TSTP Solution File: SWW473+2 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWW473+2 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 12:24:06 EDT 2023
% Result : Theorem 22.45s 6.06s
% Output : Refutation 23.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 1192
% Syntax : Number of formulae : 2107 ( 530 unt; 279 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 : 372 ( 372 >; 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_type,type,
hBOOL: $i > $o ).
thf(hAPP_fun_a_bool_bool_type,type,
hAPP_fun_a_bool_bool: $i > $i > $i ).
thf(hAPP_f1631501043l_bool_type,type,
hAPP_f1631501043l_bool: $i > $i > $i ).
thf(ord_le1311769555a_bool_type,type,
ord_le1311769555a_bool: $i ).
thf(insert_a_type,type,
insert_a: $i > $i > $i ).
thf(hAPP_pname_a_type,type,
hAPP_pname_a: $i > $i > $i ).
thf(mgt_call_type,type,
mgt_call: $i ).
thf(pn_type,type,
pn: $i ).
thf(g_type,type,
g: $i ).
thf(image_pname_a_type,type,
image_pname_a: $i > $i > $i ).
thf(u_type,type,
u: $i ).
thf(hAPP_nat_nat_type,type,
hAPP_nat_nat: $i > $i > $i ).
thf(plus_plus_nat_type,type,
plus_plus_nat: $i > $i ).
thf(suc_type,type,
suc: $i ).
thf(one_one_nat_type,type,
one_one_nat: $i ).
thf(is_fun1661590463l_bool_type,type,
is_fun1661590463l_bool: $i > $o ).
thf(hAPP_n850744903l_bool_type,type,
hAPP_n850744903l_bool: $i > $i > $i ).
thf(is_fun_a_bool_type,type,
is_fun_a_bool: $i > $o ).
thf(is_a_type,type,
is_a: $i > $o ).
thf(is_bool_type,type,
is_bool: $i > $o ).
thf(hAPP_a_bool_type,type,
hAPP_a_bool: $i > $i > $i ).
thf(bot_bot_fun_a_bool_type,type,
bot_bot_fun_a_bool: $i ).
thf(hAPP_f1637334154l_bool_type,type,
hAPP_f1637334154l_bool: $i > $i > $i ).
thf(finite2012431853t_bool_type,type,
finite2012431853t_bool: $i ).
thf(hAPP_f1772781669l_bool_type,type,
hAPP_f1772781669l_bool: $i > $i > $i ).
thf(ord_le1454342156l_bool_type,type,
ord_le1454342156l_bool: $i ).
thf(image_2129980159t_bool_type,type,
image_2129980159t_bool: $i > $i > $i ).
thf(is_fun_pname_bool_type,type,
is_fun_pname_bool: $i > $o ).
thf(hAPP_f1664156314l_bool_type,type,
hAPP_f1664156314l_bool: $i > $i > $i ).
thf(hAPP_f434788991l_bool_type,type,
hAPP_f434788991l_bool: $i > $i > $i ).
thf(ord_le313189616e_bool_type,type,
ord_le313189616e_bool: $i ).
thf(finite_finite_pname_type,type,
finite_finite_pname: $i ).
thf(hAPP_nat_bool_type,type,
hAPP_nat_bool: $i > $i > $i ).
thf(hAPP_n1699378549t_bool_type,type,
hAPP_n1699378549t_bool: $i > $i > $i ).
thf(ord_less_nat_type,type,
ord_less_nat: $i ).
thf(cOMBK_bool_nat_type,type,
cOMBK_bool_nat: $i > $i ).
thf(hAPP_f54304608l_bool_type,type,
hAPP_f54304608l_bool: $i > $i > $i ).
thf(cOMBK_1994329625t_bool_type,type,
cOMBK_1994329625t_bool: $i > $i ).
thf(hAPP_p338031245l_bool_type,type,
hAPP_p338031245l_bool: $i > $i > $i ).
thf(member_pname_type,type,
member_pname: $i ).
thf(hAPP_n215258509l_bool_type,type,
hAPP_n215258509l_bool: $i > $i > $i ).
thf(member_nat_type,type,
member_nat: $i ).
thf(hAPP_pname_nat_type,type,
hAPP_pname_nat: $i > $i > $i ).
thf(image_pname_nat_type,type,
image_pname_nat: $i > $i > $i ).
thf(bot_bot_bool_type,type,
bot_bot_bool: $i ).
thf(cOMBS_350070575l_bool_type,type,
cOMBS_350070575l_bool: $i > $i > $i ).
thf(bot_bo844097828e_bool_type,type,
bot_bo844097828e_bool: $i ).
thf(insert_nat_type,type,
insert_nat: $i > $i > $i ).
thf(bot_bot_fun_nat_bool_type,type,
bot_bot_fun_nat_bool: $i ).
thf(image_47868345e_bool_type,type,
image_47868345e_bool: $i > $i > $i ).
thf(ord_less_eq_nat_type,type,
ord_less_eq_nat: $i ).
thf(insert_fun_nat_bool_type,type,
insert_fun_nat_bool: $i > $i > $i ).
thf(collect_fun_nat_bool_type,type,
collect_fun_nat_bool: $i > $i ).
thf(cOMBS_1187019125l_bool_type,type,
cOMBS_1187019125l_bool: $i > $i > $i ).
thf(cOMBB_444170502t_bool_type,type,
cOMBB_444170502t_bool: $i > $i > $i ).
thf(fdisj_type,type,
fdisj: $i ).
thf(hAPP_f103356543l_bool_type,type,
hAPP_f103356543l_bool: $i > $i > $i ).
thf(cOMBC_1693257480l_bool_type,type,
cOMBC_1693257480l_bool: $i > $i ).
thf(fequal_fun_nat_bool_type,type,
fequal_fun_nat_bool: $i ).
thf(hAPP_f1246832597l_bool_type,type,
hAPP_f1246832597l_bool: $i > $i > $i ).
thf(cOMBC_1245412066l_bool_type,type,
cOMBC_1245412066l_bool: $i > $i ).
thf(member_fun_nat_bool_type,type,
member_fun_nat_bool: $i ).
thf(wt_type,type,
wt: $i > $i ).
thf(is_fun949378684l_bool_type,type,
is_fun949378684l_bool: $i > $o ).
thf(cOMBB_2140588453a_bool_type,type,
cOMBB_2140588453a_bool: $i > $i > $i ).
thf(finite_finite_nat_type,type,
finite_finite_nat: $i ).
thf(collect_nat_type,type,
collect_nat: $i > $i ).
thf(cOMBS_nat_bool_bool_type,type,
cOMBS_nat_bool_bool: $i > $i > $i ).
thf(cOMBB_1015721476ol_nat_type,type,
cOMBB_1015721476ol_nat: $i > $i > $i ).
thf(fconj_type,type,
fconj: $i ).
thf(cOMBC_nat_nat_bool_type,type,
cOMBC_nat_nat_bool: $i > $i ).
thf(hAPP_f389811538l_bool_type,type,
hAPP_f389811538l_bool: $i > $i > $i ).
thf(hAPP_bool_bool_type,type,
hAPP_bool_bool: $i > $i > $i ).
thf(hAPP_b589554111l_bool_type,type,
hAPP_b589554111l_bool: $i > $i > $i ).
thf(ord_less_eq_bool_type,type,
ord_less_eq_bool: $i ).
thf(hAPP_pname_bool_type,type,
hAPP_pname_bool: $i > $i > $i ).
thf(bot_bot_nat_type,type,
bot_bot_nat: $i ).
thf(zero_zero_nat_type,type,
zero_zero_nat: $i ).
thf(collect_a_type,type,
collect_a: $i > $i ).
thf(cOMBK_bool_a_type,type,
cOMBK_bool_a: $i > $i ).
thf(fFalse_type,type,
fFalse: $i ).
thf(minus_minus_nat_type,type,
minus_minus_nat: $i > $i ).
thf(hAPP_f1935102916l_bool_type,type,
hAPP_f1935102916l_bool: $i > $i > $i ).
thf(hAPP_f510955609l_bool_type,type,
hAPP_f510955609l_bool: $i > $i > $i ).
thf(cOMBC_7971162l_bool_type,type,
cOMBC_7971162l_bool: $i > $i ).
thf(ord_le1568362934t_bool_type,type,
ord_le1568362934t_bool: $i ).
thf(is_pname_type,type,
is_pname: $i > $o ).
thf(image_nat_pname_type,type,
image_nat_pname: $i > $i > $i ).
thf(hAPP_nat_pname_type,type,
hAPP_nat_pname: $i > $i > $i ).
thf(image_112932426a_bool_type,type,
image_112932426a_bool: $i > $i > $i ).
thf(image_1283814551_pname_type,type,
image_1283814551_pname: $i > $i > $i ).
thf(ord_le675606854l_bool_type,type,
ord_le675606854l_bool: $i ).
thf(finite595471783e_bool_type,type,
finite595471783e_bool: $i ).
thf(hAPP_a_a_type,type,
hAPP_a_a: $i > $i > $i ).
thf(cOMBC_385542954t_bool_type,type,
cOMBC_385542954t_bool: $i > $i ).
thf(hAPP_f800510211t_bool_type,type,
hAPP_f800510211t_bool: $i > $i > $i ).
thf(cOMBB_647938656_pname_type,type,
cOMBB_647938656_pname: $i > $i > $i ).
thf(image_fun_a_bool_nat_type,type,
image_fun_a_bool_nat: $i > $i > $i ).
thf(hAPP_f621171935l_bool_type,type,
hAPP_f621171935l_bool: $i > $i > $i ).
thf(hAPP_f1434722111l_bool_type,type,
hAPP_f1434722111l_bool: $i > $i > $i ).
thf(ord_le1375614389l_bool_type,type,
ord_le1375614389l_bool: $i ).
thf(finite347923420a_bool_type,type,
finite347923420a_bool: $i ).
thf(image_1854862208_pname_type,type,
image_1854862208_pname: $i > $i > $i ).
thf(collect_fun_a_bool_type,type,
collect_fun_a_bool: $i > $i ).
thf(hAPP_p61793385e_bool_type,type,
hAPP_p61793385e_bool: $i > $i > $i ).
thf(insert_pname_type,type,
insert_pname: $i > $i > $i ).
thf(hAPP_f1748468828l_bool_type,type,
hAPP_f1748468828l_bool: $i > $i > $i ).
thf(hAPP_n1006566506l_bool_type,type,
hAPP_n1006566506l_bool: $i > $i > $i ).
thf(cOMBB_bool_bool_nat_type,type,
cOMBB_bool_bool_nat: $i > $i > $i ).
thf(image_nat_fun_a_bool_type,type,
image_nat_fun_a_bool: $i > $i > $i ).
thf(hAPP_f22106695ol_nat_type,type,
hAPP_f22106695ol_nat: $i > $i > $i ).
thf(finite_card_nat_type,type,
finite_card_nat: $i ).
thf(hAPP_f921600141ol_nat_type,type,
hAPP_f921600141ol_nat: $i > $i > $i ).
thf(finite_card_pname_type,type,
finite_card_pname: $i ).
thf(hAPP_f759274231e_bool_type,type,
hAPP_f759274231e_bool: $i > $i > $i ).
thf(cOMBC_1058051404l_bool_type,type,
cOMBC_1058051404l_bool: $i > $i ).
thf(insert1325755072e_bool_type,type,
insert1325755072e_bool: $i > $i > $i ).
thf(collec1974731493e_bool_type,type,
collec1974731493e_bool: $i > $i ).
thf(cOMBB_2095475776e_bool_type,type,
cOMBB_2095475776e_bool: $i > $i > $i ).
thf(cOMBC_1284144636l_bool_type,type,
cOMBC_1284144636l_bool: $i > $i ).
thf(fequal533582459e_bool_type,type,
fequal533582459e_bool: $i ).
thf(hAPP_f559147733l_bool_type,type,
hAPP_f559147733l_bool: $i > $i > $i ).
thf(cOMBC_1988546018l_bool_type,type,
cOMBC_1988546018l_bool: $i > $i ).
thf(member799430823e_bool_type,type,
member799430823e_bool: $i ).
thf(hAPP_f2009550088ol_nat_type,type,
hAPP_f2009550088ol_nat: $i > $i > $i ).
thf(finite1306199131a_bool_type,type,
finite1306199131a_bool: $i ).
thf(insert_fun_a_bool_type,type,
insert_fun_a_bool: $i > $i > $i ).
thf(hAPP_p1534023578a_bool_type,type,
hAPP_p1534023578a_bool: $i > $i > $i ).
thf(cOMBC_a_pname_bool_type,type,
cOMBC_a_pname_bool: $i > $i ).
thf(hAPP_a93125764e_bool_type,type,
hAPP_a93125764e_bool: $i > $i > $i ).
thf(hAPP_f1549043526a_bool_type,type,
hAPP_f1549043526a_bool: $i > $i > $i ).
thf(cOMBC_777206479l_bool_type,type,
cOMBC_777206479l_bool: $i > $i ).
thf(hAPP_a1392362872l_bool_type,type,
hAPP_a1392362872l_bool: $i > $i > $i ).
thf(hAPP_f1476298914l_bool_type,type,
hAPP_f1476298914l_bool: $i > $i > $i ).
thf(undefined_a_type,type,
undefined_a: $i > $i ).
thf(x_a_type,type,
x_a: $i ).
thf(fequal_nat_type,type,
fequal_nat: $i ).
thf(hAPP_f1794073134e_bool_type,type,
hAPP_f1794073134e_bool: $i > $i > $i ).
thf(cOMBB_1693087065a_bool_type,type,
cOMBB_1693087065a_bool: $i > $i > $i ).
thf(hAPP_f1128469712_pname_type,type,
hAPP_f1128469712_pname: $i > $i > $i ).
thf(collect_pname_type,type,
collect_pname: $i > $i ).
thf(cOMBC_1149511130e_bool_type,type,
cOMBC_1149511130e_bool: $i > $i ).
thf(fequal_pname_type,type,
fequal_pname: $i ).
thf(cOMBB_743407885bool_a_type,type,
cOMBB_743407885bool_a: $i > $i > $i ).
thf(hAPP_a_fun_nat_bool_type,type,
hAPP_a_fun_nat_bool: $i > $i > $i ).
thf(hAPP_f1051908748a_bool_type,type,
hAPP_f1051908748a_bool: $i > $i > $i ).
thf(bot_bo1649642514l_bool_type,type,
bot_bo1649642514l_bool: $i ).
thf(cOMBB_610033911bool_a_type,type,
cOMBB_610033911bool_a: $i > $i > $i ).
thf(hAPP_a_pname_type,type,
hAPP_a_pname: $i > $i > $i ).
thf(cOMBB_800536526ol_nat_type,type,
cOMBB_800536526ol_nat: $i > $i > $i ).
thf(hAPP_f292226953l_bool_type,type,
hAPP_f292226953l_bool: $i > $i > $i ).
thf(hAPP_a217006258l_bool_type,type,
hAPP_a217006258l_bool: $i > $i > $i ).
thf(cOMBB_1137537805bool_a_type,type,
cOMBB_1137537805bool_a: $i > $i > $i ).
thf(hAPP_a_fun_a_bool_type,type,
hAPP_a_fun_a_bool: $i > $i > $i ).
thf(cOMBC_a_a_bool_type,type,
cOMBC_a_a_bool: $i > $i ).
thf(hAPP_a_fun_bool_bool_type,type,
hAPP_a_fun_bool_bool: $i > $i > $i ).
thf(cOMBB_1972296269bool_a_type,type,
cOMBB_1972296269bool_a: $i > $i > $i ).
thf(cOMBC_nat_a_bool_type,type,
cOMBC_nat_a_bool: $i > $i ).
thf(hAPP_nat_fun_a_bool_type,type,
hAPP_nat_fun_a_bool: $i > $i > $i ).
thf(hAPP_f654413245e_bool_type,type,
hAPP_f654413245e_bool: $i > $i > $i ).
thf(cOMBB_141086128t_bool_type,type,
cOMBB_141086128t_bool: $i > $i > $i ).
thf(hAPP_f1291551745_pname_type,type,
hAPP_f1291551745_pname: $i > $i > $i ).
thf(hAPP_f55526627ol_nat_type,type,
hAPP_f55526627ol_nat: $i > $i > $i ).
thf(finite1340463720e_bool_type,type,
finite1340463720e_bool: $i ).
thf(cOMBC_1666426608t_bool_type,type,
cOMBC_1666426608t_bool: $i > $i ).
thf(hAPP_f1066163005t_bool_type,type,
hAPP_f1066163005t_bool: $i > $i > $i ).
thf(image_1921560913_pname_type,type,
image_1921560913_pname: $i > $i > $i ).
thf(cOMBC_595898202l_bool_type,type,
cOMBC_595898202l_bool: $i > $i ).
thf(cOMBC_226598744l_bool_type,type,
cOMBC_226598744l_bool: $i > $i ).
thf(cOMBS_568398431l_bool_type,type,
cOMBS_568398431l_bool: $i > $i > $i ).
thf(image_fun_nat_bool_a_type,type,
image_fun_nat_bool_a: $i > $i > $i ).
thf(hAPP_n1025906991e_bool_type,type,
hAPP_n1025906991e_bool: $i > $i > $i ).
thf(cOMBB_1212655066ol_nat_type,type,
cOMBB_1212655066ol_nat: $i > $i > $i ).
thf(hAPP_p130839763l_bool_type,type,
hAPP_p130839763l_bool: $i > $i > $i ).
thf(cOMBC_615407716e_bool_type,type,
cOMBC_615407716e_bool: $i > $i ).
thf(image_pname_pname_type,type,
image_pname_pname: $i > $i > $i ).
thf(cOMBB_bool_bool_a_type,type,
cOMBB_bool_bool_a: $i > $i > $i ).
thf(cOMBB_2026977092ol_nat_type,type,
cOMBB_2026977092ol_nat: $i > $i > $i ).
thf(cOMBC_267053842l_bool_type,type,
cOMBC_267053842l_bool: $i > $i ).
thf(cOMBB_307249310e_bool_type,type,
cOMBB_307249310e_bool: $i > $i > $i ).
thf(image_1551609309ol_nat_type,type,
image_1551609309ol_nat: $i > $i > $i ).
thf(image_26036933t_bool_type,type,
image_26036933t_bool: $i > $i > $i ).
thf(cOMBC_331553030l_bool_type,type,
cOMBC_331553030l_bool: $i > $i ).
thf(cOMBK_1857069011e_bool_type,type,
cOMBK_1857069011e_bool: $i > $i ).
thf(fTrue_type,type,
fTrue: $i ).
thf(image_nat_a_type,type,
image_nat_a: $i > $i > $i ).
thf(hAPP_f2050579477a_bool_type,type,
hAPP_f2050579477a_bool: $i > $i > $i ).
thf(fimplies_type,type,
fimplies: $i ).
thf(fNot_type,type,
fNot: $i ).
thf(cOMBC_pname_a_bool_type,type,
cOMBC_pname_a_bool: $i > $i ).
thf(cOMBK_bool_pname_type,type,
cOMBK_bool_pname: $i > $i ).
thf(hAPP_p1824510254l_bool_type,type,
hAPP_p1824510254l_bool: $i > $i > $i ).
thf(hAPP_n1414589940l_bool_type,type,
hAPP_n1414589940l_bool: $i > $i > $i ).
thf(cOMBB_675860798_pname_type,type,
cOMBB_675860798_pname: $i > $i > $i ).
thf(hAPP_p393069232l_bool_type,type,
hAPP_p393069232l_bool: $i > $i > $i ).
thf(image_876012084bool_a_type,type,
image_876012084bool_a: $i > $i > $i ).
thf(mgt_type,type,
mgt: $i > $i ).
thf(cOMBC_pname_nat_bool_type,type,
cOMBC_pname_nat_bool: $i > $i ).
thf(hAPP_p1499970991t_bool_type,type,
hAPP_p1499970991t_bool: $i > $i > $i ).
thf(hAPP_f1951378235l_bool_type,type,
hAPP_f1951378235l_bool: $i > $i > $i ).
thf(cOMBB_408569982_pname_type,type,
cOMBB_408569982_pname: $i > $i > $i ).
thf(cOMBC_a_nat_bool_type,type,
cOMBC_a_nat_bool: $i > $i ).
thf(cOMBS_a_bool_bool_type,type,
cOMBS_a_bool_bool: $i > $i > $i ).
thf(hAPP_f696928925ol_nat_type,type,
hAPP_f696928925ol_nat: $i > $i > $i ).
thf(finite346522414t_bool_type,type,
finite346522414t_bool: $i ).
thf(cOMBB_1896684278e_bool_type,type,
cOMBB_1896684278e_bool: $i > $i > $i ).
thf(image_819518260e_bool_type,type,
image_819518260e_bool: $i > $i > $i ).
thf(cOMBB_598082538e_bool_type,type,
cOMBB_598082538e_bool: $i > $i > $i ).
thf(hAPP_f1297739591_pname_type,type,
hAPP_f1297739591_pname: $i > $i > $i ).
thf(image_1655916159e_bool_type,type,
image_1655916159e_bool: $i > $i > $i ).
thf(cOMBB_1321347587bool_a_type,type,
cOMBB_1321347587bool_a: $i > $i > $i ).
thf(hAPP_a_nat_type,type,
hAPP_a_nat: $i > $i > $i ).
thf(cOMBS_1035972772l_bool_type,type,
cOMBS_1035972772l_bool: $i > $i > $i ).
thf(bot_bo1389914601l_bool_type,type,
bot_bo1389914601l_bool: $i ).
thf(undefined_pname_type,type,
undefined_pname: $i > $i ).
thf(pname_type,type,
pname: $i ).
thf(image_a_pname_type,type,
image_a_pname: $i > $i > $i ).
thf(hAPP_f937997336l_bool_type,type,
hAPP_f937997336l_bool: $i > $i > $i ).
thf(cOMBK_324466864a_bool_type,type,
cOMBK_324466864a_bool: $i > $i ).
thf(finite_finite_a_type,type,
finite_finite_a: $i ).
thf(cOMBB_1250273980t_bool_type,type,
cOMBB_1250273980t_bool: $i > $i > $i ).
thf(hAPP_nat_a_type,type,
hAPP_nat_a: $i > $i > $i ).
thf(bot_bo1701429464l_bool_type,type,
bot_bo1701429464l_bool: $i ).
thf(image_a_a_type,type,
image_a_a: $i > $i > $i ).
thf(hAPP_f2117159681l_bool_type,type,
hAPP_f2117159681l_bool: $i > $i > $i ).
thf(image_fun_a_bool_a_type,type,
image_fun_a_bool_a: $i > $i > $i ).
thf(cOMBC_386238098l_bool_type,type,
cOMBC_386238098l_bool: $i > $i ).
thf(cOMBC_nat_pname_bool_type,type,
cOMBC_nat_pname_bool: $i > $i ).
thf(cOMBC_1004116266e_bool_type,type,
cOMBC_1004116266e_bool: $i > $i ).
thf(p_type,type,
p: $i > $i ).
thf(cOMBB_2117322052ol_nat_type,type,
cOMBB_2117322052ol_nat: $i > $i > $i ).
thf(hAPP_a85458249l_bool_type,type,
hAPP_a85458249l_bool: $i > $i > $i ).
thf(hAPP_pname_pname_type,type,
hAPP_pname_pname: $i > $i > $i ).
thf(cOMBB_542850580_pname_type,type,
cOMBB_542850580_pname: $i > $i > $i ).
thf(cOMBB_928955006_pname_type,type,
cOMBB_928955006_pname: $i > $i > $i ).
thf(cOMBB_1885489796ol_nat_type,type,
cOMBB_1885489796ol_nat: $i > $i > $i ).
thf(cOMBB_238756964t_bool_type,type,
cOMBB_238756964t_bool: $i > $i > $i ).
thf(cOMBB_a_fun_a_bool_a_type,type,
cOMBB_a_fun_a_bool_a: $i > $i > $i ).
thf(cOMBB_523834888_pname_type,type,
cOMBB_523834888_pname: $i > $i > $i ).
thf(hAPP_f282463732t_bool_type,type,
hAPP_f282463732t_bool: $i > $i > $i ).
thf(cOMBB_164527437a_bool_type,type,
cOMBB_164527437a_bool: $i > $i > $i ).
thf(hAPP_fun_a_bool_nat_type,type,
hAPP_fun_a_bool_nat: $i > $i > $i ).
thf(image_496248727ol_nat_type,type,
image_496248727ol_nat: $i > $i > $i ).
thf(cOMBC_1834145417l_bool_type,type,
cOMBC_1834145417l_bool: $i > $i ).
thf(hAPP_f556039215l_bool_type,type,
hAPP_f556039215l_bool: $i > $i > $i ).
thf(image_a_fun_a_bool_type,type,
image_a_fun_a_bool: $i > $i > $i ).
thf(image_nat_nat_type,type,
image_nat_nat: $i > $i > $i ).
thf(member_a_type,type,
member_a: $i ).
thf(image_a_nat_type,type,
image_a_nat: $i > $i > $i ).
thf(fequal_a_type,type,
fequal_a: $i ).
thf(cOMBK_a_pname_type,type,
cOMBK_a_pname: $i > $i ).
thf(cOMBB_338059395a_bool_type,type,
cOMBB_338059395a_bool: $i > $i > $i ).
thf(cOMBC_1732670874l_bool_type,type,
cOMBC_1732670874l_bool: $i > $i ).
thf(fequal_fun_a_bool_type,type,
fequal_fun_a_bool: $i ).
thf(finite1701474069l_bool_type,type,
finite1701474069l_bool: $i ).
thf(collec1015864663l_bool_type,type,
collec1015864663l_bool: $i > $i ).
thf(cOMBB_392435466_pname_type,type,
cOMBB_392435466_pname: $i > $i > $i ).
thf(cOMBC_1880041174l_bool_type,type,
cOMBC_1880041174l_bool: $i > $i ).
thf(member_fun_a_bool_type,type,
member_fun_a_bool: $i ).
thf(finite_card_a_type,type,
finite_card_a: $i ).
thf(na_type,type,
na: $i ).
thf(hAPP_f285962445l_bool_type,type,
hAPP_f285962445l_bool: $i > $i > $i ).
thf(cOMBC_1355376034l_bool_type,type,
cOMBC_1355376034l_bool: $i > $i ).
thf(cOMBB_1823939024ol_nat_type,type,
cOMBB_1823939024ol_nat: $i > $i > $i ).
thf(the_com_type,type,
the_com: $i > $i ).
thf(body_type,type,
body: $i > $i ).
thf(cOMBC_1928494297l_bool_type,type,
cOMBC_1928494297l_bool: $i > $i ).
thf(hAPP_f198738859l_bool_type,type,
hAPP_f198738859l_bool: $i > $i > $i ).
thf(cOMBB_472261505bool_a_type,type,
cOMBB_472261505bool_a: $i > $i > $i ).
thf(cOMBB_1897541054_pname_type,type,
cOMBB_1897541054_pname: $i > $i > $i ).
thf(cOMBC_619334683t_bool_type,type,
cOMBC_619334683t_bool: $i > $i ).
thf(cOMBC_445755039l_bool_type,type,
cOMBC_445755039l_bool: $i > $i ).
thf(finite1381704300l_bool_type,type,
finite1381704300l_bool: $i ).
thf(collec707592106l_bool_type,type,
collec707592106l_bool: $i > $i ).
thf(cOMBC_1738168533e_bool_type,type,
cOMBC_1738168533e_bool: $i > $i ).
thf(image_a_fun_nat_bool_type,type,
image_a_fun_nat_bool: $i > $i > $i ).
thf(nat_case_bool_type,type,
nat_case_bool: $i > $i > $i ).
thf(finite786885583l_bool_type,type,
finite786885583l_bool: $i ).
thf(collec1613912337l_bool_type,type,
collec1613912337l_bool: $i > $i ).
thf(396,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ ( insert_pname @ B @ A ) ) )
<=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_326_subset__insert) ).
thf(2163,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
=> ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ ( insert_pname @ B @ A ) ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ ( insert_pname @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(847,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_a_bool @ A @ B ) )
=> ( ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ ( hAPP_a_fun_a_bool @ fequal_a @ B ) ) @ A ) )
= ( insert_a @ B @ bot_bot_fun_a_bool ) ) )
& ( ~ ( hBOOL @ ( hAPP_a_bool @ A @ B ) )
=> ( ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ ( hAPP_a_fun_a_bool @ fequal_a @ B ) ) @ A ) )
= bot_bot_fun_a_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_478_Collect__conv__if2) ).
thf(3873,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_a_bool @ A @ B ) )
=> ( ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ ( hAPP_a_fun_a_bool @ fequal_a @ B ) ) @ A ) )
= ( insert_a @ B @ bot_bot_fun_a_bool ) ) )
& ( ~ ( hBOOL @ ( hAPP_a_bool @ A @ B ) )
=> ( ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ ( hAPP_a_fun_a_bool @ fequal_a @ B ) ) @ A ) )
= bot_bot_fun_a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).
thf(475,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ C ) )
=> ( ( insert_nat @ ( hAPP_a_nat @ A @ B ) @ ( image_a_nat @ A @ C ) )
= ( image_a_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_341_insert__image) ).
thf(2452,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ C ) )
=> ( ( insert_nat @ ( hAPP_a_nat @ A @ B ) @ ( image_a_nat @ A @ C ) )
= ( image_a_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(518,axiom,
! [A: $i,B: $i,C: $i] :
( ( B = C )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_531_xt1_I3_J) ).
thf(2612,plain,
! [A: $i,B: $i,C: $i] :
( ( B = C )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(563,axiom,
! [A: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_370_order__refl) ).
thf(2778,plain,
! [A: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(268,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f1066163005t_bool @ ( cOMBB_1896684278e_bool @ A @ B ) @ C )
= ( hAPP_n1699378549t_bool @ A @ ( hAPP_f921600141ol_nat @ B @ C ) ) ),
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(1767,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f1066163005t_bool @ ( cOMBB_1896684278e_bool @ A @ B ) @ C )
= ( hAPP_n1699378549t_bool @ A @ ( hAPP_f921600141ol_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(862,axiom,
! [A: $i,B: $i] :
( ( B = bot_bot_fun_nat_bool )
=> ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_395_equals0D) ).
thf(3930,plain,
! [A: $i,B: $i] :
( ( B = bot_bot_fun_nat_bool )
=> ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).
thf(210,axiom,
is_bool @ fTrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_fTrue) ).
thf(1559,plain,
is_bool @ fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(507,axiom,
! [A: $i,B: $i] :
( ( A = B )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_549_order__eq__refl) ).
thf(2559,plain,
! [A: $i,B: $i] :
( ( A = B )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(91,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( is_fun_pname_bool @ A )
& ( is_fun_pname_bool @ C ) )
=> ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
=> ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ A ) )
=> ( ( ( insert_pname @ B @ C )
= ( insert_pname @ B @ A ) )
<=> ( C = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_insert__ident) ).
thf(1179,plain,
! [A: $i,B: $i,C: $i] :
( ( ( is_fun_pname_bool @ A )
& ( is_fun_pname_bool @ C ) )
=> ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
=> ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ A ) )
=> ( ( ( ( insert_pname @ B @ C )
= ( insert_pname @ B @ A ) )
=> ( C = A ) )
& ( ( C = A )
=> ( ( insert_pname @ B @ C )
= ( insert_pname @ B @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(766,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ C )
<=> ( hBOOL @ B ) )
=> ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_530_xt1_I3_J) ).
thf(3566,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hBOOL @ C )
=> ( hBOOL @ B ) )
& ( ( hBOOL @ B )
=> ( hBOOL @ C ) ) )
=> ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).
thf(128,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ ( image_pname_nat @ B @ C ) ) )
=> ~ ! [D: $i] :
( ( is_pname @ D )
=> ( ( A
= ( hAPP_pname_nat @ B @ D ) )
=> ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_354_imageE) ).
thf(1295,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ ( image_pname_nat @ B @ C ) ) )
=> ~ ! [D: $i] :
( ( is_pname @ D )
=> ( ( A
= ( hAPP_pname_nat @ B @ D ) )
=> ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(327,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
=> ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) )
= ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_Nat_Odiff__diff__eq) ).
thf(1956,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
=> ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) )
= ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(706,axiom,
! [A: $i,B: $i,C: $i] :
( ( is_a @ A )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ ( image_pname_a @ B @ C ) ) )
=> ~ ! [D: $i] :
( ( is_pname @ D )
=> ( ( A
= ( hAPP_pname_a @ B @ D ) )
=> ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_356_imageE) ).
thf(3345,plain,
! [A: $i,B: $i,C: $i] :
( ( is_a @ A )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ ( image_pname_a @ B @ C ) ) )
=> ~ ! [D: $i] :
( ( is_pname @ D )
=> ( ( A
= ( hAPP_pname_a @ B @ D ) )
=> ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(881,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( insert_nat @ A @ B ) ) @ ( insert_nat @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_332_insert__mono) ).
thf(4005,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( insert_nat @ A @ B ) ) @ ( insert_nat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).
thf(377,axiom,
! [A: $i,B: $i] : ( is_pname @ ( hAPP_f1291551745_pname @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Com__Opname) ).
thf(2109,plain,
! [A: $i,B: $i] : ( is_pname @ ( hAPP_f1291551745_pname @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(384,axiom,
! [A: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ suc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_680_zero__less__Suc) ).
thf(2131,plain,
! [A: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(354,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_659_less__Suc__eq__le) ).
thf(2031,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(885,axiom,
hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ bot_bo1649642514l_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_387_finite_OemptyI) ).
thf(4022,plain,
hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ bot_bo1649642514l_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).
thf(255,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_not__less__eq__eq) ).
thf(1729,plain,
! [A: $i,B: $i] :
( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ B ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ B ) ) @ A ) )
=> ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(602,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ C ) )
=> ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ A ) @ ( image_nat_fun_a_bool @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_finite__surj) ).
thf(2921,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ C ) )
=> ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ A ) @ ( image_nat_fun_a_bool @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(742,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( p @ ( insert_a @ ( hAPP_pname_a @ mgt_call @ A ) @ B ) ) @ ( insert_a @ ( mgt @ ( the_com @ ( body @ A ) ) ) @ bot_bot_fun_a_bool ) ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( p @ B ) @ ( insert_a @ ( hAPP_pname_a @ mgt_call @ A ) @ bot_bot_fun_a_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_562_assms_I2_J) ).
thf(3477,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( p @ ( insert_a @ ( hAPP_pname_a @ mgt_call @ A ) @ B ) ) @ ( insert_a @ ( mgt @ ( the_com @ ( body @ A ) ) ) @ bot_bot_fun_a_bool ) ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( p @ B ) @ ( insert_a @ ( hAPP_pname_a @ mgt_call @ A ) @ bot_bot_fun_a_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).
thf(479,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
=> ( ( insert_pname @ ( hAPP_pname_pname @ A @ B ) @ ( image_pname_pname @ A @ C ) )
= ( image_pname_pname @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_338_insert__image) ).
thf(2463,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
=> ( ( insert_pname @ ( hAPP_pname_pname @ A @ B ) @ ( image_pname_pname @ A @ C ) )
= ( image_pname_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(308,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_set__rev__mp) ).
thf(1899,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(295,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( is_pname @ A )
& ( is_pname @ B ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( insert_pname @ B @ C ) ) )
<=> ( ( A = B )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_insert__iff) ).
thf(1850,plain,
! [A: $i,B: $i,C: $i] :
( ( ( is_pname @ A )
& ( is_pname @ B ) )
=> ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( insert_pname @ B @ C ) ) )
=> ( ( A = B )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) ) )
& ( ( ( A = B )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( insert_pname @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(488,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( is_a @ D )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ D ) @ C ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ ( hAPP_a_nat @ A @ D ) ) @ B ) ) ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( image_a_nat @ A @ C ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_362_image__subsetI) ).
thf(2499,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( is_a @ D )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ D ) @ C ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ ( hAPP_a_nat @ A @ D ) ) @ B ) ) ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( image_a_nat @ A @ C ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( is_bool @ A )
=> ( ( hAPP_f54304608l_bool @ ( cOMBK_1994329625t_bool @ A ) @ B )
= 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(962,plain,
! [A: $i,B: $i] :
( ( is_bool @ A )
=> ( ( hAPP_f54304608l_bool @ ( cOMBK_1994329625t_bool @ A ) @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(470,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
=> ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( image_26036933t_bool @ A @ B ) ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ ( hAPP_f800510211t_bool @ ( cOMBC_226598744l_bool @ member_nat ) @ B ) ) @ ( hAPP_f800510211t_bool @ ( cOMBC_226598744l_bool @ ( cOMBB_2026977092ol_nat @ fequal_fun_nat_bool @ A ) ) @ ( hAPP_n1699378549t_bool @ A @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_pigeonhole__infinite) ).
thf(2427,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
=> ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( image_26036933t_bool @ A @ B ) ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ ( hAPP_f800510211t_bool @ ( cOMBC_226598744l_bool @ member_nat ) @ B ) ) @ ( hAPP_f800510211t_bool @ ( cOMBC_226598744l_bool @ ( cOMBB_2026977092ol_nat @ fequal_fun_nat_bool @ A ) ) @ ( hAPP_n1699378549t_bool @ A @ C ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(484,axiom,
! [A: $i,B: $i] :
( ( is_a @ A )
=> ( ( hAPP_pname_a @ ( cOMBK_a_pname @ A ) @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000t__a_000tc__Com__Opname_U) ).
thf(2480,plain,
! [A: $i,B: $i] :
( ( is_a @ A )
=> ( ( hAPP_pname_a @ ( cOMBK_a_pname @ A ) @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(427,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) )
=> ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_628_less__SucE) ).
thf(2280,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) )
=> ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(667,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ A ) @ B ) ) ) )
<=> ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ A ) ) )
& ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_finite__Collect__disjI) ).
thf(3172,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ A ) @ B ) ) ) )
=> ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ A ) ) )
& ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ B ) ) ) ) )
& ( ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ A ) ) )
& ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ B ) ) ) )
=> ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(759,axiom,
~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( hAPP_pname_a @ mgt_call @ pn ) ) @ g ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_5) ).
thf(3534,plain,
~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( hAPP_pname_a @ mgt_call @ pn ) ) @ g ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).
thf(262,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) )
=> ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( A
= ( hAPP_nat_nat @ suc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_le__SucE) ).
thf(1750,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) )
=> ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( A
= ( hAPP_nat_nat @ suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(876,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ A ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_card__mono) ).
thf(3990,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ A ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).
thf(458,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
=> ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
=> ( ( hAPP_f921600141ol_nat @ finite_card_pname @ ( insert_pname @ A @ B ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f921600141ol_nat @ finite_card_pname @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_card__insert__disjoint) ).
thf(2381,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
=> ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
=> ( ( hAPP_f921600141ol_nat @ finite_card_pname @ ( insert_pname @ A @ B ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f921600141ol_nat @ finite_card_pname @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(59,axiom,
! [A: $i,B: $i] :
( ( is_pname @ B )
=> ( is_fun_pname_bool @ ( hAPP_p61793385e_bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).
thf(1073,plain,
! [A: $i,B: $i] :
( ( is_pname @ B )
=> ( is_fun_pname_bool @ ( hAPP_p61793385e_bool @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(855,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_p1534023578a_bool @ ( cOMBB_1897541054_pname @ A @ B ) @ C )
= ( hAPP_a_fun_a_bool @ A @ ( hAPP_pname_a @ B @ C ) ) ),
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(3910,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_p1534023578a_bool @ ( cOMBB_1897541054_pname @ A @ B ) @ C )
= ( hAPP_a_fun_a_bool @ A @ ( hAPP_pname_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).
thf(628,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ ( insert_a @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_insertI1) ).
thf(3012,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ ( insert_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(373,axiom,
! [A: $i,B: $i] : ( is_bool @ ( hAPP_nat_bool @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool) ).
thf(2099,plain,
! [A: $i,B: $i] : ( is_bool @ ( hAPP_nat_bool @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(277,axiom,
! [A: $i,B: $i,C: $i] :
( ( insert_pname @ A @ ( insert_pname @ B @ C ) )
= ( insert_pname @ B @ ( insert_pname @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_insert__commute) ).
