%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SCT171+1 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:27:27 AM UTC 2026
% Result : Theorem 16.02s 5.01s
% Output : Refutation 17.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 322
% Syntax : Number of formulae : 646 ( 240 unt; 0 typ; 0 def)
% Number of atoms : 1755 ( 327 equ; 0 cnn)
% Maximal formula atoms : 28 ( 2 avg)
% Number of connectives : 8592 ( 260 ~; 21 |; 185 &;7223 @)
% ( 50 <=>; 853 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 229 ( 227 usr; 63 con; 0-2 aty)
% Number of variables : 1387 ( 0 ^;1385 !; 2 ?;1387 :)
% Comments :
%------------------------------------------------------------------------------
thf(hBOOL_decl,type,
hBOOL: $i > $o ).
thf(hAPP_f745298353l_bool_decl,type,
hAPP_f745298353l_bool: $i > $i > $i ).
thf(member1056080916le_alt_decl,type,
member1056080916le_alt: $i > $i ).
thf(produc171383831le_alt_decl,type,
produc171383831le_alt: $i > $i > $i ).
thf(c_decl,type,
c: $i ).
thf(d_decl,type,
d: $i ).
thf(hAPP_f695124765t_bool_decl,type,
hAPP_f695124765t_bool: $i > $i > $i ).
thf(f_decl,type,
f: $i ).
thf(p_decl,type,
p: $i ).
thf(hAPP_A1333445289t_bool_decl,type,
hAPP_A1333445289t_bool: $i > $i > $i ).
thf(cOMBS_102864562t_bool_decl,type,
cOMBS_102864562t_bool: $i > $i > $i ).
thf(hAPP_f159424297t_bool_decl,type,
hAPP_f159424297t_bool: $i > $i > $i ).
thf(hAPP_A869356733t_bool_decl,type,
hAPP_A869356733t_bool: $i > $i > $i ).
thf(hAPP_A1374816149t_bool_decl,type,
hAPP_A1374816149t_bool: $i > $i > $i ).
thf(is_fun282293932t_bool_decl,type,
is_fun282293932t_bool: $i > $o ).
thf(hAPP_f1673487381t_bool_decl,type,
hAPP_f1673487381t_bool: $i > $i > $i ).
thf(hAPP_b1915039793t_bool_decl,type,
hAPP_b1915039793t_bool: $i > $i > $i ).
thf(if_fun1419651289t_bool_decl,type,
if_fun1419651289t_bool: $i ).
thf(fFalse_decl,type,
fFalse: $i ).
thf(cOMBC_481590946t_bool_decl,type,
cOMBC_481590946t_bool: $i > $i > $i ).
thf(is_fun959573582l_bool_decl,type,
is_fun959573582l_bool: $i > $o ).
thf(collec1580242420t_bool_decl,type,
collec1580242420t_bool: $i > $i ).
thf(hAPP_f1507266205t_bool_decl,type,
hAPP_f1507266205t_bool: $i > $i > $i ).
thf(cOMBK_1152753196e_indi_decl,type,
cOMBK_1152753196e_indi: $i ).
thf(is_fun917378774i_bool_decl,type,
is_fun917378774i_bool: $i > $o ).
thf(top_to1256827021i_bool_decl,type,
top_to1256827021i_bool: $i ).
thf(cOMBC_277798809t_bool_decl,type,
cOMBC_277798809t_bool: $i > $i > $i ).
thf(is_fun631676118l_bool_decl,type,
is_fun631676118l_bool: $i > $o ).
thf(top_to40512653l_bool_decl,type,
top_to40512653l_bool: $i ).
thf(hAPP_b1719629739l_bool_decl,type,
hAPP_b1719629739l_bool: $i > $i > $i ).
thf(hAPP_f371807573l_bool_decl,type,
hAPP_f371807573l_bool: $i > $i > $i ).
thf(cOMBK_697604314l_bool_decl,type,
cOMBK_697604314l_bool: $i ).
thf(top_to2005687013l_bool_decl,type,
top_to2005687013l_bool: $i ).
thf(collec874260222t_bool_decl,type,
collec874260222t_bool: $i > $i ).
thf(hAPP_b1965422783l_bool_decl,type,
hAPP_b1965422783l_bool: $i > $i > $i ).
thf(cOMBK_977355664t_bool_decl,type,
cOMBK_977355664t_bool: $i ).
thf(fTrue_decl,type,
fTrue: $i ).
thf(is_Arr553848933le_alt_decl,type,
is_Arr553848933le_alt: $i > $o ).
thf(b_decl,type,
b: $i ).
thf(arrow_413697182e_Prof_decl,type,
arrow_413697182e_Prof: $i ).
thf(hAPP_f355113919i_bool_decl,type,
hAPP_f355113919i_bool: $i > $i > $i ).
thf(hAPP_f1677452273i_bool_decl,type,
hAPP_f1677452273i_bool: $i > $i > $i ).
thf(cOMBK_1372975190t_bool_decl,type,
cOMBK_1372975190t_bool: $i ).
thf(pi_fun433100839t_bool_decl,type,
pi_fun433100839t_bool: $i > $i > $i ).
thf(collec1520786044t_bool_decl,type,
collec1520786044t_bool: $i > $i ).
thf(hAPP_b990649139l_bool_decl,type,
hAPP_b990649139l_bool: $i > $i > $i ).
thf(cOMBK_580911210t_bool_decl,type,
cOMBK_580911210t_bool: $i ).
thf(hAPP_f497468491l_bool_decl,type,
hAPP_f497468491l_bool: $i > $i > $i ).
thf(hAPP_f1235573641l_bool_decl,type,
hAPP_f1235573641l_bool: $i > $i > $i ).
thf(cOMBK_1072228194t_bool_decl,type,
cOMBK_1072228194t_bool: $i ).
thf(hAPP_f352490559i_bool_decl,type,
hAPP_f352490559i_bool: $i > $i > $i ).
thf(hAPP_f1903519657i_bool_decl,type,
hAPP_f1903519657i_bool: $i > $i > $i ).
thf(cOMBK_2076140708t_bool_decl,type,
cOMBK_2076140708t_bool: $i ).
thf(is_bool_decl,type,
is_bool: $i > $o ).
thf(hAPP_f453661011l_bool_decl,type,
hAPP_f453661011l_bool: $i > $i > $i ).
thf(top_to2034604131t_bool_decl,type,
top_to2034604131t_bool: $i ).
thf(hAPP_f483434675l_bool_decl,type,
hAPP_f483434675l_bool: $i > $i > $i ).
thf(is_fun432044380l_bool_decl,type,
is_fun432044380l_bool: $i > $o ).
thf(hAPP_f503012287l_bool_decl,type,
hAPP_f503012287l_bool: $i > $i > $i ).
