( A @ ( suc @ hAPP_nat_nat ) @ ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_665_diff__less__Suc) ).
thf(1617,plain,
! [A: $i,B: $i] : ( A @ ( suc @ hAPP_nat_nat ) @ ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(529,axiom,
bot_bot_fun_nat_bool @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_391_finite_OemptyI) ).
thf(2760,plain,
bot_bot_fun_nat_bool @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(891,axiom,
! [A: $i] :
( ( A @ ( bot_bot_fun_a_bool @ hAPP_a_bool ) @ hBOOL )
<=> ( bot_bot_bool @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_430_bot__apply) ).
thf(4289,plain,
! [A: $i] :
( ( ( bot_bot_bool @ hBOOL )
=> ( A @ ( bot_bot_fun_a_bool @ hAPP_a_bool ) @ hBOOL ) )
& ( ( A @ ( bot_bot_fun_a_bool @ hAPP_a_bool ) @ hBOOL )
=> ( bot_bot_bool @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).
thf(854,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/sandbox/benchmark/theBenchmark.p',fact_337_image__insert) ).
thf(4138,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)],[854]) ).
thf(351,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( A @ minus_minus_nat @ hAPP_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_683_diff__add__0) ).
thf(2088,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( A @ minus_minus_nat @ hAPP_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(268,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_1896684278e_bool ) @ hAPP_f1066163005t_bool ) )
= ( C @ ( B @ hAPP_f921600141ol_nat ) @ ( A @ hAPP_n1699378549t_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__014) ).
thf(1817,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_1896684278e_bool ) @ hAPP_f1066163005t_bool ) )
= ( C @ ( B @ hAPP_f921600141ol_nat ) @ ( A @ hAPP_n1699378549t_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(129,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) )
= zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_684_diff__is__0__eq_H) ).
thf(1321,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) )
= zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(224,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun1661590463l_bool )
=> ( B @ ( A @ image_876012084bool_a ) @ is_fun_a_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000t__a) ).
thf(1654,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)],[224]) ).
thf(189,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/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool) ).
thf(1517,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)],[189]) ).
thf(72,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( ( A = B )
| ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_640_le__eq__less__or__eq) ).
thf(1126,plain,
! [A: $i,B: $i] :
( ( ( ( A = B )
| ( B @ ( A @ ( ord_less_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 )
| ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(419,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( C @ minus_minus_nat @ hAPP_nat_nat ) @ ( A @ plus_plus_nat @ hAPP_nat_nat ) )
= ( B @ ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_601_add__diff__assoc) ).
thf(2342,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( C @ minus_minus_nat @ hAPP_nat_nat ) @ ( A @ plus_plus_nat @ hAPP_nat_nat ) )
= ( B @ ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(345,axiom,
! [A: $i,B: $i] :
( ( A @ is_bool )
=> ( ( B @ ( A @ cOMBK_bool_a @ hAPP_a_bool ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000t__a_U) ).
thf(2071,plain,
! [A: $i,B: $i] :
( ( A @ is_bool )
=> ( ( B @ ( A @ cOMBK_bool_a @ hAPP_a_bool ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(565,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( C @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( bot_bo1389914601l_bool @ ( A @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ! [D: $i,E: $i] :
( ( ( E @ is_fun949378684l_bool )
& ( D @ is_fun_a_bool ) )
=> ( ( E @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( D @ ( member_fun_a_bool @ hAPP_f285962445l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ~ ( E @ ( D @ ( member_fun_a_bool @ hAPP_f285962445l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( E @ ( A @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( E @ ( D @ insert_fun_a_bool ) @ ( A @ hAPP_f621171935l_bool ) @ hBOOL ) ) ) ) ) )
=> ( C @ ( A @ hAPP_f621171935l_bool ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_561_finite__subset__induct) ).
thf(2907,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( C @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( bot_bo1389914601l_bool @ ( A @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ! [D: $i,E: $i] :
( ( ( E @ is_fun949378684l_bool )
& ( D @ is_fun_a_bool ) )
=> ( ( E @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( D @ ( member_fun_a_bool @ hAPP_f285962445l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ~ ( E @ ( D @ ( member_fun_a_bool @ hAPP_f285962445l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( E @ ( A @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( E @ ( D @ insert_fun_a_bool ) @ ( A @ hAPP_f621171935l_bool ) @ hBOOL ) ) ) ) ) )
=> ( C @ ( A @ hAPP_f621171935l_bool ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(555,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/sandbox/benchmark/theBenchmark.p',fact_102_finite__insert) ).
thf(2875,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)],[555]) ).
thf(632,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_650_less__not__refl3) ).
thf(3168,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(301,axiom,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f937997336l_bool ) @ is_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HO) ).
thf(1940,plain,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f937997336l_bool ) @ is_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(722,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/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__) ).
thf(3584,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)],[722]) ).
thf(625,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/sandbox/benchmark/theBenchmark.p',fact_112_rev__finite__subset) ).
thf(3139,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)],[625]) ).
thf(335,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/sandbox/benchmark/theBenchmark.p',fact_44_card__mono) ).
thf(2045,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)],[335]) ).
thf(610,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_47868345e_bool ) @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ? [C: $i] :
( ~ ( C @ ( A @ hAPP_p61793385e_bool ) @ ( A @ ( fequal533582459e_bool @ cOMBB_408569982_pname ) @ cOMBC_1058051404l_bool @ hAPP_f759274231e_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/sandbox/benchmark/theBenchmark.p',fact_204_pigeonhole__infinite) ).
thf(3092,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_47868345e_bool ) @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ? [C: $i] :
( ~ ( C @ ( A @ hAPP_p61793385e_bool ) @ ( A @ ( fequal533582459e_bool @ cOMBB_408569982_pname ) @ cOMBC_1058051404l_bool @ hAPP_f759274231e_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)],[610]) ).
thf(708,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/sandbox/benchmark/theBenchmark.p',fact_254_insert__code) ).
thf(3533,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)],[708]) ).
thf(690,axiom,
! [A: $i] :
( ? [B: $i] : ( A @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
<=> ( A != bot_bot_fun_nat_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_413_ex__in__conv) ).
thf(3447,plain,
! [A: $i] :
( ( ( A != bot_bot_fun_nat_bool )
=> ? [B: $i] : ( A @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
& ( ? [B: $i] : ( A @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A != bot_bot_fun_nat_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(408,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( C @ ( A @ image_nat_pname ) @ ( B @ ( A @ hAPP_nat_pname ) @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_305_imageI) ).
thf(2310,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( C @ ( A @ image_nat_pname ) @ ( B @ ( A @ hAPP_nat_pname ) @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(277,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ insert_pname ) @ ( A @ insert_pname ) )
= ( C @ ( A @ insert_pname ) @ ( B @ insert_pname ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_insert__commute) ).
thf(1844,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)],[277]) ).
thf(636,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_2129980159t_bool ) @ ( A @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( A @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_finite__surj) ).
thf(3188,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_2129980159t_bool ) @ ( 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)],[636]) ).
thf(712,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/sandbox/benchmark/theBenchmark.p',fact_41_card__image__le) ).
thf(3548,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)],[712]) ).
thf(414,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_1885489796ol_nat ) @ hAPP_nat_fun_a_bool ) )
= ( C @ ( B @ hAPP_nat_a ) @ ( A @ hAPP_a_fun_a_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Nat__Onat) ).
thf(2325,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_1885489796ol_nat ) @ hAPP_nat_fun_a_bool ) )
= ( C @ ( B @ hAPP_nat_a ) @ ( A @ hAPP_a_fun_a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(801,axiom,
! [A: $i,B: $i] :
( ( A = B )
| ~ ( B @ ( A @ ( fequal_fun_nat_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T) ).
thf(3928,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)],[801]) ).
thf(587,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/sandbox/benchmark/theBenchmark.p',fact_259_insert__ident) ).
thf(2997,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)],[587]) ).
thf(170,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/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000t__a_U) ).
thf(1448,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)],[170]) ).
thf(822,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/sandbox/benchmark/theBenchmark.p',fact_519_order__antisym) ).
thf(4006,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)],[822]) ).
thf(118,axiom,
! [A: $i,B: $i] :
( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_626_Suc__less__SucD) ).
thf(1289,plain,
! [A: $i,B: $i] :
( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(602,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_nat_fun_a_bool ) @ ( A @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( A @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_finite__surj) ).
thf(3056,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_nat_fun_a_bool ) @ ( 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)],[602]) ).
thf(501,axiom,
! [A: $i] : ( A @ ( bot_bot_fun_nat_bool @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_393_empty__subsetI) ).