thf(1793,plain,
! [A: $i,B: $i,C: $i] :
( ( insert_pname @ A @ ( insert_pname @ B @ C ) )
= ( insert_pname @ B @ ( insert_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(493,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ zero_zero_nat ) )
<=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_698_le__0__eq) ).
thf(2512,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ zero_zero_nat ) )
=> ( A = zero_zero_nat ) )
& ( ( A = zero_zero_nat )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(619,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ bot_bot_nat ) )
<=> ( A = bot_bot_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_440_bot__unique) ).
thf(2976,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ bot_bot_nat ) )
=> ( A = bot_bot_nat ) )
& ( ( A = bot_bot_nat )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ bot_bot_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(647,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( image_1551609309ol_nat @ A @ B ) ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_card__image__le) ).
thf(3072,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( image_1551609309ol_nat @ A @ B ) ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(34,axiom,
bot_bot_nat = zero_zero_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_697_bot__nat__def) ).
thf(1005,plain,
bot_bot_nat = zero_zero_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(57,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ C ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( image_1854862208_pname @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_finite__surj) ).
thf(1068,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ C ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( image_1854862208_pname @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(842,axiom,
hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ bot_bo844097828e_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_390_finite_OemptyI) ).
thf(3858,plain,
hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ bot_bo844097828e_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).
thf(569,axiom,
! [A: $i,B: $i,C: $i] :
( ( B = C )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_536_ord__eq__le__trans) ).
thf(2808,plain,
! [A: $i,B: $i,C: $i] :
( ( B = C )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(813,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
=> ( B = A ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ ( insert_pname @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_insertCI) ).
thf(3762,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
=> ( B = A ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ ( insert_pname @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(282,axiom,
! [A: $i] :
( ( collect_pname @ ( hAPP_p61793385e_bool @ fequal_pname @ A ) )
= ( insert_pname @ A @ bot_bo844097828e_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_489_singleton__conv2) ).
thf(1808,plain,
! [A: $i] :
( ( collect_pname @ ( hAPP_p61793385e_bool @ fequal_pname @ A ) )
= ( insert_pname @ A @ bot_bo844097828e_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(532,axiom,
! [A: $i] :
( ( ( collect_fun_nat_bool @ A )
= bot_bo1701429464l_bool )
<=> ! [B: $i] :
~ ( hBOOL @ ( hAPP_f54304608l_bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_399_Collect__empty__eq) ).
thf(2659,plain,
! [A: $i] :
( ( ( ( collect_fun_nat_bool @ A )
= bot_bo1701429464l_bool )
=> ! [B: $i] :
~ ( hBOOL @ ( hAPP_f54304608l_bool @ A @ B ) ) )
& ( ! [B: $i] :
~ ( hBOOL @ ( hAPP_f54304608l_bool @ A @ B ) )
=> ( ( collect_fun_nat_bool @ A )
= bot_bo1701429464l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(726,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ ( insert_nat @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_insertI2) ).
thf(3417,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ ( insert_nat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).
thf(752,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1854862208_pname @ A @ B ) ) )
=> ? [C: $i] :
( ( is_fun_a_bool @ C )
& ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fconj @ ( hAPP_f2117159681l_bool @ ( cOMBC_1880041174l_bool @ member_fun_a_bool ) @ B ) ) @ ( hAPP_p1824510254l_bool @ ( cOMBC_1738168533e_bool @ ( cOMBB_1693087065a_bool @ fequal_pname @ A ) ) @ ( hAPP_f1128469712_pname @ A @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_pigeonhole__infinite) ).
thf(3509,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1854862208_pname @ A @ B ) ) )
=> ? [C: $i] :
( ( is_fun_a_bool @ C )
& ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fconj @ ( hAPP_f2117159681l_bool @ ( cOMBC_1880041174l_bool @ member_fun_a_bool ) @ B ) ) @ ( hAPP_p1824510254l_bool @ ( cOMBC_1738168533e_bool @ ( cOMBB_1693087065a_bool @ fequal_pname @ A ) ) @ ( hAPP_f1128469712_pname @ A @ C ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).
thf(227,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( image_nat_pname @ A @ B ) ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_card__image__le) ).
thf(1618,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( image_nat_pname @ A @ B ) ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(636,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
=> ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ A ) @ ( image_2129980159t_bool @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_finite__surj) ).
thf(3040,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
=> ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ A ) @ ( image_2129980159t_bool @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(663,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ A @ B ) ) @ ( insert_pname @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_331_insert__mono) ).
thf(3153,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ A @ B ) ) @ ( insert_pname @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(513,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
& ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_set__eq__subset) ).
thf(2590,plain,
! [A: $i,B: $i] :
( ( ( A = B )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
& ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
& ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(162,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_629_less__trans__Suc) ).
thf(1401,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(170,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_a_bool @ ( cOMBB_bool_bool_a @ A @ B ) @ C )
= ( hAPP_bool_bool @ A @ ( hAPP_a_bool @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000t__a_U) ).
thf(1422,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_a_bool @ ( cOMBB_bool_bool_a @ A @ B ) @ C )
= ( hAPP_bool_bool @ A @ ( hAPP_a_bool @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(214,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) )
<=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_635_less__Suc__eq) ).
thf(1569,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
| ( A = B ) ) )
& ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
| ( A = B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(320,axiom,
( bot_bo1701429464l_bool
= ( collect_fun_nat_bool @ ( cOMBK_1994329625t_bool @ fFalse ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_420_empty__def) ).
thf(1939,plain,
( bot_bo1701429464l_bool
= ( collect_fun_nat_bool @ ( cOMBK_1994329625t_bool @ fFalse ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(868,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ A @ B ) )
=> ( ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fconj @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ B ) ) @ A ) )
= ( insert_fun_nat_bool @ B @ bot_bo1701429464l_bool ) ) )
& ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ A @ B ) )
=> ( ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fconj @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ B ) ) @ A ) )
= bot_bo1701429464l_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_479_Collect__conv__if2) ).
thf(3959,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ A @ B ) )
=> ( ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fconj @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ B ) ) @ A ) )
= ( insert_fun_nat_bool @ B @ bot_bo1701429464l_bool ) ) )
& ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ A @ B ) )
=> ( ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fconj @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ B ) ) @ A ) )
= bot_bo1701429464l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).
thf(78,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B
= ( hAPP_nat_pname @ C @ D ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ D ) @ A ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ ( image_nat_pname @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_image__eqI) ).
thf(1142,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B
= ( hAPP_nat_pname @ C @ D ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ D ) @ A ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ ( image_nat_pname @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(118,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ ( hAPP_nat_nat @ suc @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_626_Suc__less__SucD) ).
thf(1269,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ ( hAPP_nat_nat @ suc @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(824,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_504_xt1_I6_J) ).
thf(3794,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).
thf(264,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_a_bool @ ( cOMBS_a_bool_bool @ A @ B ) @ C )
= ( hAPP_bool_bool @ ( hAPP_a_fun_bool_bool @ A @ C ) @ ( hAPP_a_bool @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000t__a_000tc__HOL__Obool_000tc__HOL__Obool_U) ).
thf(1756,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_a_bool @ ( cOMBS_a_bool_bool @ A @ B ) @ C )
= ( hAPP_bool_bool @ ( hAPP_a_fun_bool_bool @ A @ C ) @ ( hAPP_a_bool @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(712,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_pname_a @ A @ B ) ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_card__image__le) ).
thf(3367,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_pname_a @ A @ B ) ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(399,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) ) @ A )
= ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_596_add__diff__assoc2) ).
thf(2184,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) ) @ A )
= ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(472,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ A ) @ B ) )
| ~ ( hBOOL @ A )
| ( hBOOL @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_3_1_U) ).
thf(2434,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ A ) @ B ) )
| ~ ( hBOOL @ A )
| ( hBOOL @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(141,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ B ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( insert_nat @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_card__insert__le) ).
thf(1342,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ B ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( insert_nat @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(182,axiom,
! [A: $i,B: $i] :
( ( is_fun_a_bool @ B )
=> ( is_fun_pname_bool @ ( hAPP_f1794073134e_bool @ A @ B ) ) ),
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(1458,plain,
! [A: $i,B: $i] :
( ( is_fun_a_bool @ B )
=> ( is_fun_pname_bool @ ( hAPP_f1794073134e_bool @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(402,axiom,
( bot_bo1649642514l_bool
= ( collec1974731493e_bool @ ( cOMBK_1857069011e_bool @ fFalse ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_421_empty__def) ).
thf(2195,plain,
( bot_bo1649642514l_bool
= ( collec1974731493e_bool @ ( cOMBK_1857069011e_bool @ fFalse ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(247,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
=> ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ B ) )
=> ( ( hAPP_f22106695ol_nat @ finite_card_nat @ ( insert_nat @ A @ B ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f22106695ol_nat @ finite_card_nat @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_card__insert__disjoint) ).
thf(1705,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
=> ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ B ) )
=> ( ( hAPP_f22106695ol_nat @ finite_card_nat @ ( insert_nat @ A @ B ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f22106695ol_nat @ finite_card_nat @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(905,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) )
=> ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ ( collec1613912337l_bool @ ( hAPP_f510955609l_bool @ ( cOMBC_7971162l_bool @ ord_le675606854l_bool ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_finite__Collect__subsets) ).
thf(4090,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) )
=> ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ ( collec1613912337l_bool @ ( hAPP_f510955609l_bool @ ( cOMBC_7971162l_bool @ ord_le675606854l_bool ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).
thf(235,axiom,
! [A: $i] :
( ( hAPP_nat_nat @ suc @ A )
!= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_694_Suc__not__Zero) ).
thf(1655,plain,
! [A: $i] :
( ( hAPP_nat_nat @ suc @ A )
!= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(639,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f198738859l_bool @ ( cOMBB_338059395a_bool @ A @ B ) @ C )
= ( hAPP_b589554111l_bool @ A @ ( hAPP_fun_a_bool_bool @ B @ C ) ) ),
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(3049,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f198738859l_bool @ ( cOMBB_338059395a_bool @ A @ B ) @ C )
= ( hAPP_b589554111l_bool @ A @ ( hAPP_fun_a_bool_bool @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(809,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
=> ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ A ) @ ( image_112932426a_bool @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_finite__surj) ).
thf(3745,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
=> ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ A ) @ ( image_112932426a_bool @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).
thf(76,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ A ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_card__mono) ).
thf(1137,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ A ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(711,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ ( insert_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_320_subset__insertI) ).
thf(3365,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ ( insert_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(551,axiom,
hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ na ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_pname_a @ mgt_call @ u ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
thf(2740,plain,
hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ na ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_pname_a @ mgt_call @ u ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(601,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ ( insert_nat @ B @ C ) ) )
=> ( ( A != B )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_insertE) ).
thf(2918,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ ( insert_nat @ B @ C ) ) )
=> ( ( A != B )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(887,axiom,
! [A: $i,B: $i,C: $i] :
( ( B = C )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_534_xt1_I3_J) ).
thf(4026,plain,
! [A: $i,B: $i,C: $i] :
( ( B = C )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).
thf(638,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ A @ B ) ) )
<=> ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_finite__insert) ).
thf(3044,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ A @ B ) ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) ) )
& ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(86,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_a_bool @ ( hAPP_p1534023578a_bool @ ( cOMBC_a_pname_bool @ A ) @ B ) @ C )
= ( hAPP_pname_bool @ ( hAPP_a93125764e_bool @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000t__a_000tc__Com__Opname_000tc__HOL__Obool_U) ).
thf(1164,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_a_bool @ ( hAPP_p1534023578a_bool @ ( cOMBC_a_pname_bool @ A ) @ B ) @ C )
= ( hAPP_pname_bool @ ( hAPP_a93125764e_bool @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(343,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_Suc__n__not__le__n) ).
thf(1999,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(777,axiom,
hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ pn ) @ u ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_4) ).
thf(3616,plain,
hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ pn ) @ u ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).
thf(108,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_a1392362872l_bool @ ( cOMBB_743407885bool_a @ A @ B ) @ C )
= ( hAPP_f103356543l_bool @ A @ ( hAPP_a_fun_nat_bool @ B @ C ) ) ),
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(1233,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_a1392362872l_bool @ ( cOMBB_743407885bool_a @ A @ B ) @ C )
= ( hAPP_f103356543l_bool @ A @ ( hAPP_a_fun_nat_bool @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(482,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_finite_OinsertI) ).
thf(2476,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(115,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_a93125764e_bool @ ( cOMBB_610033911bool_a @ A @ B ) @ C )
= ( hAPP_p61793385e_bool @ A @ ( hAPP_a_pname @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob) ).
thf(1260,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_a93125764e_bool @ ( cOMBB_610033911bool_a @ A @ B ) @ C )
= ( hAPP_p61793385e_bool @ A @ ( hAPP_a_pname @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(339,axiom,
! [A: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_612_lessI) ).
thf(1988,plain,
! [A: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(833,axiom,
is_fun_a_bool @ g,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_G) ).
thf(3826,plain,
is_fun_a_bool @ g,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).
thf(478,axiom,
! [A: $i,B: $i,C: $i] :
( ( B = C )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_539_ord__eq__le__trans) ).
thf(2459,plain,
! [A: $i,B: $i,C: $i] :
( ( B = C )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(596,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_555_linorder__linear) ).
thf(2901,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(10,axiom,
! [A: $i,B: $i] : ( is_fun1661590463l_bool @ ( hAPP_n850744903l_bool @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool) ).
thf(945,plain,
! [A: $i,B: $i] : ( is_fun1661590463l_bool @ ( hAPP_n850744903l_bool @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(851,axiom,
! [A: $i,B: $i] :
( ( ( is_fun_a_bool @ A )
& ( is_fun_a_bool @ B ) )
=> ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ A ) @ B ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__fun_It__a_Mtc__HOL__Obool_J_T) ).
thf(3895,plain,
! [A: $i,B: $i] :
( ( ( is_fun_a_bool @ A )
& ( is_fun_a_bool @ B ) )
=> ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ A ) @ B ) )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).
thf(449,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( is_pname @ C )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ B ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_358_subsetI) ).
thf(2360,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( is_pname @ C )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ B ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(68,axiom,
! [A: $i,B: $i] :
( ( ( is_fun_pname_bool @ A )
& ( is_fun_pname_bool @ B ) )
=> ( ( A = B )
<=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_552_order__eq__iff) ).
thf(1095,plain,
! [A: $i,B: $i] :
( ( ( is_fun_pname_bool @ A )
& ( is_fun_pname_bool @ B ) )
=> ( ( ( A = B )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(260,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_590_add__le__mono1) ).
thf(1746,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(779,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_516_order__antisym) ).
thf(3629,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).
thf(32,axiom,
! [A: $i,B: $i] : ( is_bool @ ( hAPP_f389811538l_bool @ A @ B ) ),
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(1001,plain,
! [A: $i,B: $i] : ( is_bool @ ( hAPP_f389811538l_bool @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(617,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ C ) )
=> ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ A ) @ ( image_26036933t_bool @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_finite__surj) ).
thf(2972,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ C ) )
=> ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ A ) @ ( image_26036933t_bool @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(749,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ ( insert_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_insertI1) ).
thf(3502,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ ( insert_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(49,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_662_Suc__leI) ).
thf(1046,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(233,axiom,
! [A: $i,B: $i] :
( ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) )
= ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ one_one_nat ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_568_diff__Suc__eq__diff__pred) ).
thf(1645,plain,
! [A: $i,B: $i] :
( ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) )
= ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ one_one_nat ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(146,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_617_add__lessD1) ).
thf(1359,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(157,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ C @ D ) ) @ ( hAPP_nat_nat @ C @ ( hAPP_nat_nat @ suc @ D ) ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ C @ A ) ) @ ( hAPP_nat_nat @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_lift__Suc__mono__le) ).
thf(1386,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ C @ D ) ) @ ( hAPP_nat_nat @ C @ ( hAPP_nat_nat @ suc @ D ) ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ C @ A ) ) @ ( hAPP_nat_nat @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(852,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_508_xt1_I5_J) ).
thf(3898,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).
thf(888,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ A @ B ) ) )
<=> ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_finite__insert) ).
thf(4030,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ A @ B ) ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) ) )
& ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).
thf(149,axiom,
! [A: $i,B: $i] :
( ( is_fun_pname_bool @ B )
=> ( is_fun_pname_bool @ ( cOMBS_568398431l_bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool) ).
thf(1366,plain,
! [A: $i,B: $i] :
( ( is_fun_pname_bool @ B )
=> ( is_fun_pname_bool @ ( cOMBS_568398431l_bool @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(364,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_set__mp) ).
thf(2067,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(848,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_513_order__trans) ).
thf(3880,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).
thf(229,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
<=> ! [C: $i] :
( ( is_pname @ C )
=> ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_pname_bool @ A @ C ) ) @ ( hAPP_pname_bool @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_374_le__fun__def) ).
thf(1623,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
=> ! [C: $i] :
( ( is_pname @ C )
=> ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_pname_bool @ A @ C ) ) @ ( hAPP_pname_bool @ B @ C ) ) ) ) )
& ( ! [C: $i] :
( ( is_pname @ C )
=> ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_pname_bool @ A @ C ) ) @ ( hAPP_pname_bool @ B @ C ) ) ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(857,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_fun_a_bool_nat @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_finite__imageI) ).
thf(3915,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_fun_a_bool_nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).
thf(272,axiom,
! [A: $i,B: $i] :
( ( is_fun_a_bool @ B )
=> ( is_fun1661590463l_bool @ ( image_819518260e_bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000t__a_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).
thf(1782,plain,
! [A: $i,B: $i] :
( ( is_fun_a_bool @ B )
=> ( is_fun1661590463l_bool @ ( image_819518260e_bool @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(351,axiom,
! [A: $i,B: $i] :
( ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_683_diff__add__0) ).
thf(2020,plain,
! [A: $i,B: $i] :
( ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(753,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ bot_bot_fun_nat_bool ) )
<=> ( A = bot_bot_fun_nat_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_438_bot__unique) ).
thf(3513,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ bot_bot_fun_nat_bool ) )
=> ( A = bot_bot_fun_nat_bool ) )
& ( ( A = bot_bot_fun_nat_bool )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ bot_bot_fun_nat_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).
thf(310,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ A @ C ) )
=> ( ! [D: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ A @ ( hAPP_nat_nat @ suc @ D ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ A @ D ) ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_672_inc__induct) ).
thf(1904,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ A @ C ) )
=> ( ! [D: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ A @ ( hAPP_nat_nat @ suc @ D ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ A @ D ) ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(246,axiom,
! [A: $i,B: $i] : ( is_fun_pname_bool @ ( hAPP_f654413245e_bool @ A @ B ) ),
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(1703,plain,
! [A: $i,B: $i] : ( is_fun_pname_bool @ ( hAPP_f654413245e_bool @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(531,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f1637334154l_bool @ A @ bot_bo1701429464l_bool ) )
=> ( ! [C: $i,D: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ D ) )
=> ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_f1637334154l_bool @ A @ D ) )
=> ( hBOOL @ ( hAPP_f1637334154l_bool @ A @ ( insert_fun_nat_bool @ C @ D ) ) ) ) ) )
=> ( hBOOL @ ( hAPP_f1637334154l_bool @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_563_finite__induct) ).
thf(2654,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f1637334154l_bool @ A @ bot_bo1701429464l_bool ) )
=> ( ! [C: $i,D: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ D ) )
=> ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_f1637334154l_bool @ A @ D ) )
=> ( hBOOL @ ( hAPP_f1637334154l_bool @ A @ ( insert_fun_nat_bool @ C @ D ) ) ) ) ) )
=> ( hBOOL @ ( hAPP_f1637334154l_bool @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(688,axiom,
! [A: $i] :
( ( bot_bot_fun_a_bool
= ( collect_a @ A ) )
<=> ! [B: $i] :
( ( is_a @ B )
=> ~ ( hBOOL @ ( hAPP_a_bool @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_411_empty__Collect__eq) ).
thf(3263,plain,
! [A: $i] :
( ( ( bot_bot_fun_a_bool
= ( collect_a @ A ) )
=> ! [B: $i] :
( ( is_a @ B )
=> ~ ( hBOOL @ ( hAPP_a_bool @ A @ B ) ) ) )
& ( ! [B: $i] :
( ( is_a @ B )
=> ~ ( hBOOL @ ( hAPP_a_bool @ A @ B ) ) )
=> ( bot_bot_fun_a_bool
= ( collect_a @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(443,axiom,
! [A: $i,B: $i] :
( ( insert_nat @ A @ B )
!= bot_bot_fun_nat_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_459_insert__not__empty) ).
thf(2328,plain,
! [A: $i,B: $i] :
( ( insert_nat @ A @ B )
!= bot_bot_fun_nat_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(338,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ A ) @ B ) @ C )
= ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Com__Opname_000tc__HOL__Obool_U) ).
thf(1985,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ A ) @ B ) @ C )
= ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(690,axiom,
! [A: $i] :
( ? [B: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ A ) )
<=> ( A != bot_bot_fun_nat_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_413_ex__in__conv) ).
thf(3275,plain,
! [A: $i] :
( ( ? [B: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ A ) )
=> ( A != bot_bot_fun_nat_bool ) )
& ( ( A != bot_bot_fun_nat_bool )
=> ? [B: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(898,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ A ) @ B ) )
| ( hBOOL @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
thf(4070,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ A ) @ B ) )
| ( hBOOL @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).
thf(794,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_pname_bool @ bot_bo844097828e_bool @ A ) )
<=> ( hBOOL @ bot_bot_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_428_bot__apply) ).
thf(3689,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_pname_bool @ bot_bo844097828e_bool @ A ) )
=> ( hBOOL @ bot_bot_bool ) )
& ( ( hBOOL @ bot_bot_bool )
=> ( hBOOL @ ( hAPP_pname_bool @ bot_bo844097828e_bool @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(746,axiom,
! [A: $i,B: $i] :
( ( is_fun_a_bool @ B )
=> ( is_fun949378684l_bool @ ( hAPP_f1631501043l_bool @ A @ B ) ) ),
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(3495,plain,
! [A: $i,B: $i] :
( ( is_fun_a_bool @ B )
=> ( is_fun949378684l_bool @ ( hAPP_f1631501043l_bool @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(299,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( is_pname @ A )
& ( is_pname @ B ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( insert_pname @ B @ C ) ) )
=> ( ( A != B )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_insertE) ).
thf(1871,plain,
! [A: $i,B: $i,C: $i] :
( ( ( is_pname @ A )
& ( is_pname @ B ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( insert_pname @ B @ C ) ) )
=> ( ( A != B )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(644,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_finite_OinsertI) ).
thf(3061,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(778,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ bot_bot_bool ) )
<=> ( ( hBOOL @ A )
<=> ( hBOOL @ bot_bot_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_437_bot__unique) ).
thf(3617,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ bot_bot_bool ) )
=> ( ( ( hBOOL @ A )
=> ( hBOOL @ bot_bot_bool ) )
& ( ( hBOOL @ bot_bot_bool )
=> ( hBOOL @ A ) ) ) )
& ( ( ( ( hBOOL @ A )
=> ( hBOOL @ bot_bot_bool ) )
& ( ( hBOOL @ bot_bot_bool )
=> ( hBOOL @ A ) ) )
=> ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ bot_bot_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).
thf(744,axiom,
! [A: $i,B: $i] :
( ( ( is_fun_a_bool @ A )
& ( is_fun_a_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ A ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_544_order__antisym__conv) ).
thf(3485,plain,
! [A: $i,B: $i] :
( ( ( is_fun_a_bool @ A )
& ( is_fun_a_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).
thf(761,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ A @ B ) @ C ) )
<=> ( ( A = C )
| ( hBOOL @ ( hAPP_nat_bool @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_insert__code) ).
thf(3542,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ A @ B ) @ C ) )
=> ( ( A = C )
| ( hBOOL @ ( hAPP_nat_bool @ B @ C ) ) ) )
& ( ( ( A = C )
| ( hBOOL @ ( hAPP_nat_bool @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ A @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(94,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f1476298914l_bool @ ( cOMBB_2095475776e_bool @ A @ B ) @ C )
= ( hAPP_b589554111l_bool @ A @ ( hAPP_f1664156314l_bool @ B @ C ) ) ),
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(1191,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f1476298914l_bool @ ( cOMBB_2095475776e_bool @ A @ B ) @ C )
= ( hAPP_b589554111l_bool @ A @ ( hAPP_f1664156314l_bool @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(708,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( is_pname @ A )
& ( is_pname @ C ) )
=> ( ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ A @ B ) @ C ) )
<=> ( ( A = C )
| ( hBOOL @ ( hAPP_pname_bool @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_insert__code) ).
thf(3353,plain,
! [A: $i,B: $i,C: $i] :
( ( ( is_pname @ A )
& ( is_pname @ C ) )
=> ( ( ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ A @ B ) @ C ) )
=> ( ( A = C )
| ( hBOOL @ ( hAPP_pname_bool @ B @ C ) ) ) )
& ( ( ( A = C )
| ( hBOOL @ ( hAPP_pname_bool @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ A @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(184,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i,E: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ D ) @ E ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ C @ D ) ) @ ( hAPP_nat_nat @ C @ E ) ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ C @ A ) ) @ B ) ) @ ( hAPP_nat_nat @ C @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_671_mono__nat__linear__lb) ).
thf(1462,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i,E: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ D ) @ E ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ C @ D ) ) @ ( hAPP_nat_nat @ C @ E ) ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ C @ A ) ) @ B ) ) @ ( hAPP_nat_nat @ C @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(542,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
=> ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ A ) @ B ) )
=> ( ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( insert_fun_a_bool @ A @ B ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_card__insert__disjoint) ).
thf(2703,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
=> ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ A ) @ B ) )
=> ( ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( insert_fun_a_bool @ A @ B ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(684,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_fun_a_bool_bool @ ( hAPP_p1824510254l_bool @ ( cOMBC_1738168533e_bool @ A ) @ B ) @ C )
= ( hAPP_pname_bool @ ( hAPP_f1794073134e_bool @ A @ C ) @ B ) ),
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(3248,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_fun_a_bool_bool @ ( hAPP_p1824510254l_bool @ ( cOMBC_1738168533e_bool @ A ) @ B ) @ C )
= ( hAPP_pname_bool @ ( hAPP_f1794073134e_bool @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(673,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ ( image_a_nat @ B @ C ) ) )
<=> ? [D: $i] :
( ( is_fun_a_bool @ D )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ D ) @ C ) )
& ( A
= ( image_a_nat @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_346_subset__image__iff) ).
thf(3204,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ ( image_a_nat @ B @ C ) ) )
=> ? [D: $i] :
( ( is_fun_a_bool @ D )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ D ) @ C ) )
& ( A
= ( image_a_nat @ B @ D ) ) ) )
& ( ? [D: $i] :
( ( is_fun_a_bool @ D )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ D ) @ C ) )
& ( A
= ( image_a_nat @ B @ D ) ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ ( image_a_nat @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(53,axiom,
! [A: $i,B: $i] :
( ( ( is_fun_pname_bool @ A )
& ( is_pname @ B ) )
=> ( is_bool @ ( hAPP_pname_bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Com__Opname_000tc__HOL__Obool) ).
thf(1055,plain,
! [A: $i,B: $i] :
( ( ( is_fun_pname_bool @ A )
& ( is_pname @ B ) )
=> ( is_bool @ ( hAPP_pname_bool @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(166,axiom,
! [A: $i,B: $i] :
( ( ( hAPP_nat_nat @ suc @ A )
= ( hAPP_nat_nat @ suc @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_Suc__inject) ).
thf(1409,plain,
! [A: $i,B: $i] :
( ( ( hAPP_nat_nat @ suc @ A )
= ( hAPP_nat_nat @ suc @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(136,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f654413245e_bool @ ( cOMBB_141086128t_bool @ A @ B ) @ C )
= ( hAPP_p61793385e_bool @ A @ ( hAPP_f1291551745_pname @ B @ C ) ) ),
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(1323,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f654413245e_bool @ ( cOMBB_141086128t_bool @ A @ B ) @ C )
= ( hAPP_p61793385e_bool @ A @ ( hAPP_f1291551745_pname @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(776,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( is_a @ A )
& ( is_a @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ ( insert_a @ B @ C ) ) )
=> ( ( A != B )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_insertE) ).
thf(3612,plain,
! [A: $i,B: $i,C: $i] :
( ( ( is_a @ A )
& ( is_a @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ ( insert_a @ B @ C ) ) )
=> ( ( A != B )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).
thf(839,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_511_order__trans) ).
thf(3845,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).
thf(886,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
=> ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ B ) )
=> ( ( hAPP_fun_a_bool_nat @ finite_card_a @ ( insert_a @ A @ B ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_fun_a_bool_nat @ finite_card_a @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_card__insert__disjoint) ).
thf(4023,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
=> ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ B ) )
=> ( ( hAPP_fun_a_bool_nat @ finite_card_a @ ( insert_a @ A @ B ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_fun_a_bool_nat @ finite_card_a @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).
thf(651,axiom,
! [A: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_371_order__refl) ).
thf(3089,plain,
! [A: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(382,axiom,
! [A: $i] :
( ( is_fun_pname_bool @ A )
=> ( ( collect_pname @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_Collect__def) ).
thf(2126,plain,
! [A: $i] :
( ( is_fun_pname_bool @ A )
=> ( ( collect_pname @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(827,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ C ) )
=> ( ( B = A )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_524_xt1_I4_J) ).
thf(3803,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ C ) )
=> ( ( B = A )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).
thf(480,axiom,
! [A: $i] :
( ( collect_a @ ( hAPP_a_fun_a_bool @ fequal_a @ A ) )
= ( insert_a @ A @ bot_bot_fun_a_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_490_singleton__conv2) ).
thf(2466,plain,
! [A: $i] :
( ( collect_a @ ( hAPP_a_fun_a_bool @ fequal_a @ A ) )
= ( insert_a @ A @ bot_bot_fun_a_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(12,axiom,
is_fun_a_bool @ bot_bot_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(949,plain,
is_fun_a_bool @ bot_bot_fun_a_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(800,axiom,
! [A: $i,B: $i] :
( ( is_pname @ B )
=> ( is_a @ ( hAPP_pname_a @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Com__Opname_000t__a) ).
thf(3713,plain,
! [A: $i,B: $i] :
( ( is_pname @ B )
=> ( is_a @ ( hAPP_pname_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).
thf(469,axiom,
! [A: $i,B: $i] :
( ( A = B )
=> ~ ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
=> ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_301_equalityE) ).
thf(2420,plain,
! [A: $i,B: $i] :
( ( A = B )
=> ~ ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
=> ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(198,axiom,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_624_not__add__less2) ).
thf(1514,plain,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(38,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_655_less__add__Suc1) ).
thf(1013,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(629,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1283814551_pname @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_finite__imageI) ).
thf(3014,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1283814551_pname @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(353,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B )
= A )
<=> ( C
= ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_598_le__imp__diff__is__add) ).
thf(2024,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( ( ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B )
= A )
=> ( C
= ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) )
& ( ( C
= ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) )
=> ( ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(192,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_pname_bool @ B @ A ) ) @ ( hAPP_pname_bool @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_380_le__funE) ).
thf(1494,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_pname_bool @ B @ A ) ) @ ( hAPP_pname_bool @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(582,axiom,
hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ g ) @ ( image_pname_a @ mgt_call @ u ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(2852,plain,
hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ g ) @ ( image_pname_a @ mgt_call @ u ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(294,axiom,
! [A: $i] :
( ( is_fun_a_bool @ A )
=> ( ( collect_a @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_Collect__def) ).
thf(1847,plain,
! [A: $i] :
( ( is_fun_a_bool @ A )
=> ( ( collect_a @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(822,axiom,
! [A: $i,B: $i] :
( ( ( is_fun_a_bool @ A )
& ( is_fun_a_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ A ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_519_order__antisym) ).
thf(3788,plain,
! [A: $i,B: $i] :
( ( ( is_fun_a_bool @ A )
& ( is_fun_a_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ A ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).
thf(913,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ bot_bot_nat ) )
=> ( A = bot_bot_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_435_le__bot) ).
thf(4119,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ bot_bot_nat ) )
=> ( A = bot_bot_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[913]) ).
thf(879,axiom,
! [A: $i] : ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_367_order__refl) ).
thf(3998,plain,
! [A: $i] : ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).
thf(738,axiom,
! [A: $i,B: $i] :
( ( A = B )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_eq__imp__le) ).
thf(3463,plain,
! [A: $i,B: $i] :
( ( A = B )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(717,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_subset__trans) ).
thf(3385,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).
thf(454,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_Suc__leD) ).
thf(2373,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(859,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ C ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ ( image_nat_nat @ A @ B ) ) )
=> ? [D: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ D ) @ B ) )
& ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ D ) )
& ( C
= ( image_nat_nat @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_finite__subset__image) ).
thf(3919,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ C ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ ( image_nat_nat @ A @ B ) ) )
=> ? [D: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ D ) @ B ) )
& ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ D ) )
& ( C
= ( image_nat_nat @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).
thf(72,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
<=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_640_le__eq__less__or__eq) ).
thf(1115,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
| ( A = B ) ) )
& ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
| ( A = B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(740,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_503_xt1_I6_J) ).
thf(3470,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(764,axiom,
! [A: $i] :
( ( bot_bo1701429464l_bool
= ( collect_fun_nat_bool @ A ) )
<=> ! [B: $i] :
~ ( hBOOL @ ( hAPP_f54304608l_bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_408_empty__Collect__eq) ).
thf(3557,plain,
! [A: $i] :
( ( ( bot_bo1701429464l_bool
= ( collect_fun_nat_bool @ A ) )
=> ! [B: $i] :
~ ( hBOOL @ ( hAPP_f54304608l_bool @ A @ B ) ) )
& ( ! [B: $i] :
~ ( hBOOL @ ( hAPP_f54304608l_bool @ A @ B ) )
=> ( bot_bo1701429464l_bool
= ( collect_fun_nat_bool @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).
thf(300,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
=> ( ( ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B )
= ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) )
<=> ( C = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_eq__diff__iff) ).
thf(1875,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
=> ( ( ( ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B )
= ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) )
=> ( C = A ) )
& ( ( C = A )
=> ( ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B )
= ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(477,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ B ) )
=> ( ( insert_nat @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_insert__absorb) ).
thf(2456,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ B ) )
=> ( ( insert_nat @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(238,axiom,
! [A: $i,B: $i] :
( ( is_bool @ B )
=> ( is_bool @ ( hAPP_bool_bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool) ).
thf(1664,plain,
! [A: $i,B: $i] :
( ( is_bool @ B )
=> ( is_bool @ ( hAPP_bool_bool @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(863,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ B ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( insert_a @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_card__insert__le) ).
thf(3934,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ B ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( insert_a @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).
thf(804,axiom,
! [A: $i,B: $i] :
( ( insert_a @ A @ ( collect_a @ B ) )
= ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fimplies @ ( cOMBB_bool_bool_a @ fNot @ ( hAPP_a_fun_a_bool @ ( cOMBC_a_a_bool @ fequal_a ) @ A ) ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_insert__Collect) ).
thf(3724,plain,
! [A: $i,B: $i] :
( ( insert_a @ A @ ( collect_a @ B ) )
= ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fimplies @ ( cOMBB_bool_bool_a @ fNot @ ( hAPP_a_fun_a_bool @ ( cOMBC_a_a_bool @ fequal_a ) @ A ) ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).
thf(419,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) )
= ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_601_add__diff__assoc) ).
thf(2259,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) )
= ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(529,axiom,
hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ bot_bot_fun_nat_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_391_finite_OemptyI) ).
thf(2650,plain,
hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ bot_bot_fun_nat_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(411,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_622_trans__less__add1) ).
thf(2236,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(755,axiom,
! [A: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_le__refl) ).
thf(3525,plain,
! [A: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).
thf(816,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ A @ B ) )
=> ( ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fconj @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ B ) ) @ A ) )
= ( insert_fun_a_bool @ B @ bot_bo1389914601l_bool ) ) )
& ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ A @ B ) )
=> ( ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fconj @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ B ) ) @ A ) )
= bot_bo1389914601l_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_481_Collect__conv__if2) ).
thf(3771,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ A @ B ) )
=> ( ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fconj @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ B ) ) @ A ) )
= ( insert_fun_a_bool @ B @ bot_bo1389914601l_bool ) ) )
& ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ A @ B ) )
=> ( ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fconj @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ B ) ) @ A ) )
= bot_bo1389914601l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(519,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_n1414589940l_bool @ ( cOMBB_1823939024ol_nat @ A @ B ) @ C )
= ( hAPP_f1631501043l_bool @ A @ ( hAPP_nat_fun_a_bool @ B @ C ) ) ),
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(2616,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_n1414589940l_bool @ ( cOMBB_1823939024ol_nat @ A @ B ) @ C )
= ( hAPP_f1631501043l_bool @ A @ ( hAPP_nat_fun_a_bool @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(323,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) @ C )
= ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ C ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_diff__commute) ).
thf(1946,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) @ C )
= ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ C ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(185,axiom,
! [A: $i,B: $i] :
( ( ( insert_nat @ A @ bot_bot_fun_nat_bool )
= ( insert_nat @ B @ bot_bot_fun_nat_bool ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_447_singleton__inject) ).
thf(1465,plain,
! [A: $i,B: $i] :
( ( ( insert_nat @ A @ bot_bot_fun_nat_bool )
= ( insert_nat @ B @ bot_bot_fun_nat_bool ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(869,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ ( insert_a @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_insertI2) ).
thf(3966,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ ( insert_a @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).
thf(250,axiom,
! [A: $i] :
( ( is_fun1661590463l_bool @ A )
=> ( ( collec1974731493e_bool @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_Collect__def) ).
thf(1714,plain,
! [A: $i] :
( ( is_fun1661590463l_bool @ A )
=> ( ( collec1974731493e_bool @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(376,axiom,
! [A: $i] :
( zero_zero_nat
!= ( hAPP_nat_nat @ suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_692_Zero__neq__Suc) ).
thf(2105,plain,
! [A: $i] :
( zero_zero_nat
!= ( hAPP_nat_nat @ suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(899,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_rev__finite__subset) ).
thf(4072,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[899]) ).
thf(283,axiom,
! [A: $i,B: $i,C: $i] :
( ( is_fun_pname_bool @ C )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ ( image_1854862208_pname @ A @ B ) ) )
=> ? [D: $i] :
( ( is_fun949378684l_bool @ D )
& ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ D ) @ B ) )
& ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ D ) )
& ( C
= ( image_1854862208_pname @ A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_finite__subset__image) ).
thf(1811,plain,
! [A: $i,B: $i,C: $i] :
( ( is_fun_pname_bool @ C )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ ( image_1854862208_pname @ A @ B ) ) )
=> ? [D: $i] :
( ( is_fun949378684l_bool @ D )
& ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ D ) @ B ) )
& ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ D ) )
& ( C
= ( image_1854862208_pname @ A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(179,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_pname_bool @ ( hAPP_f654413245e_bool @ ( cOMBC_267053842l_bool @ A ) @ B ) @ C )
= ( hAPP_f54304608l_bool @ ( hAPP_p130839763l_bool @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Oboo) ).
thf(1450,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_pname_bool @ ( hAPP_f654413245e_bool @ ( cOMBC_267053842l_bool @ A ) @ B ) @ C )
= ( hAPP_f54304608l_bool @ ( hAPP_p130839763l_bool @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(884,axiom,
! [A: $i,B: $i] :
( bot_bot_fun_a_bool
!= ( insert_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_463_empty__not__insert) ).
thf(4018,plain,
! [A: $i,B: $i] :
( bot_bot_fun_a_bool
!= ( insert_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).
thf(371,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_diff__le__mono) ).
thf(2090,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(720,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( image_1655916159e_bool @ A @ B ) ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ ( hAPP_f800510211t_bool @ ( cOMBC_226598744l_bool @ member_nat ) @ B ) ) @ ( hAPP_f1066163005t_bool @ ( cOMBC_386238098l_bool @ ( cOMBB_2117322052ol_nat @ fequal533582459e_bool @ A ) ) @ ( hAPP_n1025906991e_bool @ A @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_pigeonhole__infinite) ).