thf(hAPP_f1012384989l_bool_decl,type,
hAPP_f1012384989l_bool: $i > $i > $i ).
thf(hAPP_f1550037191l_bool_decl,type,
hAPP_f1550037191l_bool: $i > $i > $i ).
thf(top_to1194196741l_bool_decl,type,
top_to1194196741l_bool: $i ).
thf(arrow_1239002508le_Lin_decl,type,
arrow_1239002508le_Lin: $i ).
thf(hAPP_A702630576t_bool_decl,type,
hAPP_A702630576t_bool: $i > $i > $i ).
thf(cOMBB_1292070696e_indi_decl,type,
cOMBB_1292070696e_indi: $i > $i > $i ).
thf(hAPP_f1290184496t_bool_decl,type,
hAPP_f1290184496t_bool: $i > $i > $i ).
thf(hAPP_f234874197l_bool_decl,type,
hAPP_f234874197l_bool: $i > $i > $i ).
thf(hAPP_P2075002375t_bool_decl,type,
hAPP_P2075002375t_bool: $i > $i > $i ).
thf(hAPP_b1024867081t_bool_decl,type,
hAPP_b1024867081t_bool: $i > $i > $i ).
thf(cOMBK_2069093696le_alt_decl,type,
cOMBK_2069093696le_alt: $i ).
thf(hAPP_nat_bool_decl,type,
hAPP_nat_bool: $i > $i > $i ).
thf(pi_Pro2135156861t_bool_decl,type,
pi_Pro2135156861t_bool: $i > $i > $i ).
thf(hAPP_f1724001331l_bool_decl,type,
hAPP_f1724001331l_bool: $i > $i > $i ).
thf(cOMBK_2008994872le_alt_decl,type,
cOMBK_2008994872le_alt: $i ).
thf(top_to1647826457l_bool_decl,type,
top_to1647826457l_bool: $i ).
thf(hAPP_f749892423i_bool_decl,type,
hAPP_f749892423i_bool: $i > $i > $i ).
thf(collec45183100e_indi_decl,type,
collec45183100e_indi: $i > $i ).
thf(is_fun1016509681e_indi_decl,type,
is_fun1016509681e_indi: $i > $o ).
thf(hilber1792103167di_nat_decl,type,
hilber1792103167di_nat: $i > $i > $i ).
thf(hAPP_P907763049i_bool_decl,type,
hAPP_P907763049i_bool: $i > $i > $i ).
thf(hAPP_f1970593179i_bool_decl,type,
hAPP_f1970593179i_bool: $i > $i > $i ).
thf(cOMBK_100791596le_alt_decl,type,
cOMBK_100791596le_alt: $i ).
thf(hAPP_b1018211123i_bool_decl,type,
hAPP_b1018211123i_bool: $i > $i > $i ).
thf(cOMBK_1157044842e_indi_decl,type,
cOMBK_1157044842e_indi: $i ).
thf(hAPP_A1944296755l_bool_decl,type,
hAPP_A1944296755l_bool: $i > $i > $i ).
thf(hAPP_f1979025587l_bool_decl,type,
hAPP_f1979025587l_bool: $i > $i > $i ).
thf(cOMBK_1158753900e_indi_decl,type,
cOMBK_1158753900e_indi: $i ).
thf(hAPP_f387058535l_bool_decl,type,
hAPP_f387058535l_bool: $i > $i > $i ).
thf(hAPP_f1636546729l_bool_decl,type,
hAPP_f1636546729l_bool: $i > $i > $i ).
thf(hAPP_A1466488369i_bool_decl,type,
hAPP_A1466488369i_bool: $i > $i > $i ).
thf(hAPP_A1922697556t_bool_decl,type,
hAPP_A1922697556t_bool: $i > $i > $i ).
thf(pi_Arr688267935t_bool_decl,type,
pi_Arr688267935t_bool: $i > $i > $i ).
thf(hAPP_f592909149l_bool_decl,type,
hAPP_f592909149l_bool: $i > $i > $i ).
thf(cOMBC_437064334t_bool_decl,type,
cOMBC_437064334t_bool: $i > $i > $i ).
thf(is_Arr625519182e_indi_decl,type,
is_Arr625519182e_indi: $i > $o ).
thf(undefi818645567e_indi_decl,type,
undefi818645567e_indi: $i > $i ).
thf(arrow_2110637339e_indi_decl,type,
arrow_2110637339e_indi: $i ).
thf(a_decl,type,
a: $i ).
thf(lba_decl,type,
lba: $i ).
thf(hAPP_f204273237l_bool_decl,type,
hAPP_f204273237l_bool: $i > $i > $i ).
thf(hAPP_f919661787l_bool_decl,type,
hAPP_f919661787l_bool: $i > $i > $i ).
thf(hAPP_bool_bool_decl,type,
hAPP_bool_bool: $i > $i > $i ).
thf(hAPP_f1818473245e_indi_decl,type,
hAPP_f1818473245e_indi: $i > $i > $i ).
thf(hAPP_f1895985727l_bool_decl,type,
hAPP_f1895985727l_bool: $i > $i > $i ).
thf(undefi802509179t_bool_decl,type,
undefi802509179t_bool: $i > $i ).
thf(fun_decl,type,
fun: $i > $i > $i ).
thf(product_prod_decl,type,
product_prod: $i > $i > $i ).
thf(arrow_1812558424le_alt_decl,type,
arrow_1812558424le_alt: $i ).
thf(bool_decl,type,
bool: $i ).
thf(arrow_467566751nimity_decl,type,
arrow_467566751nimity: $i ).
thf(undefi1301554228le_alt_decl,type,
undefi1301554228le_alt: $i > $i ).
thf(hAPP_P2127852789l_bool_decl,type,
hAPP_P2127852789l_bool: $i > $i > $i ).
thf(hAPP_f618619045e_indi_decl,type,
hAPP_f618619045e_indi: $i > $i > $i ).
thf(hAPP_f313042899l_bool_decl,type,
hAPP_f313042899l_bool: $i > $i > $i ).
thf(hAPP_f219827985l_bool_decl,type,
hAPP_f219827985l_bool: $i > $i > $i ).
thf(cOMBK_886533338t_bool_decl,type,
cOMBK_886533338t_bool: $i ).
thf(hAPP_f2056167603l_bool_decl,type,
hAPP_f2056167603l_bool: $i > $i > $i ).
thf(lab_decl,type,
lab: $i ).
thf(cOMBC_1778077589t_bool_decl,type,
cOMBC_1778077589t_bool: $i > $i > $i ).
thf(hAPP_A619995676t_bool_decl,type,
hAPP_A619995676t_bool: $i > $i > $i ).