thf(2643,plain,
! [A: $i] : ( A @ ( bot_bot_fun_nat_bool @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(759,axiom,
~ ( g @ ( pn @ ( mgt_call @ hAPP_pname_a ) @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_5) ).
thf(3729,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)],[759]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( A @ is_bool )
=> ( ( B @ ( A @ cOMBK_bool_nat @ hAPP_nat_bool ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Nat__Onat_U) ).
thf(961,plain,
! [A: $i,B: $i] :
( ( A @ is_bool )
=> ( ( B @ ( A @ cOMBK_bool_nat @ hAPP_nat_bool ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(134,axiom,
! [A: $i,B: $i] :
( ( B @ is_pname )
=> ( B @ ( A @ hAPP_p338031245l_bool ) @ is_fun1661590463l_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obo) ).
thf(1341,plain,
! [A: $i,B: $i] :
( ( B @ is_pname )
=> ( B @ ( A @ hAPP_p338031245l_bool ) @ is_fun1661590463l_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(294,axiom,
! [A: $i] :
( ( A @ is_fun_a_bool )
=> ( ( A @ collect_a )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_Collect__def) ).
thf(1903,plain,
! [A: $i] :
( ( A @ is_fun_a_bool )
=> ( ( A @ collect_a )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(53,axiom,
! [A: $i,B: $i] :
( ( ( B @ is_pname )
& ( A @ is_fun_pname_bool ) )
=> ( B @ ( A @ hAPP_pname_bool ) @ is_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Com__Opname_000tc__HOL__Obool) ).
thf(1062,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)],[53]) ).
thf(180,axiom,
! [A: $i,B: $i] :
( ( bot_bot_fun_nat_bool @ ( B @ insert_nat ) @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A
= ( bot_bot_fun_nat_bool @ ( B @ insert_nat ) ) )
| ( A = bot_bot_fun_nat_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_494_subset__singletonD) ).
thf(1481,plain,
! [A: $i,B: $i] :
( ( bot_bot_fun_nat_bool @ ( B @ insert_nat ) @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A
= ( bot_bot_fun_nat_bool @ ( B @ insert_nat ) ) )
| ( A = bot_bot_fun_nat_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(646,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/sandbox/benchmark/theBenchmark.p',fact_286_set__mp) ).
thf(3220,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)],[646]) ).
thf(320,axiom,
( bot_bo1701429464l_bool
= ( fFalse @ cOMBK_1994329625t_bool @ collect_fun_nat_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_420_empty__def) ).
thf(2004,plain,
( bot_bo1701429464l_bool
= ( fFalse @ cOMBK_1994329625t_bool @ collect_fun_nat_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(244,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_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_661_le__imp__less__Suc) ).
thf(1745,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_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(531,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( bot_bo1701429464l_bool @ ( A @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ! [C: $i,D: $i] :
( ( D @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ~ ( D @ ( C @ ( member_fun_nat_bool @ hAPP_f1951378235l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( D @ ( A @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( D @ ( C @ insert_fun_nat_bool ) @ ( A @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ) )
=> ( B @ ( A @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_563_finite__induct) ).
thf(2764,plain,
! [A: $i,B: $i] :
( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( bot_bo1701429464l_bool @ ( A @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ! [C: $i,D: $i] :
( ( D @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ~ ( D @ ( C @ ( member_fun_nat_bool @ hAPP_f1951378235l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( D @ ( A @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( D @ ( C @ insert_fun_nat_bool ) @ ( A @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ) )
=> ( B @ ( A @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(399,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ minus_minus_nat @ hAPP_nat_nat ) @ plus_plus_nat @ hAPP_nat_nat ) )
= ( B @ ( A @ ( C @ plus_plus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_596_add__diff__assoc2) ).
thf(2262,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ minus_minus_nat @ hAPP_nat_nat ) @ plus_plus_nat @ hAPP_nat_nat ) )
= ( B @ ( A @ ( C @ plus_plus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(694,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/sandbox/benchmark/theBenchmark.p',fact_554_order__eq__iff) ).
thf(3465,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)],[694]) ).
thf(208,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/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000t__a_000tc__HOL__Obool_U) ).
thf(1590,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)],[208]) ).
thf(374,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun949378684l_bool )
=> ( B @ ( A @ image_1854862208_pname ) @ is_fun_pname_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opname) ).
thf(2174,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)],[374]) ).
thf(404,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/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc_) ).
thf(2283,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)],[404]) ).
thf(436,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/sandbox/benchmark/theBenchmark.p',fact_127_diff__diff__cancel) ).
thf(2389,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)],[436]) ).
thf(844,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/sandbox/benchmark/theBenchmark.p',fact_222_insertCI) ).
thf(4089,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)],[844]) ).
thf(478,axiom,
! [A: $i,B: $i,C: $i] :
( ( B = C )
=> ( ( 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/sandbox/benchmark/theBenchmark.p',fact_539_ord__eq__le__trans) ).
thf(2554,plain,
! [A: $i,B: $i,C: $i] :
( ( B = C )
=> ( ( 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)],[478]) ).
thf(762,axiom,
! [A: $i,B: $i,C: $i] :
( ( B = C )
=> ( ( 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/sandbox/benchmark/theBenchmark.p',fact_538_ord__eq__le__trans) ).
thf(3748,plain,
! [A: $i,B: $i,C: $i] :
( ( B = C )
=> ( ( 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)],[762]) ).
thf(732,axiom,
! [A: $i] : ( A @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_266_subset__refl) ).
thf(3630,plain,
! [A: $i] : ( A @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(322,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun_pname_bool )
=> ( B @ ( A @ image_pname_pname ) @ is_fun_pname_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__Com__Opname_000tc__Com__Opname) ).
thf(2009,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)],[322]) ).
thf(813,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/sandbox/benchmark/theBenchmark.p',fact_223_insertCI) ).
thf(3978,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)],[813]) ).
thf(749,axiom,
! [A: $i,B: $i] : ( B @ ( A @ insert_nat ) @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_insertI1) ).
thf(3694,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)],[749]) ).
thf(333,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun949378684l_bool )
=> ( B @ ( A @ hAPP_f2117159681l_bool ) @ is_fun949378684l_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J_000tc___001) ).
thf(2041,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)],[333]) ).
thf(657,axiom,
! [A: $i,B: $i] :
( ( A != B )
<=> ( ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
| ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_646_nat__neq__iff) ).
thf(3267,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
| ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( A != B ) )
& ( ( A != B )
=> ( ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
| ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(627,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ is_fun949378684l_bool )
=> ( ( C @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_a_fun_a_bool ) @ ( C @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ image_a_fun_a_bool ) ) )
& ( D @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( D @ is_fun_a_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_finite__subset__image) ).
thf(3149,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ is_fun949378684l_bool )
=> ( ( C @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_a_fun_a_bool ) @ ( C @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ image_a_fun_a_bool ) ) )
& ( D @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( D @ is_fun_a_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(214,axiom,
! [A: $i,B: $i] :
( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( ( A = B )
| ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_635_less__Suc__eq) ).
thf(1607,plain,
! [A: $i,B: $i] :
( ( ( ( A = B )
| ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A = B )
| ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(410,axiom,
! [A: $i] :
( ( A @ ( fequal533582459e_bool @ hAPP_f434788991l_bool ) @ collec1974731493e_bool )
= ( bot_bo1649642514l_bool @ ( A @ insert1325755072e_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_492_singleton__conv2) ).
thf(2315,plain,
! [A: $i] :
( ( A @ ( fequal533582459e_bool @ hAPP_f434788991l_bool ) @ collec1974731493e_bool )
= ( bot_bo1649642514l_bool @ ( A @ insert1325755072e_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(914,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/sandbox/benchmark/theBenchmark.p',fact_74_finite__Collect__conjI) ).
thf(4372,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)],[914]) ).
thf(318,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun_a_bool )
=> ( B @ ( A @ image_a_a ) @ is_fun_a_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000t__a_000t__a) ).
thf(1994,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)],[318]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i,E: $i] :
( ( E @ ( D @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( E @ ( C @ hAPP_nat_nat ) @ ( D @ ( C @ hAPP_nat_nat ) @ ( ord_less_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/sandbox/benchmark/theBenchmark.p',fact_675_less__mono__imp__le__mono) ).
thf(1045,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i,E: $i] :
( ( E @ ( D @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( E @ ( C @ hAPP_nat_nat ) @ ( D @ ( C @ hAPP_nat_nat ) @ ( ord_less_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)],[46]) ).