thf(3393,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( image_1655916159e_bool @ A @ B ) ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ ( hAPP_f800510211t_bool @ ( cOMBC_226598744l_bool @ member_nat ) @ B ) ) @ ( hAPP_f1066163005t_bool @ ( cOMBC_386238098l_bool @ ( cOMBB_2117322052ol_nat @ fequal533582459e_bool @ A ) ) @ ( hAPP_n1025906991e_bool @ A @ C ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).
thf(312,axiom,
! [A: $i,B: $i,C: $i] :
( ( is_fun_pname_bool @ C )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ ( image_1921560913_pname @ A @ B ) ) )
=> ? [D: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ D ) @ B ) )
& ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ D ) )
& ( C
= ( image_1921560913_pname @ A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_finite__subset__image) ).
thf(1911,plain,
! [A: $i,B: $i,C: $i] :
( ( is_fun_pname_bool @ C )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ ( image_1921560913_pname @ A @ B ) ) )
=> ? [D: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ D ) @ B ) )
& ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ D ) )
& ( C
= ( image_1921560913_pname @ A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(565,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ C ) )
=> ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f621171935l_bool @ A @ bot_bo1389914601l_bool ) )
=> ( ! [D: $i,E: $i] :
( ( ( is_fun_a_bool @ D )
& ( is_fun949378684l_bool @ E ) )
=> ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ E ) )
=> ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ D ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP_f621171935l_bool @ A @ E ) )
=> ( hBOOL @ ( hAPP_f621171935l_bool @ A @ ( insert_fun_a_bool @ D @ E ) ) ) ) ) ) ) )
=> ( hBOOL @ ( hAPP_f621171935l_bool @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_561_finite__subset__induct) ).
thf(2782,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ C ) )
=> ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f621171935l_bool @ A @ bot_bo1389914601l_bool ) )
=> ( ! [D: $i,E: $i] :
( ( ( is_fun_a_bool @ D )
& ( is_fun949378684l_bool @ E ) )
=> ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ E ) )
=> ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ D ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP_f621171935l_bool @ A @ E ) )
=> ( hBOOL @ ( hAPP_f621171935l_bool @ A @ ( insert_fun_a_bool @ D @ E ) ) ) ) ) ) ) )
=> ( hBOOL @ ( hAPP_f621171935l_bool @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(70,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_le__diff__iff) ).
thf(1109,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(481,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
<=> ! [C: $i] :
( ( is_a @ C )
=> ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_a_bool @ A @ C ) ) @ ( hAPP_a_bool @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_376_le__fun__def) ).
thf(2469,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
=> ! [C: $i] :
( ( is_a @ C )
=> ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_a_bool @ A @ C ) ) @ ( hAPP_a_bool @ B @ C ) ) ) ) )
& ( ! [C: $i] :
( ( is_a @ C )
=> ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_a_bool @ A @ C ) ) @ ( hAPP_a_bool @ B @ C ) ) ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(138,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ A ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_card__mono) ).
thf(1334,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ A ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(756,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_subsetD) ).
thf(3527,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).
thf(591,axiom,
! [A: $i,B: $i] :
( ( B = bot_bot_fun_a_bool )
=> ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_397_equals0D) ).
thf(2880,plain,
! [A: $i,B: $i] :
( ( B = bot_bot_fun_a_bool )
=> ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(240,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_pname_bool @ ( hAPP_n1025906991e_bool @ ( cOMBC_pname_nat_bool @ A ) @ B ) @ C )
= ( hAPP_nat_bool @ ( hAPP_p1499970991t_bool @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Nat__Onat_000tc__HOL__Obool_U) ).
thf(1682,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_pname_bool @ ( hAPP_n1025906991e_bool @ ( cOMBC_pname_nat_bool @ A ) @ B ) @ C )
= ( hAPP_nat_bool @ ( hAPP_p1499970991t_bool @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(289,axiom,
is_pname @ ( undefined_pname @ pname ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_HOL_Oundefined_000tc__Com__Opname) ).
thf(1828,plain,
is_pname @ ( undefined_pname @ pname ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(335,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ A ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_card__mono) ).
thf(1978,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ A ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(431,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_631_less__SucI) ).
thf(2291,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(156,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_n1025906991e_bool @ ( cOMBB_1212655066ol_nat @ A @ B ) @ C )
= ( hAPP_p61793385e_bool @ A @ ( hAPP_nat_pname @ B @ C ) ) ),
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(1383,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_n1025906991e_bool @ ( cOMBB_1212655066ol_nat @ A @ B ) @ C )
= ( hAPP_p61793385e_bool @ A @ ( hAPP_nat_pname @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ( ( is_fun_pname_bool @ A )
& ( is_fun_pname_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_equalityI) ).
thf(1020,plain,
! [A: $i,B: $i] :
( ( ( is_fun_pname_bool @ A )
& ( is_fun_pname_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(506,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ C ) )
=> ( ( C = A )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_529_ord__le__eq__trans) ).
thf(2555,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ C ) )
=> ( ( C = A )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(695,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( is_a @ A )
& ( is_a @ B )
& ( is_a @ C )
& ( is_a @ D ) )
=> ( ( ( insert_a @ A @ ( insert_a @ B @ bot_bot_fun_a_bool ) )
= ( insert_a @ C @ ( insert_a @ D @ bot_bot_fun_a_bool ) ) )
<=> ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_454_doubleton__eq__iff) ).
thf(3300,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( is_a @ A )
& ( is_a @ B )
& ( is_a @ C )
& ( is_a @ D ) )
=> ( ( ( ( insert_a @ A @ ( insert_a @ B @ bot_bot_fun_a_bool ) )
= ( insert_a @ C @ ( insert_a @ D @ bot_bot_fun_a_bool ) ) )
=> ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) )
& ( ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) )
=> ( ( insert_a @ A @ ( insert_a @ B @ bot_bot_fun_a_bool ) )
= ( insert_a @ C @ ( insert_a @ D @ bot_bot_fun_a_bool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(653,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( is_a @ A )
& ( is_a @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ ( insert_a @ B @ C ) ) )
<=> ( ( A = B )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_insert__iff) ).
thf(3093,plain,
! [A: $i,B: $i,C: $i] :
( ( ( is_a @ A )
& ( is_a @ B ) )
=> ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ ( insert_a @ B @ C ) ) )
=> ( ( A = B )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ C ) ) ) )
& ( ( ( A = B )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ C ) ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ ( insert_a @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(445,axiom,
! [A: $i,B: $i] :
( ( is_fun_a_bool @ B )
=> ( is_pname @ ( hAPP_f1128469712_pname @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opname) ).
thf(2335,plain,
! [A: $i,B: $i] :
( ( is_fun_a_bool @ B )
=> ( is_pname @ ( hAPP_f1128469712_pname @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( ( is_fun1661590463l_bool @ A )
& ( is_fun_pname_bool @ B ) )
=> ( is_bool @ ( hAPP_f1664156314l_bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__Obool) ).
thf(966,plain,
! [A: $i,B: $i] :
( ( ( is_fun1661590463l_bool @ A )
& ( is_fun_pname_bool @ B ) )
=> ( is_bool @ ( hAPP_f1664156314l_bool @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(124,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_639_less__imp__le__nat) ).
thf(1283,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(367,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ A ) @ B ) @ C )
= ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__HOL__Obool_U) ).
thf(2073,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ A ) @ B ) @ C )
= ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(806,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ C ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ ( image_fun_nat_bool_a @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_finite__surj) ).
thf(3739,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ C ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ ( image_fun_nat_bool_a @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).
thf(585,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_subset__trans) ).
thf(2861,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(306,axiom,
is_fun949378684l_bool @ finite_finite_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Finite__Set_Ofinite_000t__a) ).
thf(1896,plain,
is_fun949378684l_bool @ finite_finite_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(303,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_658_less__eq__Suc__le) ).
thf(1886,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(278,axiom,
! [A: $i,B: $i,C: $i] :
( ( is_fun1661590463l_bool @ C )
=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ C ) )
=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ C ) @ ( image_1655916159e_bool @ A @ B ) ) )
=> ? [D: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ D ) @ B ) )
& ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ D ) )
& ( C
= ( image_1655916159e_bool @ A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_finite__subset__image) ).
thf(1796,plain,
! [A: $i,B: $i,C: $i] :
( ( is_fun1661590463l_bool @ C )
=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ C ) )
=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ C ) @ ( image_1655916159e_bool @ A @ B ) ) )
=> ? [D: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ D ) @ B ) )
& ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ D ) )
& ( C
= ( image_1655916159e_bool @ A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(453,axiom,
! [A: $i,B: $i] :
( ( is_fun_a_bool @ B )
=> ( is_fun949378684l_bool @ ( image_a_fun_a_bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
thf(2371,plain,
! [A: $i,B: $i] :
( ( is_fun_a_bool @ B )
=> ( is_fun949378684l_bool @ ( image_a_fun_a_bool @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(387,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ B ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( insert_fun_nat_bool @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_card__insert__le) ).
thf(2137,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ B ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( insert_fun_nat_bool @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(344,axiom,
! [A: $i,B: $i] :
( ( is_fun949378684l_bool @ B )
=> ( is_fun_a_bool @ ( image_fun_a_bool_a @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_It__a_Mtc__HOL__Obool_J_000t__a) ).
thf(2002,plain,
! [A: $i,B: $i] :
( ( is_fun949378684l_bool @ B )
=> ( is_fun_a_bool @ ( image_fun_a_bool_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(568,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ ( insert_nat @ B @ C ) ) )
<=> ( ( A = B )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_insert__iff) ).
thf(2799,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ ( insert_nat @ B @ C ) ) )
=> ( ( A = B )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ C ) ) ) )
& ( ( ( A = B )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ C ) ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ ( insert_nat @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(701,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( insert_pname @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_insertI1) ).
thf(3327,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( insert_pname @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(99,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( insert_nat @ A @ B ) ) @ C ) )
<=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ C ) )
& ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_322_insert__subset) ).
thf(1201,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( insert_nat @ A @ B ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ C ) )
& ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) ) ) )
& ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ C ) )
& ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( insert_nat @ A @ B ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(724,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ C ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ ( image_fun_a_bool_a @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_finite__surj) ).
thf(3406,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ C ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ ( image_fun_a_bool_a @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).
thf(592,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ A ) @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Nat__Onat_T) ).
thf(2884,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ A ) @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(875,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ D ) )
=> ( ( A
= ( hAPP_pname_a @ B @ C ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ ( image_pname_a @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_312_rev__image__eqI) ).
thf(3986,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ D ) )
=> ( ( A
= ( hAPP_pname_a @ B @ C ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ ( image_pname_a @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).
thf(361,axiom,
! [A: $i] :
( ( is_bool @ A )
=> ( is_fun_pname_bool @ ( cOMBK_bool_pname @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_COMBK_000tc__HOL__Obool_000tc__Com__Opname) ).
thf(2058,plain,
! [A: $i] :
( ( is_bool @ A )
=> ( is_fun_pname_bool @ ( cOMBK_bool_pname @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(178,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ D ) )
=> ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ D )
= ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_618_less__add__eq__less) ).
thf(1447,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ D ) )
=> ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ D )
= ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_616_termination__basic__simps_I2_J) ).
thf(956,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(375,axiom,
( bot_bo844097828e_bool
= ( collect_pname @ ( cOMBK_bool_pname @ fFalse ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_419_empty__def) ).
thf(2103,plain,
( bot_bo844097828e_bool
= ( collect_pname @ ( cOMBK_bool_pname @ fFalse ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(164,axiom,
! [A: $i,B: $i] : ( is_bool @ ( hAPP_f1637334154l_bool @ A @ B ) ),
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(1405,plain,
! [A: $i,B: $i] : ( is_bool @ ( hAPP_f1637334154l_bool @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(69,axiom,
! [A: $i,B: $i,C: $i] :
( ( is_fun949378684l_bool @ C )
=> ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ C ) )
=> ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ C ) @ ( image_nat_fun_a_bool @ A @ B ) ) )
=> ? [D: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ D ) @ B ) )
& ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ D ) )
& ( C
= ( image_nat_fun_a_bool @ A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_finite__subset__image) ).
thf(1104,plain,
! [A: $i,B: $i,C: $i] :
( ( is_fun949378684l_bool @ C )
=> ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ C ) )
=> ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ C ) @ ( image_nat_fun_a_bool @ A @ B ) ) )
=> ? [D: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ D ) @ B ) )
& ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ D ) )
& ( C
= ( image_nat_fun_a_bool @ A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(244,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_661_le__imp__less__Suc) ).
thf(1697,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(775,axiom,
! [A: $i,B: $i] :
( ( ( is_a @ A )
& ( is_a @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ ( insert_a @ B @ bot_bot_fun_a_bool ) ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_457_singleton__iff) ).
thf(3606,plain,
! [A: $i,B: $i] :
( ( ( is_a @ A )
& ( is_a @ B ) )
=> ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ ( insert_a @ B @ bot_bot_fun_a_bool ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ ( insert_a @ B @ bot_bot_fun_a_bool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).
thf(461,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ C ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ ( image_nat_nat @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_finite__surj) ).
thf(2392,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ C ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ ( image_nat_nat @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(297,axiom,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_625_not__add__less1) ).
thf(1863,plain,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(610,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( image_47868345e_bool @ A @ B ) ) )
=> ? [C: $i] :
( ( is_pname @ C )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ ( hAPP_f759274231e_bool @ ( cOMBC_1058051404l_bool @ member_pname ) @ B ) ) @ ( hAPP_f759274231e_bool @ ( cOMBC_1058051404l_bool @ ( cOMBB_408569982_pname @ fequal533582459e_bool @ A ) ) @ ( hAPP_p61793385e_bool @ A @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_pigeonhole__infinite) ).
thf(2954,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( image_47868345e_bool @ A @ B ) ) )
=> ? [C: $i] :
( ( is_pname @ C )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ ( hAPP_f759274231e_bool @ ( cOMBC_1058051404l_bool @ member_pname ) @ B ) ) @ ( hAPP_f759274231e_bool @ ( cOMBC_1058051404l_bool @ ( cOMBB_408569982_pname @ fequal533582459e_bool @ A ) ) @ ( hAPP_p61793385e_bool @ A @ C ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(347,axiom,
is_bool @ fFalse,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_fFalse) ).
thf(2011,plain,
is_bool @ fFalse,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(175,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_585_le__add1) ).
thf(1438,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(131,axiom,
! [A: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ ord_less_nat ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_614_finite__Collect__less__nat) ).
thf(1306,plain,
! [A: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ ord_less_nat ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(380,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ C ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ A @ bot_bot_fun_nat_bool ) )
=> ( ! [D: $i,E: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ E ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ D ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ A @ E ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ A @ ( insert_nat @ D @ E ) ) ) ) ) ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_556_finite__subset__induct) ).
thf(2118,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ C ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ A @ bot_bot_fun_nat_bool ) )
=> ( ! [D: $i,E: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ E ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ D ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ A @ E ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ A @ ( insert_nat @ D @ E ) ) ) ) ) ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(248,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_p338031245l_bool @ ( cOMBB_408569982_pname @ A @ B ) @ C )
= ( hAPP_f434788991l_bool @ A @ ( hAPP_p61793385e_bool @ B @ C ) ) ),
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(1708,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_p338031245l_bool @ ( cOMBB_408569982_pname @ A @ B ) @ C )
= ( hAPP_f434788991l_bool @ A @ ( hAPP_p61793385e_bool @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(901,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ A @ B ) )
=> ( ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fconj @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ fequal_fun_a_bool ) @ B ) ) @ A ) )
= ( insert_fun_a_bool @ B @ bot_bo1389914601l_bool ) ) )
& ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ A @ B ) )
=> ( ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fconj @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ fequal_fun_a_bool ) @ B ) ) @ A ) )
= bot_bo1389914601l_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_475_Collect__conv__if) ).
thf(4076,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ A @ B ) )
=> ( ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fconj @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ fequal_fun_a_bool ) @ B ) ) @ A ) )
= ( insert_fun_a_bool @ B @ bot_bo1389914601l_bool ) ) )
& ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ A @ B ) )
=> ( ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fconj @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ fequal_fun_a_bool ) @ B ) ) @ A ) )
= bot_bo1389914601l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).
thf(566,axiom,
! [A: $i,B: $i,C: $i] :
( ( is_fun_pname_bool @ C )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ ( image_a_pname @ A @ B ) ) )
=> ? [D: $i] :
( ( is_fun_a_bool @ D )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ D ) @ B ) )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ D ) )
& ( C
= ( image_a_pname @ A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_finite__subset__image) ).
thf(2790,plain,
! [A: $i,B: $i,C: $i] :
( ( is_fun_pname_bool @ C )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ ( image_a_pname @ A @ B ) ) )
=> ? [D: $i] :
( ( is_fun_a_bool @ D )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ D ) @ B ) )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ D ) )
& ( C
= ( image_a_pname @ A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(561,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_2_1_U) ).
thf(2773,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(771,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ C ) )
=> ( ( ( hBOOL @ B )
<=> ( hBOOL @ A ) )
=> ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_520_xt1_I4_J) ).
thf(3591,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ C ) )
=> ( ( ( ( hBOOL @ B )
=> ( hBOOL @ A ) )
& ( ( hBOOL @ A )
=> ( hBOOL @ B ) ) )
=> ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).
thf(599,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
=> ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( image_a_fun_a_bool @ A @ B ) ) )
=> ? [C: $i] :
( ( is_a @ C )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ ( hAPP_f2050579477a_bool @ ( cOMBC_1355376034l_bool @ member_a ) @ B ) ) @ ( hAPP_f2050579477a_bool @ ( cOMBC_1355376034l_bool @ ( cOMBB_472261505bool_a @ fequal_fun_a_bool @ A ) ) @ ( hAPP_a_fun_a_bool @ A @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_pigeonhole__infinite) ).
thf(2910,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
=> ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( image_a_fun_a_bool @ A @ B ) ) )
=> ? [C: $i] :
( ( is_a @ C )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ ( hAPP_f2050579477a_bool @ ( cOMBC_1355376034l_bool @ member_a ) @ B ) ) @ ( hAPP_f2050579477a_bool @ ( cOMBC_1355376034l_bool @ ( cOMBB_472261505bool_a @ fequal_fun_a_bool @ A ) ) @ ( hAPP_a_fun_a_bool @ A @ C ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(874,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ ( image_pname_a @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_finite__surj) ).
thf(3984,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ ( image_pname_a @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).
thf(666,axiom,
! [A: $i,B: $i] :
( ( ( is_fun_a_bool @ A )
& ( is_fun_a_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ A ) )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_509_xt1_I5_J) ).
thf(3169,plain,
! [A: $i,B: $i] :
( ( ( is_fun_a_bool @ A )
& ( is_fun_a_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ A ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ B ) )
<=> ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_574_nat__add__right__cancel) ).
thf(925,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ B ) )
=> ( A = C ) )
& ( ( A = C )
=> ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(98,axiom,
! [A: $i,B: $i] : ( is_pname @ ( hAPP_nat_pname @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__Com__Opname) ).
thf(1199,plain,
! [A: $i,B: $i] : ( is_pname @ ( hAPP_nat_pname @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(450,axiom,
! [A: $i,B: $i] : ( is_fun_a_bool @ ( hAPP_f1549043526a_bool @ A @ B ) ),
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(2364,plain,
! [A: $i,B: $i] : ( is_fun_a_bool @ ( hAPP_f1549043526a_bool @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(878,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ B ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ A ) ) ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_finite__Collect__conjI) ).
thf(3995,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ B ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ A ) ) ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).
thf(357,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_n1006566506l_bool @ ( cOMBB_1015721476ol_nat @ A @ B ) @ C )
= ( hAPP_b589554111l_bool @ A @ ( hAPP_nat_bool @ B @ C ) ) ),
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(2047,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_n1006566506l_bool @ ( cOMBB_1015721476ol_nat @ A @ B ) @ C )
= ( hAPP_b589554111l_bool @ A @ ( hAPP_nat_bool @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(697,axiom,
hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ bot_bo1389914601l_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_388_finite_OemptyI) ).
thf(3318,plain,
hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ bot_bo1389914601l_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(133,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ A @ B ) )
=> ( ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ ( hAPP_n1699378549t_bool @ fequal_nat @ B ) ) @ A ) )
= ( insert_nat @ B @ bot_bot_fun_nat_bool ) ) )
& ( ~ ( hBOOL @ ( hAPP_nat_bool @ A @ B ) )
=> ( ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ ( hAPP_n1699378549t_bool @ fequal_nat @ B ) ) @ A ) )
= bot_bot_fun_nat_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_476_Collect__conv__if2) ).
thf(1311,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ A @ B ) )
=> ( ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ ( hAPP_n1699378549t_bool @ fequal_nat @ B ) ) @ A ) )
= ( insert_nat @ B @ bot_bot_fun_nat_bool ) ) )
& ( ~ ( hBOOL @ ( hAPP_nat_bool @ A @ B ) )
=> ( ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ ( hAPP_n1699378549t_bool @ fequal_nat @ B ) ) @ A ) )
= bot_bot_fun_nat_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(814,axiom,
! [A: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_subset__refl) ).
thf(3767,plain,
! [A: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).
thf(433,axiom,
! [A: $i,B: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_571_add__Suc__right) ).
thf(2296,plain,
! [A: $i,B: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(54,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_pname_bool @ ( cOMBB_647938656_pname @ A @ B ) @ C )
= ( hAPP_bool_bool @ A @ ( hAPP_pname_bool @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname_U) ).
thf(1057,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_pname_bool @ ( cOMBB_647938656_pname @ A @ B ) @ C )
= ( hAPP_bool_bool @ A @ ( hAPP_pname_bool @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(791,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ A @ B ) ) )
<=> ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_finite__insert) ).
thf(3679,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ A @ B ) ) )
=> ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) ) )
& ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
=> ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).
thf(253,axiom,
! [A: $i] :
( ( is_fun_pname_bool @ A )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ bot_bo844097828e_bool ) )
=> ( A = bot_bo844097828e_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_431_le__bot) ).
thf(1723,plain,
! [A: $i] :
( ( is_fun_pname_bool @ A )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ bot_bo844097828e_bool ) )
=> ( A = bot_bo844097828e_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(687,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_finite__subset) ).
thf(3261,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(416,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) ) ) @ A )
= ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ suc @ C ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_608_diff__Suc__diff__eq2) ).
thf(2249,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) ) ) @ A )
= ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ suc @ C ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(845,axiom,
! [A: $i,B: $i,C: $i] :
( ( B = C )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_537_ord__eq__le__trans) ).
thf(3867,plain,
! [A: $i,B: $i,C: $i] :
( ( B = C )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).
thf(216,axiom,
! [A: $i,B: $i] : ( is_fun949378684l_bool @ ( hAPP_n1414589940l_bool @ A @ B ) ),
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(1580,plain,
! [A: $i,B: $i] : ( is_fun949378684l_bool @ ( hAPP_n1414589940l_bool @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(113,axiom,
! [A: $i,B: $i] :
( ( is_fun_pname_bool @ B )
=> ( is_fun_a_bool @ ( hAPP_f1051908748a_bool @ A @ B ) ) ),
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(1255,plain,
! [A: $i,B: $i] :
( ( is_fun_pname_bool @ B )
=> ( is_fun_a_bool @ ( hAPP_f1051908748a_bool @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(391,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_p130839763l_bool @ ( cOMBB_928955006_pname @ A @ B ) @ C )
= ( hAPP_f103356543l_bool @ A @ ( hAPP_p1499970991t_bool @ B @ C ) ) ),
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(2147,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_p130839763l_bool @ ( cOMBB_928955006_pname @ A @ B ) @ C )
= ( hAPP_f103356543l_bool @ A @ ( hAPP_p1499970991t_bool @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(239,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( insert_nat @ A @ ( insert_nat @ B @ bot_bot_fun_nat_bool ) )
= ( insert_nat @ C @ ( insert_nat @ D @ bot_bot_fun_nat_bool ) ) )
<=> ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_453_doubleton__eq__iff) ).
thf(1666,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( insert_nat @ A @ ( insert_nat @ B @ bot_bot_fun_nat_bool ) )
= ( insert_nat @ C @ ( insert_nat @ D @ bot_bot_fun_nat_bool ) ) )
=> ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) )
& ( ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) )
=> ( ( insert_nat @ A @ ( insert_nat @ B @ bot_bot_fun_nat_bool ) )
= ( insert_nat @ C @ ( insert_nat @ D @ bot_bot_fun_nat_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(515,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_le__trans) ).
thf(2606,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(392,axiom,
! [A: $i,B: $i] : ( is_fun1661590463l_bool @ ( image_1655916159e_bool @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).
thf(2150,plain,
! [A: $i,B: $i] : ( is_fun1661590463l_bool @ ( image_1655916159e_bool @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(830,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ B ) ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ A ) ) ) )
=> ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fconj @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_finite__Collect__conjI) ).
thf(3814,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ B ) ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ A ) ) ) )
=> ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fconj @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).
thf(463,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ ( insert_a @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_330_subset__insertI2) ).
thf(2396,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ ( insert_a @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(514,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
=> ( ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ A ) @ B ) )
=> ( ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( insert_fun_a_bool @ A @ B ) )
= ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ B ) ) )
& ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ A ) @ B ) )
=> ( ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( insert_fun_a_bool @ A @ B ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_card__insert__if) ).
thf(2601,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
=> ( ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ A ) @ B ) )
=> ( ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( insert_fun_a_bool @ A @ B ) )
= ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ B ) ) )
& ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ A ) @ B ) )
=> ( ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( insert_fun_a_bool @ A @ B ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(834,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_501_xt1_I6_J) ).
thf(3827,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).
thf(799,axiom,
! [A: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ bot_bot_fun_a_bool ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_394_empty__subsetI) ).
thf(3711,plain,
! [A: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ bot_bot_fun_a_bool ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).
thf(883,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_rev__finite__subset) ).
thf(4016,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).
thf(47,axiom,
! [A: $i,B: $i] :
( ( is_a @ B )
=> ( is_a @ ( hAPP_a_a @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000t__a_000t__a) ).
thf(1042,plain,
! [A: $i,B: $i] :
( ( is_a @ B )
=> ( is_a @ ( hAPP_a_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(500,axiom,
! [A: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_369_order__refl) ).
thf(2541,plain,
! [A: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(90,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ B ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_287_mem__def) ).
thf(1174,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ B @ A ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ B @ A ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(385,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_nat_bool @ B @ A ) ) @ ( hAPP_nat_bool @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_378_le__funD) ).
thf(2133,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_nat_bool @ B @ A ) ) @ ( hAPP_nat_bool @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(705,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ C ) )
=> ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ A ) )
=> ( ( ( insert_nat @ B @ C )
= ( insert_nat @ B @ A ) )
<=> ( C = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_insert__ident) ).
thf(3339,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ C ) )
=> ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ A ) )
=> ( ( ( ( insert_nat @ B @ C )
= ( insert_nat @ B @ A ) )
=> ( C = A ) )
& ( ( C = A )
=> ( ( insert_nat @ B @ C )
= ( insert_nat @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(817,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ ( insert_pname @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_insertI2) ).
thf(3778,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ ( insert_pname @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).
thf(349,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_nat_bool @ ( hAPP_f1066163005t_bool @ ( cOMBC_386238098l_bool @ A ) @ B ) @ C )
= ( hAPP_f1664156314l_bool @ ( hAPP_n850744903l_bool @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Oboo) ).
thf(2015,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_nat_bool @ ( hAPP_f1066163005t_bool @ ( cOMBC_386238098l_bool @ A ) @ B ) @ C )
= ( hAPP_f1664156314l_bool @ ( hAPP_n850744903l_bool @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(302,axiom,
! [A: $i] :
( ( hAPP_nat_nat @ ( minus_minus_nat @ zero_zero_nat ) @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_690_diff__0__eq__0) ).
thf(1883,plain,
! [A: $i] :
( ( hAPP_nat_nat @ ( minus_minus_nat @ zero_zero_nat ) @ A )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(211,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_600_le__diff__conv2) ).
thf(1560,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(611,axiom,
is_fun_pname_bool @ u,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_U) ).
thf(2958,plain,
is_fun_pname_bool @ u,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_578_nat__add__commute) ).
thf(916,plain,
! [A: $i,B: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(556,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ C ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ ( image_a_nat @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_finite__surj) ).
thf(2758,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ C ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ ( image_a_nat @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(315,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_660_Suc__le__eq) ).
thf(1920,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(893,axiom,
! [A: $i,B: $i] :
( ( A = B )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_276_equalityD2) ).
thf(4053,plain,
! [A: $i,B: $i] :
( ( A = B )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).
thf(325,axiom,
( bot_bo1389914601l_bool
= ( collect_fun_a_bool @ ( cOMBK_324466864a_bool @ fFalse ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_422_empty__def) ).
thf(1951,plain,
( bot_bo1389914601l_bool
= ( collect_fun_a_bool @ ( cOMBK_324466864a_bool @ fFalse ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(802,axiom,
! [A: $i,B: $i] :
( ( insert_a @ A @ B )
= ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ ( hAPP_a_fun_a_bool @ ( cOMBC_a_a_bool @ fequal_a ) @ A ) ) @ ( hAPP_f2050579477a_bool @ ( cOMBC_1355376034l_bool @ member_a ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_318_insert__compr__raw) ).
thf(3718,plain,
! [A: $i,B: $i] :
( ( insert_a @ A @ B )
= ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ ( hAPP_a_fun_a_bool @ ( cOMBC_a_a_bool @ fequal_a ) @ A ) ) @ ( hAPP_f2050579477a_bool @ ( cOMBC_1355376034l_bool @ member_a ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).
thf(285,axiom,
is_fun949378684l_bool @ bot_bo1389914601l_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(1819,plain,
is_fun949378684l_bool @ bot_bo1389914601l_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(84,axiom,
! [A: $i,B: $i] :
( ( insert1325755072e_bool @ A @ B )
= ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ A ) ) @ ( hAPP_f559147733l_bool @ ( cOMBC_1988546018l_bool @ member799430823e_bool ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_insert__compr) ).
thf(1159,plain,
! [A: $i,B: $i] :
( ( insert1325755072e_bool @ A @ B )
= ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ A ) ) @ ( hAPP_f559147733l_bool @ ( cOMBC_1988546018l_bool @ member799430823e_bool ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(101,axiom,
! [A: $i] :
( ( collect_nat @ ( hAPP_n1699378549t_bool @ fequal_nat @ A ) )
= ( insert_nat @ A @ bot_bot_fun_nat_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_488_singleton__conv2) ).
thf(1210,plain,
! [A: $i] :
( ( collect_nat @ ( hAPP_n1699378549t_bool @ fequal_nat @ A ) )
= ( insert_nat @ A @ bot_bot_fun_nat_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(407,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( is_pname @ A )
& ( is_pname @ B )
& ( is_pname @ C )
& ( is_pname @ D ) )
=> ( ( ( insert_pname @ A @ ( insert_pname @ B @ bot_bo844097828e_bool ) )
= ( insert_pname @ C @ ( insert_pname @ D @ bot_bo844097828e_bool ) ) )
<=> ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_452_doubleton__eq__iff) ).
thf(2213,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( is_pname @ A )
& ( is_pname @ B )
& ( is_pname @ C )
& ( is_pname @ D ) )
=> ( ( ( ( insert_pname @ A @ ( insert_pname @ B @ bot_bo844097828e_bool ) )
= ( insert_pname @ C @ ( insert_pname @ D @ bot_bo844097828e_bool ) ) )
=> ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) )
& ( ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) )
=> ( ( insert_pname @ A @ ( insert_pname @ B @ bot_bo844097828e_bool ) )
= ( insert_pname @ C @ ( insert_pname @ D @ bot_bo844097828e_bool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(21,axiom,
is_bool @ bot_bot_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Orderings_Obot__class_Obot_000tc__HOL__Obool) ).
thf(974,plain,
is_bool @ bot_bot_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(733,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_645_less__not__refl) ).
thf(3445,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(873,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ C ) @ D ) )
=> ( ( A
= ( hAPP_a_nat @ B @ C ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ ( image_a_nat @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_309_rev__image__eqI) ).
thf(3980,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ C ) @ D ) )
=> ( ( A
= ( hAPP_a_nat @ B @ C ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ ( image_a_nat @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).
thf(292,axiom,
! [A: $i] :
( ( is_fun_pname_bool @ A )
=> ( ? [B: $i] :
( ( is_pname @ B )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ A ) ) )
<=> ( A != bot_bo844097828e_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_414_ex__in__conv) ).
thf(1837,plain,
! [A: $i] :
( ( is_fun_pname_bool @ A )
=> ( ( ? [B: $i] :
( ( is_pname @ B )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ A ) ) )
=> ( A != bot_bo844097828e_bool ) )
& ( ( A != bot_bo844097828e_bool )
=> ? [B: $i] :
( ( is_pname @ B )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(534,axiom,
! [A: $i,B: $i] :
( ( A = B )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_equalityD1) ).
thf(2670,plain,
! [A: $i,B: $i] :
( ( A = B )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(829,axiom,
! [A: $i,B: $i] :
( ( A != B )
| ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ fequal_pname @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Com__Opname_T) ).
thf(3810,plain,
! [A: $i,B: $i] :
( ( A != B )
| ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ fequal_pname @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).
thf(723,axiom,
! [A: $i] :
( ( image_pname_a @ A @ bot_bo844097828e_bool )
= bot_bot_fun_a_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_468_image__empty) ).
thf(3403,plain,
! [A: $i] :
( ( image_pname_a @ A @ bot_bo844097828e_bool )
= bot_bot_fun_a_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(332,axiom,
! [A: $i,B: $i,C: $i] :
( ( is_fun1661590463l_bool @ C )
=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ C ) )
=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ C ) @ ( image_47868345e_bool @ A @ B ) ) )
=> ? [D: $i] :
( ( is_fun_pname_bool @ D )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ D ) @ B ) )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ D ) )
& ( C
= ( image_47868345e_bool @ A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_finite__subset__image) ).
thf(1968,plain,
! [A: $i,B: $i,C: $i] :
( ( is_fun1661590463l_bool @ C )
=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ C ) )
=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ C ) @ ( image_47868345e_bool @ A @ B ) ) )
=> ? [D: $i] :
( ( is_fun_pname_bool @ D )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ D ) @ B ) )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ D ) )
& ( C
= ( image_47868345e_bool @ A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(444,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f1664156314l_bool @ ( hAPP_f559147733l_bool @ ( cOMBC_1988546018l_bool @ A ) @ B ) @ C )
= ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ A @ C ) @ B ) ),
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(2332,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f1664156314l_bool @ ( hAPP_f559147733l_bool @ ( cOMBC_1988546018l_bool @ A ) @ B ) @ C )
= ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(575,axiom,
! [A: $i] :
( ( is_fun_a_bool @ A )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ bot_bot_fun_a_bool ) )
<=> ( A = bot_bot_fun_a_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_439_bot__unique) ).
thf(2826,plain,
! [A: $i] :
( ( is_fun_a_bool @ A )
=> ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ bot_bot_fun_a_bool ) )
=> ( A = bot_bot_fun_a_bool ) )
& ( ( A = bot_bot_fun_a_bool )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ bot_bot_fun_a_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(573,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_506_xt1_I5_J) ).
thf(2820,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(96,axiom,
! [A: $i] :
( ( is_bool @ A )
=> ( is_fun_a_bool @ ( cOMBK_bool_a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_COMBK_000tc__HOL__Obool_000t__a) ).
thf(1195,plain,
! [A: $i] :
( ( is_bool @ A )
=> ( is_fun_a_bool @ ( cOMBK_bool_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(165,axiom,
! [A: $i,B: $i] : ( is_fun_pname_bool @ ( image_1921560913_pname @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Com__Opname) ).
thf(1407,plain,
! [A: $i,B: $i] : ( is_fun_pname_bool @ ( image_1921560913_pname @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(503,axiom,
! [A: $i,B: $i] :
( ( insert_fun_a_bool @ A @ B )
= ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ fequal_fun_a_bool ) @ A ) ) @ ( hAPP_f2117159681l_bool @ ( cOMBC_1880041174l_bool @ member_fun_a_bool ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_315_insert__compr__raw) ).
thf(2547,plain,
! [A: $i,B: $i] :
( ( insert_fun_a_bool @ A @ B )
= ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ fequal_fun_a_bool ) @ A ) ) @ ( hAPP_f2117159681l_bool @ ( cOMBC_1880041174l_bool @ member_fun_a_bool ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(448,axiom,
! [A: $i,B: $i] :
( ( ( hAPP_nat_nat @ suc @ zero_zero_nat )
= ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) )
<=> ( ( ( A
= ( hAPP_nat_nat @ suc @ zero_zero_nat ) )
& ( B = zero_zero_nat ) )
| ( ( A = zero_zero_nat )
& ( B
= ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_682_one__is__add) ).
thf(2344,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP_nat_nat @ suc @ zero_zero_nat )
= ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) )
=> ( ( ( A
= ( hAPP_nat_nat @ suc @ zero_zero_nat ) )
& ( B = zero_zero_nat ) )
| ( ( A = zero_zero_nat )
& ( B
= ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) ) ) )
& ( ( ( ( A
= ( hAPP_nat_nat @ suc @ zero_zero_nat ) )
& ( B = zero_zero_nat ) )
| ( ( A = zero_zero_nat )
& ( B
= ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) ) )
=> ( ( hAPP_nat_nat @ suc @ zero_zero_nat )
= ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(805,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ B )
<=> ( hBOOL @ A ) )
<=> ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ A ) )
& ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_550_order__eq__iff) ).
thf(3727,plain,
! [A: $i,B: $i] :
( ( ( ( ( hBOOL @ B )
=> ( hBOOL @ A ) )
& ( ( hBOOL @ A )
=> ( hBOOL @ B ) ) )
=> ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ A ) )
& ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ B ) ) ) )
& ( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ A ) )
& ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ B ) ) )
=> ( ( ( hBOOL @ B )
=> ( hBOOL @ A ) )
& ( ( hBOOL @ A )
=> ( hBOOL @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).
thf(552,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ C ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ ( image_nat_a @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_finite__surj) ).
thf(2741,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ C ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ ( image_nat_a @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(787,axiom,
! [A: $i,B: $i,C: $i] :
( ( B = C )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_532_xt1_I3_J) ).
thf(3667,plain,
! [A: $i,B: $i,C: $i] :
( ( B = C )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).
thf(408,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( hAPP_nat_pname @ A @ B ) ) @ ( image_nat_pname @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_305_imageI) ).
thf(2228,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( hAPP_nat_pname @ A @ B ) ) @ ( image_nat_pname @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(725,axiom,
! [A: $i,B: $i,C: $i] :
( ( is_fun_a_bool @ A )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ ( image_pname_a @ B @ C ) ) )
<=> ? [D: $i] :
( ( is_fun_pname_bool @ D )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ D ) @ C ) )
& ( A
= ( image_pname_a @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_347_subset__image__iff) ).
thf(3408,plain,
! [A: $i,B: $i,C: $i] :
( ( is_fun_a_bool @ A )
=> ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ ( image_pname_a @ B @ C ) ) )
=> ? [D: $i] :
( ( is_fun_pname_bool @ D )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ D ) @ C ) )
& ( A
= ( image_pname_a @ B @ D ) ) ) )
& ( ? [D: $i] :
( ( is_fun_pname_bool @ D )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ D ) @ C ) )
& ( A
= ( image_pname_a @ B @ D ) ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ ( image_pname_a @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(258,axiom,
! [A: $i,B: $i] :
( ( ( is_fun_pname_bool @ A )
& ( is_fun_pname_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ B ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ A ) ) )
=> ( A = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_card__seteq) ).
thf(1740,plain,
! [A: $i,B: $i] :
( ( ( is_fun_pname_bool @ A )
& ( is_fun_pname_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ B ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ A ) ) )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(337,axiom,
! [A: $i,B: $i] :
( ( is_fun1661590463l_bool @ B )
=> ( is_fun1661590463l_bool @ ( hAPP_f559147733l_bool @ A @ B ) ) ),
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(1983,plain,
! [A: $i,B: $i] :
( ( is_fun1661590463l_bool @ B )
=> ( is_fun1661590463l_bool @ ( hAPP_f559147733l_bool @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(456,axiom,
! [A: $i,B: $i] :
( ( is_a @ B )
=> ( is_fun_a_bool @ ( hAPP_a_fun_a_bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
thf(2377,plain,
! [A: $i,B: $i] :
( ( is_a @ B )
=> ( is_fun_a_bool @ ( hAPP_a_fun_a_bool @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(326,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_669_less__diff__iff) ).