thf(hAPP_f417299659l_bool_decl,type,
hAPP_f417299659l_bool: $i > $i > $i ).
thf(hAPP_f1667233577l_bool_decl,type,
hAPP_f1667233577l_bool: $i > $i > $i ).
thf(cOMBK_1015076504t_bool_decl,type,
cOMBK_1015076504t_bool: $i ).
thf(hAPP_n385347014e_indi_decl,type,
hAPP_n385347014e_indi: $i > $i > $i ).
thf(hAPP_A1964572607l_bool_decl,type,
hAPP_A1964572607l_bool: $i > $i > $i ).
thf(hAPP_f1697527281l_bool_decl,type,
hAPP_f1697527281l_bool: $i > $i > $i ).
thf(cOMBK_1292462166e_indi_decl,type,
cOMBK_1292462166e_indi: $i ).
thf(hAPP_f1659504677e_indi_decl,type,
hAPP_f1659504677e_indi: $i > $i > $i ).
thf(hAPP_f1766869725l_bool_decl,type,
hAPP_f1766869725l_bool: $i > $i > $i ).
thf(hAPP_f448497509l_bool_decl,type,
hAPP_f448497509l_bool: $i > $i > $i ).
thf(cOMBK_1268833122l_bool_decl,type,
cOMBK_1268833122l_bool: $i ).
thf(hAPP_f861484971l_bool_decl,type,
hAPP_f861484971l_bool: $i > $i > $i ).
thf(hAPP_f20355883l_bool_decl,type,
hAPP_f20355883l_bool: $i > $i > $i ).
thf(cOMBK_1088865252t_bool_decl,type,
cOMBK_1088865252t_bool: $i ).
thf(hAPP_f526292585l_bool_decl,type,
hAPP_f526292585l_bool: $i > $i > $i ).
thf(cOMBK_789167586t_bool_decl,type,
cOMBK_789167586t_bool: $i ).
thf(hAPP_f1279200745l_bool_decl,type,
hAPP_f1279200745l_bool: $i > $i > $i ).
thf(hAPP_f785543729l_bool_decl,type,
hAPP_f785543729l_bool: $i > $i > $i ).
thf(hAPP_f1520552209t_bool_decl,type,
hAPP_f1520552209t_bool: $i > $i > $i ).
thf(cOMBK_697786936l_bool_decl,type,
cOMBK_697786936l_bool: $i ).
thf(cOMBB_317992461e_indi_decl,type,
cOMBB_317992461e_indi: $i > $i > $i ).
thf(hAPP_n1699378549t_bool_decl,type,
hAPP_n1699378549t_bool: $i > $i > $i ).
thf(hAPP_A588601142di_nat_decl,type,
hAPP_A588601142di_nat: $i > $i > $i ).
thf(collec1711870802le_alt_decl,type,
collec1711870802le_alt: $i > $i ).
thf(hAPP_f1018082273l_bool_decl,type,
hAPP_f1018082273l_bool: $i > $i > $i ).
thf(hAPP_A1912483895l_bool_decl,type,
hAPP_A1912483895l_bool: $i > $i > $i ).
thf(arrow_1212118780le_IIA_decl,type,
arrow_1212118780le_IIA: $i ).
thf(cOMBC_493523632t_bool_decl,type,
cOMBC_493523632t_bool: $i > $i > $i ).
thf(hAPP_A384644407t_bool_decl,type,
hAPP_A384644407t_bool: $i > $i > $i ).
thf(hAPP_A460042315t_bool_decl,type,
hAPP_A460042315t_bool: $i > $i > $i ).
thf(hAPP_f460310451l_bool_decl,type,
hAPP_f460310451l_bool: $i > $i > $i ).
thf(hAPP_f1271180905l_bool_decl,type,
hAPP_f1271180905l_bool: $i > $i > $i ).
thf(inj_on24934938di_nat_decl,type,
inj_on24934938di_nat: $i > $i > $i ).
thf(top_top_bool_decl,type,
top_top_bool: $i ).
thf(cOMBB_69933763e_indi_decl,type,
cOMBB_69933763e_indi: $i > $i > $i ).
thf(hAPP_f1336478923t_bool_decl,type,
hAPP_f1336478923t_bool: $i > $i > $i ).
thf(hAPP_f500145249l_bool_decl,type,
hAPP_f500145249l_bool: $i > $i > $i ).
thf(cOMBB_963584201e_indi_decl,type,
cOMBB_963584201e_indi: $i > $i > $i ).
thf(hAPP_f213304539l_bool_decl,type,
hAPP_f213304539l_bool: $i > $i > $i ).
thf(hAPP_f813556705l_bool_decl,type,
hAPP_f813556705l_bool: $i > $i > $i ).
thf(cOMBK_116240846e_indi_decl,type,
cOMBK_116240846e_indi: $i ).
thf(cOMBS_867867294t_bool_decl,type,
cOMBS_867867294t_bool: $i > $i > $i ).
thf(hAPP_P2024088443e_indi_decl,type,
hAPP_P2024088443e_indi: $i > $i > $i ).
thf(hAPP_f681113465i_bool_decl,type,
hAPP_f681113465i_bool: $i > $i > $i ).
thf(cOMBK_454107598t_bool_decl,type,
cOMBK_454107598t_bool: $i ).
thf(hAPP_f2135750719l_bool_decl,type,
hAPP_f2135750719l_bool: $i > $i > $i ).
thf(cOMBK_971068024l_bool_decl,type,
cOMBK_971068024l_bool: $i ).
thf(e_decl,type,
e: $i ).
thf(ord_less_nat_decl,type,
ord_less_nat: $i ).
thf(hAPP_f1710416135l_bool_decl,type,
hAPP_f1710416135l_bool: $i > $i > $i ).
thf(ord_le694128617i_bool_decl,type,
ord_le694128617i_bool: $i ).
thf(h_decl,type,
h: $i ).
thf(n_decl,type,
n: $i ).
thf(arrow_78446834_mktop_decl,type,
arrow_78446834_mktop: $i ).
thf(fequal_nat_decl,type,
fequal_nat: $i ).
thf(arrow_812378712_above_decl,type,
arrow_812378712_above: $i ).
thf(arrow_2077223396_mkbot_decl,type,
arrow_2077223396_mkbot: $i ).
thf(member2074804542e_indi_decl,type,
member2074804542e_indi: $i > $i ).
thf(member765089840e_indi_decl,type,
member765089840e_indi: $i > $i ).
thf(pi_Pro437273841e_indi_decl,type,
pi_Pro437273841e_indi: $i > $i > $i ).
thf(hAPP_f281286919l_bool_decl,type,
hAPP_f281286919l_bool: $i > $i > $i ).