thf(449,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/sandbox/benchmark/theBenchmark.p',fact_358_subsetI) ).
thf(2447,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)],[449]) ).
thf(571,axiom,
! [A: $i] : ( A @ ( bot_bot_bool @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_442_bot__least) ).
thf(2944,plain,
! [A: $i] : ( A @ ( bot_bot_bool @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(484,axiom,
! [A: $i,B: $i] :
( ( A @ is_a )
=> ( ( B @ ( A @ cOMBK_a_pname @ hAPP_pname_a ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000t__a_000tc__Com__Opname_U) ).
thf(2576,plain,
! [A: $i,B: $i] :
( ( A @ is_a )
=> ( ( B @ ( A @ cOMBK_a_pname @ hAPP_pname_a ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(343,axiom,
! [A: $i] :
~ ( A @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_Suc__n__not__le__n) ).
thf(2066,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)],[343]) ).
thf(426,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/sandbox/benchmark/theBenchmark.p',fact_47_card__mono) ).
thf(2362,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)],[426]) ).
thf(371,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/sandbox/benchmark/theBenchmark.p',fact_128_diff__le__mono) ).
thf(2162,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)],[371]) ).
thf(407,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ is_pname )
& ( C @ is_pname )
& ( B @ is_pname )
& ( A @ is_pname ) )
=> ( ( ( bot_bo844097828e_bool @ ( B @ insert_pname ) @ ( A @ insert_pname ) )
= ( bot_bo844097828e_bool @ ( D @ insert_pname ) @ ( C @ insert_pname ) ) )
<=> ( ( ( B = C )
& ( A = D ) )
| ( ( B = D )
& ( A = C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_452_doubleton__eq__iff) ).
thf(2294,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ is_pname )
& ( C @ is_pname )
& ( B @ is_pname )
& ( A @ is_pname ) )
=> ( ( ( ( ( B = C )
& ( A = D ) )
| ( ( B = D )
& ( A = C ) ) )
=> ( ( bot_bo844097828e_bool @ ( B @ insert_pname ) @ ( A @ insert_pname ) )
= ( bot_bo844097828e_bool @ ( D @ insert_pname ) @ ( C @ insert_pname ) ) ) )
& ( ( ( bot_bo844097828e_bool @ ( B @ insert_pname ) @ ( A @ insert_pname ) )
= ( bot_bo844097828e_bool @ ( D @ insert_pname ) @ ( C @ insert_pname ) ) )
=> ( ( ( B = C )
& ( A = D ) )
| ( ( B = D )
& ( A = C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(126,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/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000t__a_000t__a_000tc__HOL__Obool_U) ).
thf(1309,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)],[126]) ).
thf(524,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/sandbox/benchmark/theBenchmark.p',fact_289_mem__def) ).
thf(2739,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)],[524]) ).
thf(169,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_587_nat__add__left__cancel__le) ).
thf(1442,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(366,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/sandbox/benchmark/theBenchmark.p',fact_57_card__insert__le) ).
thf(2142,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)],[366]) ).
thf(29,axiom,
! [A: $i] : ( A @ wt @ is_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_wt) ).
thf(999,plain,
! [A: $i] : ( A @ wt @ is_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(115,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_610033911bool_a ) @ hAPP_a93125764e_bool ) )
= ( C @ ( B @ hAPP_a_pname ) @ ( A @ hAPP_p61793385e_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob) ).
thf(1280,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_610033911bool_a ) @ hAPP_a93125764e_bool ) )
= ( C @ ( B @ hAPP_a_pname ) @ ( A @ hAPP_p61793385e_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(783,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 )
=> ? [C: $i] :
( ~ ( C @ ( A @ hAPP_fun_a_bool_nat ) @ ( A @ ( fequal_nat @ cOMBB_164527437a_bool ) @ cOMBC_619334683t_bool @ hAPP_n1414589940l_bool ) @ ( B @ ( member_fun_a_bool @ cOMBC_1880041174l_bool @ hAPP_f2117159681l_bool ) @ ( fconj @ cOMBB_338059395a_bool ) @ cOMBS_1035972772l_bool ) @ collect_fun_a_bool @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
& ( B @ ( C @ ( member_fun_a_bool @ hAPP_f285962445l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
& ( C @ is_fun_a_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_pigeonhole__infinite) ).
thf(3860,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 )
=> ? [C: $i] :
( ~ ( C @ ( A @ hAPP_fun_a_bool_nat ) @ ( A @ ( fequal_nat @ cOMBB_164527437a_bool ) @ cOMBC_619334683t_bool @ hAPP_n1414589940l_bool ) @ ( B @ ( member_fun_a_bool @ cOMBC_1880041174l_bool @ hAPP_f2117159681l_bool ) @ ( fconj @ cOMBB_338059395a_bool ) @ cOMBS_1035972772l_bool ) @ collect_fun_a_bool @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
& ( B @ ( C @ ( member_fun_a_bool @ hAPP_f285962445l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
& ( C @ is_fun_a_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).
thf(910,axiom,
! [A: $i] :
( ~ ( A @ hBOOL )
| ~ ( A @ ( fNot @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_1_1_U) ).
thf(4356,plain,
! [A: $i] :
( ~ ( A @ hBOOL )
| ~ ( A @ ( fNot @ hAPP_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).
thf(656,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_619334683t_bool @ hAPP_n1414589940l_bool ) @ hAPP_fun_a_bool_bool ) )
= ( B @ ( C @ ( A @ hAPP_f282463732t_bool ) @ hAPP_nat_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Nat__Onat_000tc__) ).
thf(3264,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_619334683t_bool @ hAPP_n1414589940l_bool ) @ hAPP_fun_a_bool_bool ) )
= ( B @ ( C @ ( A @ hAPP_f282463732t_bool ) @ hAPP_nat_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(613,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/sandbox/benchmark/theBenchmark.p',fact_114_rev__finite__subset) ).
thf(3100,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)],[613]) ).
thf(574,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ insert_a ) @ ( A @ insert_a ) )
= ( C @ ( A @ insert_a ) @ ( B @ insert_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_insert__commute) ).
thf(2951,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)],[574]) ).
thf(124,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_639_less__imp__le__nat) ).
thf(1303,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_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)],[124]) ).
thf(698,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( C @ ( A @ image_nat_a ) @ ( B @ ( A @ image_nat_a ) @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_350_image__mono) ).
thf(3496,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( C @ ( A @ image_nat_a ) @ ( B @ ( A @ image_nat_a ) @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(604,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( C = A )
=> ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_528_ord__le__eq__trans) ).
thf(3062,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( C = A )
=> ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(740,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( 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 )
=> ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_503_xt1_I6_J) ).
thf(3658,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( 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 )
=> ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(851,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/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__fun_It__a_Mtc__HOL__Obool_J_T) ).
thf(4125,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)],[851]) ).
thf(306,axiom,
finite_finite_a @ is_fun949378684l_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Finite__Set_Ofinite_000t__a) ).
thf(1957,plain,
finite_finite_a @ is_fun949378684l_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(850,axiom,
! [A: $i] :
( ( bot_bo1649642514l_bool
= ( A @ collec1974731493e_bool ) )
<=> ! [B: $i] :
( ( B @ is_fun_pname_bool )
=> ~ ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_409_empty__Collect__eq) ).
thf(4114,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ is_fun_pname_bool )
=> ~ ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL ) )
=> ( bot_bo1649642514l_bool
= ( A @ collec1974731493e_bool ) ) )
& ( ( bot_bo1649642514l_bool
= ( A @ collec1974731493e_bool ) )
=> ! [B: $i] :
( ( B @ is_fun_pname_bool )
=> ~ ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).
thf(582,axiom,
u @ ( mgt_call @ image_pname_a ) @ ( g @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(2983,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)],[582]) ).
thf(784,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ hAPP_a_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_a @ cOMBC_a_a_bool @ hAPP_a_fun_a_bool ) @ ( fconj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a )
= bot_bot_fun_a_bool ) )
& ( ( B @ ( A @ hAPP_a_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_a @ cOMBC_a_a_bool @ hAPP_a_fun_a_bool ) @ ( fconj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a )
= ( bot_bot_fun_a_bool @ ( B @ insert_a ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_472_Collect__conv__if) ).
thf(3865,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ hAPP_a_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_a @ cOMBC_a_a_bool @ hAPP_a_fun_a_bool ) @ ( fconj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a )
= bot_bot_fun_a_bool ) )
& ( ( B @ ( A @ hAPP_a_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_a @ cOMBC_a_a_bool @ hAPP_a_fun_a_bool ) @ ( fconj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a )
= ( bot_bot_fun_a_bool @ ( B @ insert_a ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).