thf(1953,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(579,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
=> ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ B ) )
=> ( ( hAPP_fun_a_bool_nat @ finite_card_a @ ( insert_a @ A @ B ) )
= ( hAPP_fun_a_bool_nat @ finite_card_a @ B ) ) )
& ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ B ) )
=> ( ( hAPP_fun_a_bool_nat @ finite_card_a @ ( insert_a @ A @ B ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_fun_a_bool_nat @ finite_card_a @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_card__insert__if) ).
thf(2841,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
=> ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ B ) )
=> ( ( hAPP_fun_a_bool_nat @ finite_card_a @ ( insert_a @ A @ B ) )
= ( hAPP_fun_a_bool_nat @ finite_card_a @ B ) ) )
& ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ B ) )
=> ( ( hAPP_fun_a_bool_nat @ finite_card_a @ ( insert_a @ A @ B ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_fun_a_bool_nat @ finite_card_a @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(204,axiom,
! [A: $i,B: $i] :
( ( insert1325755072e_bool @ A @ ( collec1974731493e_bool @ B ) )
= ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fimplies @ ( cOMBB_307249310e_bool @ fNot @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ A ) ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_insert__Collect) ).
thf(1540,plain,
! [A: $i,B: $i] :
( ( insert1325755072e_bool @ A @ ( collec1974731493e_bool @ B ) )
= ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fimplies @ ( cOMBB_307249310e_bool @ fNot @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ A ) ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(524,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ B ) )
<=> ( hBOOL @ ( hAPP_a_bool @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_289_mem__def) ).
thf(2631,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_a_bool @ B @ A ) ) )
& ( ( hBOOL @ ( hAPP_a_bool @ B @ A ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(548,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ C ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ A @ bot_bot_fun_a_bool ) )
=> ( ! [D: $i,E: $i] :
( ( ( is_a @ D )
& ( is_fun_a_bool @ E ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ E ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ D ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ A @ E ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ A @ ( insert_a @ D @ E ) ) ) ) ) ) ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_558_finite__subset__induct) ).
thf(2724,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ C ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ A @ bot_bot_fun_a_bool ) )
=> ( ! [D: $i,E: $i] :
( ( ( is_a @ D )
& ( is_fun_a_bool @ E ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ E ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ D ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ A @ E ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ A @ ( insert_a @ D @ E ) ) ) ) ) ) ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(780,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
=> ( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ A ) @ B ) )
=> ( ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( insert1325755072e_bool @ A @ B ) )
= ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ B ) ) )
& ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ A ) @ B ) )
=> ( ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( insert1325755072e_bool @ A @ B ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_card__insert__if) ).
thf(3632,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
=> ( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ A ) @ B ) )
=> ( ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( insert1325755072e_bool @ A @ B ) )
= ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ B ) ) )
& ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ A ) @ B ) )
=> ( ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( insert1325755072e_bool @ A @ B ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).
thf(422,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_588_trans__le__add1) ).
thf(2268,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( A != B )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_638_le__neq__implies__less) ).
thf(989,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( A != B )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(870,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_510_order__trans) ).
thf(3968,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).
thf(144,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ( cOMBC_595898202l_bool @ A ) @ B ) @ C )
= ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ A @ C ) @ B ) ),
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(1350,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ( cOMBC_595898202l_bool @ A ) @ B ) @ C )
= ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(739,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_le__antisym) ).
thf(3467,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(820,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_finite_OinsertI) ).
thf(3784,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).
thf(266,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ A ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_card__mono) ).
thf(1762,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ A ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(686,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ B ) )
=> ( ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fconj @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ B ) ) @ A ) )
= ( insert1325755072e_bool @ B @ bot_bo1649642514l_bool ) ) )
& ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ B ) )
=> ( ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fconj @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ B ) ) @ A ) )
= bot_bo1649642514l_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_474_Collect__conv__if) ).
thf(3254,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ B ) )
=> ( ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fconj @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ B ) ) @ A ) )
= ( insert1325755072e_bool @ B @ bot_bo1649642514l_bool ) ) )
& ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ B ) )
=> ( ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fconj @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ B ) ) @ A ) )
= bot_bo1649642514l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(658,axiom,
! [A: $i] :
( ( ( collect_fun_a_bool @ A )
= bot_bo1389914601l_bool )
<=> ! [B: $i] :
( ( is_fun_a_bool @ B )
=> ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_401_Collect__empty__eq) ).
thf(3122,plain,
! [A: $i] :
( ( ( ( collect_fun_a_bool @ A )
= bot_bo1389914601l_bool )
=> ! [B: $i] :
( ( is_fun_a_bool @ B )
=> ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ A @ B ) ) ) )
& ( ! [B: $i] :
( ( is_fun_a_bool @ B )
=> ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ A @ B ) ) )
=> ( ( collect_fun_a_bool @ A )
= bot_bo1389914601l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(622,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_pname_a @ A @ B ) ) @ ( image_pname_a @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_351_image__mono) ).
thf(2990,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_pname_a @ A @ B ) ) @ ( image_pname_a @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(280,axiom,
! [A: $i,B: $i] :
( ( is_fun949378684l_bool @ B )
=> ( is_fun949378684l_bool @ ( cOMBS_1035972772l_bool @ A @ B ) ) ),
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(1804,plain,
! [A: $i,B: $i] :
( ( is_fun949378684l_bool @ B )
=> ( is_fun949378684l_bool @ ( cOMBS_1035972772l_bool @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(844,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ C ) )
=> ( B = A ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ ( insert_nat @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_insertCI) ).
thf(3862,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ C ) )
=> ( B = A ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ ( insert_nat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).
thf(511,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ C ) )
=> ( B = A ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ ( insert_a @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_insertCI) ).
thf(2577,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ C ) )
=> ( B = A ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ ( insert_a @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(716,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
=> ( ( B = A )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_522_xt1_I4_J) ).
thf(3381,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
=> ( ( B = A )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(544,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_pname_bool @ bot_bo844097828e_bool @ A ) )
<=> ( hBOOL @ bot_bot_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_425_bot__fun__def) ).
thf(2709,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_pname_bool @ bot_bo844097828e_bool @ A ) )
=> ( hBOOL @ bot_bot_bool ) )
& ( ( hBOOL @ bot_bot_bool )
=> ( hBOOL @ ( hAPP_pname_bool @ bot_bo844097828e_bool @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(106,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ A ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_602_le__add__diff__inverse) ).
thf(1227,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(539,axiom,
! [A: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ bot_bot_nat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_445_bot__least) ).
thf(2692,plain,
! [A: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ bot_bot_nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(219,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ C ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_diff__le__mono2) ).
thf(1587,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ C ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(540,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ A ) @ B ) ) ) )
<=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ A ) ) )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_finite__Collect__disjI) ).
thf(2694,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ A ) @ B ) ) ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ A ) ) )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ B ) ) ) ) )
& ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ A ) ) )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ B ) ) ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(171,axiom,
! [A: $i] :
( ( collect_fun_nat_bool @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_292_Collect__def) ).
thf(1425,plain,
! [A: $i] :
( ( collect_fun_nat_bool @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(492,axiom,
! [A: $i] :
( ( collect_fun_a_bool @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ fequal_fun_a_bool ) @ A ) )
= ( insert_fun_a_bool @ A @ bot_bo1389914601l_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_487_singleton__conv) ).
thf(2509,plain,
! [A: $i] :
( ( collect_fun_a_bool @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ fequal_fun_a_bool ) @ A ) )
= ( insert_fun_a_bool @ A @ bot_bo1389914601l_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(654,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
=> ( ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ A ) @ B ) )
=> ( ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( insert_fun_nat_bool @ A @ B ) )
= ( hAPP_f696928925ol_nat @ finite346522414t_bool @ B ) ) )
& ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ A ) @ B ) )
=> ( ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( insert_fun_nat_bool @ A @ B ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_card__insert__if) ).
thf(3102,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
=> ( ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ A ) @ B ) )
=> ( ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( insert_fun_nat_bool @ A @ B ) )
= ( hAPP_f696928925ol_nat @ finite346522414t_bool @ B ) ) )
& ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ A ) @ B ) )
=> ( ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( insert_fun_nat_bool @ A @ B ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(526,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_fun_nat_bool_a @ A @ B ) ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_card__image__le) ).
thf(2638,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_fun_nat_bool_a @ A @ B ) ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(911,axiom,
! [A: $i,B: $i] :
( ( A = B )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_272_equalityD1) ).
thf(4109,plain,
! [A: $i,B: $i] :
( ( A = B )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).
thf(631,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ B )
<=> ( hBOOL @ A ) )
=> ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_545_order__eq__refl) ).
thf(3018,plain,
! [A: $i,B: $i] :
( ( ( ( hBOOL @ B )
=> ( hBOOL @ A ) )
& ( ( hBOOL @ A )
=> ( hBOOL @ B ) ) )
=> ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(161,axiom,
! [A: $i] :
( ( hAPP_nat_nat @ suc @ A )
!= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_693_nat_Osimps_I3_J) ).
thf(1397,plain,
! [A: $i] :
( ( hAPP_nat_nat @ suc @ A )
!= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(213,axiom,
! [A: $i,B: $i] :
( ( is_pname @ B )
=> ( is_fun949378684l_bool @ ( hAPP_p1824510254l_bool @ A @ B ) ) ),
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(1567,plain,
! [A: $i,B: $i] :
( ( is_pname @ B )
=> ( is_fun949378684l_bool @ ( hAPP_p1824510254l_bool @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(590,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ bot_bot_fun_nat_bool ) )
=> ( A = bot_bot_fun_nat_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_433_le__bot) ).
thf(2877,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ bot_bot_fun_nat_bool ) )
=> ( A = bot_bot_fun_nat_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(147,axiom,
! [A: $i,B: $i] :
( ( is_fun949378684l_bool @ B )
=> ( is_bool @ ( hAPP_f621171935l_bool @ A @ B ) ) ),
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(1361,plain,
! [A: $i,B: $i] :
( ( is_fun949378684l_bool @ B )
=> ( is_bool @ ( hAPP_f621171935l_bool @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(441,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) )
= ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_605_diff__diff__right) ).
thf(2323,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) )
= ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(127,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_a_fun_bool_bool @ ( cOMBB_1972296269bool_a @ A @ B ) @ C )
= ( hAPP_b589554111l_bool @ A @ ( hAPP_a_bool @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo) ).
thf(1292,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_a_fun_bool_bool @ ( cOMBB_1972296269bool_a @ A @ B ) @ C )
= ( hAPP_b589554111l_bool @ A @ ( hAPP_a_bool @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(772,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
=> ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ A ) @ B ) )
=> ( ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( insert_fun_nat_bool @ A @ B ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_card__insert__disjoint) ).
thf(3596,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
=> ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ A ) @ B ) )
=> ( ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( insert_fun_nat_bool @ A @ B ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).
thf(60,axiom,
! [A: $i,B: $i] :
( ( ( is_pname @ A )
& ( is_fun_pname_bool @ B ) )
=> ( is_fun_pname_bool @ ( insert_pname @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oinsert_000tc__Com__Opname) ).
thf(1075,plain,
! [A: $i,B: $i] :
( ( ( is_pname @ A )
& ( is_fun_pname_bool @ B ) )
=> ( is_fun_pname_bool @ ( insert_pname @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(218,axiom,
! [A: $i,B: $i] :
( ( insert_pname @ A @ B )
= ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ fequal_pname ) @ A ) ) @ ( hAPP_f759274231e_bool @ ( cOMBC_1058051404l_bool @ member_pname ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_317_insert__compr__raw) ).
thf(1584,plain,
! [A: $i,B: $i] :
( ( insert_pname @ A @ B )
= ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ fequal_pname ) @ A ) ) @ ( hAPP_f759274231e_bool @ ( cOMBC_1058051404l_bool @ member_pname ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(634,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_496248727ol_nat @ A @ B ) ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fconj @ ( hAPP_f1246832597l_bool @ ( cOMBC_1245412066l_bool @ member_fun_nat_bool ) @ B ) ) @ ( hAPP_n215258509l_bool @ ( cOMBC_385542954t_bool @ ( cOMBB_1250273980t_bool @ fequal_nat @ A ) ) @ ( hAPP_f22106695ol_nat @ A @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_pigeonhole__infinite) ).
thf(3032,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_496248727ol_nat @ A @ B ) ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fconj @ ( hAPP_f1246832597l_bool @ ( cOMBC_1245412066l_bool @ member_fun_nat_bool ) @ B ) ) @ ( hAPP_n215258509l_bool @ ( cOMBC_385542954t_bool @ ( cOMBB_1250273980t_bool @ fequal_nat @ A ) ) @ ( hAPP_f22106695ol_nat @ A @ C ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(533,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( is_pname @ D )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ C ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( hAPP_pname_a @ A @ D ) ) @ B ) ) ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_pname_a @ A @ C ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_366_image__subsetI) ).
thf(2666,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( is_pname @ D )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ C ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( hAPP_pname_a @ A @ D ) ) @ B ) ) ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_pname_a @ A @ C ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(763,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_500_xt1_I6_J) ).
thf(3555,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).
thf(439,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_a_bool @ ( hAPP_f1051908748a_bool @ ( cOMBC_1834145417l_bool @ A ) @ B ) @ C )
= ( hAPP_f1664156314l_bool @ ( hAPP_a217006258l_bool @ A @ C ) @ B ) ),
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(2317,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_a_bool @ ( hAPP_f1051908748a_bool @ ( cOMBC_1834145417l_bool @ A ) @ B ) @ C )
= ( hAPP_f1664156314l_bool @ ( hAPP_a217006258l_bool @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ( is_fun_pname_bool @ B )
=> ( is_fun949378684l_bool @ ( image_112932426a_bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__Com__Opname_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
thf(1028,plain,
! [A: $i,B: $i] :
( ( is_fun_pname_bool @ B )
=> ( is_fun949378684l_bool @ ( image_112932426a_bool @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(63,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_nat_bool @ ( cOMBS_nat_bool_bool @ A @ B ) @ C )
= ( hAPP_bool_bool @ ( hAPP_n1006566506l_bool @ A @ C ) @ ( hAPP_nat_bool @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__HOL__Obool_000tc__HOL__Obool_U) ).
thf(1082,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_nat_bool @ ( cOMBS_nat_bool_bool @ A @ B ) @ C )
= ( hAPP_bool_bool @ ( hAPP_n1006566506l_bool @ A @ C ) @ ( hAPP_nat_bool @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(352,axiom,
is_fun1661590463l_bool @ bot_bo1649642514l_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Orderings_Obot__class_Obot_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__) ).
thf(2023,plain,
is_fun1661590463l_bool @ bot_bo1649642514l_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(330,axiom,
! [A: $i,B: $i] :
( ( is_fun_a_bool @ B )
=> ( is_fun_a_bool @ ( cOMBB_bool_bool_a @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000t__a) ).
thf(1964,plain,
! [A: $i,B: $i] :
( ( is_fun_a_bool @ B )
=> ( is_fun_a_bool @ ( cOMBB_bool_bool_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(236,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_n1025906991e_bool @ C @ D ) ) @ ( hAPP_n1025906991e_bool @ C @ ( hAPP_nat_nat @ suc @ D ) ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_n1025906991e_bool @ C @ A ) ) @ ( hAPP_n1025906991e_bool @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_lift__Suc__mono__le) ).
thf(1659,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_n1025906991e_bool @ C @ D ) ) @ ( hAPP_n1025906991e_bool @ C @ ( hAPP_nat_nat @ suc @ D ) ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_n1025906991e_bool @ C @ A ) ) @ ( hAPP_n1025906991e_bool @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(438,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ C ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ ( image_496248727ol_nat @ A @ B ) ) )
=> ? [D: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ D ) @ B ) )
& ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ D ) )
& ( C
= ( image_496248727ol_nat @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_finite__subset__image) ).
thf(2312,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ C ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ ( image_496248727ol_nat @ A @ B ) ) )
=> ? [D: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ D ) @ B ) )
& ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ D ) )
& ( C
= ( image_496248727ol_nat @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(476,axiom,
hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ bot_bot_fun_a_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_389_finite_OemptyI) ).
thf(2455,plain,
hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ bot_bot_fun_a_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(168,axiom,
! [A: $i,B: $i] :
( ( ( is_pname @ A )
& ( is_pname @ B ) )
=> ( ( ( insert_pname @ A @ bot_bo844097828e_bool )
= ( insert_pname @ B @ bot_bo844097828e_bool ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_446_singleton__inject) ).
thf(1414,plain,
! [A: $i,B: $i] :
( ( ( is_pname @ A )
& ( is_pname @ B ) )
=> ( ( ( insert_pname @ A @ bot_bo844097828e_bool )
= ( insert_pname @ B @ bot_bo844097828e_bool ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(359,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( ( ( hAPP_nat_nat @ suc @ A )
!= B )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_630_Suc__lessI) ).
thf(2053,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( ( ( hAPP_nat_nat @ suc @ A )
!= B )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(276,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_nat_bool @ B @ A ) ) @ ( hAPP_nat_bool @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_381_le__funE) ).
thf(1791,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_nat_bool @ B @ A ) ) @ ( hAPP_nat_bool @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(729,axiom,
! [A: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_368_order__refl) ).
thf(3428,plain,
! [A: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(100,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) @ B )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_595_diff__add__assoc2) ).
thf(1207,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) @ B )
= ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(788,axiom,
! [A: $i,B: $i,C: $i] :
( ( B = C )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_533_xt1_I3_J) ).
thf(3671,plain,
! [A: $i,B: $i,C: $i] :
( ( B = C )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).
thf(369,axiom,
! [A: $i] :
( ( is_fun_a_bool @ A )
=> ( is_fun949378684l_bool @ ( p @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_P) ).
thf(2085,plain,
! [A: $i] :
( ( is_fun_a_bool @ A )
=> ( is_fun949378684l_bool @ ( p @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(224,axiom,
! [A: $i,B: $i] :
( ( is_fun1661590463l_bool @ B )
=> ( is_fun_a_bool @ ( image_876012084bool_a @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000t__a) ).
thf(1612,plain,
! [A: $i,B: $i] :
( ( is_fun1661590463l_bool @ B )
=> ( is_fun_a_bool @ ( image_876012084bool_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i,E: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ D ) @ E ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ C @ D ) ) @ ( hAPP_nat_nat @ C @ E ) ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ C @ A ) ) @ ( hAPP_nat_nat @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_675_less__mono__imp__le__mono) ).
thf(1039,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i,E: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ D ) @ E ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ C @ D ) ) @ ( hAPP_nat_nat @ C @ E ) ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ C @ A ) ) @ ( hAPP_nat_nat @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_279_in__mono) ).
thf(970,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(682,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ C ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( image_a_pname @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_finite__surj) ).
thf(3242,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ C ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( image_a_pname @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(181,axiom,
! [A: $i,B: $i] :
( ( is_fun1661590463l_bool @ B )
=> ( is_fun1661590463l_bool @ ( cOMBB_307249310e_bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc_) ).
thf(1456,plain,
! [A: $i,B: $i] :
( ( is_fun1661590463l_bool @ B )
=> ( is_fun1661590463l_bool @ ( cOMBB_307249310e_bool @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(808,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
=> ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( image_1655916159e_bool @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_finite__imageI) ).
thf(3743,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
=> ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( image_1655916159e_bool @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
thf(333,axiom,
! [A: $i,B: $i] :
( ( is_fun949378684l_bool @ B )
=> ( is_fun949378684l_bool @ ( hAPP_f2117159681l_bool @ A @ B ) ) ),
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(1974,plain,
! [A: $i,B: $i] :
( ( is_fun949378684l_bool @ B )
=> ( is_fun949378684l_bool @ ( hAPP_f2117159681l_bool @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(414,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_nat_fun_a_bool @ ( cOMBB_1885489796ol_nat @ A @ B ) @ C )
= ( hAPP_a_fun_a_bool @ A @ ( hAPP_nat_a @ B @ C ) ) ),
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(2243,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_nat_fun_a_bool @ ( cOMBB_1885489796ol_nat @ A @ B ) @ C )
= ( hAPP_a_fun_a_bool @ A @ ( hAPP_nat_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(319,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) )
<=> ? [B: $i] :
! [C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_652_finite__nat__set__iff__bounded) ).
thf(1932,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) )
=> ? [B: $i] :
! [C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ B ) ) ) )
& ( ? [B: $i] :
! [C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(676,axiom,
! [A: $i,B: $i] :
( ( insert_a @ A @ B )
= ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ ( hAPP_a_fun_a_bool @ ( cOMBC_a_a_bool @ fequal_a ) @ A ) ) @ ( hAPP_f2050579477a_bool @ ( cOMBC_1355376034l_bool @ member_a ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_insert__compr) ).
thf(3222,plain,
! [A: $i,B: $i] :
( ( insert_a @ A @ B )
= ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ ( hAPP_a_fun_a_bool @ ( cOMBC_a_a_bool @ fequal_a ) @ A ) ) @ ( hAPP_f2050579477a_bool @ ( cOMBC_1355376034l_bool @ member_a ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(509,axiom,
! [A: $i,B: $i] :
( ( is_bool @ A )
=> ( ( hAPP_fun_a_bool_bool @ ( cOMBK_324466864a_bool @ A ) @ B )
= 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(2566,plain,
! [A: $i,B: $i] :
( ( is_bool @ A )
=> ( ( hAPP_fun_a_bool_bool @ ( cOMBK_324466864a_bool @ A ) @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(111,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] : ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_nat_bool @ C @ D ) ) @ ( hAPP_nat_bool @ C @ ( hAPP_nat_nat @ suc @ D ) ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_nat_bool @ C @ A ) ) @ ( hAPP_nat_bool @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_lift__Suc__mono__le) ).
thf(1246,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] : ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_nat_bool @ C @ D ) ) @ ( hAPP_nat_bool @ C @ ( hAPP_nat_nat @ suc @ D ) ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_nat_bool @ C @ A ) ) @ ( hAPP_nat_bool @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(703,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ bot_bot_fun_nat_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_383_emptyE) ).
thf(3333,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ bot_bot_fun_nat_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(252,axiom,
! [A: $i,B: $i] :
( ( insert_fun_nat_bool @ A @ B )
= ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ ( hAPP_f103356543l_bool @ ( cOMBC_1693257480l_bool @ fequal_fun_nat_bool ) @ A ) ) @ ( hAPP_f1246832597l_bool @ ( cOMBC_1245412066l_bool @ member_fun_nat_bool ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_insert__compr) ).
thf(1720,plain,
! [A: $i,B: $i] :
( ( insert_fun_nat_bool @ A @ B )
= ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ ( hAPP_f103356543l_bool @ ( cOMBC_1693257480l_bool @ fequal_fun_nat_bool ) @ A ) ) @ ( hAPP_f1246832597l_bool @ ( cOMBC_1245412066l_bool @ member_fun_nat_bool ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(797,axiom,
! [A: $i,B: $i] :
( ( A != B )
| ( hBOOL @ ( hAPP_a_bool @ ( hAPP_a_fun_a_bool @ fequal_a @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000t__a_T) ).
thf(3703,plain,
! [A: $i,B: $i] :
( ( A != B )
| ( hBOOL @ ( hAPP_a_bool @ ( hAPP_a_fun_a_bool @ fequal_a @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).
thf(288,axiom,
! [A: $i,B: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B )
= ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_573_add__Suc__shift) ).
thf(1825,plain,
! [A: $i,B: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B )
= ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(270,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ D ) )
=> ( ( A
= ( hAPP_pname_nat @ B @ C ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ ( image_pname_nat @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_308_rev__image__eqI) ).
thf(1776,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ D ) )
=> ( ( A
= ( hAPP_pname_nat @ B @ C ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ ( image_pname_nat @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(116,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f1748468828l_bool @ ( cOMBB_444170502t_bool @ A @ B ) @ C )
= ( hAPP_b589554111l_bool @ A @ ( hAPP_f54304608l_bool @ B @ C ) ) ),
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(1263,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f1748468828l_bool @ ( cOMBB_444170502t_bool @ A @ B ) @ C )
= ( hAPP_b589554111l_bool @ A @ ( hAPP_f54304608l_bool @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( is_fun949378684l_bool @ B )
=> ( is_fun949378684l_bool @ ( cOMBB_2140588453a_bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_It__a_Mtc__HOL__Obool) ).
thf(997,plain,
! [A: $i,B: $i] :
( ( is_fun949378684l_bool @ B )
=> ( is_fun949378684l_bool @ ( cOMBB_2140588453a_bool @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(784,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_a_bool @ A @ B ) )
=> ( ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ ( hAPP_a_fun_a_bool @ ( cOMBC_a_a_bool @ fequal_a ) @ B ) ) @ A ) )
= ( insert_a @ B @ bot_bot_fun_a_bool ) ) )
& ( ~ ( hBOOL @ ( hAPP_a_bool @ A @ B ) )
=> ( ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ ( hAPP_a_fun_a_bool @ ( cOMBC_a_a_bool @ fequal_a ) @ B ) ) @ A ) )
= bot_bot_fun_a_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_472_Collect__conv__if) ).
thf(3656,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_a_bool @ A @ B ) )
=> ( ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ ( hAPP_a_fun_a_bool @ ( cOMBC_a_a_bool @ fequal_a ) @ B ) ) @ A ) )
= ( insert_a @ B @ bot_bot_fun_a_bool ) ) )
& ( ~ ( hBOOL @ ( hAPP_a_bool @ A @ B ) )
=> ( ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ ( hAPP_a_fun_a_bool @ ( cOMBC_a_a_bool @ fequal_a ) @ B ) ) @ A ) )
= bot_bot_fun_a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).
thf(188,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ ( insert_nat @ B @ bot_bot_fun_nat_bool ) ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_455_singleton__iff) ).
thf(1478,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ ( insert_nat @ B @ bot_bot_fun_nat_bool ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ ( insert_nat @ B @ bot_bot_fun_nat_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(494,axiom,
! [A: $i] :
( ( bot_bo1389914601l_bool
= ( collect_fun_a_bool @ A ) )
<=> ! [B: $i] :
( ( is_fun_a_bool @ B )
=> ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_410_empty__Collect__eq) ).
thf(2519,plain,
! [A: $i] :
( ( ( bot_bo1389914601l_bool
= ( collect_fun_a_bool @ A ) )
=> ! [B: $i] :
( ( is_fun_a_bool @ B )
=> ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ A @ B ) ) ) )
& ( ! [B: $i] :
( ( is_fun_a_bool @ B )
=> ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ A @ B ) ) )
=> ( bot_bo1389914601l_bool
= ( collect_fun_a_bool @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(498,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
=> ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( image_112932426a_bool @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_finite__imageI) ).
thf(2536,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
=> ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( image_112932426a_bool @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(536,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ u ) )
=> ( hBOOL @ ( wt @ ( the_com @ ( body @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_567_assms_I4_J) ).
thf(2681,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ u ) )
=> ( hBOOL @ ( wt @ ( the_com @ ( body @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(486,axiom,
! [A: $i,B: $i] :
( ( insert_fun_a_bool @ A @ ( collect_fun_a_bool @ B ) )
= ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fimplies @ ( cOMBB_2140588453a_bool @ fNot @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ fequal_fun_a_bool ) @ A ) ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_insert__Collect) ).
thf(2487,plain,
! [A: $i,B: $i] :
( ( insert_fun_a_bool @ A @ ( collect_fun_a_bool @ B ) )
= ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fimplies @ ( cOMBB_2140588453a_bool @ fNot @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ fequal_fun_a_bool ) @ A ) ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(643,axiom,
! [A: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ bot_bot_fun_nat_bool ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_443_bot__least) ).
thf(3059,plain,
! [A: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ bot_bot_fun_nat_bool ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(117,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_n1699378549t_bool @ ( cOMBB_800536526ol_nat @ A @ B ) @ C )
= ( hAPP_n1699378549t_bool @ A @ ( hAPP_nat_nat @ B @ C ) ) ),
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(1266,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_n1699378549t_bool @ ( cOMBB_800536526ol_nat @ A @ B ) @ C )
= ( hAPP_n1699378549t_bool @ A @ ( hAPP_nat_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(897,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( image_pname_pname @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_finite__surj) ).
thf(4068,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( image_pname_pname @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).
thf(55,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ C ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_642_diff__less__mono2) ).
thf(1060,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ C ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ ( cOMBC_385542954t_bool @ A ) @ B ) @ C )
= ( hAPP_nat_bool @ ( hAPP_f800510211t_bool @ A @ C ) @ B ) ),
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(1050,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ ( cOMBC_385542954t_bool @ A ) @ B ) @ C )
= ( hAPP_nat_bool @ ( hAPP_f800510211t_bool @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ ( insert_nat @ B @ bot_bot_fun_nat_bool ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_449_singletonE) ).
thf(984,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ ( insert_nat @ B @ bot_bot_fun_nat_bool ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(490,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( insert_pname @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_319_subset__insertI) ).
thf(2505,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( insert_pname @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(719,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
=> ( ( insert_a @ ( hAPP_pname_a @ A @ B ) @ ( image_pname_a @ A @ C ) )
= ( image_pname_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_343_insert__image) ).
thf(3390,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
=> ( ( insert_a @ ( hAPP_pname_a @ A @ B ) @ ( image_pname_a @ A @ C ) )
= ( image_pname_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).
thf(656,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_fun_a_bool_bool @ ( hAPP_n1414589940l_bool @ ( cOMBC_619334683t_bool @ A ) @ B ) @ C )
= ( hAPP_nat_bool @ ( hAPP_f282463732t_bool @ A @ C ) @ B ) ),
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(3109,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_fun_a_bool_bool @ ( hAPP_n1414589940l_bool @ ( cOMBC_619334683t_bool @ A ) @ B ) @ C )
= ( hAPP_nat_bool @ ( hAPP_f282463732t_bool @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(648,axiom,
! [A: $i,B: $i] :
( ( is_fun_pname_bool @ B )
=> ( ( ( image_pname_a @ A @ B )
= bot_bot_fun_a_bool )
<=> ( B = bot_bo844097828e_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_467_image__is__empty) ).
thf(3074,plain,
! [A: $i,B: $i] :
( ( is_fun_pname_bool @ B )
=> ( ( ( ( image_pname_a @ A @ B )
= bot_bot_fun_a_bool )
=> ( B = bot_bo844097828e_bool ) )
& ( ( B = bot_bo844097828e_bool )
=> ( ( image_pname_a @ A @ B )
= bot_bot_fun_a_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(672,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
=> ( ( image_pname_a @ ( cOMBK_a_pname @ A ) @ C )
= ( insert_a @ A @ bot_bot_fun_a_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_497_image__constant) ).
thf(3201,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
=> ( ( image_pname_a @ ( cOMBK_a_pname @ A ) @ C )
= ( insert_a @ A @ bot_bot_fun_a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(265,axiom,
! [A: $i] :
( ( collect_nat @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_Collect__def) ).
thf(1759,plain,
! [A: $i] :
( ( collect_nat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(160,axiom,
! [A: $i,B: $i] :
( bot_bo844097828e_bool
!= ( insert_pname @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_461_empty__not__insert) ).
thf(1393,plain,
! [A: $i,B: $i] :
( bot_bo844097828e_bool
!= ( insert_pname @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(736,axiom,
! [A: $i] :
( ( is_fun_a_bool @ A )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ bot_bot_fun_a_bool ) )
=> ( A = bot_bot_fun_a_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_434_le__bot) ).
thf(3454,plain,
! [A: $i] :
( ( is_fun_a_bool @ A )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ bot_bot_fun_a_bool ) )
=> ( A = bot_bot_fun_a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(812,axiom,
! [A: $i,B: $i] :
( ( A = B )
=> ~ ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
=> ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_300_equalityE) ).
thf(3755,plain,
! [A: $i,B: $i] :
( ( A = B )
=> ~ ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
=> ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).
thf(134,axiom,
! [A: $i,B: $i] :
( ( is_pname @ B )
=> ( is_fun1661590463l_bool @ ( hAPP_p338031245l_bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obo) ).
thf(1318,plain,
! [A: $i,B: $i] :
( ( is_pname @ B )
=> ( is_fun1661590463l_bool @ ( hAPP_p338031245l_bool @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(604,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( C = A )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_528_ord__le__eq__trans) ).
thf(2926,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( C = A )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(404,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ( cOMBC_1693257480l_bool @ A ) @ B ) @ C )
= ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ A @ C ) @ B ) ),
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(2203,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ( cOMBC_1693257480l_bool @ A ) @ B ) @ C )
= ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(212,axiom,
! [A: $i,B: $i] :
( ( is_bool @ A )
=> ( ( hAPP_pname_bool @ ( cOMBK_bool_pname @ A ) @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Com__Opname_U) ).
thf(1563,plain,
! [A: $i,B: $i] :
( ( is_bool @ A )
=> ( ( hAPP_pname_bool @ ( cOMBK_bool_pname @ A ) @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(465,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
=> ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_finite__subset) ).
thf(2408,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
=> ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(87,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_a_bool @ ( hAPP_f1549043526a_bool @ ( cOMBC_777206479l_bool @ A ) @ B ) @ C )
= ( hAPP_f54304608l_bool @ ( hAPP_a1392362872l_bool @ A @ C ) @ B ) ),
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(1167,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_a_bool @ ( hAPP_f1549043526a_bool @ ( cOMBC_777206479l_bool @ A ) @ B ) @ C )
= ( hAPP_f54304608l_bool @ ( hAPP_a1392362872l_bool @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(838,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( is_a @ C )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ C ) @ B ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ C ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_359_subsetI) ).
thf(3841,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( is_a @ C )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ C ) @ B ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ C ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).
thf(92,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) ) )
= ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ suc @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_609_diff__Suc__diff__eq1) ).
thf(1185,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) ) )
= ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(495,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_p1824510254l_bool @ ( cOMBB_392435466_pname @ A @ B ) @ C )
= ( hAPP_f1631501043l_bool @ A @ ( hAPP_p1534023578a_bool @ B @ C ) ) ),
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(2529,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_p1824510254l_bool @ ( cOMBB_392435466_pname @ A @ B ) @ C )
= ( hAPP_f1631501043l_bool @ A @ ( hAPP_p1534023578a_bool @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(828,axiom,
! [A: $i,B: $i,C: $i] :
( ( image_nat_a @ A @ ( insert_nat @ B @ C ) )
= ( insert_a @ ( hAPP_nat_a @ A @ B ) @ ( image_nat_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_336_image__insert) ).
thf(3807,plain,
! [A: $i,B: $i,C: $i] :
( ( image_nat_a @ A @ ( insert_nat @ B @ C ) )
= ( insert_a @ ( hAPP_nat_a @ A @ B ) @ ( image_nat_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).
thf(832,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( hAPP_nat_a @ A @ B ) ) @ ( image_nat_a @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_306_imageI) ).
thf(3824,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( hAPP_nat_a @ A @ B ) ) @ ( image_nat_a @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).
thf(554,axiom,
! [A: $i,B: $i] :
( ( is_fun_a_bool @ A )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ ( insert_a @ B @ bot_bot_fun_a_bool ) ) )
=> ( ( A = bot_bot_fun_a_bool )
| ( A
= ( insert_a @ B @ bot_bot_fun_a_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_496_subset__singletonD) ).
thf(2749,plain,
! [A: $i,B: $i] :
( ( is_fun_a_bool @ A )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ ( insert_a @ B @ bot_bot_fun_a_bool ) ) )
=> ( ( A = bot_bot_fun_a_bool )
| ( A
= ( insert_a @ B @ bot_bot_fun_a_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(173,axiom,
! [A: $i,B: $i] : ( is_fun_pname_bool @ ( hAPP_n1025906991e_bool @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).
thf(1434,plain,
! [A: $i,B: $i] : ( is_fun_pname_bool @ ( hAPP_n1025906991e_bool @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) )
<=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_575_nat__add__left__cancel) ).
thf(938,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) )
=> ( B = C ) )
& ( ( B = C )
=> ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(677,axiom,
! [A: $i,B: $i] :
( ( insert_fun_a_bool @ A @ B )
= ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ fequal_fun_a_bool ) @ A ) ) @ ( hAPP_f2117159681l_bool @ ( cOMBC_1880041174l_bool @ member_fun_a_bool ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_insert__compr) ).
thf(3225,plain,
! [A: $i,B: $i] :
( ( insert_fun_a_bool @ A @ B )
= ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ fequal_fun_a_bool ) @ A ) ) @ ( hAPP_f2117159681l_bool @ ( cOMBC_1880041174l_bool @ member_fun_a_bool ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(368,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) )
<=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
| ( A
= ( hAPP_nat_nat @ suc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_le__Suc__eq) ).
thf(2076,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
| ( A
= ( hAPP_nat_nat @ suc @ B ) ) ) )
& ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
| ( A
= ( hAPP_nat_nat @ suc @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(88,axiom,
! [A: $i,B: $i] : ( is_bool @ ( hAPP_f54304608l_bool @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obool) ).
thf(1170,plain,
! [A: $i,B: $i] : ( is_bool @ ( hAPP_f54304608l_bool @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(614,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ bot_bot_fun_nat_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_404_empty__iff) ).
thf(2963,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ bot_bot_fun_nat_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(699,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_1_1_U) ).
thf(3321,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(401,axiom,
! [A: $i,B: $i] :
( ( ( is_fun_pname_bool @ A )
& ( is_fun_pname_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_542_order__antisym__conv) ).
thf(2189,plain,
! [A: $i,B: $i] :
( ( ( is_fun_pname_bool @ A )
& ( is_fun_pname_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(226,axiom,
! [A: $i] : ( is_a @ ( mgt @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_mgt) ).
thf(1616,plain,
! [A: $i] : ( is_a @ ( mgt @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(624,axiom,
! [A: $i] :
( ( hBOOL @ A )
| ( hBOOL @ ( hAPP_bool_bool @ fNot @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_2_1_U) ).
thf(2995,plain,
! [A: $i] :
( ( hBOOL @ A )
| ( hBOOL @ ( hAPP_bool_bool @ fNot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(342,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) )
= ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_582_diff__cancel) ).
thf(1996,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) )
= ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(789,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_nat_fun_a_bool @ C @ D ) ) @ ( hAPP_nat_fun_a_bool @ C @ ( hAPP_nat_nat @ suc @ D ) ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_nat_fun_a_bool @ C @ A ) ) @ ( hAPP_nat_fun_a_bool @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_lift__Suc__mono__le) ).
thf(3675,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_nat_fun_a_bool @ C @ D ) ) @ ( hAPP_nat_fun_a_bool @ C @ ( hAPP_nat_nat @ suc @ D ) ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_nat_fun_a_bool @ C @ A ) ) @ ( hAPP_nat_fun_a_bool @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).
thf(122,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ ( hAPP_nat_nat @ suc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_613_Suc__mono) ).
thf(1278,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ ( hAPP_nat_nat @ suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(267,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_p393069232l_bool @ ( cOMBB_675860798_pname @ A @ B ) @ C )
= ( hAPP_b589554111l_bool @ A @ ( hAPP_pname_bool @ B @ C ) ) ),
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(1764,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_p393069232l_bool @ ( cOMBB_675860798_pname @ A @ B ) @ C )
= ( hAPP_b589554111l_bool @ A @ ( hAPP_pname_bool @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(79,axiom,
! [A: $i,B: $i] :
( ( ( is_fun_pname_bool @ A )
& ( is_fun_pname_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_507_xt1_I5_J) ).
thf(1146,plain,
! [A: $i,B: $i] :
( ( ( is_fun_pname_bool @ A )
& ( is_fun_pname_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(328,axiom,
! [A: $i,B: $i] :
( ( ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B )
= zero_zero_nat )
=> ( ( ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ A )
= zero_zero_nat )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_687_diffs0__imp__equal) ).