thf(ord_le1480133609l_bool_decl,type,
ord_le1480133609l_bool: $i ).
thf(member497701034t_bool_decl,type,
member497701034t_bool: $i > $i ).
thf(pi_boo2007389459t_bool_decl,type,
pi_boo2007389459t_bool: $i > $i > $i ).
thf(member1965683644t_bool_decl,type,
member1965683644t_bool: $i > $i ).
thf(member_bool_decl,type,
member_bool: $i > $i ).
thf(hAPP_b589554111l_bool_decl,type,
hAPP_b589554111l_bool: $i > $i > $i ).
thf(ord_less_bool_decl,type,
ord_less_bool: $i ).
thf(member1622429502t_bool_decl,type,
member1622429502t_bool: $i > $i ).
thf(member1277417654t_bool_decl,type,
member1277417654t_bool: $i > $i ).
thf(arrow_2061665457ctator_decl,type,
arrow_2061665457ctator: $i ).
thf(member387398118l_bool_decl,type,
member387398118l_bool: $i > $i ).
thf(pi_fun525942951l_bool_decl,type,
pi_fun525942951l_bool: $i > $i > $i ).
thf(member1122398042e_indi_decl,type,
member1122398042e_indi: $i > $i ).
thf(pi_fun2075749915e_indi_decl,type,
pi_fun2075749915e_indi: $i > $i > $i ).
thf(member42699324le_alt_decl,type,
member42699324le_alt: $i > $i ).
thf(pi_boo1877522301le_alt_decl,type,
pi_boo1877522301le_alt: $i > $i > $i ).
thf(hAPP_b1817367815le_alt_decl,type,
hAPP_b1817367815le_alt: $i > $i > $i ).
thf(member859582768le_alt_decl,type,
member859582768le_alt: $i > $i ).
thf(pi_Arr149813489le_alt_decl,type,
pi_Arr149813489le_alt: $i > $i > $i ).
thf(hAPP_A1736628091le_alt_decl,type,
hAPP_A1736628091le_alt: $i > $i > $i ).
thf(member1661336414l_bool_decl,type,
member1661336414l_bool: $i > $i ).
thf(pi_fun1494794527l_bool_decl,type,
pi_fun1494794527l_bool: $i > $i > $i ).
thf(member1033316428l_bool_decl,type,
member1033316428l_bool: $i > $i ).
thf(pi_fun1727820731l_bool_decl,type,
pi_fun1727820731l_bool: $i > $i > $i ).
thf(member329987264e_indi_decl,type,
member329987264e_indi: $i > $i ).
thf(pi_fun972956463e_indi_decl,type,
pi_fun972956463e_indi: $i > $i > $i ).
thf(member1833291218t_bool_decl,type,
member1833291218t_bool: $i > $i ).
thf(pi_Arr1511953043t_bool_decl,type,
pi_Arr1511953043t_bool: $i > $i > $i ).
thf(hAPP_A1594182429t_bool_decl,type,
hAPP_A1594182429t_bool: $i > $i > $i ).
thf(hAPP_f1760255479l_bool_decl,type,
hAPP_f1760255479l_bool: $i > $i > $i ).
thf(ord_le453141089l_bool_decl,type,
ord_le453141089l_bool: $i ).
thf(member1105181906e_indi_decl,type,
member1105181906e_indi: $i > $i ).
thf(pi_fun1736243859e_indi_decl,type,
pi_fun1736243859e_indi: $i > $i > $i ).
thf(member1467476314t_bool_decl,type,
member1467476314t_bool: $i > $i ).
thf(pi_Arr372473371t_bool_decl,type,
pi_Arr372473371t_bool: $i > $i > $i ).
thf(hAPP_A1062826149t_bool_decl,type,
hAPP_A1062826149t_bool: $i > $i > $i ).
thf(member1911067358t_bool_decl,type,
member1911067358t_bool: $i > $i ).
thf(pi_boo691944735t_bool_decl,type,
pi_boo691944735t_bool: $i > $i > $i ).
thf(hAPP_b833696937t_bool_decl,type,
hAPP_b833696937t_bool: $i > $i > $i ).
thf(member2081512038t_bool_decl,type,
member2081512038t_bool: $i > $i ).
thf(pi_boo71521447t_bool_decl,type,
pi_boo71521447t_bool: $i > $i > $i ).
thf(hAPP_b331122225t_bool_decl,type,
hAPP_b331122225t_bool: $i > $i > $i ).
thf(hAPP_f1669465919l_bool_decl,type,
hAPP_f1669465919l_bool: $i > $i > $i ).
thf(ord_le272605321l_bool_decl,type,
ord_le272605321l_bool: $i ).
thf(finite120254591e_indi_decl,type,
finite120254591e_indi: $i > $i ).
thf(ord_le227393471t_bool_decl,type,
ord_le227393471t_bool: $i ).
thf(297,axiom,
! [A: $i] : ( top_to40512653l_bool @ ( A @ member1622429502t_bool @ hAPP_f213304539l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_iso__tuple__UNIV__I) ).
thf(1337,plain,
! [A: $i] : ( top_to40512653l_bool @ ( A @ member1622429502t_bool @ hAPP_f213304539l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(308,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( cOMBK_1268833122l_bool @ hAPP_f448497509l_bool ) @ ( C @ pi_boo71521447t_bool ) @ ( B @ member2081512038t_bool @ hAPP_f1271180905l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_b331122225t_bool ) @ member1622429502t_bool @ hAPP_f213304539l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_funcset__mem) ).
thf(1369,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( cOMBK_1268833122l_bool @ hAPP_f448497509l_bool ) @ ( C @ pi_boo71521447t_bool ) @ ( B @ member2081512038t_bool @ hAPP_f1271180905l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_b331122225t_bool ) @ member1622429502t_bool @ hAPP_f213304539l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(71,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( cOMBK_886533338t_bool @ hAPP_f219827985l_bool ) @ hAPP_f313042899l_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc_029) ).
thf(479,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( cOMBK_886533338t_bool @ hAPP_f219827985l_bool ) @ hAPP_f313042899l_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(195,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( cOMBK_1072228194t_bool @ hAPP_f1235573641l_bool ) @ ( C @ pi_fun525942951l_bool ) @ ( B @ member387398118l_bool @ hAPP_f1279200745l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member1622429502t_bool @ hAPP_f213304539l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_f785543729l_bool ) @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_funcset__mem) ).
thf(909,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( cOMBK_1072228194t_bool @ hAPP_f1235573641l_bool ) @ ( C @ pi_fun525942951l_bool ) @ ( B @ member387398118l_bool @ hAPP_f1279200745l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member1622429502t_bool @ hAPP_f213304539l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_f785543729l_bool ) @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(291,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( ( C = A )
=> ( A @ ( B @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_ord__less__eq__trans) ).