thf(209,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ insert_nat ) @ ( A @ insert_nat ) )
= ( C @ ( A @ insert_nat ) @ ( B @ insert_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_insert__commute) ).
thf(1593,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)],[209]) ).
thf(780,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/sandbox/benchmark/theBenchmark.p',fact_61_card__insert__if) ).
thf(3837,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)],[780]) ).
thf(770,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( fimplies @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
| ( B @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_1_1_U) ).
thf(3790,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)],[770]) ).
thf(75,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/sandbox/benchmark/theBenchmark.p',fact_53_card__seteq) ).
thf(1148,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)],[75]) ).
thf(230,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ? [C: $i] :
( B
= ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_657_less__iff__Suc__add) ).
thf(1673,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( B
= ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) ) )
=> ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ? [C: $i] :
( B
= ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(622,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/sandbox/benchmark/theBenchmark.p',fact_351_image__mono) ).
thf(3132,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)],[622]) ).
thf(107,axiom,
! [A: $i] :
( ( A @ ( fequal_pname @ cOMBC_1149511130e_bool @ hAPP_p61793385e_bool ) @ collect_pname )
= ( bot_bo844097828e_bool @ ( A @ insert_pname ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_483_singleton__conv) ).
thf(1248,plain,
! [A: $i] :
( ( A @ ( fequal_pname @ cOMBC_1149511130e_bool @ hAPP_p61793385e_bool ) @ collect_pname )
= ( bot_bo844097828e_bool @ ( A @ insert_pname ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(337,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun1661590463l_bool )
=> ( B @ ( A @ hAPP_f559147733l_bool ) @ is_fun1661590463l_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo_002) ).
thf(2050,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)],[337]) ).
thf(498,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/sandbox/benchmark/theBenchmark.p',fact_9_finite__imageI) ).
thf(2636,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)],[498]) ).
thf(857,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/sandbox/benchmark/theBenchmark.p',fact_21_finite__imageI) ).
thf(4146,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)],[857]) ).
thf(140,axiom,
! [A: $i,B: $i] :
( ( B @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_579_diff__add__inverse2) ).
thf(1363,plain,
! [A: $i,B: $i] :
( ( B @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(908,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 )
=> ? [C: $i] :
( ~ ( C @ ( A @ hAPP_a_a ) @ ( A @ ( fequal_a @ cOMBB_a_fun_a_bool_a ) @ cOMBC_a_a_bool @ hAPP_a_fun_a_bool ) @ ( B @ ( member_a @ cOMBC_1355376034l_bool @ hAPP_f2050579477a_bool ) @ ( fconj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( C @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( C @ is_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_pigeonhole__infinite) ).
thf(4350,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 )
=> ? [C: $i] :
( ~ ( C @ ( A @ hAPP_a_a ) @ ( A @ ( fequal_a @ cOMBB_a_fun_a_bool_a ) @ cOMBC_a_a_bool @ hAPP_a_fun_a_bool ) @ ( B @ ( member_a @ cOMBC_1355376034l_bool @ hAPP_f2050579477a_bool ) @ ( fconj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( C @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( C @ is_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).
thf(417,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B
!= ( A @ ( suc @ hAPP_nat_nat ) ) )
=> ~ ! [C: $i] :
( ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B
!= ( C @ ( suc @ hAPP_nat_nat ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_677_lessE) ).
thf(2334,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B
!= ( A @ ( suc @ hAPP_nat_nat ) ) )
=> ~ ! [C: $i] :
( ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B
!= ( C @ ( suc @ hAPP_nat_nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(890,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ hAPP_pname_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_pname @ cOMBC_1149511130e_bool @ hAPP_p61793385e_bool ) @ ( fconj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname )
= bot_bo844097828e_bool ) )
& ( ( B @ ( A @ hAPP_pname_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_pname @ cOMBC_1149511130e_bool @ hAPP_p61793385e_bool ) @ ( fconj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname )
= ( bot_bo844097828e_bool @ ( B @ insert_pname ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_471_Collect__conv__if) ).
thf(4281,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ hAPP_pname_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_pname @ cOMBC_1149511130e_bool @ hAPP_p61793385e_bool ) @ ( fconj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname )
= bot_bo844097828e_bool ) )
& ( ( B @ ( A @ hAPP_pname_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_pname @ cOMBC_1149511130e_bool @ hAPP_p61793385e_bool ) @ ( fconj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname )
= ( bot_bo844097828e_bool @ ( B @ insert_pname ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).
thf(786,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/sandbox/benchmark/theBenchmark.p',fact_4_finite__Collect__subsets) ).
thf(3875,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)],[786]) ).
thf(444,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/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_024) ).
thf(2417,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)],[444]) ).
thf(352,axiom,
bot_bo1649642514l_bool @ is_fun1661590463l_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Orderings_Obot__class_Obot_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__) ).
thf(2091,plain,
bot_bo1649642514l_bool @ is_fun1661590463l_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(516,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/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Oboo) ).
thf(2714,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)],[516]) ).
thf(830,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/sandbox/benchmark/theBenchmark.p',fact_73_finite__Collect__conjI) ).
thf(4034,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)],[830]) ).
thf(536,axiom,
! [A: $i] :
( ( u @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ body @ the_com @ wt @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_567_assms_I4_J) ).
thf(2795,plain,
! [A: $i] :
( ( u @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ body @ the_com @ wt @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(418,axiom,
! [A: $i,B: $i] : ( B @ ( A @ image_nat_fun_a_bool ) @ is_fun949378684l_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
thf(2340,plain,
! [A: $i,B: $i] : ( B @ ( A @ image_nat_fun_a_bool ) @ is_fun949378684l_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(534,axiom,
! [A: $i,B: $i] :
( ( A = B )
=> ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_equalityD1) ).
thf(2783,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)],[534]) ).
thf(793,axiom,
! [A: $i,B: $i] :
( ( A != B )
=> ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_647_linorder__neqE__nat) ).
thf(3897,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).
thf(382,axiom,
! [A: $i] :
( ( A @ is_fun_pname_bool )
=> ( ( A @ collect_pname )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_Collect__def) ).
thf(2201,plain,
! [A: $i] :
( ( A @ is_fun_pname_bool )
=> ( ( A @ collect_pname )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(316,axiom,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_nat_a ) @ is_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000t__a) ).
thf(1989,plain,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_nat_a ) @ is_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(835,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 )
=> ? [C: $i] :
( ~ ( C @ ( A @ hAPP_a_nat ) @ ( A @ ( fequal_nat @ cOMBB_1321347587bool_a ) @ cOMBC_a_nat_bool @ hAPP_nat_fun_a_bool ) @ ( B @ ( member_a @ cOMBC_1355376034l_bool @ hAPP_f2050579477a_bool ) @ ( fconj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( C @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( C @ is_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_pigeonhole__infinite) ).
thf(4051,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 )
=> ? [C: $i] :
( ~ ( C @ ( A @ hAPP_a_nat ) @ ( A @ ( fequal_nat @ cOMBB_1321347587bool_a ) @ cOMBC_a_nat_bool @ hAPP_nat_fun_a_bool ) @ ( B @ ( member_a @ cOMBC_1355376034l_bool @ hAPP_f2050579477a_bool ) @ ( fconj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( C @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( C @ is_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).
thf(234,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ? [C: $i] :
( B
= ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_586_le__iff__add) ).
thf(1693,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( B
= ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) ) )
=> ( 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 )
=> ? [C: $i] :
( B
= ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(482,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/sandbox/benchmark/theBenchmark.p',fact_26_finite_OinsertI) ).
thf(2572,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)],[482]) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun_pname_bool )
=> ( B @ ( A @ image_112932426a_bool ) @ is_fun949378684l_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__Com__Opname_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
thf(1033,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)],[43]) ).
thf(576,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/sandbox/benchmark/theBenchmark.p',fact_30_card__image__le) ).
thf(2961,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)],[576]) ).
thf(238,axiom,
! [A: $i,B: $i] :
( ( B @ is_bool )
=> ( B @ ( A @ hAPP_bool_bool ) @ is_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool) ).
thf(1710,plain,
! [A: $i,B: $i] :
( ( B @ is_bool )
=> ( B @ ( A @ hAPP_bool_bool ) @ is_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(867,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/sandbox/benchmark/theBenchmark.p',fact_13_finite__imageI) ).
thf(4193,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)],[867]) ).