thf(1959,plain,
! [A: $i,B: $i] :
( ( ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B )
= zero_zero_nat )
=> ( ( ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ A )
= zero_zero_nat )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(846,axiom,
! [A: $i,B: $i] :
( ( ( is_fun949378684l_bool @ A )
& ( is_fun_a_bool @ B ) )
=> ( is_bool @ ( hAPP_fun_a_bool_bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool) ).
thf(3871,plain,
! [A: $i,B: $i] :
( ( ( is_fun949378684l_bool @ A )
& ( is_fun_a_bool @ B ) )
=> ( is_bool @ ( hAPP_fun_a_bool_bool @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).
thf(637,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ ( insert_pname @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_subset__insertI2) ).
thf(3042,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ ( insert_pname @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(546,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( p @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_assms_I1_J) ).
thf(2717,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( p @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(745,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
=> ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( image_a_fun_nat_bool @ A @ B ) ) )
=> ? [C: $i] :
( ( is_a @ C )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ ( hAPP_f2050579477a_bool @ ( cOMBC_1355376034l_bool @ member_a ) @ B ) ) @ ( hAPP_f1549043526a_bool @ ( cOMBC_777206479l_bool @ ( cOMBB_743407885bool_a @ fequal_fun_nat_bool @ A ) ) @ ( hAPP_a_fun_nat_bool @ A @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_pigeonhole__infinite) ).
thf(3491,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
=> ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( image_a_fun_nat_bool @ A @ B ) ) )
=> ? [C: $i] :
( ( is_a @ C )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ ( hAPP_f2050579477a_bool @ ( cOMBC_1355376034l_bool @ member_a ) @ B ) ) @ ( hAPP_f1549043526a_bool @ ( cOMBC_777206479l_bool @ ( cOMBB_743407885bool_a @ fequal_fun_nat_bool @ A ) ) @ ( hAPP_a_fun_nat_bool @ A @ C ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).
thf(120,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_a217006258l_bool @ ( cOMBB_1137537805bool_a @ A @ B ) @ C )
= ( hAPP_f434788991l_bool @ A @ ( hAPP_a93125764e_bool @ B @ C ) ) ),
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(1273,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_a217006258l_bool @ ( cOMBB_1137537805bool_a @ A @ B ) @ C )
= ( hAPP_f434788991l_bool @ A @ ( hAPP_a93125764e_bool @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(510,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ bot_bo1649642514l_bool ) )
=> ( ! [C: $i,D: $i] :
( ( ( is_fun_pname_bool @ C )
& ( is_fun1661590463l_bool @ D ) )
=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ D ) )
=> ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ D ) )
=> ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ ( insert1325755072e_bool @ C @ D ) ) ) ) ) ) )
=> ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_564_finite__induct) ).
thf(2570,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ bot_bo1649642514l_bool ) )
=> ( ! [C: $i,D: $i] :
( ( ( is_fun_pname_bool @ C )
& ( is_fun1661590463l_bool @ D ) )
=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ D ) )
=> ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ D ) )
=> ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ ( insert1325755072e_bool @ C @ D ) ) ) ) ) ) )
=> ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(317,axiom,
! [A: $i] :
( ( collect_fun_nat_bool @ ( hAPP_f103356543l_bool @ ( cOMBC_1693257480l_bool @ fequal_fun_nat_bool ) @ A ) )
= ( insert_fun_nat_bool @ A @ bot_bo1701429464l_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_485_singleton__conv) ).
thf(1927,plain,
! [A: $i] :
( ( collect_fun_nat_bool @ ( hAPP_f103356543l_bool @ ( cOMBC_1693257480l_bool @ fequal_fun_nat_bool ) @ A ) )
= ( insert_fun_nat_bool @ A @ bot_bo1701429464l_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(693,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
=> ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_finite_OinsertI) ).
thf(3289,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
=> ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(714,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( wt @ B ) )
=> ( ! [C: $i] :
( ( is_pname @ C )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ u ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( p @ A ) @ ( insert_a @ ( hAPP_pname_a @ mgt_call @ C ) @ bot_bot_fun_a_bool ) ) ) ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( p @ A ) @ ( insert_a @ ( mgt @ B ) @ bot_bot_fun_a_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_373_assms_I3_J) ).
thf(3375,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( wt @ B ) )
=> ( ! [C: $i] :
( ( is_pname @ C )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ u ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( p @ A ) @ ( insert_a @ ( hAPP_pname_a @ mgt_call @ C ) @ bot_bot_fun_a_bool ) ) ) ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( p @ A ) @ ( insert_a @ ( mgt @ B ) @ bot_bot_fun_a_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(793,axiom,
! [A: $i,B: $i] :
( ( A != B )
=> ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_647_linorder__neqE__nat) ).
thf(3686,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).
thf(721,axiom,
! [A: $i,B: $i] :
( ( A != B )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ 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(3396,plain,
! [A: $i,B: $i] :
( ( A != B )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(607,axiom,
! [A: $i,B: $i] :
( ( is_fun_pname_bool @ B )
=> ( ( ( B = bot_bo844097828e_bool )
=> ( ( image_pname_a @ ( cOMBK_a_pname @ A ) @ B )
= bot_bot_fun_a_bool ) )
& ( ( B != bot_bo844097828e_bool )
=> ( ( image_pname_a @ ( cOMBK_a_pname @ A ) @ B )
= ( insert_a @ A @ bot_bot_fun_a_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_498_image__constant__conv) ).
thf(2936,plain,
! [A: $i,B: $i] :
( ( is_fun_pname_bool @ B )
=> ( ( ( B = bot_bo844097828e_bool )
=> ( ( image_pname_a @ ( cOMBK_a_pname @ A ) @ B )
= bot_bot_fun_a_bool ) )
& ( ( B != bot_bo844097828e_bool )
=> ( ( image_pname_a @ ( cOMBK_a_pname @ A ) @ B )
= ( insert_a @ A @ bot_bot_fun_a_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(234,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
<=> ? [C: $i] :
( B
= ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_586_le__iff__add) ).
thf(1648,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ? [C: $i] :
( B
= ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) )
& ( ? [C: $i] :
( B
= ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(798,axiom,
! [A: $i,B: $i] :
( ( A = B )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_equalityD2) ).
thf(3707,plain,
! [A: $i,B: $i] :
( ( A = B )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).
thf(196,axiom,
! [A: $i,B: $i] :
( ( is_fun_a_bool @ B )
=> ( is_fun_a_bool @ ( hAPP_f2050579477a_bool @ A @ B ) ) ),
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(1510,plain,
! [A: $i,B: $i] :
( ( is_fun_a_bool @ B )
=> ( is_fun_a_bool @ ( hAPP_f2050579477a_bool @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(594,axiom,
! [A: $i,B: $i] :
( ( A = B )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_equalityD1) ).
thf(2894,plain,
! [A: $i,B: $i] :
( ( A = B )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(152,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_589_trans__le__add2) ).
thf(1374,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(807,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ~ ( hBOOL @ A )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
thf(3741,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ~ ( hBOOL @ A )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).
thf(646,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_set__mp) ).
thf(3070,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(313,axiom,
! [A: $i,B: $i] :
( ( is_fun_a_bool @ B )
=> ( is_fun_a_bool @ ( cOMBS_a_bool_bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_COMBS_000t__a_000tc__HOL__Obool_000tc__HOL__Obool) ).
thf(1916,plain,
! [A: $i,B: $i] :
( ( is_fun_a_bool @ B )
=> ( is_fun_a_bool @ ( cOMBS_a_bool_bool @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(679,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B
= ( hAPP_nat_a @ C @ D ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ D ) @ A ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ ( image_nat_a @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_image__eqI) ).
thf(3234,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B
= ( hAPP_nat_a @ C @ D ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ D ) @ A ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ ( image_nat_a @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(750,axiom,
! [A: $i,B: $i] :
( ( ( is_a @ A )
& ( is_a @ B ) )
=> ( ( ( insert_a @ A @ bot_bot_fun_a_bool )
= ( insert_a @ B @ bot_bot_fun_a_bool ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_448_singleton__inject) ).
thf(3504,plain,
! [A: $i,B: $i] :
( ( ( is_a @ A )
& ( is_a @ B ) )
=> ( ( ( insert_a @ A @ bot_bot_fun_a_bool )
= ( insert_a @ B @ bot_bot_fun_a_bool ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).
thf(273,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ ( image_pname_nat @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_finite__surj) ).
thf(1784,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ ( image_pname_nat @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(681,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ ( hAPP_a_nat @ A @ B ) ) @ ( image_a_nat @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_304_imageI) ).
thf(3240,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ ( hAPP_a_nat @ A @ B ) ) @ ( image_a_nat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(581,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ A ) )
=> ( ( hBOOL @ B )
<=> ( hBOOL @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_505_xt1_I5_J) ).
thf(2849,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ A ) )
=> ( ( ( hBOOL @ B )
=> ( hBOOL @ A ) )
& ( ( hBOOL @ A )
=> ( hBOOL @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(650,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ B ) ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ A ) ) ) )
=> ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fconj @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_finite__Collect__conjI) ).
thf(3086,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ B ) ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ A ) ) ) )
=> ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fconj @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(865,axiom,
! [A: $i] :
( ( is_fun_a_bool @ A )
=> ( ? [B: $i] :
( ( is_a @ B )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ A ) ) )
<=> ( A != bot_bot_fun_a_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_415_ex__in__conv) ).
thf(3945,plain,
! [A: $i] :
( ( is_fun_a_bool @ A )
=> ( ( ? [B: $i] :
( ( is_a @ B )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ A ) ) )
=> ( A != bot_bot_fun_a_bool ) )
& ( ( A != bot_bot_fun_a_bool )
=> ? [B: $i] :
( ( is_a @ B )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).
thf(464,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ A @ C ) @ B ) ) )
=> ( ( ( B = C )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ A @ C ) @ B ) ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ A @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ A @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_651_nat__less__cases) ).
thf(2398,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ A @ C ) @ B ) ) )
=> ( ( ( B = C )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ A @ C ) @ B ) ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ A @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ A @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(774,axiom,
! [A: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ bot_bo844097828e_bool ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_392_empty__subsetI) ).
thf(3604,plain,
! [A: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ bot_bo844097828e_bool ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(73,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
<=> ! [C: $i] : ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_nat_bool @ A @ C ) ) @ ( hAPP_nat_bool @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_375_le__fun__def) ).
thf(1124,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
=> ! [C: $i] : ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_nat_bool @ A @ C ) ) @ ( hAPP_nat_bool @ B @ C ) ) ) )
& ( ! [C: $i] : ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_nat_bool @ A @ C ) ) @ ( hAPP_nat_bool @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(190,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_627_Suc__lessD) ).
thf(1488,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(773,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ A ) )
<=> ( hBOOL @ bot_bot_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_426_bot__fun__def) ).
thf(3599,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ A ) )
=> ( hBOOL @ bot_bot_bool ) )
& ( ( hBOOL @ bot_bot_bool )
=> ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).
thf(760,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ C ) )
=> ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f1637334154l_bool @ A @ bot_bo1701429464l_bool ) )
=> ( ! [D: $i,E: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ E ) )
=> ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ D ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP_f1637334154l_bool @ A @ E ) )
=> ( hBOOL @ ( hAPP_f1637334154l_bool @ A @ ( insert_fun_nat_bool @ D @ E ) ) ) ) ) ) )
=> ( hBOOL @ ( hAPP_f1637334154l_bool @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_559_finite__subset__induct) ).
thf(3536,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ C ) )
=> ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f1637334154l_bool @ A @ bot_bo1701429464l_bool ) )
=> ( ! [D: $i,E: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ E ) )
=> ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ D ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP_f1637334154l_bool @ A @ E ) )
=> ( hBOOL @ ( hAPP_f1637334154l_bool @ A @ ( insert_fun_nat_bool @ D @ E ) ) ) ) ) ) )
=> ( hBOOL @ ( hAPP_f1637334154l_bool @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).
thf(82,axiom,
! [A: $i,B: $i] :
( ( is_fun_pname_bool @ B )
=> ( is_fun_pname_bool @ ( cOMBB_647938656_pname @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname) ).
thf(1154,plain,
! [A: $i,B: $i] :
( ( is_fun_pname_bool @ B )
=> ( is_fun_pname_bool @ ( cOMBB_647938656_pname @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(880,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ A ) )
<=> ( hBOOL @ bot_bot_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_429_bot__apply) ).
thf(4000,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ A ) )
=> ( hBOOL @ bot_bot_bool ) )
& ( ( hBOOL @ bot_bot_bool )
=> ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).
thf(22,axiom,
is_fun1661590463l_bool @ finite_finite_pname,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Finite__Set_Ofinite_000tc__Com__Opname) ).
thf(975,plain,
is_fun1661590463l_bool @ finite_finite_pname,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(718,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ bot_bo844097828e_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_405_empty__iff) ).
thf(3387,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ bot_bo844097828e_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).
thf(616,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ ( insert_nat @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_329_subset__insertI2) ).
thf(2970,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ ( insert_nat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(35,axiom,
( bot_bot_fun_a_bool
= ( collect_a @ ( cOMBK_bool_a @ fFalse ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_423_empty__def) ).
thf(1007,plain,
( bot_bot_fun_a_bool
= ( collect_a @ ( cOMBK_bool_a @ fFalse ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(698,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_nat_a @ A @ B ) ) @ ( image_nat_a @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_350_image__mono) ).
thf(3319,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_nat_a @ A @ B ) ) @ ( image_nat_a @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(228,axiom,
! [A: $i,B: $i] :
( ( ( is_fun1661590463l_bool @ A )
& ( is_fun1661590463l_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ B ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ A ) ) )
=> ( A = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_card__seteq) ).
thf(1620,plain,
! [A: $i,B: $i] :
( ( ( is_fun1661590463l_bool @ A )
& ( is_fun1661590463l_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ B ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ A ) ) )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(741,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ A @ B ) ) )
<=> ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_finite__insert) ).
thf(3472,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ A @ B ) ) )
=> ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) ) )
& ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
=> ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(691,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( image_819518260e_bool @ A @ B ) ) )
=> ? [C: $i] :
( ( is_a @ C )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ ( hAPP_f2050579477a_bool @ ( cOMBC_1355376034l_bool @ member_a ) @ B ) ) @ ( hAPP_f1051908748a_bool @ ( cOMBC_1834145417l_bool @ ( cOMBB_1137537805bool_a @ fequal533582459e_bool @ A ) ) @ ( hAPP_a93125764e_bool @ A @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_pigeonhole__infinite) ).
thf(3283,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( image_819518260e_bool @ A @ B ) ) )
=> ? [C: $i] :
( ( is_a @ C )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ ( hAPP_f2050579477a_bool @ ( cOMBC_1355376034l_bool @ member_a ) @ B ) ) @ ( hAPP_f1051908748a_bool @ ( cOMBC_1834145417l_bool @ ( cOMBB_1137537805bool_a @ fequal533582459e_bool @ A ) ) @ ( hAPP_a93125764e_bool @ A @ C ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(535,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f621171935l_bool @ A @ bot_bo1389914601l_bool ) )
=> ( ! [C: $i,D: $i] :
( ( ( is_fun_a_bool @ C )
& ( is_fun949378684l_bool @ D ) )
=> ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ D ) )
=> ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_f621171935l_bool @ A @ D ) )
=> ( hBOOL @ ( hAPP_f621171935l_bool @ A @ ( insert_fun_a_bool @ C @ D ) ) ) ) ) ) )
=> ( hBOOL @ ( hAPP_f621171935l_bool @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_565_finite__induct) ).
thf(2674,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f621171935l_bool @ A @ bot_bo1389914601l_bool ) )
=> ( ! [C: $i,D: $i] :
( ( ( is_fun_a_bool @ C )
& ( is_fun949378684l_bool @ D ) )
=> ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ D ) )
=> ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_f621171935l_bool @ A @ D ) )
=> ( hBOOL @ ( hAPP_f621171935l_bool @ A @ ( insert_fun_a_bool @ C @ D ) ) ) ) ) ) )
=> ( hBOOL @ ( hAPP_f621171935l_bool @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(158,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
=> ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ ord_le313189616e_bool ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_finite__Collect__subsets) ).
thf(1388,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
=> ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ ord_le313189616e_bool ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(914,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ B ) ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ A ) ) ) )
=> ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fconj @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_finite__Collect__conjI) ).
thf(4122,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ B ) ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ A ) ) ) )
=> ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fconj @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( is_bool @ A )
=> ( ( hAPP_nat_bool @ ( cOMBK_bool_nat @ A ) @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Nat__Onat_U) ).
thf(958,plain,
! [A: $i,B: $i] :
( ( is_bool @ A )
=> ( ( hAPP_nat_bool @ ( cOMBK_bool_nat @ A ) @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(163,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_611_termination__basic__simps_I4_J) ).
thf(1403,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(612,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ ( insert_a @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_321_subset__insertI) ).
thf(2959,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ ( insert_a @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(674,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ A @ B ) )
=> ( ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fconj @ ( hAPP_f103356543l_bool @ ( cOMBC_1693257480l_bool @ fequal_fun_nat_bool ) @ B ) ) @ A ) )
= ( insert_fun_nat_bool @ B @ bot_bo1701429464l_bool ) ) )
& ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ A @ B ) )
=> ( ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fconj @ ( hAPP_f103356543l_bool @ ( cOMBC_1693257480l_bool @ fequal_fun_nat_bool ) @ B ) ) @ A ) )
= bot_bo1701429464l_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_473_Collect__conv__if) ).
thf(3213,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ A @ B ) )
=> ( ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fconj @ ( hAPP_f103356543l_bool @ ( cOMBC_1693257480l_bool @ fequal_fun_nat_bool ) @ B ) ) @ A ) )
= ( insert_fun_nat_bool @ B @ bot_bo1701429464l_bool ) ) )
& ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ A @ B ) )
=> ( ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fconj @ ( hAPP_f103356543l_bool @ ( cOMBC_1693257480l_bool @ fequal_fun_nat_bool ) @ B ) ) @ A ) )
= bot_bo1701429464l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(172,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ C ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ ( image_pname_nat @ A @ B ) ) )
=> ? [D: $i] :
( ( is_fun_pname_bool @ D )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ D ) @ B ) )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ D ) )
& ( C
= ( image_pname_nat @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_finite__subset__image) ).
thf(1428,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ C ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ ( image_pname_nat @ A @ B ) ) )
=> ? [D: $i] :
( ( is_fun_pname_bool @ D )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ D ) @ B ) )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ D ) )
& ( C
= ( image_pname_nat @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(811,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_a_pname @ A @ B ) ) )
=> ? [C: $i] :
( ( is_a @ C )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ ( hAPP_f2050579477a_bool @ ( cOMBC_1355376034l_bool @ member_a ) @ B ) ) @ ( hAPP_p1534023578a_bool @ ( cOMBC_a_pname_bool @ ( cOMBB_610033911bool_a @ fequal_pname @ A ) ) @ ( hAPP_a_pname @ A @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_pigeonhole__infinite) ).
thf(3751,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_a_pname @ A @ B ) ) )
=> ? [C: $i] :
( ( is_a @ C )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ ( hAPP_f2050579477a_bool @ ( cOMBC_1355376034l_bool @ member_a ) @ B ) ) @ ( hAPP_p1534023578a_bool @ ( cOMBC_a_pname_bool @ ( cOMBB_610033911bool_a @ fequal_pname @ A ) ) @ ( hAPP_a_pname @ A @ C ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).
thf(442,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ C ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ ( image_496248727ol_nat @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_finite__surj) ).
thf(2326,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ C ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ ( image_496248727ol_nat @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(432,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_p1499970991t_bool @ ( cOMBB_523834888_pname @ A @ B ) @ C )
= ( hAPP_n1699378549t_bool @ A @ ( hAPP_pname_nat @ B @ C ) ) ),
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(2293,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_p1499970991t_bool @ ( cOMBB_523834888_pname @ A @ B ) @ C )
= ( hAPP_n1699378549t_bool @ A @ ( hAPP_pname_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(550,axiom,
! [A: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_679_le0) ).
thf(2738,plain,
! [A: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(785,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_pname_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_finite__imageI) ).
thf(3663,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_pname_a @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).
thf(110,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) )
<=> ? [B: $i] :
! [C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_372_finite__nat__set__iff__bounded__le) ).
thf(1239,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) )
=> ? [B: $i] :
! [C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ B ) ) ) )
& ( ? [B: $i] :
! [C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(758,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_514_order__trans) ).
thf(3532,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).
thf(77,axiom,
! [A: $i,B: $i] :
( ( insert_pname @ A @ ( insert_pname @ A @ B ) )
= ( insert_pname @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_insert__absorb2) ).
thf(1139,plain,
! [A: $i,B: $i] :
( ( insert_pname @ A @ ( insert_pname @ A @ B ) )
= ( insert_pname @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(825,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ ( image_a_nat @ B @ C ) ) )
=> ~ ! [D: $i] :
( ( is_a @ D )
=> ( ( A
= ( hAPP_a_nat @ B @ D ) )
=> ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ D ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_355_imageE) ).
thf(3796,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ ( image_a_nat @ B @ C ) ) )
=> ~ ! [D: $i] :
( ( is_a @ D )
=> ( ( A
= ( hAPP_a_nat @ B @ D ) )
=> ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ D ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).
thf(274,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f759274231e_bool @ ( cOMBB_598082538e_bool @ A @ B ) @ C )
= ( hAPP_p61793385e_bool @ A @ ( hAPP_f1297739591_pname @ B @ C ) ) ),
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(1786,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f759274231e_bool @ ( cOMBB_598082538e_bool @ A @ B ) @ C )
= ( hAPP_p61793385e_bool @ A @ ( hAPP_f1297739591_pname @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(632,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_650_less__not__refl3) ).
thf(3023,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(119,axiom,
! [A: $i,B: $i] : ( is_bool @ ( hAPP_f292226953l_bool @ A @ B ) ),
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(1271,plain,
! [A: $i,B: $i] : ( is_bool @ ( hAPP_f292226953l_bool @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(437,axiom,
! [A: $i] :
( zero_zero_nat
!= ( hAPP_nat_nat @ suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_696_Zero__not__Suc) ).
thf(2308,plain,
! [A: $i] :
( zero_zero_nat
!= ( hAPP_nat_nat @ suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(474,axiom,
! [A: $i] :
( ( ( collect_pname @ A )
= bot_bo844097828e_bool )
<=> ! [B: $i] :
( ( is_pname @ B )
=> ~ ( hBOOL @ ( hAPP_pname_bool @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_398_Collect__empty__eq) ).
thf(2442,plain,
! [A: $i] :
( ( ( ( collect_pname @ A )
= bot_bo844097828e_bool )
=> ! [B: $i] :
( ( is_pname @ B )
=> ~ ( hBOOL @ ( hAPP_pname_bool @ A @ B ) ) ) )
& ( ! [B: $i] :
( ( is_pname @ B )
=> ~ ( hBOOL @ ( hAPP_pname_bool @ A @ B ) ) )
=> ( ( collect_pname @ A )
= bot_bo844097828e_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(555,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ A @ B ) ) )
<=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_finite__insert) ).
thf(2753,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ A @ B ) ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) ) )
& ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(819,axiom,
hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ bot_bo1701429464l_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_386_finite_OemptyI) ).
thf(3783,plain,
hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ bot_bo1701429464l_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).
thf(67,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_nat_bool @ ( cOMBB_bool_bool_nat @ A @ B ) @ C )
= ( hAPP_bool_bool @ A @ ( hAPP_nat_bool @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Nat__Onat_U) ).
thf(1092,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_nat_bool @ ( cOMBB_bool_bool_nat @ A @ B ) @ C )
= ( hAPP_bool_bool @ A @ ( hAPP_nat_bool @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(895,axiom,
! [A: $i,B: $i,C: $i] :
( ( is_fun_a_bool @ C )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ C ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C ) @ ( image_pname_a @ A @ B ) ) )
=> ? [D: $i] :
( ( is_fun_pname_bool @ D )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ D ) @ B ) )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ D ) )
& ( C
= ( image_pname_a @ A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_finite__subset__image) ).
thf(4060,plain,
! [A: $i,B: $i,C: $i] :
( ( is_fun_a_bool @ C )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ C ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C ) @ ( image_pname_a @ A @ B ) ) )
=> ? [D: $i] :
( ( is_fun_pname_bool @ D )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ D ) @ B ) )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ D ) )
& ( C
= ( image_pname_a @ A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).
thf(543,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
=> ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( image_nat_fun_a_bool @ A @ B ) ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ ( hAPP_f800510211t_bool @ ( cOMBC_226598744l_bool @ member_nat ) @ B ) ) @ ( hAPP_f282463732t_bool @ ( cOMBC_1928494297l_bool @ ( cOMBB_1823939024ol_nat @ fequal_fun_a_bool @ A ) ) @ ( hAPP_nat_fun_a_bool @ A @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_pigeonhole__infinite) ).
thf(2706,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
=> ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( image_nat_fun_a_bool @ A @ B ) ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ ( hAPP_f800510211t_bool @ ( cOMBC_226598744l_bool @ member_nat ) @ B ) ) @ ( hAPP_f282463732t_bool @ ( cOMBC_1928494297l_bool @ ( cOMBB_1823939024ol_nat @ fequal_fun_a_bool @ A ) ) @ ( hAPP_nat_fun_a_bool @ A @ C ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(397,axiom,
! [A: $i,B: $i] :
( ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B )
= ( hAPP_nat_nat @ suc @ zero_zero_nat ) )
<=> ( ( ( A
= ( hAPP_nat_nat @ suc @ zero_zero_nat ) )
& ( B = zero_zero_nat ) )
| ( ( A = zero_zero_nat )
& ( B
= ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_681_add__is__1) ).
thf(2166,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B )
= ( hAPP_nat_nat @ suc @ zero_zero_nat ) )
=> ( ( ( A
= ( hAPP_nat_nat @ suc @ zero_zero_nat ) )
& ( B = zero_zero_nat ) )
| ( ( A = zero_zero_nat )
& ( B
= ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) ) ) )
& ( ( ( ( A
= ( hAPP_nat_nat @ suc @ zero_zero_nat ) )
& ( B = zero_zero_nat ) )
| ( ( A = zero_zero_nat )
& ( B
= ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) ) )
=> ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B )
= ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(66,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_603_le__add__diff) ).
thf(1090,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(307,axiom,
! [A: $i,B: $i] :
( ( is_pname @ B )
=> ( is_fun_a_bool @ ( hAPP_p1534023578a_bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Com__Opname_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
thf(1897,plain,
! [A: $i,B: $i] :
( ( is_pname @ B )
=> ( is_fun_a_bool @ ( hAPP_p1534023578a_bool @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ C ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_577_nat__add__left__commute) ).
thf(919,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ C ) )
= ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(782,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
& ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_551_order__eq__iff) ).
thf(3641,plain,
! [A: $i,B: $i] :
( ( ( A = B )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
& ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
& ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).
thf(652,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ C ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ ( image_876012084bool_a @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_finite__surj) ).
thf(3091,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ C ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ ( image_876012084bool_a @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( ( is_fun_a_bool @ A )
& ( is_a @ B ) )
=> ( is_bool @ ( hAPP_a_bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000t__a_000tc__HOL__Obool) ).
thf(947,plain,
! [A: $i,B: $i] :
( ( ( is_fun_a_bool @ A )
& ( is_a @ B ) )
=> ( is_bool @ ( hAPP_a_bool @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(95,axiom,
is_a @ ( undefined_a @ x_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_HOL_Oundefined_000t__a) ).
thf(1194,plain,
is_a @ ( undefined_a @ x_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(499,axiom,
! [A: $i,B: $i,C: $i] :
( ( image_a_pname @ A @ ( insert_a @ B @ C ) )
= ( insert_pname @ ( hAPP_a_pname @ A @ B ) @ ( image_a_pname @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_334_image__insert) ).
thf(2538,plain,
! [A: $i,B: $i,C: $i] :
( ( image_a_pname @ A @ ( insert_a @ B @ C ) )
= ( insert_pname @ ( hAPP_a_pname @ A @ B ) @ ( image_a_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(664,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
=> ( ( C = A )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_526_ord__le__eq__trans) ).
thf(3155,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
=> ( ( C = A )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(680,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ A ) @ B ) )
| ( hBOOL @ A )
| ( hBOOL @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_3_1_U) ).
thf(3238,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ A ) @ B ) )
| ( hBOOL @ A )
| ( hBOOL @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(762,axiom,
! [A: $i,B: $i,C: $i] :
( ( B = C )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_538_ord__eq__le__trans) ).
thf(3551,plain,
! [A: $i,B: $i,C: $i] :
( ( B = C )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).
thf(379,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_591_add__le__mono) ).
thf(2116,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ D ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(279,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_a_fun_nat_bool @ ( cOMBB_1321347587bool_a @ A @ B ) @ C )
= ( hAPP_n1699378549t_bool @ A @ ( hAPP_a_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_) ).
thf(1801,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_a_fun_nat_bool @ ( cOMBB_1321347587bool_a @ A @ B ) @ C )
= ( hAPP_n1699378549t_bool @ A @ ( hAPP_a_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(748,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( image_fun_a_bool_nat @ A @ B ) ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_card__image__le) ).
thf(3500,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( image_fun_a_bool_nat @ A @ B ) ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(483,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_finite__subset) ).
thf(2478,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(685,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ bot_bo844097828e_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_384_emptyE) ).
thf(3251,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ bot_bo844097828e_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(467,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ A @ B ) ) @ ( insert_a @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_333_insert__mono) ).
thf(2415,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ A @ B ) ) @ ( insert_a @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(621,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ D ) @ C ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( hAPP_nat_a @ A @ D ) ) @ B ) ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_nat_a @ A @ C ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_365_image__subsetI) ).
thf(2987,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ D ) @ C ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( hAPP_nat_a @ A @ D ) ) @ B ) ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_nat_a @ A @ C ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(281,axiom,
! [A: $i,B: $i] :
( ( is_a @ B )
=> ( is_fun_pname_bool @ ( hAPP_a93125764e_bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000t__a_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).
thf(1806,plain,
! [A: $i,B: $i] :
( ( is_a @ B )
=> ( is_fun_pname_bool @ ( hAPP_a93125764e_bool @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_668_diff__less__mono) ).
thf(1011,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(867,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
=> ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( image_nat_fun_a_bool @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_finite__imageI) ).
thf(3957,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
=> ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( image_nat_fun_a_bool @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).
thf(692,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_in__mono) ).
thf(3287,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(727,axiom,
! [A: $i,B: $i] :
( ( A = B )
=> ~ ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
=> ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_299_equalityE) ).
thf(3419,plain,
! [A: $i,B: $i] :
( ( A = B )
=> ~ ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
=> ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).
thf(50,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_set__mp) ).
thf(1048,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(418,axiom,
! [A: $i,B: $i] : ( is_fun949378684l_bool @ ( image_nat_fun_a_bool @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
thf(2257,plain,
! [A: $i,B: $i] : ( is_fun949378684l_bool @ ( image_nat_fun_a_bool @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(220,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
=> ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
=> ( ( hAPP_f921600141ol_nat @ finite_card_pname @ ( insert_pname @ A @ B ) )
= ( hAPP_f921600141ol_nat @ finite_card_pname @ B ) ) )
& ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
=> ( ( hAPP_f921600141ol_nat @ finite_card_pname @ ( insert_pname @ A @ B ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f921600141ol_nat @ finite_card_pname @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_card__insert__if) ).
thf(1589,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
=> ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
=> ( ( hAPP_f921600141ol_nat @ finite_card_pname @ ( insert_pname @ A @ B ) )
= ( hAPP_f921600141ol_nat @ finite_card_pname @ B ) ) )
& ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
=> ( ( hAPP_f921600141ol_nat @ finite_card_pname @ ( insert_pname @ A @ B ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f921600141ol_nat @ finite_card_pname @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(415,axiom,
! [A: $i,B: $i] :
( ( insert_nat @ A @ ( collect_nat @ B ) )
= ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fimplies @ ( cOMBB_bool_bool_nat @ fNot @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ fequal_nat ) @ A ) ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_insert__Collect) ).
thf(2246,plain,
! [A: $i,B: $i] :
( ( insert_nat @ A @ ( collect_nat @ B ) )
= ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fimplies @ ( cOMBB_bool_bool_nat @ fNot @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ fequal_nat ) @ A ) ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(223,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
<=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
& ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_641_nat__less__le) ).
thf(1603,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
& ( A != B ) ) )
& ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
& ( A != B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(434,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f282463732t_bool @ ( cOMBB_164527437a_bool @ A @ B ) @ C )
= ( hAPP_n1699378549t_bool @ A @ ( hAPP_fun_a_bool_nat @ B @ C ) ) ),
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(2299,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f282463732t_bool @ ( cOMBB_164527437a_bool @ A @ B ) @ C )
= ( hAPP_n1699378549t_bool @ A @ ( hAPP_fun_a_bool_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(769,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_518_order__antisym) ).
thf(3586,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).
thf(242,axiom,
! [A: $i,B: $i] :
( ( insert_pname @ A @ B )
!= bot_bo844097828e_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_458_insert__not__empty) ).
thf(1690,plain,
! [A: $i,B: $i] :
( ( insert_pname @ A @ B )
!= bot_bo844097828e_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(669,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ A ) @ B ) ) ) )
<=> ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ A ) ) )
& ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_finite__Collect__disjI) ).
thf(3182,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ A ) @ B ) ) ) )
=> ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ A ) ) )
& ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ B ) ) ) ) )
& ( ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ A ) ) )
& ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ B ) ) ) )
=> ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(588,axiom,
! [A: $i,B: $i] :
( ( A != B )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Nat__Onat_T) ).
thf(2871,plain,
! [A: $i,B: $i] :
( ( A != B )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(153,axiom,
! [A: $i,B: $i] : ( is_fun_a_bool @ ( image_fun_nat_bool_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000t__a) ).
thf(1376,plain,
! [A: $i,B: $i] : ( is_fun_a_bool @ ( image_fun_nat_bool_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(403,axiom,
! [A: $i] :
( ( is_fun_pname_bool @ A )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ bot_bo844097828e_bool ) )
<=> ( A = bot_bo844097828e_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_436_bot__unique) ).
thf(2197,plain,
! [A: $i] :
( ( is_fun_pname_bool @ A )
=> ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ bot_bo844097828e_bool ) )
=> ( A = bot_bo844097828e_bool ) )
& ( ( A = bot_bo844097828e_bool )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ bot_bo844097828e_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(910,axiom,
! [A: $i] :
( ~ ( hBOOL @ ( hAPP_bool_bool @ fNot @ A ) )
| ~ ( hBOOL @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_1_1_U) ).
thf(4107,plain,
! [A: $i] :
( ~ ( hBOOL @ ( hAPP_bool_bool @ fNot @ A ) )
| ~ ( hBOOL @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).
thf(398,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_664_Suc__le__lessD) ).
thf(2182,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(810,axiom,
! [A: $i,B: $i] :
( ( A = B )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_546_order__eq__refl) ).
thf(3747,plain,
! [A: $i,B: $i] :
( ( A = B )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).
thf(641,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_1551609309ol_nat @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_finite__imageI) ).
thf(3055,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_1551609309ol_nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(383,axiom,
! [A: $i,B: $i] :
( ( is_pname @ B )
=> ( is_pname @ ( hAPP_pname_pname @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Com__Opname_000tc__Com__Opname) ).
thf(2129,plain,
! [A: $i,B: $i] :
( ( is_pname @ B )
=> ( is_pname @ ( hAPP_pname_pname @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(378,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ C ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_667_less__diff__conv) ).
thf(2111,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(564,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
=> ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( image_47868345e_bool @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_finite__imageI) ).
thf(2780,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
=> ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( image_47868345e_bool @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(85,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ B ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( insert_fun_a_bool @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_card__insert__le) ).
thf(1162,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ B ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( insert_fun_a_bool @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(627,axiom,
! [A: $i,B: $i,C: $i] :
( ( is_fun949378684l_bool @ C )
=> ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ C ) )
=> ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ C ) @ ( image_a_fun_a_bool @ A @ B ) ) )
=> ? [D: $i] :
( ( is_fun_a_bool @ D )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ D ) @ B ) )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ D ) )
& ( C
= ( image_a_fun_a_bool @ A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_finite__subset__image) ).
thf(3006,plain,
! [A: $i,B: $i,C: $i] :
( ( is_fun949378684l_bool @ C )
=> ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ C ) )
=> ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ C ) @ ( image_a_fun_a_bool @ A @ B ) ) )
=> ? [D: $i] :
( ( is_fun_a_bool @ D )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ D ) @ B ) )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ D ) )
& ( C
= ( image_a_fun_a_bool @ A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(80,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_pname_bool @ ( hAPP_f759274231e_bool @ ( cOMBC_1058051404l_bool @ A ) @ B ) @ C )
= ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob) ).
thf(1149,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_pname_bool @ ( hAPP_f759274231e_bool @ ( cOMBC_1058051404l_bool @ A ) @ B ) @ C )
= ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(1,conjecture,
hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ ( hAPP_pname_a @ mgt_call @ pn ) @ g ) ) @ ( image_pname_a @ mgt_call @ u ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_6) ).
thf(2,negated_conjecture,
~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ ( hAPP_pname_a @ mgt_call @ pn ) @ g ) ) @ ( image_pname_a @ mgt_call @ u ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(915,plain,
~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ ( hAPP_pname_a @ mgt_call @ pn ) @ g ) ) @ ( image_pname_a @ mgt_call @ u ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(142,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ D ) )
=> ( ( A
= ( hAPP_nat_pname @ B @ C ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( image_nat_pname @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_310_rev__image__eqI) ).
thf(1344,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ D ) )
=> ( ( A
= ( hAPP_nat_pname @ B @ C ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( image_nat_pname @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(417,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( ( B
!= ( hAPP_nat_nat @ suc @ A ) )
=> ~ ! [C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) )
=> ( B
!= ( hAPP_nat_nat @ suc @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_677_lessE) ).
thf(2252,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( ( B
!= ( hAPP_nat_nat @ suc @ A ) )
=> ~ ! [C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) )
=> ( B
!= ( hAPP_nat_nat @ suc @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(618,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_502_xt1_I6_J) ).
thf(2974,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ C )
= ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_576_nat__add__assoc) ).
thf(932,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ C )
= ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(286,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( image_pname_nat @ A @ B ) ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_card__image__le) ).
thf(1820,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( image_pname_nat @ A @ B ) ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(71,axiom,
! [A: $i] :
( ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_688_diff__self__eq__0) ).
thf(1112,plain,
! [A: $i] :
( ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ A )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(570,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
=> ( ( C = A )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_527_ord__le__eq__trans) ).
thf(2812,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
=> ( ( C = A )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(62,axiom,
( one_one_nat
= ( hAPP_nat_nat @ suc @ zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_686_One__nat__def) ).
thf(1080,plain,
( one_one_nat
= ( hAPP_nat_nat @ suc @ zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(140,axiom,
! [A: $i,B: $i] :
( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_579_diff__add__inverse2) ).
thf(1339,plain,
! [A: $i,B: $i] :
( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(633,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ A @ B ) ) )
<=> ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_finite__insert) ).
thf(3027,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ A @ B ) ) )
=> ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) ) )
& ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
=> ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(230,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
<=> ? [C: $i] :
( B
= ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_657_less__iff__Suc__add) ).
thf(1630,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ? [C: $i] :
( B
= ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) ) )
& ( ? [C: $i] :
( B
= ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(341,axiom,
! [A: $i] :
( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ one_one_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_569_diff__Suc__1) ).
thf(1993,plain,
! [A: $i] :
( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(466,axiom,
! [A: $i,B: $i,C: $i] :
( ( is_a @ A )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ ( image_nat_a @ B @ C ) ) )
=> ~ ! [D: $i] :
( ( A
= ( hAPP_nat_a @ B @ D ) )
=> ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ D ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_353_imageE) ).