thf(1315,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( ( C = A )
=> ( A @ ( B @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(254,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ~ ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_order__less__not__sym) ).
thf(1179,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ~ ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(100,axiom,
! [A: $i,B: $i] :
( ( B @ is_Arr625519182e_indi )
=> ( B @ ( A @ hAPP_A1912483895l_bool ) @ is_fun959573582l_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000tc__fun_It) ).
thf(555,plain,
! [A: $i,B: $i] :
( ( B @ is_Arr625519182e_indi )
=> ( B @ ( A @ hAPP_A1912483895l_bool ) @ is_fun959573582l_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(286,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( cOMBK_2008994872le_alt @ hAPP_f1724001331l_bool ) @ ( C @ pi_Pro2135156861t_bool ) @ ( B @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_P2075002375t_bool ) @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_funcset__mem) ).
thf(1295,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( cOMBK_2008994872le_alt @ hAPP_f1724001331l_bool ) @ ( C @ pi_Pro2135156861t_bool ) @ ( B @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_P2075002375t_bool ) @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( A @ is_fun917378774i_bool )
=> ( ( B @ ( A @ ( cOMBK_1372975190t_bool @ hAPP_f1677452273i_bool ) @ hAPP_f355113919i_bool ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg___037) ).
thf(352,plain,
! [A: $i,B: $i] :
( ( A @ is_fun917378774i_bool )
=> ( ( B @ ( A @ ( cOMBK_1372975190t_bool @ hAPP_f1677452273i_bool ) @ hAPP_f355113919i_bool ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(138,axiom,
e @ ( p @ ( arrow_2077223396_mkbot @ cOMBB_1292070696e_indi ) @ cOMBC_1778077589t_bool ) @ ( e @ ( c @ ( p @ ( arrow_812378712_above @ cOMBB_69933763e_indi ) @ cOMBC_493523632t_bool ) @ cOMBC_1778077589t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_317992461e_indi ) @ cOMBC_277798809t_bool ) @ ( if_fun1419651289t_bool @ cOMBB_963584201e_indi ) @ cOMBS_102864562t_bool ) @ cOMBS_867867294t_bool ) @ ( e @ ( p @ ( arrow_78446834_mktop @ cOMBB_1292070696e_indi ) @ cOMBC_1778077589t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_317992461e_indi ) @ cOMBC_277798809t_bool ) @ ( if_fun1419651289t_bool @ cOMBB_963584201e_indi ) @ cOMBS_102864562t_bool ) @ cOMBS_867867294t_bool ) @ ( f @ hAPP_f695124765t_bool ) @ ( e @ ( c @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto) ).
thf(645,plain,
e @ ( p @ ( arrow_2077223396_mkbot @ cOMBB_1292070696e_indi ) @ cOMBC_1778077589t_bool ) @ ( e @ ( c @ ( p @ ( arrow_812378712_above @ cOMBB_69933763e_indi ) @ cOMBC_493523632t_bool ) @ cOMBC_1778077589t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_317992461e_indi ) @ cOMBC_277798809t_bool ) @ ( if_fun1419651289t_bool @ cOMBB_963584201e_indi ) @ cOMBS_102864562t_bool ) @ cOMBS_867867294t_bool ) @ ( e @ ( p @ ( arrow_78446834_mktop @ cOMBB_1292070696e_indi ) @ cOMBC_1778077589t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_317992461e_indi ) @ cOMBC_277798809t_bool ) @ ( if_fun1419651289t_bool @ cOMBB_963584201e_indi ) @ cOMBS_102864562t_bool ) @ cOMBS_867867294t_bool ) @ ( f @ hAPP_f695124765t_bool ) @ ( e @ ( c @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(189,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ is_Arr625519182e_indi )
& ( A @ is_Arr625519182e_indi ) )
=> ( ( D @ ( C @ inj_on24934938di_nat ) @ hBOOL )
=> ( ( ( A @ ( C @ hAPP_A588601142di_nat ) )
= ( B @ ( C @ hAPP_A588601142di_nat ) ) )
=> ( ( D @ ( A @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( ( D @ ( B @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( A = B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_inj__onD) ).
thf(892,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ is_Arr625519182e_indi )
& ( A @ is_Arr625519182e_indi ) )
=> ( ( D @ ( C @ inj_on24934938di_nat ) @ hBOOL )
=> ( ( ( A @ ( C @ hAPP_A588601142di_nat ) )
= ( B @ ( C @ hAPP_A588601142di_nat ) ) )
=> ( ( D @ ( A @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( ( D @ ( B @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( A = B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(233,axiom,
! [A: $i] : ( top_to1194196741l_bool @ ( A @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_iso__tuple__UNIV__I) ).
thf(1083,plain,
! [A: $i] : ( top_to1194196741l_bool @ ( A @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(64,axiom,
! [A: $i,B: $i] :
( ( B @ is_bool )
=> ( B @ ( A @ hAPP_b1018211123i_bool ) @ is_fun917378774i_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabelle____fjew) ).
thf(468,plain,
! [A: $i,B: $i] :
( ( B @ is_bool )
=> ( B @ ( A @ hAPP_b1018211123i_bool ) @ is_fun917378774i_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(113,axiom,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f500145249l_bool ) @ is_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____fjew_015) ).
thf(582,plain,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f500145249l_bool ) @ is_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(50,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_437064334t_bool ) @ hAPP_A1374816149t_bool ) )
= ( B @ ( C @ ( A @ hAPP_A1333445289t_bool ) @ hAPP_f1673487381t_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000_034) ).
thf(440,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_437064334t_bool ) @ hAPP_A1374816149t_bool ) )
= ( B @ ( C @ ( A @ hAPP_A1333445289t_bool ) @ hAPP_f1673487381t_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(124,axiom,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f355113919i_bool ) @ is_fun917378774i_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__O_013) ).
thf(614,plain,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f355113919i_bool ) @ is_fun917378774i_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(263,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_Arr688267935t_bool ) @ ( B @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_A1944296755l_bool ) @ ( A @ ( B @ hAPP_A1374816149t_bool ) @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_PiE) ).
thf(1205,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_Arr688267935t_bool ) @ ( B @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_A1944296755l_bool ) @ ( A @ ( B @ hAPP_A1374816149t_bool ) @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(55,axiom,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f204273237l_bool ) @ is_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__O) ).
thf(449,plain,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f204273237l_bool ) @ is_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(244,axiom,
~ ( lba @ ( b @ ( a @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196__096_Ia_M_Ab_J_A_126_058_ALba_096) ).
thf(1142,plain,
~ ( lba @ ( b @ ( a @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(26,axiom,
top_to1194196741l_bool @ is_fun959573582l_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__fun_Itc__Arrow____Order____Mira) ).