thf(686,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal533582459e_bool @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ ( fconj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool )
= bot_bo1649642514l_bool ) )
& ( ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal533582459e_bool @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ ( fconj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool )
= ( bot_bo1649642514l_bool @ ( B @ insert1325755072e_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_474_Collect__conv__if) ).
thf(3424,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal533582459e_bool @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ ( fconj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool )
= bot_bo1649642514l_bool ) )
& ( ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal533582459e_bool @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ ( fconj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool )
= ( bot_bo1649642514l_bool @ ( B @ insert1325755072e_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(702,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/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__fun_It__a_Mtc__HOL__Obool_J_T) ).
thf(3506,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)],[702]) ).
thf(781,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_112932426a_bool ) @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ? [C: $i] :
( ~ ( C @ ( A @ hAPP_p1534023578a_bool ) @ ( A @ ( fequal_fun_a_bool @ cOMBB_392435466_pname ) @ cOMBC_445755039l_bool @ hAPP_f1794073134e_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/sandbox/benchmark/theBenchmark.p',fact_205_pigeonhole__infinite) ).
thf(3843,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_112932426a_bool ) @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ? [C: $i] :
( ~ ( C @ ( A @ hAPP_p1534023578a_bool ) @ ( A @ ( fequal_fun_a_bool @ cOMBB_392435466_pname ) @ cOMBC_445755039l_bool @ hAPP_f1794073134e_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)],[781]) ).
thf(136,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_141086128t_bool ) @ hAPP_f654413245e_bool ) )
= ( C @ ( B @ hAPP_f1291551745_pname ) @ ( A @ hAPP_p61793385e_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_015) ).
thf(1346,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_141086128t_bool ) @ hAPP_f654413245e_bool ) )
= ( C @ ( B @ hAPP_f1291551745_pname ) @ ( A @ hAPP_p61793385e_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(342,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) )
= ( C @ ( B @ minus_minus_nat @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_582_diff__cancel) ).
thf(2063,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) )
= ( C @ ( B @ minus_minus_nat @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(899,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/sandbox/benchmark/theBenchmark.p',fact_113_rev__finite__subset) ).
thf(4318,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)],[899]) ).
thf(243,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/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__021) ).
thf(1742,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)],[243]) ).
thf(652,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_876012084bool_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/sandbox/benchmark/theBenchmark.p',fact_133_finite__surj) ).
thf(3244,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_876012084bool_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)],[652]) ).
thf(360,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_1283814551_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_finite__surj) ).
thf(2127,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_1283814551_pname ) @ ( 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)],[360]) ).
thf(370,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_2117322052ol_nat ) @ hAPP_n850744903l_bool ) )
= ( C @ ( B @ hAPP_n1025906991e_bool ) @ ( A @ hAPP_f434788991l_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_023) ).
thf(2159,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_2117322052ol_nat ) @ hAPP_n850744903l_bool ) )
= ( C @ ( B @ hAPP_n1025906991e_bool ) @ ( A @ hAPP_f434788991l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(621,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( C @ ( D @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( D @ ( A @ hAPP_nat_a ) @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
=> ( B @ ( C @ ( A @ image_nat_a ) @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_365_image__subsetI) ).
thf(3128,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( C @ ( D @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( D @ ( A @ hAPP_nat_a ) @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
=> ( B @ ( C @ ( A @ image_nat_a ) @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(270,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_nat ) ) )
=> ( D @ ( B @ image_pname_nat ) @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_308_rev__image__eqI) ).
thf(1827,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_nat ) ) )
=> ( D @ ( B @ image_pname_nat ) @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(457,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/sandbox/benchmark/theBenchmark.p',fact_79_finite__Collect__le__nat) ).
thf(2467,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)],[457]) ).
thf(199,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_1551609309ol_nat ) @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ image_1551609309ol_nat ) ) )
& ( D @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
& ( D @ is_fun1661590463l_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_finite__subset__image) ).
thf(1550,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_1551609309ol_nat ) @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ image_1551609309ol_nat ) ) )
& ( D @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
& ( D @ is_fun1661590463l_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(486,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/sandbox/benchmark/theBenchmark.p',fact_242_insert__Collect) ).
thf(2583,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)],[486]) ).
thf(880,axiom,
! [A: $i] :
( ( A @ ( bot_bot_fun_nat_bool @ hAPP_nat_bool ) @ hBOOL )
<=> ( bot_bot_bool @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_429_bot__apply) ).
thf(4239,plain,
! [A: $i] :
( ( ( bot_bot_bool @ hBOOL )
=> ( A @ ( bot_bot_fun_nat_bool @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( A @ ( bot_bot_fun_nat_bool @ hAPP_nat_bool ) @ hBOOL )
=> ( bot_bot_bool @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).
thf(902,axiom,
! [A: $i] : ( A @ ( bot_bot_fun_a_bool @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_444_bot__least) ).
thf(4330,plain,
! [A: $i] : ( A @ ( bot_bot_fun_a_bool @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).
thf(618,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_502_xt1_I6_J) ).
thf(3113,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(364,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/sandbox/benchmark/theBenchmark.p',fact_284_set__mp) ).
thf(2138,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)],[364]) ).
thf(64,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ ( B @ plus_plus_nat @ hAPP_nat_nat ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_666_add__diff__inverse) ).
thf(1093,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ ( B @ plus_plus_nat @ hAPP_nat_nat ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(423,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_a_fun_a_bool_a ) @ hAPP_a_fun_a_bool ) )
= ( C @ ( B @ hAPP_a_a ) @ ( A @ hAPP_a_fun_a_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000t__a_U) ).
thf(2353,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_a_fun_a_bool_a ) @ hAPP_a_fun_a_bool ) )
= ( C @ ( B @ hAPP_a_a ) @ ( A @ hAPP_a_fun_a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(448,axiom,
! [A: $i,B: $i] :
( ( ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) )
= ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) ) )
<=> ( ( ( B
= ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) )
& ( A = zero_zero_nat ) )
| ( ( B = zero_zero_nat )
& ( A
= ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_682_one__is__add) ).
thf(2430,plain,
! [A: $i,B: $i] :
( ( ( ( ( B
= ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) )
& ( A = zero_zero_nat ) )
| ( ( B = zero_zero_nat )
& ( A
= ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) ) ) )
=> ( ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) )
= ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) ) ) )
& ( ( ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) )
= ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) ) )
=> ( ( ( B
= ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) )
& ( A = zero_zero_nat ) )
| ( ( B = zero_zero_nat )
& ( A
= ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(710,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/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_It__a_Mtc__HO) ).
thf(3543,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)],[710]) ).
thf(752,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_1854862208_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ? [C: $i] :
( ~ ( C @ ( A @ hAPP_f1128469712_pname ) @ ( A @ ( fequal_pname @ cOMBB_1693087065a_bool ) @ cOMBC_1738168533e_bool @ hAPP_p1824510254l_bool ) @ ( B @ ( member_fun_a_bool @ cOMBC_1880041174l_bool @ hAPP_f2117159681l_bool ) @ ( fconj @ cOMBB_338059395a_bool ) @ cOMBS_1035972772l_bool ) @ collect_fun_a_bool @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
& ( B @ ( C @ ( member_fun_a_bool @ hAPP_f285962445l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
& ( C @ is_fun_a_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_pigeonhole__infinite) ).
thf(3701,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_1854862208_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ? [C: $i] :
( ~ ( C @ ( A @ hAPP_f1128469712_pname ) @ ( A @ ( fequal_pname @ cOMBB_1693087065a_bool ) @ cOMBC_1738168533e_bool @ hAPP_p1824510254l_bool ) @ ( B @ ( member_fun_a_bool @ cOMBC_1880041174l_bool @ hAPP_f2117159681l_bool ) @ ( fconj @ cOMBB_338059395a_bool ) @ cOMBS_1035972772l_bool ) @ collect_fun_a_bool @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
& ( B @ ( C @ ( member_fun_a_bool @ hAPP_f285962445l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
& ( C @ is_fun_a_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).
thf(718,axiom,
! [A: $i] :
~ ( bot_bo844097828e_bool @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_405_empty__iff) ).
thf(3570,plain,
! [A: $i] :
~ ( bot_bo844097828e_bool @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).
thf(146,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_617_add__lessD1) ).
thf(1384,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(682,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_a_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_finite__surj) ).
thf(3411,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_a_pname ) @ ( 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)],[682]) ).
thf(463,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/sandbox/benchmark/theBenchmark.p',fact_330_subset__insertI2) ).
thf(2485,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)],[463]) ).