thf(2410,plain,
! [A: $i,B: $i,C: $i] :
( ( is_a @ A )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ ( image_nat_a @ B @ C ) ) )
=> ~ ! [D: $i] :
( ( A
= ( hAPP_nat_a @ B @ D ) )
=> ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ D ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(603,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_nat_pname @ A @ B ) ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ ( hAPP_f800510211t_bool @ ( cOMBC_226598744l_bool @ member_nat ) @ B ) ) @ ( hAPP_p1499970991t_bool @ ( cOMBC_nat_pname_bool @ ( cOMBB_1212655066ol_nat @ fequal_pname @ A ) ) @ ( hAPP_nat_pname @ A @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_pigeonhole__infinite) ).
thf(2923,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_nat_pname @ A @ B ) ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ ( hAPP_f800510211t_bool @ ( cOMBC_226598744l_bool @ member_nat ) @ B ) ) @ ( hAPP_p1499970991t_bool @ ( cOMBC_nat_pname_bool @ ( cOMBB_1212655066ol_nat @ fequal_pname @ A ) ) @ ( hAPP_nat_pname @ A @ C ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(209,axiom,
! [A: $i,B: $i,C: $i] :
( ( insert_nat @ A @ ( insert_nat @ B @ C ) )
= ( insert_nat @ B @ ( insert_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_insert__commute) ).
thf(1556,plain,
! [A: $i,B: $i,C: $i] :
( ( insert_nat @ A @ ( insert_nat @ B @ C ) )
= ( insert_nat @ B @ ( insert_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(183,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ C ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ ( image_1551609309ol_nat @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_finite__surj) ).
thf(1460,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ C ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ ( image_1551609309ol_nat @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(430,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_278_in__mono) ).
thf(2289,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(426,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ A ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_card__mono) ).
thf(2278,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ A ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(505,axiom,
( ( hAPP_fun_a_bool_nat @ finite_card_a @ g )
= ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_pname_a @ mgt_call @ u ) ) ) @ ( hAPP_nat_nat @ suc @ na ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_3) ).
thf(2553,plain,
( ( hAPP_fun_a_bool_nat @ finite_card_a @ g )
= ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_pname_a @ mgt_call @ u ) ) ) @ ( hAPP_nat_nat @ suc @ na ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(201,axiom,
! [A: $i,B: $i] :
( ( is_fun_pname_bool @ B )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
=> ( ( insert_pname @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_insert__absorb) ).
thf(1528,plain,
! [A: $i,B: $i] :
( ( is_fun_pname_bool @ B )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
=> ( ( insert_pname @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(232,axiom,
! [A: $i,B: $i] :
( ( is_fun_pname_bool @ B )
=> ( is_fun_pname_bool @ ( hAPP_f759274231e_bool @ A @ B ) ) ),
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(1643,plain,
! [A: $i,B: $i] :
( ( is_fun_pname_bool @ B )
=> ( is_fun_pname_bool @ ( hAPP_f759274231e_bool @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(858,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( image_a_pname @ A @ B ) ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_card__image__le) ).
thf(3917,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( image_a_pname @ A @ B ) ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).
thf(388,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_p61793385e_bool @ ( cOMBB_542850580_pname @ A @ B ) @ C )
= ( hAPP_p61793385e_bool @ A @ ( hAPP_pname_pname @ B @ C ) ) ),
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(2139,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_p61793385e_bool @ ( cOMBB_542850580_pname @ A @ B ) @ C )
= ( hAPP_p61793385e_bool @ A @ ( hAPP_pname_pname @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(374,axiom,
! [A: $i,B: $i] :
( ( is_fun949378684l_bool @ B )
=> ( is_fun_pname_bool @ ( image_1854862208_pname @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opname) ).
thf(2101,plain,
! [A: $i,B: $i] :
( ( is_fun949378684l_bool @ B )
=> ( is_fun_pname_bool @ ( image_1854862208_pname @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(254,axiom,
! [A: $i,B: $i] :
( ( ( is_fun949378684l_bool @ A )
& ( is_fun949378684l_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ B ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ A ) ) )
=> ( A = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_card__seteq) ).
thf(1726,plain,
! [A: $i,B: $i] :
( ( ( is_fun949378684l_bool @ A )
& ( is_fun949378684l_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ B ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ A ) ) )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(193,axiom,
! [A: $i] :
( ( is_bool @ A )
=> ( ( A = fTrue )
| ( A = fFalse ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
thf(1496,plain,
! [A: $i] :
( ( is_bool @ A )
=> ( ( A = fTrue )
| ( A = fFalse ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(668,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1283814551_pname @ A @ B ) ) )
=> ? [C: $i] :
( ( is_fun_pname_bool @ C )
& ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fconj @ ( hAPP_f559147733l_bool @ ( cOMBC_1988546018l_bool @ member799430823e_bool ) @ B ) ) @ ( hAPP_p338031245l_bool @ ( cOMBC_1004116266e_bool @ ( cOMBB_598082538e_bool @ fequal_pname @ A ) ) @ ( hAPP_f1297739591_pname @ A @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_pigeonhole__infinite) ).
thf(3178,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1283814551_pname @ A @ B ) ) )
=> ? [C: $i] :
( ( is_fun_pname_bool @ C )
& ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fconj @ ( hAPP_f559147733l_bool @ ( cOMBC_1988546018l_bool @ member799430823e_bool ) @ B ) ) @ ( hAPP_p338031245l_bool @ ( cOMBC_1004116266e_bool @ ( cOMBB_598082538e_bool @ fequal_pname @ A ) ) @ ( hAPP_f1297739591_pname @ A @ C ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(626,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ B ) )
=> ( ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fconj @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ B ) ) @ A ) )
= ( insert1325755072e_bool @ B @ bot_bo1649642514l_bool ) ) )
& ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ B ) )
=> ( ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fconj @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ B ) ) @ A ) )
= bot_bo1649642514l_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_480_Collect__conv__if2) ).
thf(2999,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ B ) )
=> ( ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fconj @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ B ) ) @ A ) )
= ( insert1325755072e_bool @ B @ bot_bo1649642514l_bool ) ) )
& ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ B ) )
=> ( ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fconj @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ B ) ) @ A ) )
= bot_bo1649642514l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(365,axiom,
! [A: $i,B: $i] :
( ( is_fun_pname_bool @ B )
=> ( is_fun1661590463l_bool @ ( hAPP_f434788991l_bool @ A @ B ) ) ),
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(2069,plain,
! [A: $i,B: $i] :
( ( is_fun_pname_bool @ B )
=> ( is_fun1661590463l_bool @ ( hAPP_f434788991l_bool @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(221,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_pname_bool @ ( cOMBS_568398431l_bool @ A @ B ) @ C )
= ( hAPP_bool_bool @ ( hAPP_p393069232l_bool @ A @ C ) @ ( hAPP_pname_bool @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool_U) ).
thf(1594,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_pname_bool @ ( cOMBS_568398431l_bool @ A @ B ) @ C )
= ( hAPP_bool_bool @ ( hAPP_p393069232l_bool @ A @ C ) @ ( hAPP_pname_bool @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(245,axiom,
! [A: $i] :
( zero_zero_nat
!= ( hAPP_nat_nat @ suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_695_nat_Osimps_I2_J) ).
thf(1699,plain,
! [A: $i] :
( zero_zero_nat
!= ( hAPP_nat_nat @ suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(102,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f1794073134e_bool @ ( cOMBB_1693087065a_bool @ A @ B ) @ C )
= ( hAPP_p61793385e_bool @ A @ ( hAPP_f1128469712_pname @ B @ C ) ) ),
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(1213,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f1794073134e_bool @ ( cOMBB_1693087065a_bool @ A @ B ) @ C )
= ( hAPP_p61793385e_bool @ A @ ( hAPP_f1128469712_pname @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(837,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ bot_bot_fun_a_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_406_empty__iff) ).
thf(3838,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ bot_bot_fun_a_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).
thf(558,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ C ) )
=> ( ( insert_a @ ( hAPP_nat_a @ A @ B ) @ ( image_nat_a @ A @ C ) )
= ( image_nat_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_342_insert__image) ).
thf(2765,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ C ) )
=> ( ( insert_a @ ( hAPP_nat_a @ A @ B ) @ ( image_nat_a @ A @ C ) )
= ( image_nat_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(48,axiom,
! [A: $i,B: $i] : ( is_fun_pname_bool @ ( image_nat_pname @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__Com__Opname) ).
thf(1044,plain,
! [A: $i,B: $i] : ( is_fun_pname_bool @ ( image_nat_pname @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(504,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_nat_nat @ A @ B ) ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ ( hAPP_f800510211t_bool @ ( cOMBC_226598744l_bool @ member_nat ) @ B ) ) @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ ( cOMBB_800536526ol_nat @ fequal_nat @ A ) ) @ ( hAPP_nat_nat @ A @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_pigeonhole__infinite) ).
thf(2550,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_nat_nat @ A @ B ) ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ ( hAPP_f800510211t_bool @ ( cOMBC_226598744l_bool @ member_nat ) @ B ) ) @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ ( cOMBB_800536526ol_nat @ fequal_nat @ A ) ) @ ( hAPP_nat_nat @ A @ C ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(903,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
=> ( ( insert_nat @ ( hAPP_pname_nat @ A @ B ) @ ( image_pname_nat @ A @ C ) )
= ( image_pname_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_339_insert__image) ).
thf(4085,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
=> ( ( insert_nat @ ( hAPP_pname_nat @ A @ B ) @ ( image_pname_nat @ A @ C ) )
= ( image_pname_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).
thf(665,axiom,
! [A: $i] :
( ( bot_bo844097828e_bool
= ( collect_pname @ A ) )
<=> ! [B: $i] :
( ( is_pname @ B )
=> ~ ( hBOOL @ ( hAPP_pname_bool @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_407_empty__Collect__eq) ).
thf(3159,plain,
! [A: $i] :
( ( ( bot_bo844097828e_bool
= ( collect_pname @ A ) )
=> ! [B: $i] :
( ( is_pname @ B )
=> ~ ( hBOOL @ ( hAPP_pname_bool @ A @ B ) ) ) )
& ( ! [B: $i] :
( ( is_pname @ B )
=> ~ ( hBOOL @ ( hAPP_pname_bool @ A @ B ) ) )
=> ( bot_bo844097828e_bool
= ( collect_pname @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(452,axiom,
! [A: $i] :
( ( is_fun1661590463l_bool @ A )
=> ( is_fun1661590463l_bool @ ( collec1974731493e_bool @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_OCollect_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).
thf(2369,plain,
! [A: $i] :
( ( is_fun1661590463l_bool @ A )
=> ( is_fun1661590463l_bool @ ( collec1974731493e_bool @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ( cOMBC_7971162l_bool @ A ) @ B ) @ C )
= ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ A @ C ) @ B ) ),
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(1015,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ( cOMBC_7971162l_bool @ A ) @ B ) @ C )
= ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(866,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_pname_nat @ A @ B ) ) )
=> ? [C: $i] :
( ( is_pname @ C )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ ( hAPP_f759274231e_bool @ ( cOMBC_1058051404l_bool @ member_pname ) @ B ) ) @ ( hAPP_n1025906991e_bool @ ( cOMBC_pname_nat_bool @ ( cOMBB_523834888_pname @ fequal_nat @ A ) ) @ ( hAPP_pname_nat @ A @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_pigeonhole__infinite) ).
thf(3953,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_pname_nat @ A @ B ) ) )
=> ? [C: $i] :
( ( is_pname @ C )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ ( hAPP_f759274231e_bool @ ( cOMBC_1058051404l_bool @ member_pname ) @ B ) ) @ ( hAPP_n1025906991e_bool @ ( cOMBC_pname_nat_bool @ ( cOMBB_523834888_pname @ fequal_nat @ A ) ) @ ( hAPP_pname_nat @ A @ C ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).
thf(630,axiom,
! [A: $i,B: $i] :
( ( is_fun_pname_bool @ B )
=> ( is_fun_a_bool @ ( image_pname_a @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__Com__Opname_000t__a) ).
thf(3016,plain,
! [A: $i,B: $i] :
( ( is_fun_pname_bool @ B )
=> ( is_fun_a_bool @ ( image_pname_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(243,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f54304608l_bool @ ( hAPP_f1246832597l_bool @ ( cOMBC_1245412066l_bool @ A ) @ B ) @ C )
= ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ A @ C ) @ B ) ),
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(1694,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f54304608l_bool @ ( hAPP_f1246832597l_bool @ ( cOMBC_1245412066l_bool @ A ) @ B ) @ C )
= ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(5,axiom,
! [A: $i] :
( ( hAPP_nat_nat @ suc @ A )
= ( hAPP_nat_nat @ ( plus_plus_nat @ one_one_nat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_607_Suc__eq__plus1__left) ).
thf(922,plain,
! [A: $i] :
( ( hAPP_nat_nat @ suc @ A )
= ( hAPP_nat_nat @ ( plus_plus_nat @ one_one_nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(864,axiom,
! [A: $i,B: $i] :
( ( ( is_fun_a_bool @ A )
& ( is_fun_a_bool @ B ) )
=> ( ( A = B )
<=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_271_set__eq__subset) ).
thf(3936,plain,
! [A: $i,B: $i] :
( ( ( is_fun_a_bool @ A )
& ( is_fun_a_bool @ B ) )
=> ( ( ( A = B )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ A ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).
thf(768,axiom,
! [A: $i] :
( ( ( collect_a @ A )
= bot_bot_fun_a_bool )
<=> ! [B: $i] :
( ( is_a @ B )
=> ~ ( hBOOL @ ( hAPP_a_bool @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_402_Collect__empty__eq) ).
thf(3576,plain,
! [A: $i] :
( ( ( ( collect_a @ A )
= bot_bot_fun_a_bool )
=> ! [B: $i] :
( ( is_a @ B )
=> ~ ( hBOOL @ ( hAPP_a_bool @ A @ B ) ) ) )
& ( ! [B: $i] :
( ( is_a @ B )
=> ~ ( hBOOL @ ( hAPP_a_bool @ A @ B ) ) )
=> ( ( collect_a @ A )
= bot_bot_fun_a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).
thf(489,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
=> ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( image_2129980159t_bool @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_finite__imageI) ).
thf(2503,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
=> ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( image_2129980159t_bool @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(381,axiom,
! [A: $i,B: $i] :
( ( is_a @ B )
=> ( is_fun949378684l_bool @ ( hAPP_a85458249l_bool @ A @ B ) ) ),
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(2124,plain,
! [A: $i,B: $i] :
( ( is_a @ B )
=> ( is_fun949378684l_bool @ ( hAPP_a85458249l_bool @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(523,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_rev__finite__subset) ).
thf(2629,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(340,axiom,
! [A: $i,B: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B )
= ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_572_add__Suc) ).
thf(1990,plain,
! [A: $i,B: $i] :
( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B )
= ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_subsetD) ).
thf(968,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(600,axiom,
! [A: $i,B: $i] :
( ( insert_a @ A @ B )
!= bot_bot_fun_a_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_460_insert__not__empty) ).
thf(2914,plain,
! [A: $i,B: $i] :
( ( insert_a @ A @ B )
!= bot_bot_fun_a_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(571,axiom,
! [A: $i] : ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ bot_bot_bool ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_442_bot__least) ).
thf(2816,plain,
! [A: $i] : ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ bot_bot_bool ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(75,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ B ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ A ) ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_card__seteq) ).
thf(1134,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ B ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ A ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(661,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_pname_bool @ ( hAPP_f1794073134e_bool @ ( cOMBC_445755039l_bool @ A ) @ B ) @ C )
= ( hAPP_fun_a_bool_bool @ ( hAPP_p1824510254l_bool @ A @ C ) @ B ) ),
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(3146,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_pname_bool @ ( hAPP_f1794073134e_bool @ ( cOMBC_445755039l_bool @ A ) @ B ) @ C )
= ( hAPP_fun_a_bool_bool @ ( hAPP_p1824510254l_bool @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(912,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ A ) @ B ) ) ) )
<=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ A ) ) )
& ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_finite__Collect__disjI) ).
thf(4113,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ A ) @ B ) ) ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ A ) ) )
& ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ B ) ) ) ) )
& ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ A ) ) )
& ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ B ) ) ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).
thf(580,axiom,
! [A: $i,B: $i] :
( ( ( is_a @ A )
& ( is_a @ B ) )
=> ( ~ ( hBOOL @ ( hAPP_a_bool @ ( hAPP_a_fun_a_bool @ fequal_a @ A ) @ B ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000t__a_T) ).
thf(2846,plain,
! [A: $i,B: $i] :
( ( ( is_a @ A )
& ( is_a @ B ) )
=> ( ~ ( hBOOL @ ( hAPP_a_bool @ ( hAPP_a_fun_a_bool @ fequal_a @ A ) @ B ) )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( hAPP_n1699378549t_bool @ C @ D ) ) @ ( hAPP_n1699378549t_bool @ C @ ( hAPP_nat_nat @ suc @ D ) ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( hAPP_n1699378549t_bool @ C @ A ) ) @ ( hAPP_n1699378549t_bool @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_lift__Suc__mono__le) ).
thf(1018,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( hAPP_n1699378549t_bool @ C @ D ) ) @ ( hAPP_n1699378549t_bool @ C @ ( hAPP_nat_nat @ suc @ D ) ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( hAPP_n1699378549t_bool @ C @ A ) ) @ ( hAPP_n1699378549t_bool @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(512,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ C ) )
=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ bot_bo1649642514l_bool ) )
=> ( ! [D: $i,E: $i] :
( ( ( is_fun_pname_bool @ D )
& ( is_fun1661590463l_bool @ E ) )
=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ E ) )
=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ D ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ E ) )
=> ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ ( insert1325755072e_bool @ D @ E ) ) ) ) ) ) ) )
=> ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_560_finite__subset__induct) ).
thf(2582,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ C ) )
=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ bot_bo1649642514l_bool ) )
=> ( ! [D: $i,E: $i] :
( ( ( is_fun_pname_bool @ D )
& ( is_fun1661590463l_bool @ E ) )
=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ E ) )
=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ D ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ E ) )
=> ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ ( insert1325755072e_bool @ D @ E ) ) ) ) ) ) ) )
=> ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(767,axiom,
! [A: $i,B: $i,C: $i] :
( ( is_fun_a_bool @ C )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ C ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C ) @ ( image_nat_a @ A @ B ) ) )
=> ? [D: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ D ) @ B ) )
& ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ D ) )
& ( C
= ( image_nat_a @ A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_finite__subset__image) ).
thf(3571,plain,
! [A: $i,B: $i,C: $i] :
( ( is_fun_a_bool @ C )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ C ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C ) @ ( image_nat_a @ A @ B ) ) )
=> ? [D: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ D ) @ B ) )
& ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ D ) )
& ( C
= ( image_nat_a @ A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).
thf(608,axiom,
! [A: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_subset__refl) ).
thf(2942,plain,
! [A: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(293,axiom,
! [A: $i,B: $i] :
( ( is_fun_a_bool @ B )
=> ( is_fun_pname_bool @ ( image_a_pname @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000t__a_000tc__Com__Opname) ).
thf(1845,plain,
! [A: $i,B: $i] :
( ( is_fun_a_bool @ B )
=> ( is_fun_pname_bool @ ( image_a_pname @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(889,axiom,
! [A: $i,B: $i] :
( ( A = B )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_275_equalityD2) ).
thf(4035,plain,
! [A: $i,B: $i] :
( ( A = B )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).
thf(751,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( image_496248727ol_nat @ A @ B ) ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_card__image__le) ).
thf(3507,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( image_496248727ol_nat @ A @ B ) ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(856,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
=> ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_finite_OinsertI) ).
thf(3913,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
=> ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).
thf(348,axiom,
! [A: $i,B: $i] :
( ( insert_pname @ A @ ( collect_pname @ B ) )
= ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fimplies @ ( cOMBB_647938656_pname @ fNot @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ fequal_pname ) @ A ) ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_insert__Collect) ).
thf(2012,plain,
! [A: $i,B: $i] :
( ( insert_pname @ A @ ( collect_pname @ B ) )
= ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fimplies @ ( cOMBB_647938656_pname @ fNot @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ fequal_pname ) @ A ) ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(836,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ A ) )
<=> ( hBOOL @ bot_bot_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_427_bot__fun__def) ).
thf(3833,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ A ) )
=> ( hBOOL @ bot_bot_bool ) )
& ( ( hBOOL @ bot_bot_bool )
=> ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).
thf(271,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_584_le__add2) ).
thf(1780,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(202,axiom,
! [A: $i,B: $i,C: $i] :
( ( is_fun_pname_bool @ C )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ ( image_nat_pname @ A @ B ) ) )
=> ? [D: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ D ) @ B ) )
& ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ D ) )
& ( C
= ( image_nat_pname @ A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_finite__subset__image) ).
thf(1531,plain,
! [A: $i,B: $i,C: $i] :
( ( is_fun_pname_bool @ C )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ ( image_nat_pname @ A @ B ) ) )
=> ? [D: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ D ) @ B ) )
& ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ D ) )
& ( C
= ( image_nat_pname @ A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(107,axiom,
! [A: $i] :
( ( collect_pname @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ fequal_pname ) @ A ) )
= ( insert_pname @ A @ bot_bo844097828e_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_483_singleton__conv) ).
thf(1230,plain,
! [A: $i] :
( ( collect_pname @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ fequal_pname ) @ A ) )
= ( insert_pname @ A @ bot_bo844097828e_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(206,axiom,
! [A: $i,B: $i] :
( ( ( is_pname @ A )
& ( is_pname @ B ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( insert_pname @ B @ bot_bo844097828e_bool ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_450_singletonE) ).
thf(1547,plain,
! [A: $i,B: $i] :
( ( ( is_pname @ A )
& ( is_pname @ B ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( insert_pname @ B @ bot_bo844097828e_bool ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(261,axiom,
! [A: $i] :
( ( is_bool @ A )
=> ( is_fun1661590463l_bool @ ( cOMBK_1857069011e_bool @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).
thf(1748,plain,
! [A: $i] :
( ( is_bool @ A )
=> ( is_fun1661590463l_bool @ ( cOMBK_1857069011e_bool @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_pname_bool @ B @ A ) ) @ ( hAPP_pname_bool @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_377_le__funD) ).
thf(1003,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_pname_bool @ B @ A ) ) @ ( hAPP_pname_bool @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(269,axiom,
! [A: $i,B: $i] :
( ( ( is_pname @ A )
& ( is_pname @ B ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( insert_pname @ B @ bot_bo844097828e_bool ) ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_456_singleton__iff) ).
thf(1770,plain,
! [A: $i,B: $i] :
( ( ( is_pname @ A )
& ( is_pname @ B ) )
=> ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( insert_pname @ B @ bot_bo844097828e_bool ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( insert_pname @ B @ bot_bo844097828e_bool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(586,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_499_linorder__le__cases) ).
thf(2863,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(696,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_nat_a @ A @ B ) ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ ( hAPP_f800510211t_bool @ ( cOMBC_226598744l_bool @ member_nat ) @ B ) ) @ ( hAPP_a_fun_nat_bool @ ( cOMBC_nat_a_bool @ ( cOMBB_1885489796ol_nat @ fequal_a @ A ) ) @ ( hAPP_nat_a @ A @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_pigeonhole__infinite) ).
thf(3315,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_nat_a @ A @ B ) ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ ( hAPP_f800510211t_bool @ ( cOMBC_226598744l_bool @ member_nat ) @ B ) ) @ ( hAPP_a_fun_nat_bool @ ( cOMBC_nat_a_bool @ ( cOMBB_1885489796ol_nat @ fequal_a @ A ) ) @ ( hAPP_nat_a @ A @ C ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(58,axiom,
! [A: $i] :
( ( is_fun949378684l_bool @ A )
=> ( ( collect_fun_a_bool @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_Collect__def) ).
thf(1070,plain,
! [A: $i] :
( ( is_fun949378684l_bool @ A )
=> ( ( collect_fun_a_bool @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(657,axiom,
! [A: $i,B: $i] :
( ( A != B )
<=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_646_nat__neq__iff) ).
thf(3112,plain,
! [A: $i,B: $i] :
( ( ( A != B )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(455,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ B ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( insert1325755072e_bool @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_card__insert__le) ).
thf(2375,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ B ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( insert1325755072e_bool @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(83,axiom,
! [A: $i] :
( ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ zero_zero_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_689_minus__nat_Odiff__0) ).
thf(1156,plain,
! [A: $i] :
( ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ zero_zero_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(362,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f1664156314l_bool @ ( cOMBS_350070575l_bool @ A @ B ) @ C )
= ( hAPP_bool_bool @ ( hAPP_f1476298914l_bool @ A @ C ) @ ( hAPP_f1664156314l_bool @ B @ C ) ) ),
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(2060,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f1664156314l_bool @ ( cOMBS_350070575l_bool @ A @ B ) @ C )
= ( hAPP_bool_bool @ ( hAPP_f1476298914l_bool @ A @ C ) @ ( hAPP_f1664156314l_bool @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(259,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ? [C: $i] :
( B
= ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_673_less__imp__Suc__add) ).
thf(1743,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ? [C: $i] :
( B
= ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(549,axiom,
! [A: $i,B: $i,C: $i] :
( ( is_fun_a_bool @ C )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ C ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C ) @ ( image_a_a @ A @ B ) ) )
=> ? [D: $i] :
( ( is_fun_a_bool @ D )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ D ) @ B ) )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ D ) )
& ( C
= ( image_a_a @ A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_finite__subset__image) ).
thf(2732,plain,
! [A: $i,B: $i,C: $i] :
( ( is_fun_a_bool @ C )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ C ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C ) @ ( image_a_a @ A @ B ) ) )
=> ? [D: $i] :
( ( is_fun_a_bool @ D )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ D ) @ B ) )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ D ) )
& ( C
= ( image_a_a @ A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(321,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) @ B )
= ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_597_diff__add__assoc) ).
thf(1941,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) @ B )
= ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(150,axiom,
! [A: $i] :
( ( hAPP_nat_nat @ suc @ A )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_Suc__n__not__n) ).
thf(1368,plain,
! [A: $i] :
( ( hAPP_nat_nat @ suc @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(678,axiom,
! [A: $i,B: $i,C: $i] :
( ( is_fun1661590463l_bool @ C )
=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ C ) )
=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ C ) @ ( image_819518260e_bool @ A @ B ) ) )
=> ? [D: $i] :
( ( is_fun_a_bool @ D )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ D ) @ B ) )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ D ) )
& ( C
= ( image_819518260e_bool @ A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_finite__subset__image) ).
thf(3228,plain,
! [A: $i,B: $i,C: $i] :
( ( is_fun1661590463l_bool @ C )
=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ C ) )
=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ C ) @ ( image_819518260e_bool @ A @ B ) ) )
=> ? [D: $i] :
( ( is_fun_a_bool @ D )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ D ) @ B ) )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ D ) )
& ( C
= ( image_819518260e_bool @ A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(263,axiom,
! [A: $i,B: $i] :
( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ ( hAPP_nat_nat @ suc @ B ) )
= ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_diff__Suc__Suc) ).
thf(1753,plain,
! [A: $i,B: $i] :
( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ ( hAPP_nat_nat @ suc @ B ) )
= ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(821,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_512_order__trans) ).
thf(3786,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).
thf(460,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ A @ B ) ) @ C ) )
<=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_323_insert__subset) ).
thf(2386,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ A @ B ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) ) ) )
& ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ A @ B ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(734,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_649_less__not__refl2) ).
thf(3448,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).
thf(850,axiom,
! [A: $i] :
( ( bot_bo1649642514l_bool
= ( collec1974731493e_bool @ A ) )
<=> ! [B: $i] :
( ( is_fun_pname_bool @ B )
=> ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_409_empty__Collect__eq) ).
thf(3885,plain,
! [A: $i] :
( ( ( bot_bo1649642514l_bool
= ( collec1974731493e_bool @ A ) )
=> ! [B: $i] :
( ( is_fun_pname_bool @ B )
=> ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ B ) ) ) )
& ( ! [B: $i] :
( ( is_fun_pname_bool @ B )
=> ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ B ) ) )
=> ( bot_bo1649642514l_bool
= ( collec1974731493e_bool @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).
thf(645,axiom,
! [A: $i] :
( ( bot_bot_fun_nat_bool
= ( collect_nat @ A ) )
<=> ! [B: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_412_empty__Collect__eq) ).
thf(3063,plain,
! [A: $i] :
( ( ( bot_bot_fun_nat_bool
= ( collect_nat @ A ) )
=> ! [B: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ A @ B ) ) )
& ( ! [B: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ A @ B ) )
=> ( bot_bot_fun_nat_bool
= ( collect_nat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(446,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ suc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_636_not__less__eq) ).
thf(2337,plain,
! [A: $i,B: $i] :
( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ suc @ A ) ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ suc @ A ) ) )
=> ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(309,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f800510211t_bool @ ( cOMBB_1250273980t_bool @ A @ B ) @ C )
= ( hAPP_n1699378549t_bool @ A @ ( hAPP_f22106695ol_nat @ B @ C ) ) ),
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(1901,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f800510211t_bool @ ( cOMBB_1250273980t_bool @ A @ B ) @ C )
= ( hAPP_n1699378549t_bool @ A @ ( hAPP_f22106695ol_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(64,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_666_add__diff__inverse) ).
thf(1085,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(765,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ A ) @ ( image_47868345e_bool @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_finite__surj) ).
thf(3564,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ A ) @ ( image_47868345e_bool @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).
thf(801,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ A ) @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T) ).
thf(3715,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ A ) @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).
thf(249,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ B @ C ) )
=> ( ! [D: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ B @ ( hAPP_nat_nat @ suc @ D ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ B @ D ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ B @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_zero__induct__lemma) ).
thf(1711,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ B @ C ) )
=> ( ! [D: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ B @ ( hAPP_nat_nat @ suc @ D ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ B @ D ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ B @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(649,axiom,
! [A: $i,B: $i,C: $i] :
( ( is_fun_a_bool @ C )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ C ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C ) @ ( image_876012084bool_a @ A @ B ) ) )
=> ? [D: $i] :
( ( is_fun1661590463l_bool @ D )
& ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ D ) @ B ) )
& ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ D ) )
& ( C
= ( image_876012084bool_a @ A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_finite__subset__image) ).
thf(3080,plain,
! [A: $i,B: $i,C: $i] :
( ( is_fun_a_bool @ C )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ C ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C ) @ ( image_876012084bool_a @ A @ B ) ) )
=> ? [D: $i] :
( ( is_fun1661590463l_bool @ D )
& ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ D ) @ B ) )
& ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ D ) )
& ( C
= ( image_876012084bool_a @ A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(52,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) )
=> ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( hAPP_f103356543l_bool @ ( cOMBC_1693257480l_bool @ ord_le1568362934t_bool ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_finite__Collect__subsets) ).
thf(1053,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) )
=> ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( hAPP_f103356543l_bool @ ( cOMBC_1693257480l_bool @ ord_le1568362934t_bool ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(194,axiom,
! [A: $i,B: $i] :
( ( ( is_fun_pname_bool @ A )
& ( is_fun_pname_bool @ B ) )
=> ( ( A = B )
<=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_set__eq__subset) ).
thf(1499,plain,
! [A: $i,B: $i] :
( ( ( is_fun_pname_bool @ A )
& ( is_fun_pname_bool @ B ) )
=> ( ( ( A = B )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(372,axiom,
! [A: $i,B: $i] :
( ( ( hAPP_nat_nat @ suc @ A )
= ( hAPP_nat_nat @ suc @ B ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_nat_Oinject) ).
thf(2092,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP_nat_nat @ suc @ A )
= ( hAPP_nat_nat @ suc @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( hAPP_nat_nat @ suc @ A )
= ( hAPP_nat_nat @ suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(906,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ C ) )
=> ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ C ) @ ( image_a_fun_nat_bool @ A @ B ) ) )
=> ? [D: $i] :
( ( is_fun_a_bool @ D )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ D ) @ B ) )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ D ) )
& ( C
= ( image_a_fun_nat_bool @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_finite__subset__image) ).
thf(4092,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ C ) )
=> ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ C ) @ ( image_a_fun_nat_bool @ A @ B ) ) )
=> ? [D: $i] :
( ( is_fun_a_bool @ D )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ D ) @ B ) )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ D ) )
& ( C
= ( image_a_fun_nat_bool @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).
thf(129,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B )
= zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_684_diff__is__0__eq_H) ).
thf(1300,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B )
= zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(231,axiom,
! [A: $i,B: $i,C: $i] :
( ( is_fun949378684l_bool @ C )
=> ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ C ) )
=> ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ C ) @ ( image_112932426a_bool @ A @ B ) ) )
=> ? [D: $i] :
( ( is_fun_pname_bool @ D )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ D ) @ B ) )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ D ) )
& ( C
= ( image_112932426a_bool @ A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_finite__subset__image) ).
thf(1637,plain,
! [A: $i,B: $i,C: $i] :
( ( is_fun949378684l_bool @ C )
=> ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ C ) )
=> ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ C ) @ ( image_112932426a_bool @ A @ B ) ) )
=> ? [D: $i] :
( ( is_fun_pname_bool @ D )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ D ) @ B ) )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ D ) )
& ( C
= ( image_112932426a_bool @ A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(689,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_subset__trans) ).
thf(3273,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(823,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ B ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ A ) ) ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_finite__Collect__conjI) ).
thf(3791,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ B ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ A ) ) ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).
thf(93,axiom,
! [A: $i,B: $i] :
( ( insert1325755072e_bool @ A @ B )
= ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ A ) ) @ ( hAPP_f559147733l_bool @ ( cOMBC_1988546018l_bool @ member799430823e_bool ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_insert__compr__raw) ).
thf(1188,plain,
! [A: $i,B: $i] :
( ( insert1325755072e_bool @ A @ B )
= ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ A ) ) @ ( hAPP_f559147733l_bool @ ( cOMBC_1988546018l_bool @ member799430823e_bool ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(541,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_nat_bool @ ( hAPP_f282463732t_bool @ ( cOMBC_1928494297l_bool @ A ) @ B ) @ C )
= ( hAPP_fun_a_bool_bool @ ( hAPP_n1414589940l_bool @ A @ C ) @ B ) ),
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(2700,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_nat_bool @ ( hAPP_f282463732t_bool @ ( cOMBC_1928494297l_bool @ A ) @ B ) @ C )
= ( hAPP_fun_a_bool_bool @ ( hAPP_n1414589940l_bool @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(425,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_644_termination__basic__simps_I5_J) ).
thf(2276,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(826,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_a_bool @ B @ A ) ) @ ( hAPP_a_bool @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_382_le__funE) ).
thf(3801,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_a_bool @ B @ A ) ) @ ( hAPP_a_bool @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).
thf(336,axiom,
! [A: $i,B: $i] :
( ( insert_nat @ A @ B )
= ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ fequal_nat ) @ A ) ) @ ( hAPP_f800510211t_bool @ ( cOMBC_226598744l_bool @ member_nat ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_316_insert__compr__raw) ).
thf(1980,plain,
! [A: $i,B: $i] :
( ( insert_nat @ A @ B )
= ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ fequal_nat ) @ A ) ) @ ( hAPP_f800510211t_bool @ ( cOMBC_226598744l_bool @ member_nat ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(597,axiom,
! [A: $i,B: $i] :
( ( A = B )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_548_order__eq__refl) ).
thf(2903,plain,
! [A: $i,B: $i] :
( ( A = B )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(502,axiom,
! [A: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ bot_bo844097828e_bool ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_441_bot__least) ).
thf(2545,plain,
! [A: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ bot_bo844097828e_bool ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(840,axiom,
! [A: $i] :
( ( ( collect_nat @ A )
= bot_bot_fun_nat_bool )
<=> ! [B: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_403_Collect__empty__eq) ).
thf(3847,plain,
! [A: $i] :
( ( ( ( collect_nat @ A )
= bot_bot_fun_nat_bool )
=> ! [B: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ A @ B ) ) )
& ( ! [B: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ A @ B ) )
=> ( ( collect_nat @ A )
= bot_bot_fun_nat_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).
thf(702,axiom,
! [A: $i,B: $i] :
( ( A != B )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__fun_It__a_Mtc__HOL__Obool_J_T) ).
thf(3329,plain,
! [A: $i,B: $i] :
( ( A != B )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(356,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_nat_bool @ ( hAPP_p1499970991t_bool @ ( cOMBC_nat_pname_bool @ A ) @ B ) @ C )
= ( hAPP_pname_bool @ ( hAPP_n1025906991e_bool @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Com__Opname_000tc__HOL__Obool_U) ).
thf(2044,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_nat_bool @ ( hAPP_p1499970991t_bool @ ( cOMBC_nat_pname_bool @ A ) @ B ) @ C )
= ( hAPP_pname_bool @ ( hAPP_n1025906991e_bool @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(125,axiom,
! [A: $i] :
( A
!= ( hAPP_nat_nat @ suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_n__not__Suc__n) ).
thf(1285,plain,
! [A: $i] :
( A
!= ( hAPP_nat_nat @ suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(104,axiom,
! [A: $i] :
( ( collect_nat @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ fequal_nat ) @ A ) )
= ( insert_nat @ A @ bot_bot_fun_nat_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_482_singleton__conv) ).
thf(1218,plain,
! [A: $i] :
( ( collect_nat @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ fequal_nat ) @ A ) )
= ( insert_nat @ A @ bot_bot_fun_nat_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(139,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f1664156314l_bool @ ( hAPP_n850744903l_bool @ ( cOMBC_1666426608t_bool @ A ) @ B ) @ C )
= ( hAPP_nat_bool @ ( hAPP_f1066163005t_bool @ A @ C ) @ B ) ),
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(1336,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f1664156314l_bool @ ( hAPP_n850744903l_bool @ ( cOMBC_1666426608t_bool @ A ) @ B ) @ C )
= ( hAPP_nat_bool @ ( hAPP_f1066163005t_bool @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(815,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
=> ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( image_26036933t_bool @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_finite__imageI) ).
thf(3769,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
=> ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( image_26036933t_bool @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).
thf(360,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ C ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( image_1283814551_pname @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_finite__surj) ).
thf(2056,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ C ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( image_1283814551_pname @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(796,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ A ) @ B ) ) ) )
<=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ A ) ) )
& ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_finite__Collect__disjI) ).
thf(3697,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ A ) @ B ) ) ) )
=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ A ) ) )
& ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ B ) ) ) ) )
& ( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ A ) ) )
& ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ B ) ) ) )
=> ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i] :
( ( is_pname @ A )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( image_nat_pname @ B @ C ) ) )
=> ~ ! [D: $i] :
( ( A
= ( hAPP_nat_pname @ B @ D ) )
=> ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ D ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_352_imageE) ).
thf(1023,plain,
! [A: $i,B: $i,C: $i] :
( ( is_pname @ A )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( image_nat_pname @ B @ C ) ) )
=> ~ ! [D: $i] :
( ( A
= ( hAPP_nat_pname @ B @ D ) )
=> ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ D ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(457,axiom,
! [A: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ ord_less_eq_nat ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_finite__Collect__le__nat) ).
thf(2379,plain,
! [A: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ ord_less_eq_nat ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(501,axiom,
! [A: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ bot_bot_fun_nat_bool ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_393_empty__subsetI) ).
thf(2543,plain,
! [A: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ bot_bot_fun_nat_bool ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(105,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ suc @ A ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_663_le__less__Suc__eq) ).
thf(1221,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ suc @ A ) ) )
=> ( B = A ) )
& ( ( B = A )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ suc @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(891,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ A ) )
<=> ( hBOOL @ bot_bot_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_430_bot__apply) ).
thf(4046,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ A ) )
=> ( hBOOL @ bot_bot_bool ) )
& ( ( hBOOL @ bot_bot_bool )
=> ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).
thf(24,axiom,
! [A: $i] :
( ( is_fun_pname_bool @ A )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ bot_bo844097828e_bool ) )
<=> ( A = bot_bo844097828e_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_465_subset__empty) ).
thf(978,plain,
! [A: $i] :
( ( is_fun_pname_bool @ A )
=> ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ bot_bo844097828e_bool ) )
=> ( A = bot_bo844097828e_bool ) )
& ( ( A = bot_bo844097828e_bool )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ bot_bo844097828e_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(251,axiom,
! [A: $i,B: $i] :
( ( insert_pname @ A @ B )
= ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ fequal_pname ) @ A ) ) @ ( hAPP_f759274231e_bool @ ( cOMBC_1058051404l_bool @ member_pname ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_insert__compr) ).