thf(379,plain,
top_to1194196741l_bool @ is_fun959573582l_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(252,axiom,
! [A: $i,B: $i,C: $i] :
( ( B = C )
=> ( ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_xt1_I1_J) ).
thf(1173,plain,
! [A: $i,B: $i,C: $i] :
( ( B = C )
=> ( ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(323,axiom,
! [A: $i] :
~ ( A @ ( top_to2005687013l_bool @ ( ord_le272605321l_bool @ hAPP_f1669465919l_bool ) @ hAPP_f503012287l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_not__top__less) ).
thf(1486,plain,
! [A: $i] :
~ ( A @ ( top_to2005687013l_bool @ ( ord_le272605321l_bool @ hAPP_f1669465919l_bool ) @ hAPP_f503012287l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(230,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( cOMBK_1158753900e_indi @ hAPP_f1979025587l_bool ) @ ( C @ pi_Arr688267935t_bool ) @ ( B @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_A1374816149t_bool ) @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_funcset__mem) ).
thf(1078,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( cOMBK_1158753900e_indi @ hAPP_f1979025587l_bool ) @ ( C @ pi_Arr688267935t_bool ) @ ( B @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_A1374816149t_bool ) @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(92,axiom,
! [A: $i,B: $i] :
( ( A @ is_bool )
=> ( ( B @ ( A @ ( cOMBK_580911210t_bool @ hAPP_b990649139l_bool ) @ hAPP_f785543729l_bool ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Arrow____Order__) ).
thf(533,plain,
! [A: $i,B: $i] :
( ( A @ is_bool )
=> ( ( B @ ( A @ ( cOMBK_580911210t_bool @ hAPP_b990649139l_bool ) @ hAPP_f785543729l_bool ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(79,axiom,
! [A: $i,B: $i] :
( ( A @ is_fun631676118l_bool )
=> ( ( B @ ( A @ ( cOMBK_1292462166e_indi @ hAPP_f1697527281l_bool ) @ hAPP_A1964572607l_bool ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel_038) ).
thf(500,plain,
! [A: $i,B: $i] :
( ( A @ is_fun631676118l_bool )
=> ( ( B @ ( A @ ( cOMBK_1292462166e_indi @ hAPP_f1697527281l_bool ) @ hAPP_A1964572607l_bool ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(155,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( arrow_2061665457ctator @ hAPP_f355113919i_bool ) @ hAPP_A1466488369i_bool ) @ hBOOL )
<=> ! [C: $i] :
( ( arrow_413697182e_Prof @ ( C @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL )
=> ( ( C @ ( A @ hAPP_f695124765t_bool ) )
= ( B @ ( C @ hAPP_A1374816149t_bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_dictator__def) ).
thf(715,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( arrow_413697182e_Prof @ ( C @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL )
=> ( ( C @ ( A @ hAPP_f695124765t_bool ) )
= ( B @ ( C @ hAPP_A1374816149t_bool ) ) ) )
=> ( B @ ( A @ ( arrow_2061665457ctator @ hAPP_f355113919i_bool ) @ hAPP_A1466488369i_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( arrow_2061665457ctator @ hAPP_f355113919i_bool ) @ hAPP_A1466488369i_bool ) @ hBOOL )
=> ! [C: $i] :
( ( arrow_413697182e_Prof @ ( C @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL )
=> ( ( C @ ( A @ hAPP_f695124765t_bool ) )
= ( B @ ( C @ hAPP_A1374816149t_bool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(67,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( cOMBK_2008994872le_alt @ hAPP_f1724001331l_bool ) @ hAPP_P2127852789l_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__prod_It) ).
thf(472,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( cOMBK_2008994872le_alt @ hAPP_f1724001331l_bool ) @ hAPP_P2127852789l_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(294,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_boo691944735t_bool ) @ ( B @ member1911067358t_bool @ hAPP_f1018082273l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_b1719629739l_bool ) @ ( A @ ( B @ hAPP_b833696937t_bool ) @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_Pi__mem) ).
thf(1327,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_boo691944735t_bool ) @ ( B @ member1911067358t_bool @ hAPP_f1018082273l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_b1719629739l_bool ) @ ( A @ ( B @ hAPP_b833696937t_bool ) @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(273,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( cOMBK_1292462166e_indi @ hAPP_f1697527281l_bool ) @ ( C @ pi_Arr372473371t_bool ) @ ( B @ member1467476314t_bool @ hAPP_f1012384989l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_A1062826149t_bool ) @ member1622429502t_bool @ hAPP_f213304539l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_funcset__mem) ).
thf(1260,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( cOMBK_1292462166e_indi @ hAPP_f1697527281l_bool ) @ ( C @ pi_Arr372473371t_bool ) @ ( B @ member1467476314t_bool @ hAPP_f1012384989l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_A1062826149t_bool ) @ member1622429502t_bool @ hAPP_f213304539l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(300,axiom,
arrow_1239002508le_Lin @ ( lab @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117__096Lab_A_058_ALin_096) ).
thf(1342,plain,
arrow_1239002508le_Lin @ ( lab @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(305,axiom,
! [A: $i] :
~ ( A @ ( top_to2034604131t_bool @ ( ord_le227393471t_bool @ hAPP_f2056167603l_bool ) @ hAPP_f745298353l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_not__top__less) ).
thf(1354,plain,
! [A: $i] :
~ ( A @ ( top_to2034604131t_bool @ ( ord_le227393471t_bool @ hAPP_f2056167603l_bool ) @ hAPP_f745298353l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(223,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_fun1494794527l_bool ) @ ( B @ member1661336414l_bool @ hAPP_f500145249l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_f313042899l_bool ) @ ( A @ ( B @ hAPP_f1636546729l_bool ) @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_PiE) ).
thf(1063,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_fun1494794527l_bool ) @ ( B @ member1661336414l_bool @ hAPP_f500145249l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_f313042899l_bool ) @ ( A @ ( B @ hAPP_f1636546729l_bool ) @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(8,axiom,
top_to1256827021i_bool @ is_fun917378774i_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__Arrow____Order____Mirabelle____) ).