thf(400,axiom,
( bot_bot_fun_nat_bool
= ( fFalse @ cOMBK_bool_nat @ collect_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_424_empty__def) ).
thf(2265,plain,
( bot_bot_fun_nat_bool
= ( fFalse @ cOMBK_bool_nat @ collect_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(39,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/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_) ).
thf(1019,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)],[39]) ).
thf(811,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 )
=> ? [C: $i] :
( ~ ( C @ ( A @ hAPP_a_pname ) @ ( A @ ( fequal_pname @ cOMBB_610033911bool_a ) @ cOMBC_a_pname_bool @ hAPP_p1534023578a_bool ) @ ( B @ ( member_a @ cOMBC_1355376034l_bool @ hAPP_f2050579477a_bool ) @ ( fconj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( C @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( C @ is_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_pigeonhole__infinite) ).
thf(3965,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 )
=> ? [C: $i] :
( ~ ( C @ ( A @ hAPP_a_pname ) @ ( A @ ( fequal_pname @ cOMBB_610033911bool_a ) @ cOMBC_a_pname_bool @ hAPP_p1534023578a_bool ) @ ( B @ ( member_a @ cOMBC_1355376034l_bool @ hAPP_f2050579477a_bool ) @ ( fconj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( C @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( C @ is_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).
thf(298,axiom,
! [A: $i,B: $i] :
( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_634_Suc__less__eq) ).
thf(1923,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(593,axiom,
! [A: $i] :
( ! [B: $i] :
~ ( A @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
<=> ( A = bot_bot_fun_nat_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_416_all__not__in__conv) ).
thf(3020,plain,
! [A: $i] :
( ( ( A = bot_bot_fun_nat_bool )
=> ! [B: $i] :
~ ( A @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
& ( ! [B: $i] :
~ ( A @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A = bot_bot_fun_nat_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(211,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( C @ minus_minus_nat @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( C @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_600_le__diff__conv2) ).
thf(1597,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( C @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( C @ minus_minus_nat @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( B @ ( C @ minus_minus_nat @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(553,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 )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_541_order__antisym__conv) ).
thf(2864,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( ( B = A )
=> ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
& ( ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(152,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_589_trans__le__add2) ).
thf(1399,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(888,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/sandbox/benchmark/theBenchmark.p',fact_101_finite__insert) ).
thf(4271,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)],[888]) ).
thf(217,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/sandbox/benchmark/theBenchmark.p',fact_281_set__rev__mp) ).
thf(1621,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)],[217]) ).
thf(591,axiom,
! [A: $i,B: $i] :
( ( B = bot_bot_fun_a_bool )
=> ~ ( B @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_397_equals0D) ).
thf(3013,plain,
! [A: $i,B: $i] :
( ( B = bot_bot_fun_a_bool )
=> ~ ( B @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(904,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/sandbox/benchmark/theBenchmark.p',fact_32_card__image__le) ).
thf(4335,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)],[904]) ).
thf(309,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_1250273980t_bool ) @ hAPP_f800510211t_bool ) )
= ( C @ ( B @ hAPP_f22106695ol_nat ) @ ( A @ hAPP_n1699378549t_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__012) ).
thf(1962,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_1250273980t_bool ) @ hAPP_f800510211t_bool ) )
= ( C @ ( B @ hAPP_f22106695ol_nat ) @ ( A @ hAPP_n1699378549t_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(384,axiom,
! [A: $i] : ( A @ ( suc @ hAPP_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_680_zero__less__Suc) ).
thf(2206,plain,
! [A: $i] : ( A @ ( suc @ hAPP_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(174,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_593_add__leD1) ).
thf(1463,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(687,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/sandbox/benchmark/theBenchmark.p',fact_108_finite__subset) ).
thf(3432,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)],[687]) ).
thf(252,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/sandbox/benchmark/theBenchmark.p',fact_233_insert__compr) ).
thf(1769,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)],[252]) ).
thf(836,axiom,
! [A: $i] :
( ( A @ ( bot_bot_fun_a_bool @ hAPP_a_bool ) @ hBOOL )
<=> ( bot_bot_bool @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_427_bot__fun__def) ).
thf(4056,plain,
! [A: $i] :
( ( ( bot_bot_bool @ hBOOL )
=> ( A @ ( bot_bot_fun_a_bool @ hAPP_a_bool ) @ hBOOL ) )
& ( ( A @ ( bot_bot_fun_a_bool @ hAPP_a_bool ) @ hBOOL )
=> ( bot_bot_bool @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).
thf(355,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( bot_bo844097828e_bool @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ! [D: $i,E: $i] :
( ( ( E @ is_fun_pname_bool )
& ( D @ is_pname ) )
=> ( ( E @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ~ ( E @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( E @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( E @ ( D @ insert_pname ) @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ) ) )
=> ( C @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_557_finite__subset__induct) ).
thf(2106,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( bot_bo844097828e_bool @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ! [D: $i,E: $i] :
( ( ( E @ is_fun_pname_bool )
& ( D @ is_pname ) )
=> ( ( E @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ~ ( E @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( E @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( E @ ( D @ insert_pname ) @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ) ) )
=> ( C @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(56,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_fun_a_bool_nat ) @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ image_fun_a_bool_nat ) ) )
& ( D @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
& ( D @ is_fun949378684l_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_finite__subset__image) ).
thf(1069,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_fun_a_bool_nat ) @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ image_fun_a_bool_nat ) ) )
& ( D @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
& ( D @ is_fun949378684l_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(596,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/sandbox/benchmark/theBenchmark.p',fact_555_linorder__linear) ).
thf(3035,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)],[596]) ).
thf(820,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/sandbox/benchmark/theBenchmark.p',fact_28_finite_OinsertI) ).
thf(4002,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)],[820]) ).
thf(284,axiom,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_nat_fun_a_bool ) @ is_fun_a_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
thf(1870,plain,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_nat_fun_a_bool ) @ is_fun_a_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(721,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( fequal533582459e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
| ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T) ).
thf(3580,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)],[721]) ).
thf(692,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/sandbox/benchmark/theBenchmark.p',fact_280_in__mono) ).
thf(3461,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)],[692]) ).
thf(799,axiom,
! [A: $i] : ( A @ ( bot_bot_fun_a_bool @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_394_empty__subsetI) ).
thf(3924,plain,
! [A: $i] : ( A @ ( bot_bot_fun_a_bool @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).
thf(556,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_a_nat ) @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_finite__surj) ).
thf(2881,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_a_nat ) @ ( 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)],[556]) ).
thf(303,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_658_less__eq__Suc__le) ).
thf(1945,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_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(645,axiom,
! [A: $i] :
( ( bot_bot_fun_nat_bool
= ( A @ collect_nat ) )
<=> ! [B: $i] :
~ ( B @ ( A @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_412_empty__Collect__eq) ).
thf(3212,plain,
! [A: $i] :
( ( ! [B: $i] :
~ ( B @ ( A @ hAPP_nat_bool ) @ hBOOL )
=> ( bot_bot_fun_nat_bool
= ( A @ collect_nat ) ) )
& ( ( bot_bot_fun_nat_bool
= ( A @ collect_nat ) )
=> ! [B: $i] :
~ ( B @ ( A @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(34,axiom,
bot_bot_nat = zero_zero_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_697_bot__nat__def) ).
thf(1009,plain,
bot_bot_nat = zero_zero_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(231,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ is_fun949378684l_bool )
=> ( ( C @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_112932426a_bool ) @ ( C @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ image_112932426a_bool ) ) )
& ( 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/sandbox/benchmark/theBenchmark.p',fact_172_finite__subset__image) ).
thf(1681,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ is_fun949378684l_bool )
=> ( ( C @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_112932426a_bool ) @ ( C @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ image_112932426a_bool ) ) )
& ( 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)],[231]) ).
thf(88,axiom,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f54304608l_bool ) @ is_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obool) ).
thf(1184,plain,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f54304608l_bool ) @ is_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(326,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_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( A @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_669_less__diff__iff) ).
thf(2018,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_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_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_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(861,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/sandbox/benchmark/theBenchmark.p',fact_33_card__image__le) ).
thf(4161,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)],[861]) ).
thf(545,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/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000tc_) ).
thf(2832,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)],[545]) ).
thf(395,axiom,
bot_bo844097828e_bool @ is_fun_pname_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Orderings_Obot__class_Obot_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).
thf(2238,plain,
bot_bo844097828e_bool @ is_fun_pname_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(184,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i,E: $i] :
( ( E @ ( D @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( E @ ( C @ hAPP_nat_nat ) @ ( D @ ( C @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( C @ hAPP_nat_nat ) @ ( B @ ( A @ ( C @ hAPP_nat_nat ) @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_671_mono__nat__linear__lb) ).