thf(1717,plain,
! [A: $i,B: $i] :
( ( insert_pname @ A @ B )
= ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ fequal_pname ) @ A ) ) @ ( hAPP_f759274231e_bool @ ( cOMBC_1058051404l_bool @ member_pname ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(151,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ C ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( image_nat_pname @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_finite__surj) ).
thf(1372,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ C ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( image_nat_pname @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(301,axiom,
! [A: $i,B: $i] : ( is_bool @ ( hAPP_f937997336l_bool @ A @ B ) ),
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(1881,plain,
! [A: $i,B: $i] : ( is_bool @ ( hAPP_f937997336l_bool @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(754,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( nat_case_bool @ fFalse @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_570_less__eq__nat_Osimps_I2_J) ).
thf(3520,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( nat_case_bool @ fFalse @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( nat_case_bool @ fFalse @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).
thf(792,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_finite__subset) ).
thf(3684,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).
thf(205,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) )
=> ~ ! [C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) )
=> ( B
!= ( hAPP_nat_nat @ suc @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_676_Suc__lessE) ).
thf(1543,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) )
=> ~ ! [C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) )
=> ( B
!= ( hAPP_nat_nat @ suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(655,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ C ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ ( image_a_a @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_finite__surj) ).
thf(3107,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ C ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ ( image_a_a @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(894,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ B ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ A ) ) ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_finite__Collect__conjI) ).
thf(4057,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ B ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ A ) ) ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).
thf(783,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_fun_a_bool_nat @ A @ B ) ) )
=> ? [C: $i] :
( ( is_fun_a_bool @ C )
& ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fconj @ ( hAPP_f2117159681l_bool @ ( cOMBC_1880041174l_bool @ member_fun_a_bool ) @ B ) ) @ ( hAPP_n1414589940l_bool @ ( cOMBC_619334683t_bool @ ( cOMBB_164527437a_bool @ fequal_nat @ A ) ) @ ( hAPP_fun_a_bool_nat @ A @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_pigeonhole__infinite) ).
thf(3652,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_fun_a_bool_nat @ A @ B ) ) )
=> ? [C: $i] :
( ( is_fun_a_bool @ C )
& ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fconj @ ( hAPP_f2117159681l_bool @ ( cOMBC_1880041174l_bool @ member_fun_a_bool ) @ B ) ) @ ( hAPP_n1414589940l_bool @ ( cOMBC_619334683t_bool @ ( cOMBB_164527437a_bool @ fequal_nat @ A ) ) @ ( hAPP_fun_a_bool_nat @ A @ C ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).
thf(114,axiom,
! [A: $i] :
( ( collec1974731493e_bool @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ A ) )
= ( insert1325755072e_bool @ A @ bot_bo1649642514l_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_486_singleton__conv) ).
thf(1257,plain,
! [A: $i] :
( ( collec1974731493e_bool @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ A ) )
= ( insert1325755072e_bool @ A @ bot_bo1649642514l_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(578,axiom,
! [A: $i,B: $i,C: $i] :
( ( image_a_nat @ A @ ( insert_a @ B @ C ) )
= ( insert_nat @ ( hAPP_a_nat @ A @ B ) @ ( image_a_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_335_image__insert) ).
thf(2838,plain,
! [A: $i,B: $i,C: $i] :
( ( image_a_nat @ A @ ( insert_a @ B @ C ) )
= ( insert_nat @ ( hAPP_a_nat @ A @ B ) @ ( image_a_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(871,axiom,
! [A: $i,B: $i] :
( ( B = bot_bo844097828e_bool )
=> ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_396_equals0D) ).
thf(3970,plain,
! [A: $i,B: $i] :
( ( B = bot_bo844097828e_bool )
=> ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).
thf(835,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_a_nat @ A @ B ) ) )
=> ? [C: $i] :
( ( is_a @ C )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ ( hAPP_f2050579477a_bool @ ( cOMBC_1355376034l_bool @ member_a ) @ B ) ) @ ( hAPP_nat_fun_a_bool @ ( cOMBC_a_nat_bool @ ( cOMBB_1321347587bool_a @ fequal_nat @ A ) ) @ ( hAPP_a_nat @ A @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_pigeonhole__infinite) ).
thf(3829,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_a_nat @ A @ B ) ) )
=> ? [C: $i] :
( ( is_a @ C )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ ( hAPP_f2050579477a_bool @ ( cOMBC_1355376034l_bool @ member_a ) @ B ) ) @ ( hAPP_nat_fun_a_bool @ ( cOMBC_a_nat_bool @ ( cOMBB_1321347587bool_a @ fequal_nat @ A ) ) @ ( hAPP_a_nat @ A @ C ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).
thf(623,axiom,
! [A: $i,B: $i] :
( ( ( is_fun_a_bool @ A )
& ( is_fun_a_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ B ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ A ) ) )
=> ( A = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_card__seteq) ).
thf(2992,plain,
! [A: $i,B: $i] :
( ( ( is_fun_a_bool @ A )
& ( is_fun_a_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ B ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ A ) ) )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(203,axiom,
! [A: $i,B: $i] :
( bot_bot_fun_nat_bool
!= ( insert_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_462_empty__not__insert) ).
thf(1536,plain,
! [A: $i,B: $i] :
( bot_bot_fun_nat_bool
!= ( insert_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(145,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_633_not__less__less__Suc__eq) ).
thf(1353,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(390,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_619_add__less__mono) ).
thf(2145,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ D ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(189,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ( cOMBC_331553030l_bool @ A ) @ B ) @ C )
= ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ A @ C ) @ B ) ),
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(1485,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ( cOMBC_331553030l_bool @ A ) @ B ) @ C )
= ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(440,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_nat_bool @ ( hAPP_f800510211t_bool @ ( cOMBC_226598744l_bool @ A ) @ B ) @ C )
= ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_) ).
thf(2320,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_nat_bool @ ( hAPP_f800510211t_bool @ ( cOMBC_226598744l_bool @ A ) @ B ) @ C )
= ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(909,axiom,
is_pname @ pn,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_pn) ).
thf(4106,plain,
is_pname @ pn,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).
thf(557,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ C ) )
=> ( ( ( hBOOL @ C )
<=> ( hBOOL @ A ) )
=> ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_525_ord__le__eq__trans) ).
thf(2760,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ C ) )
=> ( ( ( ( hBOOL @ C )
=> ( hBOOL @ A ) )
& ( ( hBOOL @ A )
=> ( hBOOL @ C ) ) )
=> ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(722,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_fun_a_bool_bool @ ( hAPP_f2117159681l_bool @ ( cOMBC_1880041174l_bool @ A ) @ B ) @ C )
= ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ A @ C ) @ B ) ),
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(3400,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_fun_a_bool_bool @ ( hAPP_f2117159681l_bool @ ( cOMBC_1880041174l_bool @ A ) @ B ) @ C )
= ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(660,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ bot_bot_fun_nat_bool ) )
<=> ( A = bot_bot_fun_nat_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_464_subset__empty) ).
thf(3139,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ bot_bot_fun_nat_bool ) )
=> ( A = bot_bot_fun_nat_bool ) )
& ( ( A = bot_bot_fun_nat_bool )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ bot_bot_fun_nat_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(735,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
=> ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_finite__subset) ).
thf(3452,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
=> ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(770,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ B )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_1_1_U) ).
thf(3589,plain,
! [A: $i,B: $i] :
( ( hBOOL @ B )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).
thf(572,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1854862208_pname @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_finite__imageI) ).
thf(2818,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1854862208_pname @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(331,axiom,
! [A: $i,B: $i] :
( ( is_a @ B )
=> ( is_pname @ ( hAPP_a_pname @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000t__a_000tc__Com__Opname) ).
thf(1966,plain,
! [A: $i,B: $i] :
( ( is_a @ B )
=> ( is_pname @ ( hAPP_a_pname @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(241,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_623_nat__add__left__cancel__less) ).
thf(1685,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(208,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_pname_bool @ ( hAPP_a93125764e_bool @ ( cOMBC_pname_a_bool @ A ) @ B ) @ C )
= ( hAPP_a_bool @ ( hAPP_p1534023578a_bool @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000t__a_000tc__HOL__Obool_U) ).
thf(1553,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_pname_bool @ ( hAPP_a93125764e_bool @ ( cOMBC_pname_a_bool @ A ) @ B ) @ C )
= ( hAPP_a_bool @ ( hAPP_p1534023578a_bool @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(324,axiom,
! [A: $i,B: $i] :
( ( is_fun_pname_bool @ B )
=> ( is_pname @ ( hAPP_f1297739591_pname @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__Opname) ).
thf(1949,plain,
! [A: $i,B: $i] :
( ( is_fun_pname_bool @ B )
=> ( is_pname @ ( hAPP_f1297739591_pname @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(284,axiom,
! [A: $i,B: $i] : ( is_fun_a_bool @ ( hAPP_nat_fun_a_bool @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
thf(1817,plain,
! [A: $i,B: $i] : ( is_fun_a_bool @ ( hAPP_nat_fun_a_bool @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(291,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ A ) ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_599_le__add__diff__inverse2) ).
thf(1834,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ A ) ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( is_fun1661590463l_bool @ B )
=> ( is_fun1661590463l_bool @ ( cOMBS_350070575l_bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__Obool_000t) ).
thf(976,plain,
! [A: $i,B: $i] :
( ( is_fun1661590463l_bool @ B )
=> ( is_fun1661590463l_bool @ ( cOMBS_350070575l_bool @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(670,axiom,
! [A: $i] :
( ( is_fun_a_bool @ A )
=> ( ! [B: $i] :
( ( is_a @ B )
=> ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ A ) ) )
<=> ( A = bot_bot_fun_a_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_418_all__not__in__conv) ).
thf(3188,plain,
! [A: $i] :
( ( is_fun_a_bool @ A )
=> ( ( ! [B: $i] :
( ( is_a @ B )
=> ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ A ) ) )
=> ( A = bot_bot_fun_a_bool ) )
& ( ( A = bot_bot_fun_a_bool )
=> ! [B: $i] :
( ( is_a @ B )
=> ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(167,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( image_pname_pname @ A @ B ) ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_card__image__le) ).
thf(1412,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( image_pname_pname @ A @ B ) ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(199,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ C ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ ( image_1551609309ol_nat @ A @ B ) ) )
=> ? [D: $i] :
( ( is_fun1661590463l_bool @ D )
& ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ D ) @ B ) )
& ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ D ) )
& ( C
= ( image_1551609309ol_nat @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_finite__subset__image) ).
thf(1517,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ C ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ ( image_1551609309ol_nat @ A @ B ) ) )
=> ? [D: $i] :
( ( is_fun1661590463l_bool @ D )
& ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ D ) @ B ) )
& ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ D ) )
& ( C
= ( image_1551609309ol_nat @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(786,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) )
=> ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ ord_le1311769555a_bool ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_finite__Collect__subsets) ).
thf(3665,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) )
=> ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ ord_le1311769555a_bool ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).
thf(587,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( is_fun_a_bool @ A )
& ( is_fun_a_bool @ C ) )
=> ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ C ) )
=> ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ A ) )
=> ( ( ( insert_a @ B @ C )
= ( insert_a @ B @ A ) )
<=> ( C = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_insert__ident) ).
thf(2865,plain,
! [A: $i,B: $i,C: $i] :
( ( ( is_fun_a_bool @ A )
& ( is_fun_a_bool @ C ) )
=> ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ C ) )
=> ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ A ) )
=> ( ( ( ( insert_a @ B @ C )
= ( insert_a @ B @ A ) )
=> ( C = A ) )
& ( ( C = A )
=> ( ( insert_a @ B @ C )
= ( insert_a @ B @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(589,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( image_a_nat @ A @ B ) ) @ ( image_a_nat @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_349_image__mono) ).
thf(2875,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( image_a_nat @ A @ B ) ) @ ( image_a_nat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(522,axiom,
! [A: $i] :
( ( collect_a @ ( hAPP_a_fun_a_bool @ ( cOMBC_a_a_bool @ fequal_a ) @ A ) )
= ( insert_a @ A @ bot_bot_fun_a_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_484_singleton__conv) ).
thf(2626,plain,
! [A: $i] :
( ( collect_a @ ( hAPP_a_fun_a_bool @ ( cOMBC_a_a_bool @ fequal_a ) @ A ) )
= ( insert_a @ A @ bot_bot_fun_a_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(314,axiom,
! [A: $i,B: $i] :
( ( ( is_fun_pname_bool @ A )
& ( is_fun1661590463l_bool @ B ) )
=> ( is_fun1661590463l_bool @ ( insert1325755072e_bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oinsert_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).
thf(1918,plain,
! [A: $i,B: $i] :
( ( ( is_fun_pname_bool @ A )
& ( is_fun1661590463l_bool @ B ) )
=> ( is_fun1661590463l_bool @ ( insert1325755072e_bool @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(737,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ C ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ ( image_a_nat @ A @ B ) ) )
=> ? [D: $i] :
( ( is_fun_a_bool @ D )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ D ) @ B ) )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ D ) )
& ( C
= ( image_a_nat @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_finite__subset__image) ).
thf(3457,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ C ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ ( image_a_nat @ A @ B ) ) )
=> ? [D: $i] :
( ( is_fun_a_bool @ D )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ D ) @ B ) )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ D ) )
& ( C
= ( image_a_nat @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).
thf(517,axiom,
hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ u ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2611,plain,
hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ u ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(861,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_fun_a_bool_a @ A @ B ) ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_card__image__le) ).
thf(3928,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_fun_a_bool_a @ A @ B ) ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).
thf(103,axiom,
! [A: $i,B: $i] :
( ( is_fun1661590463l_bool @ B )
=> ( is_fun_pname_bool @ ( image_1283814551_pname @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__Opnam) ).
thf(1216,plain,
! [A: $i,B: $i] :
( ( is_fun1661590463l_bool @ B )
=> ( is_fun_pname_bool @ ( image_1283814551_pname @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(406,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( is_pname @ D )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ C ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( hAPP_pname_pname @ A @ D ) ) @ B ) ) ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( image_pname_pname @ A @ C ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_361_image__subsetI) ).
thf(2209,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( is_pname @ D )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ C ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( hAPP_pname_pname @ A @ D ) ) @ B ) ) ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( image_pname_pname @ A @ C ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(553,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_541_order__antisym__conv) ).
thf(2743,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(625,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_rev__finite__subset) ).
thf(2997,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(487,axiom,
! [A: $i,B: $i,C: $i] :
( ( is_fun_pname_bool @ A )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( image_a_pname @ B @ C ) ) )
<=> ? [D: $i] :
( ( is_fun_a_bool @ D )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ D ) @ C ) )
& ( A
= ( image_a_pname @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_345_subset__image__iff) ).
thf(2490,plain,
! [A: $i,B: $i,C: $i] :
( ( is_fun_pname_bool @ A )
=> ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( image_a_pname @ B @ C ) ) )
=> ? [D: $i] :
( ( is_fun_a_bool @ D )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ D ) @ C ) )
& ( A
= ( image_a_pname @ B @ D ) ) ) )
& ( ? [D: $i] :
( ( is_fun_a_bool @ D )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ D ) @ C ) )
& ( A
= ( image_a_pname @ B @ D ) ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( image_a_pname @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(908,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_a_a @ A @ B ) ) )
=> ? [C: $i] :
( ( is_a @ C )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ ( hAPP_f2050579477a_bool @ ( cOMBC_1355376034l_bool @ member_a ) @ B ) ) @ ( hAPP_a_fun_a_bool @ ( cOMBC_a_a_bool @ ( cOMBB_a_fun_a_bool_a @ fequal_a @ A ) ) @ ( hAPP_a_a @ A @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_pigeonhole__infinite) ).
thf(4102,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_a_a @ A @ B ) ) )
=> ? [C: $i] :
( ( is_a @ C )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ ( hAPP_f2050579477a_bool @ ( cOMBC_1355376034l_bool @ member_a ) @ B ) ) @ ( hAPP_a_fun_a_bool @ ( cOMBC_a_a_bool @ ( cOMBB_a_fun_a_bool_a @ fequal_a @ A ) ) @ ( hAPP_a_a @ A @ C ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).
thf(400,axiom,
( bot_bot_fun_nat_bool
= ( collect_nat @ ( cOMBK_bool_nat @ fFalse ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_424_empty__def) ).
thf(2187,plain,
( bot_bot_fun_nat_bool
= ( collect_nat @ ( cOMBK_bool_nat @ fFalse ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(159,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f54304608l_bool @ ( hAPP_p130839763l_bool @ ( cOMBC_615407716e_bool @ A ) @ B ) @ C )
= ( hAPP_pname_bool @ ( hAPP_f654413245e_bool @ A @ C ) @ B ) ),
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(1390,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f54304608l_bool @ ( hAPP_p130839763l_bool @ ( cOMBC_615407716e_bool @ A ) @ B ) @ C )
= ( hAPP_pname_bool @ ( hAPP_f654413245e_bool @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(436,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_diff__diff__cancel) ).
thf(2305,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(447,axiom,
! [A: $i,B: $i] :
( ( ( is_fun_a_bool @ A )
& ( is_fun949378684l_bool @ B ) )
=> ( is_fun949378684l_bool @ ( insert_fun_a_bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oinsert_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
thf(2342,plain,
! [A: $i,B: $i] :
( ( ( is_fun_a_bool @ A )
& ( is_fun949378684l_bool @ B ) )
=> ( is_fun949378684l_bool @ ( insert_fun_a_bool @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(126,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_a_bool @ ( hAPP_a_fun_a_bool @ ( cOMBC_a_a_bool @ A ) @ B ) @ C )
= ( hAPP_a_bool @ ( hAPP_a_fun_a_bool @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000t__a_000t__a_000tc__HOL__Obool_U) ).
thf(1289,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_a_bool @ ( hAPP_a_fun_a_bool @ ( cOMBC_a_a_bool @ A ) @ B ) @ C )
= ( hAPP_a_bool @ ( hAPP_a_fun_a_bool @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(180,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ ( insert_nat @ B @ bot_bot_fun_nat_bool ) ) )
=> ( ( A = bot_bot_fun_nat_bool )
| ( A
= ( insert_nat @ B @ bot_bot_fun_nat_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_494_subset__singletonD) ).
thf(1453,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ ( insert_nat @ B @ bot_bot_fun_nat_bool ) ) )
=> ( ( A = bot_bot_fun_nat_bool )
| ( A
= ( insert_nat @ B @ bot_bot_fun_nat_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(298,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ ( hAPP_nat_nat @ suc @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_634_Suc__less__eq) ).
thf(1866,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ ( hAPP_nat_nat @ suc @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ ( hAPP_nat_nat @ suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(366,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ B ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( insert_pname @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_card__insert__le) ).
thf(2071,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ B ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( insert_pname @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(562,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1921560913_pname @ A @ B ) ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fconj @ ( hAPP_f1246832597l_bool @ ( cOMBC_1245412066l_bool @ member_fun_nat_bool ) @ B ) ) @ ( hAPP_p130839763l_bool @ ( cOMBC_615407716e_bool @ ( cOMBB_141086128t_bool @ fequal_pname @ A ) ) @ ( hAPP_f1291551745_pname @ A @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_pigeonhole__infinite) ).
thf(2775,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1921560913_pname @ A @ B ) ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fconj @ ( hAPP_f1246832597l_bool @ ( cOMBC_1245412066l_bool @ member_fun_nat_bool ) @ B ) ) @ ( hAPP_p130839763l_bool @ ( cOMBC_615407716e_bool @ ( cOMBB_141086128t_bool @ fequal_pname @ A ) ) @ ( hAPP_f1291551745_pname @ A @ C ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(256,axiom,
! [A: $i] :
( ( hAPP_f22106695ol_nat @ finite_card_nat @ ( collect_nat @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ ord_less_eq_nat ) @ A ) ) )
= ( hAPP_nat_nat @ suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_card__Collect__le__nat) ).
thf(1734,plain,
! [A: $i] :
( ( hAPP_f22106695ol_nat @ finite_card_nat @ ( collect_nat @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ ord_less_eq_nat ) @ A ) ) )
= ( hAPP_nat_nat @ suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(598,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_a85458249l_bool @ ( cOMBB_472261505bool_a @ A @ B ) @ C )
= ( hAPP_f1631501043l_bool @ A @ ( hAPP_a_fun_a_bool @ B @ C ) ) ),
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(2907,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_a85458249l_bool @ ( cOMBB_472261505bool_a @ A @ B ) @ C )
= ( hAPP_f1631501043l_bool @ A @ ( hAPP_a_fun_a_bool @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(121,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_610_termination__basic__simps_I3_J) ).
thf(1276,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(137,axiom,
! [A: $i] :
( ( is_fun_pname_bool @ A )
=> ( ! [B: $i] :
( ( is_pname @ B )
=> ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ A ) ) )
<=> ( A = bot_bo844097828e_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_417_all__not__in__conv) ).
thf(1326,plain,
! [A: $i] :
( ( is_fun_pname_bool @ A )
=> ( ( ! [B: $i] :
( ( is_pname @ B )
=> ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ A ) ) )
=> ( A = bot_bo844097828e_bool ) )
& ( ( A = bot_bo844097828e_bool )
=> ! [B: $i] :
( ( is_pname @ B )
=> ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(424,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_674_bounded__nat__set__is__finite) ).
thf(2273,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(428,axiom,
! [A: $i] :
( ( hAPP_nat_nat @ suc @ A )
!= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_691_Suc__neq__Zero) ).
thf(2283,plain,
! [A: $i] :
( ( hAPP_nat_nat @ suc @ A )
!= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(584,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_543_order__antisym__conv) ).
thf(2855,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(583,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ C ) )
=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ A ) @ ( image_1655916159e_bool @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_finite__surj) ).
thf(2853,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ C ) )
=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ A ) @ ( image_1655916159e_bool @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(386,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_615_termination__basic__simps_I1_J) ).
thf(2135,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(704,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ A ) )
=> ( ( hBOOL @ A )
<=> ( hBOOL @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_515_order__antisym) ).
thf(3336,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ A ) )
=> ( ( ( hBOOL @ A )
=> ( hBOOL @ B ) )
& ( ( hBOOL @ B )
=> ( hBOOL @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(345,axiom,
! [A: $i,B: $i] :
( ( is_bool @ A )
=> ( ( hAPP_a_bool @ ( cOMBK_bool_a @ A ) @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000t__a_U) ).
thf(2004,plain,
! [A: $i,B: $i] :
( ( is_bool @ A )
=> ( ( hAPP_a_bool @ ( cOMBK_bool_a @ A ) @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(516,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_a_bool @ ( hAPP_f2050579477a_bool @ ( cOMBC_1355376034l_bool @ A ) @ B ) @ C )
= ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ A @ C ) @ B ) ),
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(2608,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_a_bool @ ( hAPP_f2050579477a_bool @ ( cOMBC_1355376034l_bool @ A ) @ B ) @ C )
= ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(287,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ ( insert_nat @ B @ A ) ) )
<=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_325_subset__insert) ).
thf(1822,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ C ) )
=> ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ ( insert_nat @ B @ A ) ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ ( insert_nat @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(818,axiom,
! [A: $i,B: $i] :
( ( ( is_fun_pname_bool @ A )
& ( is_fun_pname_bool @ B ) )
=> ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ A ) @ B ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T) ).
thf(3780,plain,
! [A: $i,B: $i] :
( ( ( is_fun_pname_bool @ A )
& ( is_fun_pname_bool @ B ) )
=> ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ A ) @ B ) )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).
thf(462,axiom,
~ ( hBOOL @ fFalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
thf(2394,plain,
~ ( hBOOL @ fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(56,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ C ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ ( image_fun_a_bool_nat @ A @ B ) ) )
=> ? [D: $i] :
( ( is_fun949378684l_bool @ D )
& ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ D ) @ B ) )
& ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ D ) )
& ( C
= ( image_fun_a_bool_nat @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_finite__subset__image) ).
thf(1062,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ C ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ ( image_fun_a_bool_nat @ A @ B ) ) )
=> ? [D: $i] :
( ( is_fun949378684l_bool @ D )
& ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ D ) @ B ) )
& ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ D ) )
& ( C
= ( image_fun_a_bool_nat @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(496,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
=> ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_finite_OinsertI) ).
thf(2532,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
=> ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(195,axiom,
! [A: $i,B: $i] : ( is_fun_a_bool @ ( image_nat_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__Nat__Onat_000t__a) ).
thf(1508,plain,
! [A: $i,B: $i] : ( is_fun_a_bool @ ( image_nat_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(713,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ A @ B ) ) @ C ) )
<=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ C ) )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_324_insert__subset) ).
thf(3369,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ A @ B ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ C ) )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ C ) ) ) )
& ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ C ) )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ A @ B ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(574,axiom,
! [A: $i,B: $i,C: $i] :
( ( insert_a @ A @ ( insert_a @ B @ C ) )
= ( insert_a @ B @ ( insert_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_insert__commute) ).
thf(2823,plain,
! [A: $i,B: $i,C: $i] :
( ( insert_a @ A @ ( insert_a @ B @ C ) )
= ( insert_a @ B @ ( insert_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(675,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A ) )
=> ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ ( collec707592106l_bool @ ( hAPP_f1434722111l_bool @ ( cOMBC_331553030l_bool @ ord_le1375614389l_bool ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_finite__Collect__subsets) ).
thf(3220,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A ) )
=> ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ ( collec707592106l_bool @ ( hAPP_f1434722111l_bool @ ( cOMBC_331553030l_bool @ ord_le1375614389l_bool ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(200,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
| ( A = B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_637_less__or__eq__imp__le) ).
thf(1523,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
| ( A = B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(843,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ bot_bot_bool ) )
=> ( ( hBOOL @ A )
<=> ( hBOOL @ bot_bot_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_432_le__bot) ).
thf(3859,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ bot_bot_bool ) )
=> ( ( ( hBOOL @ A )
=> ( hBOOL @ bot_bot_bool ) )
& ( ( hBOOL @ bot_bot_bool )
=> ( hBOOL @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).
thf(29,axiom,
! [A: $i] : ( is_bool @ ( wt @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_wt) ).
thf(995,plain,
! [A: $i] : ( is_bool @ ( wt @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(606,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_a_pname @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_finite__imageI) ).
thf(2934,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_a_pname @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(393,axiom,
! [A: $i,B: $i] :
( ( ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B )
= zero_zero_nat )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_685_diff__is__0__eq) ).
thf(2152,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B )
= zero_zero_nat )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B )
= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(420,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f54304608l_bool @ ( cOMBB_238756964t_bool @ A @ B ) @ C )
= ( hAPP_bool_bool @ A @ ( hAPP_f54304608l_bool @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Nat__On) ).
thf(2262,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f54304608l_bool @ ( cOMBB_238756964t_bool @ A @ B ) @ C )
= ( hAPP_bool_bool @ A @ ( hAPP_f54304608l_bool @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(609,axiom,
! [A: $i] :
( ( ( collec1974731493e_bool @ A )
= bot_bo1649642514l_bool )
<=> ! [B: $i] :
( ( is_fun_pname_bool @ B )
=> ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_400_Collect__empty__eq) ).
thf(2944,plain,
! [A: $i] :
( ( ( ( collec1974731493e_bool @ A )
= bot_bo1649642514l_bool )
=> ! [B: $i] :
( ( is_fun_pname_bool @ B )
=> ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ B ) ) ) )
& ( ! [B: $i] :
( ( is_fun_pname_bool @ B )
=> ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ B ) ) )
=> ( ( collec1974731493e_bool @ A )
= bot_bo1649642514l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) @ C )
= ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_581_diff__diff__left) ).
thf(1030,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) @ C )
= ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(567,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_equalityI) ).
thf(2796,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(747,axiom,
! [A: $i,B: $i] :
( ( is_fun_a_bool @ B )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ B ) )
=> ( ( insert_a @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_insert__absorb) ).
thf(3497,plain,
! [A: $i,B: $i] :
( ( is_fun_a_bool @ B )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ B ) )
=> ( ( insert_a @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).
thf(132,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ D ) @ C ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( hAPP_nat_pname @ A @ D ) ) @ B ) ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( image_nat_pname @ A @ C ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_364_image__subsetI) ).
thf(1308,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ D ) @ C ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( hAPP_nat_pname @ A @ D ) ) @ B ) ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( image_nat_pname @ A @ C ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(757,axiom,
! [A: $i,B: $i] :
( ( ( is_pname @ A )
& ( is_pname @ B ) )
=> ( ~ ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ fequal_pname @ A ) @ B ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Com__Opname_T) ).
thf(3529,plain,
! [A: $i,B: $i] :
( ( ( is_pname @ A )
& ( is_pname @ B ) )
=> ( ~ ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ fequal_pname @ A ) @ B ) )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).
thf(707,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_nat_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_finite__imageI) ).
thf(3351,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_nat_a @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(237,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f1664156314l_bool @ ( cOMBB_307249310e_bool @ A @ B ) @ C )
= ( hAPP_bool_bool @ A @ ( hAPP_f1664156314l_bool @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Op) ).
thf(1661,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f1664156314l_bool @ ( cOMBB_307249310e_bool @ A @ B ) @ C )
= ( hAPP_bool_bool @ A @ ( hAPP_f1664156314l_bool @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(900,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( image_a_pname @ A @ B ) ) @ ( image_a_pname @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_348_image__mono) ).
thf(4074,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( image_a_pname @ A @ B ) ) @ ( image_a_pname @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).
thf(521,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C ) @ ( insert_a @ B @ A ) ) )
<=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_327_subset__insert) ).
thf(2623,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ C ) )
=> ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C ) @ ( insert_a @ B @ A ) ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C ) @ ( insert_a @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(225,axiom,
! [A: $i] :
( ( is_fun_pname_bool @ A )
=> ( is_fun_pname_bool @ ( collect_pname @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_OCollect_000tc__Com__Opname) ).
thf(1614,plain,
! [A: $i] :
( ( is_fun_pname_bool @ A )
=> ( is_fun_pname_bool @ ( collect_pname @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(459,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_643_less__imp__diff__less) ).
thf(2384,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ A ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(795,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ C ) )
=> ( ( insert_pname @ ( hAPP_a_pname @ A @ B ) @ ( image_a_pname @ A @ C ) )
= ( image_a_pname @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_340_insert__image) ).
thf(3694,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ C ) )
=> ( ( insert_pname @ ( hAPP_a_pname @ A @ B ) @ ( image_a_pname @ A @ C ) )
= ( image_a_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).
thf(528,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_496248727ol_nat @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_finite__imageI) ).
thf(2648,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_496248727ol_nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(730,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_283_set__rev__mp) ).
thf(3430,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(176,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( is_pname @ D )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ C ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ ( hAPP_pname_nat @ A @ D ) ) @ B ) ) ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( image_pname_nat @ A @ C ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_360_image__subsetI) ).
thf(1440,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( is_pname @ D )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ C ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ ( hAPP_pname_nat @ A @ D ) ) @ B ) ) ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( image_pname_nat @ A @ C ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(662,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
=> ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( image_2129980159t_bool @ A @ B ) ) )
=> ? [C: $i] :
( ( is_pname @ C )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ ( hAPP_f759274231e_bool @ ( cOMBC_1058051404l_bool @ member_pname ) @ B ) ) @ ( hAPP_f654413245e_bool @ ( cOMBC_267053842l_bool @ ( cOMBB_928955006_pname @ fequal_fun_nat_bool @ A ) ) @ ( hAPP_p1499970991t_bool @ A @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_pigeonhole__infinite) ).
thf(3149,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
=> ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( image_2129980159t_bool @ A @ B ) ) )
=> ? [C: $i] :
( ( is_pname @ C )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ ( hAPP_f759274231e_bool @ ( cOMBC_1058051404l_bool @ member_pname ) @ B ) ) @ ( hAPP_f654413245e_bool @ ( cOMBC_267053842l_bool @ ( cOMBB_928955006_pname @ fequal_fun_nat_bool @ A ) ) @ ( hAPP_p1499970991t_bool @ A @ C ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f54304608l_bool @ ( cOMBS_1187019125l_bool @ A @ B ) @ C )
= ( hAPP_bool_bool @ ( hAPP_f1748468828l_bool @ A @ C ) @ ( hAPP_f54304608l_bool @ B @ C ) ) ),
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(1077,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f54304608l_bool @ ( cOMBS_1187019125l_bool @ A @ B ) @ C )
= ( hAPP_bool_bool @ ( hAPP_f1748468828l_bool @ A @ C ) @ ( hAPP_f54304608l_bool @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(790,axiom,
! [A: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_699_less__eq__nat_Osimps_I1_J) ).
thf(3677,plain,
! [A: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).
thf(395,axiom,
is_fun_pname_bool @ bot_bo844097828e_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Orderings_Obot__class_Obot_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).
thf(2162,plain,
is_fun_pname_bool @ bot_bo844097828e_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(409,axiom,
! [A: $i] :
( ( hAPP_n1699378549t_bool @ ord_less_nat @ A )
= ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_670_less__eq__Suc__le__raw) ).
thf(2230,plain,
! [A: $i] :
( ( hAPP_n1699378549t_bool @ ord_less_nat @ A )
= ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(305,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_357_subsetI) ).
thf(1893,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(355,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ bot_bo844097828e_bool ) )
=> ( ! [D: $i,E: $i] :
( ( ( is_pname @ D )
& ( is_fun_pname_bool @ E ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ E ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ E ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ ( insert_pname @ D @ E ) ) ) ) ) ) ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_557_finite__subset__induct) ).
thf(2036,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ bot_bo844097828e_bool ) )
=> ( ! [D: $i,E: $i] :
( ( ( is_pname @ D )
& ( is_fun_pname_bool @ E ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ E ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ E ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ ( insert_pname @ D @ E ) ) ) ) ) ) ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(907,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B
= ( hAPP_pname_a @ C @ D ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ A ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ ( image_pname_a @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_image__eqI) ).
thf(4098,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B
= ( hAPP_pname_a @ C @ D ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ A ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ ( image_pname_a @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[907]) ).
thf(177,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_n215258509l_bool @ ( cOMBB_2026977092ol_nat @ A @ B ) @ C )
= ( hAPP_f103356543l_bool @ A @ ( hAPP_n1699378549t_bool @ B @ C ) ) ),
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(1444,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_n215258509l_bool @ ( cOMBB_2026977092ol_nat @ A @ B ) @ C )
= ( hAPP_f103356543l_bool @ A @ ( hAPP_n1699378549t_bool @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(605,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
=> ( ( B = A )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_521_xt1_I4_J) ).
thf(2930,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
=> ( ( B = A )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(197,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_le__SucI) ).
thf(1512,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(123,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) )
=> ? [C: $i] :
( B
= ( hAPP_nat_nat @ suc @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_Suc__le__D) ).
thf(1280,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) )
=> ? [C: $i] :
( B
= ( hAPP_nat_nat @ suc @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(215,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ suc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_665_diff__less__Suc) ).
thf(1578,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(497,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_nat__le__linear) ).
thf(2534,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ C ) )
=> ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ C ) @ ( image_2129980159t_bool @ A @ B ) ) )
=> ? [D: $i] :
( ( is_fun_pname_bool @ D )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ D ) @ B ) )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ D ) )
& ( C
= ( image_2129980159t_bool @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_finite__subset__image) ).
thf(950,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ C ) )
=> ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ C ) @ ( image_2129980159t_bool @ A @ B ) ) )
=> ? [D: $i] :
( ( is_fun_pname_bool @ D )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ D ) @ B ) )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ D ) )
& ( C
= ( image_2129980159t_bool @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(410,axiom,
! [A: $i] :
( ( collec1974731493e_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ A ) )
= ( insert1325755072e_bool @ A @ bot_bo1649642514l_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_492_singleton__conv2) ).
thf(2233,plain,
! [A: $i] :
( ( collec1974731493e_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ A ) )
= ( insert1325755072e_bool @ A @ bot_bo1649642514l_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(849,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
=> ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ A ) @ B ) )
=> ( ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( insert1325755072e_bool @ A @ B ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_card__insert__disjoint) ).
thf(3882,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
=> ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ A ) @ B ) )
=> ( ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( insert1325755072e_bool @ A @ B ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).
thf(155,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ suc @ B ) ) @ A )
= ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_Suc__diff__le) ).
thf(1380,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ suc @ B ) ) @ A )
= ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(559,axiom,
! [A: $i] :
( ( collect_fun_a_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ A ) )
= ( insert_fun_a_bool @ A @ bot_bo1389914601l_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_493_singleton__conv2) ).
thf(2768,plain,
! [A: $i] :
( ( collect_fun_a_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ A ) )
= ( insert_fun_a_bool @ A @ bot_bo1389914601l_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(389,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_632_less__antisym) ).
thf(2142,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(715,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_2_1_U) ).
thf(3379,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).
thf(877,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_648_less__irrefl__nat) ).
thf(3992,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).
thf(311,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ B ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ A ) ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_card__seteq) ).
thf(1908,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ B ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ A ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(890,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_pname_bool @ A @ B ) )
=> ( ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ fequal_pname ) @ B ) ) @ A ) )
= ( insert_pname @ B @ bot_bo844097828e_bool ) ) )
& ( ~ ( hBOOL @ ( hAPP_pname_bool @ A @ B ) )
=> ( ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ fequal_pname ) @ B ) ) @ A ) )
= bot_bo844097828e_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_471_Collect__conv__if) ).
thf(4039,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_pname_bool @ A @ B ) )
=> ( ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ fequal_pname ) @ B ) ) @ A ) )
= ( insert_pname @ B @ bot_bo844097828e_bool ) ) )
& ( ~ ( hBOOL @ ( hAPP_pname_bool @ A @ B ) )
=> ( ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ fequal_pname ) @ B ) ) @ A ) )
= bot_bo844097828e_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).
thf(143,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ C ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( image_1921560913_pname @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_finite__surj) ).
thf(1348,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ C ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( image_1921560913_pname @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(31,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ A ) @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ ord_less_nat ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_654_finite__M__bounded__by__nat) ).
thf(999,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ A ) @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ ord_less_nat ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(429,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_656_less__add__Suc2) ).
thf(2287,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(435,axiom,
! [A: $i,B: $i] :
( ( insert_nat @ A @ ( insert_nat @ A @ B ) )
= ( insert_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_insert__absorb2) ).
thf(2302,plain,
! [A: $i,B: $i] :
( ( insert_nat @ A @ ( insert_nat @ A @ B ) )
= ( insert_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(537,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_pname_bool @ A @ B ) )
=> ( ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ ( hAPP_p61793385e_bool @ fequal_pname @ B ) ) @ A ) )
= ( insert_pname @ B @ bot_bo844097828e_bool ) ) )
& ( ~ ( hBOOL @ ( hAPP_pname_bool @ A @ B ) )
=> ( ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ ( hAPP_p61793385e_bool @ fequal_pname @ B ) ) @ A ) )
= bot_bo844097828e_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_477_Collect__conv__if2) ).
thf(2683,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_pname_bool @ A @ B ) )
=> ( ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ ( hAPP_p61793385e_bool @ fequal_pname @ B ) ) @ A ) )
= ( insert_pname @ B @ bot_bo844097828e_bool ) ) )
& ( ~ ( hBOOL @ ( hAPP_pname_bool @ A @ B ) )
=> ( ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ ( hAPP_p61793385e_bool @ fequal_pname @ B ) ) @ A ) )
= bot_bo844097828e_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(694,axiom,
! [A: $i,B: $i] :
( ( ( is_fun_a_bool @ A )
& ( is_fun_a_bool @ B ) )
=> ( ( A = B )
<=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_554_order__eq__iff) ).
thf(3291,plain,
! [A: $i,B: $i] :
( ( ( is_fun_a_bool @ A )
& ( is_fun_a_bool @ B ) )
=> ( ( ( A = B )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ A ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(854,axiom,
! [A: $i,B: $i,C: $i] :
( ( image_pname_a @ A @ ( insert_pname @ B @ C ) )
= ( insert_a @ ( hAPP_pname_a @ A @ B ) @ ( image_pname_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_337_image__insert) ).