thf(340,plain,
top_to1256827021i_bool @ is_fun917378774i_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(237,axiom,
! [A: $i] :
( ( A @ ( p @ hAPP_A1374816149t_bool ) @ ( d @ ( c @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
<=> ( ( ~ ( n @ ( A @ ( h @ hAPP_A588601142di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( ( A @ ( h @ hAPP_A588601142di_nat ) )
!= n )
=> ( e @ ( A @ ( p @ hAPP_A1374816149t_bool ) @ ( arrow_2077223396_mkbot @ hAPP_f1290184496t_bool ) @ hAPP_A619995676t_bool ) @ ( d @ ( c @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) )
& ( ( ( A @ ( h @ hAPP_A588601142di_nat ) )
= n )
=> ( e @ ( c @ ( A @ ( p @ hAPP_A1374816149t_bool ) @ ( arrow_812378712_above @ hAPP_f1336478923t_bool ) @ hAPP_A384644407t_bool ) @ hAPP_A619995676t_bool ) @ ( d @ ( c @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) ) )
& ( ( n @ ( A @ ( h @ hAPP_A588601142di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( e @ ( A @ ( p @ hAPP_A1374816149t_bool ) @ ( arrow_78446834_mktop @ hAPP_f1290184496t_bool ) @ hAPP_A619995676t_bool ) @ ( d @ ( c @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ad_J) ).
thf(1095,plain,
! [A: $i] :
( ( ( ( ~ ( n @ ( A @ ( h @ hAPP_A588601142di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( ( A @ ( h @ hAPP_A588601142di_nat ) )
!= n )
=> ( e @ ( A @ ( p @ hAPP_A1374816149t_bool ) @ ( arrow_2077223396_mkbot @ hAPP_f1290184496t_bool ) @ hAPP_A619995676t_bool ) @ ( d @ ( c @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) )
& ( ( ( A @ ( h @ hAPP_A588601142di_nat ) )
= n )
=> ( e @ ( c @ ( A @ ( p @ hAPP_A1374816149t_bool ) @ ( arrow_812378712_above @ hAPP_f1336478923t_bool ) @ hAPP_A384644407t_bool ) @ hAPP_A619995676t_bool ) @ ( d @ ( c @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) ) )
& ( ( n @ ( A @ ( h @ hAPP_A588601142di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( e @ ( A @ ( p @ hAPP_A1374816149t_bool ) @ ( arrow_78446834_mktop @ hAPP_f1290184496t_bool ) @ hAPP_A619995676t_bool ) @ ( d @ ( c @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) )
=> ( A @ ( p @ hAPP_A1374816149t_bool ) @ ( d @ ( c @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) )
& ( ( A @ ( p @ hAPP_A1374816149t_bool ) @ ( d @ ( c @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
=> ( ( ~ ( n @ ( A @ ( h @ hAPP_A588601142di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( ( A @ ( h @ hAPP_A588601142di_nat ) )
!= n )
=> ( e @ ( A @ ( p @ hAPP_A1374816149t_bool ) @ ( arrow_2077223396_mkbot @ hAPP_f1290184496t_bool ) @ hAPP_A619995676t_bool ) @ ( d @ ( c @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) )
& ( ( ( A @ ( h @ hAPP_A588601142di_nat ) )
= n )
=> ( e @ ( c @ ( A @ ( p @ hAPP_A1374816149t_bool ) @ ( arrow_812378712_above @ hAPP_f1336478923t_bool ) @ hAPP_A384644407t_bool ) @ hAPP_A619995676t_bool ) @ ( d @ ( c @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) ) )
& ( ( n @ ( A @ ( h @ hAPP_A588601142di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( e @ ( A @ ( p @ hAPP_A1374816149t_bool ) @ ( arrow_78446834_mktop @ hAPP_f1290184496t_bool ) @ hAPP_A619995676t_bool ) @ ( d @ ( c @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(320,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ is_Arr553848933le_alt )
& ( D @ is_Arr553848933le_alt )
& ( B @ is_Arr553848933le_alt )
& ( A @ is_Arr553848933le_alt ) )
=> ( ( D != E )
=> ( ( arrow_1239002508le_Lin @ ( C @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL )
=> ( ( E @ ( D @ ( C @ ( arrow_812378712_above @ hAPP_f1336478923t_bool ) @ hAPP_A384644407t_bool ) @ hAPP_A619995676t_bool ) @ ( B @ ( A @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
<=> ( ( ( A != E )
=> ( ( ( B != E )
=> ( C @ ( B @ ( A @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) )
& ( ( B = E )
=> ( ( C @ ( D @ ( A @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
| ( A = D ) ) ) ) )
& ( ( A = E )
=> ( C @ ( B @ ( D @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) )
& ( A != B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_in__above) ).
thf(1441,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ is_Arr553848933le_alt )
& ( D @ is_Arr553848933le_alt )
& ( B @ is_Arr553848933le_alt )
& ( A @ is_Arr553848933le_alt ) )
=> ( ( D != E )
=> ( ( arrow_1239002508le_Lin @ ( C @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL )
=> ( ( ( ( ( A != E )
=> ( ( ( B != E )
=> ( C @ ( B @ ( A @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) )
& ( ( B = E )
=> ( ( C @ ( D @ ( A @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
| ( A = D ) ) ) ) )
& ( ( A = E )
=> ( C @ ( B @ ( D @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) )
& ( A != B ) )
=> ( E @ ( D @ ( C @ ( arrow_812378712_above @ hAPP_f1336478923t_bool ) @ hAPP_A384644407t_bool ) @ hAPP_A619995676t_bool ) @ ( B @ ( A @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) )
& ( ( E @ ( D @ ( C @ ( arrow_812378712_above @ hAPP_f1336478923t_bool ) @ hAPP_A384644407t_bool ) @ hAPP_A619995676t_bool ) @ ( B @ ( A @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
=> ( ( ( A != E )
=> ( ( ( B != E )
=> ( C @ ( B @ ( A @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) )
& ( ( B = E )
=> ( ( C @ ( D @ ( A @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
| ( A = D ) ) ) ) )
& ( ( A = E )
=> ( C @ ( B @ ( D @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) )
& ( A != B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(42,axiom,
! [A: $i,B: $i] :
( ( A @ is_fun917378774i_bool )
=> ( ( B @ ( A @ ( cOMBK_100791596le_alt @ hAPP_f1970593179i_bool ) @ hAPP_P907763049i_bool ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__) ).
thf(417,plain,
! [A: $i,B: $i] :
( ( A @ is_fun917378774i_bool )
=> ( ( B @ ( A @ ( cOMBK_100791596le_alt @ hAPP_f1970593179i_bool ) @ hAPP_P907763049i_bool ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(218,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_order__less__imp__triv) ).
thf(1046,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(307,axiom,
! [A: $i] :
( ! [B: $i] : ( B @ ( A @ hAPP_P2075002375t_bool ) @ hBOOL )
<=> ! [B: $i,C: $i] :
( ( ( C @ is_Arr553848933le_alt )
& ( B @ is_Arr553848933le_alt ) )
=> ( C @ ( B @ produc171383831le_alt ) @ ( A @ hAPP_P2075002375t_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_split__paired__All) ).