thf(1490,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i,E: $i] :
( ( E @ ( D @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( E @ ( C @ hAPP_nat_nat ) @ ( D @ ( C @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( C @ hAPP_nat_nat ) @ ( B @ ( A @ ( C @ hAPP_nat_nat ) @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(422,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( C @ plus_plus_nat @ hAPP_nat_nat ) @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_588_trans__le__add1) ).
thf(2351,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( C @ plus_plus_nat @ hAPP_nat_nat ) @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(62,axiom,
( one_one_nat
= ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_686_One__nat__def) ).
thf(1088,plain,
( one_one_nat
= ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(585,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/sandbox/benchmark/theBenchmark.p',fact_296_subset__trans) ).
thf(2993,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)],[585]) ).
thf(93,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/sandbox/benchmark/theBenchmark.p',fact_314_insert__compr__raw) ).
thf(1204,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)],[93]) ).
thf(266,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/sandbox/benchmark/theBenchmark.p',fact_42_card__mono) ).
thf(1812,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)],[266]) ).
thf(4553,plain,
$false,
inference(e,[status(thm)],[2452,1879,1411,1024,2889,2778,4062,4169,3798,3434,2463,1840,1083,4015,2331,3172,2199,1665,2822,3873,4188,1168,3345,3053,4101,3008,2131,1454,3666,1729,1315,2787,977,1211,2976,4339,1882,2527,1401,3098,1793,1305,1437,3072,1005,2210,2940,1596,1522,3762,1422,3959,2671,2014,2837,1142,3498,2380,1173,1486,3049,2607,1756,3044,2184,1275,1327,2459,3313,3848,1497,1705,3017,1078,1426,3004,3367,1872,2712,3616,1233,4247,3562,2580,3895,2360,3370,1835,3513,973,3308,1265,2405,2348,1001,2227,1391,1576,1601,1386,4030,1475,3809,1366,4322,2819,4156,1803,1623,1254,3689,3495,4224,3821,3612,2274,3776,4023,2897,3820,2654,1628,1055,3204,2603,2328,2916,1430,3644,1660,1298,4070,2667,1860,2217,949,2745,2356,1800,4358,4179,1013,1494,1100,1847,1545,2420,3517,3998,1892,3463,969,2373,1572,4141,2730,3602,3557,1875,1778,2852,3231,1465,3524,3887,3934,4072,3393,3724,4001,2650,1418,1136,1858,1151,2034,1960,1283,1051,2178,2222,4205,1415,4297,2469,3986,2367,2618,2483,1526,1405,1201,4211,2718,2586,2508,981,4230,1377,2861,1215,2190,3421,2523,1796,1119,2371,2979,3361,3955,2809,988,2286,4038,2392,3906,3510,4065,1863,2954,2204,1153,2118,2047,2737,2641,3550,3418,2011,3097,2574,3720,3984,925,3531,3635,2364,2164,2083,1067,4312,2660,2905,3037,1057,1163,952,2596,1123,1751,3134,1883,2601,2428,1343,2805,1217,2147,3752,4128,3816,1619,2032,2986,2396,3682,4021,1238,3889,2758,1920,2826,1178,1951,3546,1787,1027,2547,3727,1634,3931,916,4295,1837,3618,3403,3198,3297,3137,1296,3877,1210,1656,3028,2345,3926,1291,4080,3445,4027,4316,3731,1360,1983,2377,2895,1064,1587,2694,3916,3105,3699,2498,3909,1541,2157,2115,2100,3413,1772,2946,1017,1953,2685,1970,1227,4048,1856,1096,3102,4233,3632,4095,2638,4109,1397,4263,4320,4301,1942,2323,933,3714,2080,1842,1584,3032,2172,2472,3573,4049,1329,1160,3141,3407,2561,3210,4167,1461,2312,3010,2551,1207,1889,1644,3242,1324,1451,3787,2487,1831,3770,2243,3937,3115,3333,4259,3920,2140,1478,2519,2536,3541,2465,1060,4237,3390,3222,2006,3409,2862,3692,2052,3109,1979,3162,3201,1759,1393,4163,1333,2926,1814,2208,2883,1563,1170,2402,3639,2529,1732,3807,4148,2634,2749,1434,1991,3834,2761,4195,2043,3587,2057,1712,3592,2963,1286,1035,2408,3190,2645,2995,4004,1996,3675,1906,2936,3660,965,4131,2176,1103,2717,3491,3262,3289,3792,3111,3696,1374,3396,2121,2235,2144,1251,2413,3079,1747,3738,2028,2734,3158,2260,4144,975,1833,3070,1916,2859,1784,2016,1388,3900,1403,3604,1965,1520,1488,2134,2970,1007,3319,2225,3504,3081,1929,1701,3590,1428,1503,936,2220,1707,1312,3340,3123,2055,2706,1090,3568,3651,4099,3330,3208,4218,2457,919,3641,2474,947,4245,1224,979,1194,2079,3352,4369,3764,3957,1349,3500,3160,4337,2679,4228,3996,1853,1408,3238,2214,2383,2422,4305,1806,1011,996,1933,3066,1690,3182,2871,1439,3456,4203,2182,2267,4264,4277,915,1293,2461,1820,1688,2025,2632,2605,2610,1557,4009,2129,3668,4332,3192,2923,3614,2289,2647,1022,2664,2725,1528,2086,3687,1176,1775,2022,3706,2967,3178,922,2069,2770,2075,2212,959,1213,2835,2550,1245,2481,4085,4362,1015,3953,1113,2797,2984,1973,2506,3380,4084,1626,4207,2239,2816,1809,1662,1166,3576,1467,1509,939,1472,2564,4355,2899,1181,1049,1413,1076,3881,1873,4013,2318,3206,1277,2124,1081,2629,3278,1958,3988,1547,1798,1003,3315,2060,2192,971,1566,1368,1531,1098,993,2375,1156,1605,3754,1753,1267,3058,2386,1230,1484,3246,4314,4346,2092,3722,1038,4222,3475,1763,1901,3564,1579,2656,2747,1053,1790,3940,2454,3305,1432,3885,1300,1637,1188,1186,3655,1235,2276,3801,1085,1658,951,2903,1738,3041,1358,2948,1257,1981,2843,2320,3388,2722,3961,4150,4257,4111,2411,2500,1543,1766,2558,3970,4046,3224,978,2511,4267,2030,1372,3256,2892,2807,3156,991,1617,2760,4289,4138,2088,1817,1321,1654,1517,1126,2342,2071,2907,2875,3168,1940,3584,3139,2045,3092,3533,3447,2310,1844,3188,3548,2325,3928,2997,1448,4006,1289,3056,2643,3729,961,1341,1903,1062,1481,3220,2004,1745,2764,2262,3465,1590,2174,2283,2389,4089,2554,3748,3630,2009,3978,3694,2041,3267,3149,1607,2315,4372,1994,1045,2447,2944,2576,2066,2362,2162,2294,1309,2739,1442,2142,999,1280,3860,4356,3264,3100,2951,1303,3496,3062,3658,4125,1957,4114,2983,3865,1593,3837,3790,1148,1673,3132,1248,2050,2636,4146,1363,4350,2334,4281,3875,2417,2091,2714,4034,2795,2340,2783,3897,2201,1989,4051,1693,2572,1033,2961,1710,4193,3424,3506,3843,1346,2063,4318,1742,3244,2127,2159,3128,1827,2467,1550,2583,4239,4330,3113,2138,1093,2353,2430,3543,3701,3570,1384,3411,2485,2265,1019,3965,1923,3020,1597,2864,1399,4271,1621,3013,4335,1962,2206,1463,3432,1769,4056,2106,1069,3035,4002,1870,3580,3461,3924,2881,1945,3212,1009,1681,1184,2018,4161,2832,2238,1490,2351,1088,2993,1204,1812]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWW473+2 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.04 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.05/0.32 % Computer : n012.cluster.edu
% 0.05/0.32 % Model : x86_64 x86_64
% 0.05/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.32 % Memory : 8046.5625MB
% 0.05/0.32 % OS : Linux 6.8.0-71-generic
% 0.05/0.32 % CPULimit : 300
% 0.05/0.32 % WCLimit : 300
% 0.05/0.32 % DateTime : Sat Sep 26 16:00:50 UTC 2026
% 0.05/0.32 % CPUTime :
% 0.05/0.32 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.52/0.82 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.28/1.19 % [INFO] Parsing done (364ms).