thf(3907,plain,
! [A: $i,B: $i,C: $i] :
( ( image_pname_a @ A @ ( insert_pname @ B @ C ) )
= ( insert_a @ ( hAPP_pname_a @ A @ B ) @ ( image_pname_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).
thf(620,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_pname_a @ A @ B ) ) )
=> ? [C: $i] :
( ( is_pname @ C )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ ( hAPP_f759274231e_bool @ ( cOMBC_1058051404l_bool @ member_pname ) @ B ) ) @ ( hAPP_a93125764e_bool @ ( cOMBC_pname_a_bool @ ( cOMBB_1897541054_pname @ fequal_a @ A ) ) @ ( hAPP_pname_a @ A @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_pigeonhole__infinite) ).
thf(2983,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_pname_a @ A @ B ) ) )
=> ? [C: $i] :
( ( is_pname @ C )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ ( hAPP_f759274231e_bool @ ( cOMBC_1058051404l_bool @ member_pname ) @ B ) ) @ ( hAPP_a93125764e_bool @ ( cOMBC_pname_a_bool @ ( cOMBB_1897541054_pname @ fequal_a @ A ) ) @ ( hAPP_pname_a @ A @ C ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(547,axiom,
! [A: $i,B: $i,C: $i] :
( ( is_fun_a_bool @ C )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ C ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C ) @ ( image_fun_nat_bool_a @ A @ B ) ) )
=> ? [D: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ D ) @ B ) )
& ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ D ) )
& ( C
= ( image_fun_nat_bool_a @ A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_finite__subset__image) ).
thf(2719,plain,
! [A: $i,B: $i,C: $i] :
( ( is_fun_a_bool @ C )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ C ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C ) @ ( image_fun_nat_bool_a @ A @ B ) ) )
=> ? [D: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ D ) @ B ) )
& ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ D ) )
& ( C
= ( image_fun_nat_bool_a @ A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(346,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ C ) )
=> ~ ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) )
=> ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_594_add__leE) ).
thf(2008,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ C ) )
=> ~ ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) )
=> ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(130,axiom,
! [A: $i] :
( ( hAPP_f22106695ol_nat @ finite_card_nat @ ( collect_nat @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ ord_less_nat ) @ A ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_653_card__Collect__less__nat) ).
thf(1303,plain,
! [A: $i] :
( ( hAPP_f22106695ol_nat @ finite_card_nat @ ( collect_nat @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ ord_less_nat ) @ A ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(659,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( is_a @ A )
& ( is_a @ C ) )
=> ( ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ A @ B ) @ C ) )
<=> ( ( A = C )
| ( hBOOL @ ( hAPP_a_bool @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_insert__code) ).
thf(3132,plain,
! [A: $i,B: $i,C: $i] :
( ( ( is_a @ A )
& ( is_a @ C ) )
=> ( ( ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ A @ B ) @ C ) )
=> ( ( A = C )
| ( hBOOL @ ( hAPP_a_bool @ B @ C ) ) ) )
& ( ( ( A = C )
| ( hBOOL @ ( hAPP_a_bool @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ A @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(112,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ A @ B ) )
=> ( ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ fequal_nat ) @ B ) ) @ A ) )
= ( insert_nat @ B @ bot_bot_fun_nat_bool ) ) )
& ( ~ ( hBOOL @ ( hAPP_nat_bool @ A @ B ) )
=> ( ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ fequal_nat ) @ B ) ) @ A ) )
= bot_bot_fun_nat_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_470_Collect__conv__if) ).
thf(1248,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ A @ B ) )
=> ( ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ fequal_nat ) @ B ) ) @ A ) )
= ( insert_nat @ B @ bot_bot_fun_nat_bool ) ) )
& ( ~ ( hBOOL @ ( hAPP_nat_bool @ A @ B ) )
=> ( ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ fequal_nat ) @ B ) ) @ A ) )
= bot_bot_fun_nat_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(358,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ ( cOMBC_1004116266e_bool @ A ) @ B ) @ C )
= ( hAPP_pname_bool @ ( hAPP_f759274231e_bool @ A @ C ) @ B ) ),
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(2050,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ ( cOMBC_1004116266e_bool @ A ) @ B ) @ C )
= ( hAPP_pname_bool @ ( hAPP_f759274231e_bool @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(525,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( hAPP_pname_a @ A @ B ) ) @ ( image_pname_a @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_307_imageI) ).
thf(2636,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( hAPP_pname_a @ A @ B ) ) @ ( image_pname_a @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(892,axiom,
! [A: $i,B: $i] :
( ( ( is_a @ A )
& ( is_fun_a_bool @ B ) )
=> ( is_fun_a_bool @ ( insert_a @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oinsert_000t__a) ).
thf(4051,plain,
! [A: $i,B: $i] :
( ( ( is_a @ A )
& ( is_fun_a_bool @ B ) )
=> ( is_fun_a_bool @ ( insert_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).
thf(148,axiom,
! [A: $i,B: $i] :
( ( insert_nat @ A @ B )
= ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ fequal_nat ) @ A ) ) @ ( hAPP_f800510211t_bool @ ( cOMBC_226598744l_bool @ member_nat ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_insert__compr) ).
thf(1363,plain,
! [A: $i,B: $i] :
( ( insert_nat @ A @ B )
= ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ fequal_nat ) @ A ) ) @ ( hAPP_f800510211t_bool @ ( cOMBC_226598744l_bool @ member_nat ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(882,axiom,
! [A: $i,B: $i,C: $i] :
( ( is_a @ A )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ ( image_pname_a @ B @ C ) ) )
<=> ? [D: $i] :
( ( is_pname @ D )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ C ) )
& ( A
= ( hAPP_pname_a @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_302_image__iff) ).
thf(4007,plain,
! [A: $i,B: $i,C: $i] :
( ( is_a @ A )
=> ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ ( image_pname_a @ B @ C ) ) )
=> ? [D: $i] :
( ( is_pname @ D )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ C ) )
& ( A
= ( hAPP_pname_a @ B @ D ) ) ) )
& ( ? [D: $i] :
( ( is_pname @ D )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ C ) )
& ( A
= ( hAPP_pname_a @ B @ D ) ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ ( image_pname_a @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).
thf(902,axiom,
! [A: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ bot_bot_fun_a_bool ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_444_bot__least) ).
thf(4083,plain,
! [A: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ bot_bot_fun_a_bool ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).
thf(275,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_620_add__less__mono1) ).
thf(1789,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(451,axiom,
! [A: $i] :
( ( collect_fun_nat_bool @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ A ) )
= ( insert_fun_nat_bool @ A @ bot_bo1701429464l_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_491_singleton__conv2) ).
thf(2366,plain,
! [A: $i] :
( ( collect_fun_nat_bool @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ A ) )
= ( insert_fun_nat_bool @ A @ bot_bo1701429464l_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(700,axiom,
! [A: $i,B: $i] :
( ( A = B )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_547_order__eq__refl) ).
thf(3323,plain,
! [A: $i,B: $i] :
( ( A = B )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(187,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ ( hAPP_nat_nat @ suc @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_Suc__le__mono) ).
thf(1473,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ ( hAPP_nat_nat @ suc @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ ( hAPP_nat_nat @ suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(520,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_1551609309ol_nat @ A @ B ) ) )
=> ? [C: $i] :
( ( is_fun_pname_bool @ C )
& ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fconj @ ( hAPP_f559147733l_bool @ ( cOMBC_1988546018l_bool @ member799430823e_bool ) @ B ) ) @ ( hAPP_n850744903l_bool @ ( cOMBC_1666426608t_bool @ ( cOMBB_1896684278e_bool @ fequal_nat @ A ) ) @ ( hAPP_f921600141ol_nat @ A @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_pigeonhole__infinite) ).
thf(2619,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_1551609309ol_nat @ A @ B ) ) )
=> ? [C: $i] :
( ( is_fun_pname_bool @ C )
& ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fconj @ ( hAPP_f559147733l_bool @ ( cOMBC_1988546018l_bool @ member799430823e_bool ) @ B ) ) @ ( hAPP_n850744903l_bool @ ( cOMBC_1666426608t_bool @ ( cOMBB_1896684278e_bool @ fequal_nat @ A ) ) @ ( hAPP_f921600141ol_nat @ A @ C ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(363,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B
= ( hAPP_pname_nat @ C @ D ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ A ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ ( image_pname_nat @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_image__eqI) ).
thf(2063,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B
= ( hAPP_pname_nat @ C @ D ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ A ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ ( image_pname_nat @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(530,axiom,
! [A: $i,B: $i] :
( ( insert_a @ A @ ( insert_a @ A @ B ) )
= ( insert_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_insert__absorb2) ).
thf(2651,plain,
! [A: $i,B: $i] :
( ( insert_a @ A @ ( insert_a @ A @ B ) )
= ( insert_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(174,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_593_add__leD1) ).
thf(1436,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(296,axiom,
! [A: $i,B: $i] :
( ( is_fun_pname_bool @ A )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( insert_pname @ B @ bot_bo844097828e_bool ) ) )
=> ( ( A = bot_bo844097828e_bool )
| ( A
= ( insert_pname @ B @ bot_bo844097828e_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_495_subset__singletonD) ).
thf(1859,plain,
! [A: $i,B: $i] :
( ( is_fun_pname_bool @ A )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( insert_pname @ B @ bot_bo844097828e_bool ) ) )
=> ( ( A = bot_bo844097828e_bool )
| ( A
= ( insert_pname @ B @ bot_bo844097828e_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(89,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ C ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ ( image_fun_a_bool_nat @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_finite__surj) ).
thf(1172,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ C ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ ( image_fun_a_bool_nat @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(743,axiom,
! [A: $i,B: $i] :
( ( is_fun_pname_bool @ B )
=> ( ( bot_bot_fun_a_bool
= ( image_pname_a @ A @ B ) )
<=> ( B = bot_bo844097828e_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_469_empty__is__image) ).
thf(3479,plain,
! [A: $i,B: $i] :
( ( is_fun_pname_bool @ B )
=> ( ( ( bot_bot_fun_a_bool
= ( image_pname_a @ A @ B ) )
=> ( B = bot_bo844097828e_bool ) )
& ( ( B = bot_bo844097828e_bool )
=> ( bot_bot_fun_a_bool
= ( image_pname_a @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(468,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_678_less__zeroE) ).
thf(2417,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i] :
( ( is_fun_pname_bool @ C )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ ( image_1283814551_pname @ A @ B ) ) )
=> ? [D: $i] :
( ( is_fun1661590463l_bool @ D )
& ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ D ) @ B ) )
& ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ D ) )
& ( C
= ( image_1283814551_pname @ A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_finite__subset__image) ).
thf(1033,plain,
! [A: $i,B: $i,C: $i] :
( ( is_fun_pname_bool @ C )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ ( image_1283814551_pname @ A @ B ) ) )
=> ? [D: $i] :
( ( is_fun1661590463l_bool @ D )
& ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ D ) @ B ) )
& ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ D ) )
& ( C
= ( image_1283814551_pname @ A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(613,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_rev__finite__subset) ).
thf(2961,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(97,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_subsetD) ).
thf(1197,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(545,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_fun_a_bool_bool @ ( cOMBS_1035972772l_bool @ A @ B ) @ C )
= ( hAPP_bool_bool @ ( hAPP_f198738859l_bool @ A @ C ) @ ( hAPP_fun_a_bool_bool @ B @ C ) ) ),
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(2714,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_fun_a_bool_bool @ ( cOMBS_1035972772l_bool @ A @ B ) @ C )
= ( hAPP_bool_bool @ ( hAPP_f198738859l_bool @ A @ C ) @ ( hAPP_fun_a_bool_bool @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(671,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
<=> ( hBOOL @ ( hAPP_pname_bool @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_mem__def) ).
thf(3196,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_pname_bool @ B @ A ) ) )
& ( ( hBOOL @ ( hAPP_pname_bool @ B @ A ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(728,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_a_bool @ B @ A ) ) @ ( hAPP_a_bool @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_379_le__funD) ).
thf(3426,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_a_bool @ B @ A ) ) @ ( hAPP_a_bool @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).
thf(304,axiom,
! [A: $i] :
( ( is_bool @ A )
=> ( is_fun949378684l_bool @ ( cOMBK_324466864a_bool @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_COMBK_000tc__HOL__Obool_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
thf(1891,plain,
! [A: $i] :
( ( is_bool @ A )
=> ( is_fun949378684l_bool @ ( cOMBK_324466864a_bool @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(318,axiom,
! [A: $i,B: $i] :
( ( is_fun_a_bool @ B )
=> ( is_fun_a_bool @ ( image_a_a @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000t__a_000t__a) ).
thf(1930,plain,
! [A: $i,B: $i] :
( ( is_fun_a_bool @ B )
=> ( is_fun_a_bool @ ( image_a_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(683,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( is_a @ D )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ D ) @ C ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( hAPP_a_pname @ A @ D ) ) @ B ) ) ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( image_a_pname @ A @ C ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_363_image__subsetI) ).
thf(3244,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( is_a @ D )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ D ) @ C ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( hAPP_a_pname @ A @ D ) ) @ B ) ) ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( image_a_pname @ A @ C ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(872,axiom,
! [A: $i] :
( ( is_fun_a_bool @ A )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ bot_bot_fun_a_bool ) )
<=> ( A = bot_bot_fun_a_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_466_subset__empty) ).
thf(3974,plain,
! [A: $i] :
( ( is_fun_a_bool @ A )
=> ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ bot_bot_fun_a_bool ) )
=> ( A = bot_bot_fun_a_bool ) )
& ( ( A = bot_bot_fun_a_bool )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ bot_bot_fun_a_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).
thf(81,axiom,
! [A: $i] :
( ( is_fun949378684l_bool @ A )
=> ( is_fun949378684l_bool @ ( collect_fun_a_bool @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_OCollect_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
thf(1152,plain,
! [A: $i] :
( ( is_fun949378684l_bool @ A )
=> ( is_fun949378684l_bool @ ( collect_fun_a_bool @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(642,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_a_nat @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_finite__imageI) ).
thf(3057,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_a_nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(595,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_fun_a_bool_bool @ ( cOMBB_2140588453a_bool @ A @ B ) @ C )
= ( hAPP_bool_bool @ A @ ( hAPP_fun_a_bool_bool @ B @ C ) ) ),
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(2898,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_fun_a_bool_bool @ ( cOMBB_2140588453a_bool @ A @ B ) @ C )
= ( hAPP_bool_bool @ A @ ( hAPP_fun_a_bool_bool @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(896,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1921560913_pname @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_finite__imageI) ).
thf(4066,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1921560913_pname @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( insert_fun_nat_bool @ A @ B )
= ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ ( hAPP_f103356543l_bool @ ( cOMBC_1693257480l_bool @ fequal_fun_nat_bool ) @ A ) ) @ ( hAPP_f1246832597l_bool @ ( cOMBC_1245412066l_bool @ member_fun_nat_bool ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_313_insert__compr__raw) ).
thf(992,plain,
! [A: $i,B: $i] :
( ( insert_fun_nat_bool @ A @ B )
= ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ ( hAPP_f103356543l_bool @ ( cOMBC_1693257480l_bool @ fequal_fun_nat_bool ) @ A ) ) @ ( hAPP_f1246832597l_bool @ ( cOMBC_1245412066l_bool @ member_fun_nat_bool ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(831,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ A ) )
<=> ( ( hBOOL @ B )
<=> ( hBOOL @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_540_order__antisym__conv) ).
thf(3817,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ A ) )
=> ( ( ( hBOOL @ B )
=> ( hBOOL @ A ) )
& ( ( hBOOL @ A )
=> ( hBOOL @ B ) ) ) )
& ( ( ( ( hBOOL @ B )
=> ( hBOOL @ A ) )
& ( ( hBOOL @ A )
=> ( hBOOL @ B ) ) )
=> ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).
thf(491,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A ) )
=> ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ ( collec1015864663l_bool @ ( hAPP_f1772781669l_bool @ ( cOMBC_595898202l_bool @ ord_le1454342156l_bool ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_finite__Collect__subsets) ).
thf(2507,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A ) )
=> ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ ( collec1015864663l_bool @ ( hAPP_f1772781669l_bool @ ( cOMBC_595898202l_bool @ ord_le1454342156l_bool ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(316,axiom,
! [A: $i,B: $i] : ( is_a @ ( hAPP_nat_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000t__a) ).
thf(1925,plain,
! [A: $i,B: $i] : ( is_a @ ( hAPP_nat_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(222,axiom,
! [A: $i,B: $i,C: $i] :
( ( is_fun_pname_bool @ C )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ ( image_pname_pname @ A @ B ) ) )
=> ? [D: $i] :
( ( is_fun_pname_bool @ D )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ D ) @ B ) )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ D ) )
& ( C
= ( image_pname_pname @ A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_finite__subset__image) ).
thf(1597,plain,
! [A: $i,B: $i,C: $i] :
( ( is_fun_pname_bool @ C )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ ( image_pname_pname @ A @ B ) ) )
=> ? [D: $i] :
( ( is_fun_pname_bool @ D )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ D ) @ B ) )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ D ) )
& ( C
= ( image_pname_pname @ A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(485,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ bot_bot_fun_a_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_385_emptyE) ).
thf(2484,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ bot_bot_fun_a_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(109,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) ) @ ( hAPP_nat_nat @ suc @ C ) )
= ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_Suc__diff__diff) ).
thf(1236,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) ) @ ( hAPP_nat_nat @ suc @ C ) )
= ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(413,axiom,
! [A: $i,B: $i] :
( ( is_fun1661590463l_bool @ B )
=> ( is_bool @ ( hAPP_f1935102916l_bool @ A @ B ) ) ),
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(2241,plain,
! [A: $i,B: $i] :
( ( is_fun1661590463l_bool @ B )
=> ( is_bool @ ( hAPP_f1935102916l_bool @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( is_fun_pname_bool @ B )
=> ( is_fun1661590463l_bool @ ( image_47868345e_bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_) ).
thf(987,plain,
! [A: $i,B: $i] :
( ( is_fun_pname_bool @ B )
=> ( is_fun1661590463l_bool @ ( image_47868345e_bool @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(394,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ B ) )
= ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_583_diff__cancel2) ).
thf(2159,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ B ) )
= ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(710,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ A ) @ B ) @ C )
= ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ A @ C ) @ B ) ),
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(3362,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ A ) @ B ) @ C )
= ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(290,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
=> ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ B ) )
=> ( ( hAPP_f22106695ol_nat @ finite_card_nat @ ( insert_nat @ A @ B ) )
= ( hAPP_f22106695ol_nat @ finite_card_nat @ B ) ) )
& ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ B ) )
=> ( ( hAPP_f22106695ol_nat @ finite_card_nat @ ( insert_nat @ A @ B ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f22106695ol_nat @ finite_card_nat @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_card__insert__if) ).
thf(1829,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
=> ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ B ) )
=> ( ( hAPP_f22106695ol_nat @ finite_card_nat @ ( insert_nat @ A @ B ) )
= ( hAPP_f22106695ol_nat @ finite_card_nat @ B ) ) )
& ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ B ) )
=> ( ( hAPP_f22106695ol_nat @ finite_card_nat @ ( insert_nat @ A @ B ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_f22106695ol_nat @ finite_card_nat @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(74,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) @ C ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_604_le__diff__conv) ).
thf(1129,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ B ) ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(615,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( B = A )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_523_xt1_I4_J) ).
thf(2966,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( B = A )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(471,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B
= ( hAPP_a_nat @ C @ D ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ D ) @ A ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ ( image_a_nat @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_image__eqI) ).
thf(2430,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B
= ( hAPP_a_nat @ C @ D ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ D ) @ A ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ ( image_a_nat @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(709,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_rev__finite__subset) ).
thf(3360,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(154,axiom,
! [A: $i,B: $i] :
( ! [C: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ ( hAPP_nat_nat @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ ( cOMBB_800536526ol_nat @ ord_less_eq_nat @ B ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_566_finite__less__ub) ).
thf(1378,plain,
! [A: $i,B: $i] :
( ! [C: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ ( hAPP_nat_nat @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ ( cOMBB_800536526ol_nat @ ord_less_eq_nat @ B ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(217,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281_set__rev__mp) ).
thf(1582,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(421,axiom,
! [A: $i,B: $i] :
( ( insert_fun_nat_bool @ A @ ( collect_fun_nat_bool @ B ) )
= ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fimplies @ ( cOMBB_238756964t_bool @ fNot @ ( hAPP_f103356543l_bool @ ( cOMBC_1693257480l_bool @ fequal_fun_nat_bool ) @ A ) ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_insert__Collect) ).
thf(2265,plain,
! [A: $i,B: $i] :
( ( insert_fun_nat_bool @ A @ ( collect_fun_nat_bool @ B ) )
= ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fimplies @ ( cOMBB_238756964t_bool @ fNot @ ( hAPP_f103356543l_bool @ ( cOMBC_1693257480l_bool @ fequal_fun_nat_bool ) @ A ) ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(334,axiom,
! [A: $i,B: $i] :
( ( is_a @ B )
=> ( is_fun1661590463l_bool @ ( hAPP_a217006258l_bool @ A @ B ) ) ),
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(1976,plain,
! [A: $i,B: $i] :
( ( is_a @ B )
=> ( is_fun1661590463l_bool @ ( hAPP_a217006258l_bool @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(207,axiom,
! [A: $i,B: $i] :
( ( ( is_fun_pname_bool @ A )
& ( is_fun_pname_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_517_order__antisym) ).
thf(1550,plain,
! [A: $i,B: $i] :
( ( ( is_fun_pname_bool @ A )
& ( is_fun_pname_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(423,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_a_fun_a_bool @ ( cOMBB_a_fun_a_bool_a @ A @ B ) @ C )
= ( hAPP_a_fun_a_bool @ A @ ( hAPP_a_a @ B @ C ) ) ),
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(2270,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_a_fun_a_bool @ ( cOMBB_a_fun_a_bool_a @ A @ B ) @ C )
= ( hAPP_a_fun_a_bool @ A @ ( hAPP_a_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(904,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_876012084bool_a @ A @ B ) ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_card__image__le) ).
thf(4088,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_876012084bool_a @ A @ B ) ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).
thf(853,axiom,
! [A: $i,B: $i,C: $i] :
( ( is_fun_a_bool @ C )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ C ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C ) @ ( image_fun_a_bool_a @ A @ B ) ) )
=> ? [D: $i] :
( ( is_fun949378684l_bool @ D )
& ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ D ) @ B ) )
& ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ D ) )
& ( C
= ( image_fun_a_bool_a @ A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_finite__subset__image) ).
thf(3901,plain,
! [A: $i,B: $i,C: $i] :
( ( is_fun_a_bool @ C )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ C ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C ) @ ( image_fun_a_bool_a @ A @ B ) ) )
=> ? [D: $i] :
( ( is_fun949378684l_bool @ D )
& ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ D ) @ B ) )
& ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ D ) )
& ( C
= ( image_fun_a_bool_a @ A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).
thf(527,axiom,
! [A: $i,B: $i,C: $i] :
( ( is_fun_a_bool @ A )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ ( image_nat_a @ B @ C ) ) )
<=> ? [D: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ D ) @ C ) )
& ( A
= ( image_nat_a @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_344_subset__image__iff) ).
thf(2640,plain,
! [A: $i,B: $i,C: $i] :
( ( is_fun_a_bool @ A )
=> ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ ( image_nat_a @ B @ C ) ) )
=> ? [D: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ D ) @ C ) )
& ( A
= ( image_nat_a @ B @ D ) ) ) )
& ( ? [D: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ D ) @ C ) )
& ( A
= ( image_nat_a @ B @ D ) ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ ( image_nat_a @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(135,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_nat_bool @ ( hAPP_a_fun_nat_bool @ ( cOMBC_nat_a_bool @ A ) @ B ) @ C )
= ( hAPP_a_bool @ ( hAPP_nat_fun_a_bool @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000t__a_000tc__HOL__Obool_U) ).
thf(1320,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_nat_bool @ ( hAPP_a_fun_nat_bool @ ( cOMBC_nat_a_bool @ A ) @ B ) @ C )
= ( hAPP_a_bool @ ( hAPP_nat_fun_a_bool @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(322,axiom,
! [A: $i,B: $i] :
( ( is_fun_pname_bool @ B )
=> ( is_fun_pname_bool @ ( image_pname_pname @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__Com__Opname_000tc__Com__Opname) ).
thf(1944,plain,
! [A: $i,B: $i] :
( ( is_fun_pname_bool @ B )
=> ( is_fun_pname_bool @ ( image_pname_pname @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(329,axiom,
! [A: $i] :
( ( is_fun_a_bool @ A )
=> ( is_fun_a_bool @ ( collect_a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_OCollect_000t__a) ).
thf(1962,plain,
! [A: $i] :
( ( is_fun_a_bool @ A )
=> ( is_fun_a_bool @ ( collect_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(593,axiom,
! [A: $i] :
( ! [B: $i] :
~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ A ) )
<=> ( A = bot_bot_fun_nat_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_416_all__not__in__conv) ).
thf(2887,plain,
! [A: $i] :
( ( ! [B: $i] :
~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ A ) )
=> ( A = bot_bot_fun_nat_bool ) )
& ( ( A = bot_bot_fun_nat_bool )
=> ! [B: $i] :
~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(538,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
=> ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_finite__subset) ).
thf(2690,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
=> ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(473,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ A ) @ B ) ) ) )
<=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ A ) ) )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_finite__Collect__disjI) ).
thf(2436,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ A ) @ B ) ) ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ A ) ) )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ B ) ) ) ) )
& ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ A ) ) )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ B ) ) ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(731,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
& ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_553_order__eq__iff) ).
thf(3432,plain,
! [A: $i,B: $i] :
( ( ( A = B )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
& ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
& ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).
thf(370,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_n850744903l_bool @ ( cOMBB_2117322052ol_nat @ A @ B ) @ C )
= ( hAPP_f434788991l_bool @ A @ ( hAPP_n1025906991e_bool @ B @ C ) ) ),
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(2087,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_n850744903l_bool @ ( cOMBB_2117322052ol_nat @ A @ B ) @ C )
= ( hAPP_f434788991l_bool @ A @ ( hAPP_n1025906991e_bool @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(186,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ C ) )
=> ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ C ) @ ( image_26036933t_bool @ A @ B ) ) )
=> ? [D: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ D ) @ B ) )
& ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ D ) )
& ( C
= ( image_26036933t_bool @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_finite__subset__image) ).
thf(1468,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ C ) )
=> ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ C ) @ ( image_26036933t_bool @ A @ B ) ) )
=> ? [D: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ D ) @ B ) )
& ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ D ) )
& ( C
= ( image_26036933t_bool @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(803,axiom,
! [A: $i,B: $i] :
( ( ( is_fun_a_bool @ A )
& ( is_fun_a_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ A ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_equalityI) ).
thf(3721,plain,
! [A: $i,B: $i] :
( ( ( is_fun_a_bool @ A )
& ( is_fun_a_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ A ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).
thf(635,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ C )
<=> ( hBOOL @ B ) )
=> ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ A ) )
=> ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_535_ord__eq__le__trans) ).
thf(3035,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hBOOL @ C )
=> ( hBOOL @ B ) )
& ( ( hBOOL @ B )
=> ( hBOOL @ C ) ) )
=> ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ A ) )
=> ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(508,axiom,
! [A: $i,B: $i] :
( ( ( is_a @ A )
& ( is_a @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ ( insert_a @ B @ bot_bot_fun_a_bool ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_451_singletonE) ).
thf(2563,plain,
! [A: $i,B: $i] :
( ( ( is_a @ A )
& ( is_a @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ ( insert_a @ B @ bot_bot_fun_a_bool ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(860,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_pname_pname @ A @ B ) ) )
=> ? [C: $i] :
( ( is_pname @ C )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ ( hAPP_f759274231e_bool @ ( cOMBC_1058051404l_bool @ member_pname ) @ B ) ) @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ ( cOMBB_542850580_pname @ fequal_pname @ A ) ) @ ( hAPP_pname_pname @ A @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_pigeonhole__infinite) ).
thf(3924,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_pname_pname @ A @ B ) ) )
=> ? [C: $i] :
( ( is_pname @ C )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ ( hAPP_f759274231e_bool @ ( cOMBC_1058051404l_bool @ member_pname ) @ B ) ) @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ ( cOMBB_542850580_pname @ fequal_pname @ A ) ) @ ( hAPP_pname_pname @ A @ C ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).
thf(8,axiom,
! [A: $i] :
( ( hAPP_nat_nat @ suc @ A )
= ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ one_one_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_606_Suc__eq__plus1) ).
thf(935,plain,
! [A: $i] :
( ( hAPP_nat_nat @ suc @ A )
= ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ one_one_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_621_trans__less__add2) ).
thf(1009,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(257,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_a_bool @ ( hAPP_nat_fun_a_bool @ ( cOMBC_a_nat_bool @ A ) @ B ) @ C )
= ( hAPP_nat_bool @ ( hAPP_a_fun_nat_bool @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000t__a_000tc__Nat__Onat_000tc__HOL__Obool_U) ).
thf(1737,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_a_bool @ ( hAPP_nat_fun_a_bool @ ( cOMBC_a_nat_bool @ A ) @ B ) @ C )
= ( hAPP_nat_bool @ ( hAPP_a_fun_nat_bool @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(841,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ D ) )
=> ( ( A
= ( hAPP_nat_a @ B @ C ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ ( image_nat_a @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_rev__image__eqI) ).
thf(3854,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ D ) )
=> ( ( A
= ( hAPP_nat_a @ B @ C ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ ( image_nat_a @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).
thf(405,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ A ) @ B ) @ C )
= ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ A @ C ) @ B ) ),
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(2206,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ A ) @ B ) @ C )
= ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(350,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_592_add__leD2) ).
thf(2018,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(576,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_a_a @ A @ B ) ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_card__image__le) ).
thf(2832,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_a_a @ A @ B ) ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(412,axiom,
! [A: $i,B: $i] :
( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_580_diff__add__inverse) ).
thf(2238,plain,
! [A: $i,B: $i] :
( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(191,axiom,
! [A: $i,B: $i] :
( ( is_bool @ A )
=> ( ( hAPP_f1664156314l_bool @ ( cOMBK_1857069011e_bool @ A ) @ B )
= 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(1490,plain,
! [A: $i,B: $i] :
( ( is_bool @ A )
=> ( ( hAPP_f1664156314l_bool @ ( cOMBK_1857069011e_bool @ A ) @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(732,axiom,
! [A: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_266_subset__refl) ).
thf(3443,plain,
! [A: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(640,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ A ) @ B ) )
| ( hBOOL @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
thf(3052,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ A ) @ B ) )
| ( hBOOL @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(781,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
=> ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( image_112932426a_bool @ A @ B ) ) )
=> ? [C: $i] :
( ( is_pname @ C )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ ( hAPP_f759274231e_bool @ ( cOMBC_1058051404l_bool @ member_pname ) @ B ) ) @ ( hAPP_f1794073134e_bool @ ( cOMBC_445755039l_bool @ ( cOMBB_392435466_pname @ fequal_fun_a_bool @ A ) ) @ ( hAPP_p1534023578a_bool @ A @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_pigeonhole__infinite) ).
thf(3637,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
=> ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( image_112932426a_bool @ A @ B ) ) )
=> ? [C: $i] :
( ( is_pname @ C )
& ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ B ) )
& ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ ( hAPP_f759274231e_bool @ ( cOMBC_1058051404l_bool @ member_pname ) @ B ) ) @ ( hAPP_f1794073134e_bool @ ( cOMBC_445755039l_bool @ ( cOMBB_392435466_pname @ fequal_fun_a_bool @ A ) ) @ ( hAPP_p1534023578a_bool @ A @ C ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).
thf(577,axiom,
! [A: $i,B: $i] :
( ( A != B )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ 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(2834,plain,
! [A: $i,B: $i] :
( ( A != B )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(65,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_diff__le__self) ).
thf(1088,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(169,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_587_nat__add__left__cancel__le) ).
thf(1417,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ ( hAPP_pname_nat @ A @ B ) ) @ ( image_pname_nat @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_303_imageI) ).
thf(972,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ ( hAPP_pname_nat @ A @ B ) ) @ ( image_pname_nat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(560,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( image_a_nat @ A @ B ) ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_card__image__le) ).
thf(2771,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( image_a_nat @ A @ B ) ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(4298,plain,
$false,
inference(cvc4,[status(thm)],[2163,3873,2452,2612,2778,1767,3930,1559,2559,1179,3566,1295,1956,3345,4005,2109,2131,2031,4022,1729,2921,3477,2463,1899,1850,2499,962,2427,2480,2280,3172,3534,1750,3990,2381,1073,3910,3012,2099,1793,2512,2976,3072,1005,1068,3858,2808,3762,1808,2659,3417,3509,1618,3040,3153,2590,1401,1422,1569,1939,3959,1142,1269,3794,1756,3367,2184,2434,1342,1458,2195,1705,4090,1655,3049,3745,1137,3365,2740,2918,4026,3044,1164,1999,3616,1233,2476,1260,1988,3826,2459,2901,945,3895,2360,1095,1746,3629,1001,2972,3502,1046,1645,1359,1386,3898,4030,1366,2067,3880,1623,3915,1782,2020,3513,1904,1703,2654,3263,2328,1985,3275,4070,3689,3495,1871,3061,3617,3485,3542,1191,3353,1462,2703,3248,3204,1055,1409,1323,3612,3845,4023,3089,2126,3803,2466,949,3713,2420,1514,1013,3014,2024,1494,2852,1847,3788,4119,3998,3463,3385,2373,3919,1115,3470,3557,1875,2456,1664,3934,3724,2259,2650,2236,3525,3771,2616,1946,1465,3966,1714,2105,4072,1811,1450,4018,2090,3393,1911,2782,1109,2469,1334,3527,2880,1682,1828,1978,2291,1383,1020,2555,3300,3093,2335,966,1283,2073,3739,2861,1896,1886,1796,2371,2137,2002,2799,3327,1201,3406,2884,3986,2058,1447,956,2103,1405,1104,1697,3606,2392,1863,2954,2011,1438,1306,2118,1708,4076,2790,2773,3591,2910,3984,3169,925,1199,2364,3995,2047,3318,1311,3767,2296,1057,3679,1723,3261,2249,3867,1580,1255,2147,1666,2606,2150,3814,2396,2601,3827,3711,4016,1042,2541,1174,2133,3339,3778,2015,1883,1560,2958,916,2758,1920,4053,1951,3718,1819,1159,1210,2213,974,3445,3980,1837,2670,3810,3403,1968,2332,2826,2820,1195,1407,2547,2344,3727,2741,3667,2228,3408,1740,1983,2377,1953,2841,1540,2631,2724,3632,2268,989,3968,1350,3467,3784,1762,3254,3122,2990,1804,3862,2577,3381,2709,1227,2692,1587,2694,1425,2509,3102,2638,4109,3018,1397,1567,2877,1361,2323,1292,3596,1075,1584,3032,2666,3555,2317,1028,1082,2023,1964,1659,2312,2455,1414,2053,1791,3428,1207,3671,2085,1612,1039,970,3242,1456,3743,1974,2243,1932,3222,2566,1246,3333,1720,3703,1825,1776,1263,997,3656,1478,2519,2536,2681,2487,3059,1266,4068,1060,1050,984,2505,3390,3109,3074,3201,1759,1393,3454,3755,1318,2926,2203,1563,2408,1167,3841,1185,2529,3807,3824,2749,1434,938,3225,2076,1170,2963,3321,2189,1616,2995,1996,3675,1278,1764,1146,1959,3871,3042,2717,3491,1273,2570,1927,3289,3375,3686,3396,2936,1648,3707,1510,2894,1374,3741,3070,1916,3234,3504,1784,3240,2849,3086,3945,2398,3604,1124,1488,3599,3536,1154,4000,975,3387,2970,1007,3319,1620,3472,3283,2674,1388,4122,958,1403,2959,3213,1428,3751,2326,2293,2738,3663,1239,3532,1139,3796,1786,3023,1271,2308,2442,2753,3783,1092,4060,2706,2166,1090,1897,919,3641,3091,947,1194,2538,3155,3238,3551,2116,1801,3500,2478,3251,2415,2987,1806,1011,3957,3287,3419,1048,2257,1589,2246,1603,2299,3586,1690,3182,2871,1376,2197,4107,2182,3747,3055,2129,2111,2780,1162,3006,1149,915,1344,2252,2974,932,1820,1112,2812,1080,1339,3027,1630,1993,2410,2923,1556,1460,2289,2278,2553,1528,1643,3917,2139,2101,1726,1496,3178,2999,2069,1594,1699,1213,3838,2765,1044,2550,4085,3159,2369,1015,3953,3016,1694,922,3936,3576,2503,2124,2629,1990,968,2914,2816,1134,3146,4113,2846,1018,2582,3571,2942,1845,4035,3507,3913,2012,3833,1780,1531,1230,1547,1748,1003,1770,2863,3315,1070,3112,2375,1156,2060,1743,2732,1941,1368,3228,1753,3786,2386,3448,3885,3063,2337,1901,1085,3564,3715,1711,3080,1053,1499,2092,4092,1300,1637,3273,3791,1188,2700,2276,3801,1980,2903,2545,3847,3329,2044,1285,1218,1336,3769,2056,3697,1023,2379,2543,1221,4046,978,1717,1372,1881,3520,3684,1543,3107,4057,3652,1257,2838,3970,3829,2992,1536,1353,2145,1485,2320,4106,2760,3400,3139,3452,3589,2818,1966,1685,1553,1949,1817,1834,976,3188,1412,1517,3665,2865,2875,2626,1918,3457,2611,3928,1216,2209,2743,2997,2490,4102,2187,1390,2305,2342,1289,1453,1866,2071,2775,1734,2907,1276,1326,2273,2283,2855,2853,2135,3336,2004,2608,1822,3780,2394,1062,2532,1508,3369,2823,3220,1523,3859,995,2934,2152,2262,2944,1030,2796,3497,1308,3529,3351,1661,4074,2623,1614,2384,3694,2648,3430,1440,3149,1077,3677,2162,2230,1893,2036,4098,1444,2930,1512,1280,1578,2534,950,2233,3882,1380,2768,2142,3379,3992,1908,4039,1348,999,2287,2302,2683,3291,3907,2983,2719,2008,1303,3132,1248,2050,2636,4051,1363,4007,4083,1789,2366,3323,1473,2619,2063,2651,1436,1859,1172,3479,2417,1033,2961,1197,2714,3196,3426,1891,1930,3244,3974,1152,3057,2898,4066,992,3817,2507,1925,1597,2484,1236,2241,987,2159,3362,1829,1129,2966,2430,3360,1378,1582,2265,1976,1550,2270,4088,3901,2640,1320,1944,1962,2887,2690,2436,3432,2087,1468,3721,3035,2563,3924,935,1009,1737,3854,2206,2018,2832,2238,1490,3443,3052,3637,2834,1088,1417,972,2771]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW473+2 : TPTP v8.1.2. Released v5.3.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n028.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu May 18 22:56:49 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.83/0.87 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.64/1.14 % [INFO] Parsing done (268ms).
% 1.64/1.14 % [INFO] Running in sequential loop mode.
% 2.52/1.36 % [INFO] eprover registered as external prover.
% 2.52/1.36 % [INFO] cvc4 registered as external prover.
% 2.52/1.37 % [INFO] Scanning for conjecture ...
% 3.13/1.51 % [INFO] Found a conjecture and 916 axioms. Running axiom selection ...
% 3.98/1.74 % [INFO] Axiom selection finished. Selected 912 axioms (removed 4 axioms).
% 5.25/2.07 % [INFO] Problem is first-order (TPTP FOF).
% 5.30/2.10 % [INFO] Type checking passed.
% 5.30/2.10 % [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 ...
% 22.45/6.05 % External prover 'cvc4' found a proof!
% 22.45/6.05 % [INFO] Killing All external provers ...
% 22.45/6.05 % Time passed: 5531ms (effective reasoning time: 4904ms)
% 22.45/6.05 % 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)>
% 22.45/6.06 % 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
% 22.45/6.06 % No. of inferences in proof: 1828
% 22.45/6.06 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 5531 ms resp. 4904 ms w/o parsing
% 23.66/6.44 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 23.66/6.44 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------