% 1.43/1.20 % [INFO] Running in sequential loop mode.
% 1.96/1.53 % [INFO] eprover registered as external prover.
% 1.96/1.55 % [INFO] Scanning for conjecture ...
% 2.34/1.76 % [INFO] Found a conjecture (or negated_conjecture) and 916 axioms. Running axiom selection ...
% 3.61/2.20 % [INFO] Axiom selection finished. Selected 912 axioms (removed 4 axioms).
% 4.51/2.67 % [INFO] Problem is first-order (TPTP FOF).
% 4.78/2.71 % [INFO] Type checking passed.
% 4.78/2.71 % [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 ...
% 17.95/6.94 % External prover 'e' found a proof!
% 17.95/6.94 % [INFO] Killing All external provers ...
% 17.95/6.94 % Time passed: 6455ms (effective reasoning time: 5729ms)
% 17.95/6.94 % 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)>
% 17.95/6.94 % Axioms used in derivation (912): fact_628_less__SucE, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_It__a_Mtc__H, fact_539_ord__eq__le__trans, fact_461_empty__not__insert, fact_508_xt1_I5_J, fact_513_order__trans, fact_658_less__eq__Suc__le, fact_155_finite__subset__image, fact_183_lift__Suc__mono__le, fact_359_subsetI, fact_348_image__mono, fact_310_rev__image__eqI, fact_692_Zero__neq__Suc, fact_166_finite__subset__image, fact_180_finite__subset__image, fact_437_bot__unique, help_fimplies_2_1_U, fact_241_insert__Collect, fact_555_linorder__linear, fact_31_card__image__le, fact_208_pigeonhole__infinite, fact_43_card__mono, fact_644_termination__basic__simps_I5_J, fact_171_finite__subset__image, fact_51_card__seteq, fact_598_le__imp__diff__is__add, fact_47_card__mono, fact_411_empty__Collect__eq, fact_139_finite__surj, fact_245_insert__absorb2, gsy_c_Set_Oimage_000tc__Com__Opname_000tc__Com__Opname, fact_440_bot__unique, gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obool, fact_248_insert__commute, fact_127_diff__diff__cancel, fact_618_less__add__eq__less, fact_678_less__zeroE, gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool, fact_185_lift__Suc__mono__le, fact_260_insertI2, 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_639_less__imp__le__nat, fact_371_order__refl, fact_651_nat__less__cases, fact_179_finite__subset__image, fact_219_subsetD, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_010, fact_614_finite__Collect__less__nat, gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_Itc__Com__Op, fact_684_diff__is__0__eq_H, help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It, fact_562_assms_I2_J, gsy_c_COMBK_000tc__HOL__Obool_000tc__Com__Opname, fact_164_finite__subset__image, fact_67_card__insert__disjoint, fact_512_order__trans, fact_178_finite__subset__image, gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__, gsy_c_Orderings_Obot__class_Obot_000tc__fun_It__a_Mtc__HOL__Obool_J, fact_636_not__less__eq, fact_505_xt1_I5_J, fact_11_finite__imageI, fact_529_ord__le__eq__trans, fact_213_image__eqI, fact_655_less__add__Suc1, fact_621_trans__less__add2, fact_190_pigeonhole__infinite, fact_501_xt1_I6_J, fact_672_inc__induct, 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, fact_604_le__diff__conv, fact_33_card__image__le, fact_302_image__iff, fact_265_insert__absorb, help_fconj_3_1_U, fact_306_imageI, fact_282_set__rev__mp, fact_275_equalityD2, fact_277_equalityD2, fact_393_empty__subsetI, fact_15_finite__imageI, help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Nat__Ona, gsy_c_Set_Oimage_000tc__Com__Opname_000t__a, fact_603_le__add__diff, fact_122_Suc__diff__diff, fact_186_lift__Suc__mono__le, fact_676_Suc__lessE, fact_677_lessE, gsy_c_Set_Oimage_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_, fact_390_finite_OemptyI, fact_686_One__nat__def, fact_345_subset__image__iff, fact_346_subset__image__iff, fact_469_empty__is__image, fact_654_finite__M__bounded__by__nat, gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obo, gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opname, fact_199_pigeonhole__infinite, help_fequal_1_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T, fact_667_less__diff__conv, fact_665_diff__less__Suc, fact_376_le__fun__def, help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__, fact_563_finite__induct, gsy_c_Set_Oimage_000t__a_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J, fact_420_empty__def, fact_136_finite__surj, fact_540_order__antisym__conv, fact_458_insert__not__empty, fact_372_finite__nat__set__iff__bounded__le, help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Nat__Onat_U, fact_659_less__Suc__eq__le, gsy_c_Set_Oinsert_000tc__Com__Opname, fact_374_le__fun__def, fact_299_equalityE, gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_, gsy_c_hAPP_000tc__Com__Opname_000tc__HOL__Obool, help_fequal_2_1_fequal_000tc__Nat__Onat_T, fact_192_pigeonhole__infinite, fact_652_finite__nat__set__iff__bounded, fact_444_bot__least, fact_109_rev__finite__subset, fact_698_le__0__eq, help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__012, fact_626_Suc__less__SucD, fact_338_insert__image, help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_It__a_Mtc__HOL__Obool_J_U, fact_367_order__refl, gsy_v_mgt, fact_214_image__eqI, fact_401_Collect__empty__eq, fact_419_empty__def, conj_3, fact_313_insert__compr__raw, fact_177_finite__subset__image, help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It___019, fact_159_finite__subset__image, fact_66_card__insert__disjoint, fact_450_singletonE, fact_126_eq__diff__iff, fact_638_le__neq__implies__less, fact_605_diff__diff__right, fact_206_pigeonhole__infinite, fact_163_finite__subset__image, fact_296_subset__trans, fact_511_order__trans, fact_9_finite__imageI, fact_541_order__antisym__conv, help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__022, fact_110_rev__finite__subset, fact_616_termination__basic__simps_I2_J, fact_506_xt1_I5_J, fact_360_image__subsetI, fact_499_linorder__le__cases, fact_187_pigeonhole__infinite, fact_582_diff__cancel, fact_418_all__not__in__conv, fact_223_insertCI, help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Com__Opname_000tc__HOL__Obool_U, help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__005, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_007, fact_464_subset__empty, fact_252_insert__iff, gsy_c_Set_Oimage_000t__a_000t__a, fact_78_Suc__diff__le, fact_93_finite__Collect__disjI, gsy_c_Set_Oimage_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000t__a, gsy_c_Finite__Set_Ofinite_000t__a, fact_39_card__image__le, help_fequal_2_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T, fact_311_rev__image__eqI, fact_522_xt1_I4_J, fact_578_nat__add__commute, gsy_c_Set_Oimage_000tc__Nat__Onat_000t__a, fact_246_insert__absorb2, fact_395_equals0D, fact_365_image__subsetI, fact_304_imageI, fact_61_card__insert__if, fact_398_Collect__empty__eq, fact_484_singleton__conv, fact_354_imageE, fact_388_finite_OemptyI, fact_240_insert__Collect, fact_97_finite__insert, fact_125_Nat_Odiff__diff__eq, fact_24_finite_OinsertI, fact_251_insert__iff, fact_120_not__less__eq__eq, fact_321_subset__insertI, fact_34_card__image__le, fact_216_equalityI, fact_226_insertE, fact_485_singleton__conv, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_004, fact_378_le__funD, fact_162_finite__subset__image, fact_477_Collect__conv__if2, fact_209_pigeonhole__infinite, fact_64_card__insert__if, fact_389_finite_OemptyI, fact_493_singleton__conv2, fact_95_finite__Collect__disjI, fact_280_in__mono, fact_381_le__funE, gsy_c_Set_Oimage_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__Opnam, gsy_c_Orderings_Obot__class_Obot_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc, fact_642_diff__less__mono2, fact_674_bounded__nat__set__is__finite, fact_96_finite__Collect__disjI, fact_689_minus__nat_Odiff__0, fact_687_diffs0__imp__equal, fact_188_pigeonhole__infinite, fact_623_nat__add__left__cancel__less, fact_645_less__not__refl, gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc, fact_594_add__leE, fact_611_termination__basic__simps_I4_J, fact_519_order__antisym, 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fact_32_card__image__le, gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__Com__Opname, help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__, gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname
% 17.95/6.95 % No. of inferences in proof: 1828
% 17.95/6.95 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 6455 ms resp. 5729 ms w/o parsing
% 19.52/7.29 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 19.52/7.30 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------