thf(1359,plain,
! [A: $i] :
( ( ! [B: $i,C: $i] :
( ( ( C @ is_Arr553848933le_alt )
& ( B @ is_Arr553848933le_alt ) )
=> ( C @ ( B @ produc171383831le_alt ) @ ( A @ hAPP_P2075002375t_bool ) @ hBOOL ) )
=> ! [B: $i] : ( B @ ( A @ hAPP_P2075002375t_bool ) @ hBOOL ) )
& ( ! [B: $i] : ( B @ ( A @ hAPP_P2075002375t_bool ) @ hBOOL )
=> ! [B: $i,C: $i] :
( ( ( C @ is_Arr553848933le_alt )
& ( B @ is_Arr553848933le_alt ) )
=> ( C @ ( B @ produc171383831le_alt ) @ ( A @ hAPP_P2075002375t_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(105,axiom,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f460310451l_bool ) @ is_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fje) ).
thf(565,plain,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f460310451l_bool ) @ is_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(141,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_boo2007389459t_bool ) @ ( B @ member497701034t_bool @ hAPP_f1550037191l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_b1965422783l_bool ) @ ( A @ ( B @ hAPP_b1024867081t_bool ) @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_PiE) ).
thf(651,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_boo2007389459t_bool ) @ ( B @ member497701034t_bool @ hAPP_f1550037191l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_b1965422783l_bool ) @ ( A @ ( B @ hAPP_b1024867081t_bool ) @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(221,axiom,
! [A: $i,B: $i] :
( ( arrow_1239002508le_Lin @ ( B @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL )
=> ( arrow_1239002508le_Lin @ ( A @ ( B @ ( arrow_78446834_mktop @ hAPP_f1290184496t_bool ) @ hAPP_A619995676t_bool ) @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_mktop__Lin) ).
thf(1055,plain,
! [A: $i,B: $i] :
( ( arrow_1239002508le_Lin @ ( B @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL )
=> ( arrow_1239002508le_Lin @ ( A @ ( B @ ( arrow_78446834_mktop @ hAPP_f1290184496t_bool ) @ hAPP_A619995676t_bool ) @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(80,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun282293932t_bool )
=> ( B @ ( A @ hAPP_f1659504677e_indi ) @ is_Arr625519182e_indi ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fjewxadnqg__) ).
thf(504,plain,
! [A: $i,B: $i] :
( ( B @ is_fun282293932t_bool )
=> ( B @ ( A @ hAPP_f1659504677e_indi ) @ is_Arr625519182e_indi ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(275,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( ( B = A )
=> ( C @ ( A @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_xt1_I2_J) ).
thf(1264,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( ( B = A )
=> ( C @ ( A @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(151,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL )
=> ~ ( A @ ( B @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_order__less__not__sym) ).
thf(702,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL )
=> ~ ( A @ ( B @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( A @ is_fun959573582l_bool )
=> ( ( B @ ( A @ ( cOMBK_697604314l_bool @ hAPP_f371807573l_bool ) @ hAPP_b1719629739l_bool ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____fje) ).
thf(344,plain,
! [A: $i,B: $i] :
( ( A @ is_fun959573582l_bool )
=> ( ( B @ ( A @ ( cOMBK_697604314l_bool @ hAPP_f371807573l_bool ) @ hAPP_b1719629739l_bool ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(281,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_xt1_I10_J) ).
thf(1279,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(199,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_fun1494794527l_bool ) @ ( B @ member1661336414l_bool @ hAPP_f500145249l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_f313042899l_bool ) @ ( A @ ( B @ hAPP_f1636546729l_bool ) @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_Pi__mem) ).
thf(949,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_fun1494794527l_bool ) @ ( B @ member1661336414l_bool @ hAPP_f500145249l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_f313042899l_bool ) @ ( A @ ( B @ hAPP_f1636546729l_bool ) @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(60,axiom,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1818473245e_indi ) @ is_Arr625519182e_indi ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_Mtc__004) ).
thf(460,plain,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1818473245e_indi ) @ is_Arr625519182e_indi ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(115,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_963584201e_indi ) @ hAPP_A869356733t_bool ) )
= ( C @ ( B @ hAPP_A1466488369i_bool ) @ ( A @ hAPP_b1915039793t_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow_) ).
thf(587,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_963584201e_indi ) @ hAPP_A869356733t_bool ) )
= ( C @ ( B @ hAPP_A1466488369i_bool ) @ ( A @ hAPP_b1915039793t_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(127,axiom,
! [A: $i] :
( ( top_to2005687013l_bool @ ( cOMBK_1088865252t_bool @ hAPP_f20355883l_bool ) @ ( A @ pi_fun433100839t_bool ) )
= top_to40512653l_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_Pi__UNIV) ).
thf(619,plain,
! [A: $i] :
( ( top_to2005687013l_bool @ ( cOMBK_1088865252t_bool @ hAPP_f20355883l_bool ) @ ( A @ pi_fun433100839t_bool ) )
= top_to40512653l_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(177,axiom,
! [A: $i] : ( A @ ( top_to2005687013l_bool @ hAPP_f745298353l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_top1I) ).
thf(853,plain,
! [A: $i] : ( A @ ( top_to2005687013l_bool @ hAPP_f745298353l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(312,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_order__less__imp__not__eq) ).
thf(1379,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(247,axiom,
e @ ( p @ ( arrow_2077223396_mkbot @ cOMBB_1292070696e_indi ) @ cOMBC_1778077589t_bool ) @ ( e @ ( c @ ( p @ ( arrow_812378712_above @ cOMBB_69933763e_indi ) @ cOMBC_493523632t_bool ) @ cOMBC_1778077589t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_317992461e_indi ) @ cOMBC_277798809t_bool ) @ ( if_fun1419651289t_bool @ cOMBB_963584201e_indi ) @ cOMBS_102864562t_bool ) @ cOMBS_867867294t_bool ) @ ( e @ ( p @ ( arrow_78446834_mktop @ cOMBB_1292070696e_indi ) @ cOMBC_1778077589t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_317992461e_indi ) @ cOMBC_277798809t_bool ) @ ( if_fun1419651289t_bool @ cOMBB_963584201e_indi ) @ cOMBS_102864562t_bool ) @ cOMBS_867867294t_bool ) @ ( f @ hAPP_f695124765t_bool ) @ ( d @ ( c @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto) ).
thf(1147,plain,
e @ ( p @ ( arrow_2077223396_mkbot @ cOMBB_1292070696e_indi ) @ cOMBC_1778077589t_bool ) @ ( e @ ( c @ ( p @ ( arrow_812378712_above @ cOMBB_69933763e_indi ) @ cOMBC_493523632t_bool ) @ cOMBC_1778077589t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_317992461e_indi ) @ cOMBC_277798809t_bool ) @ ( if_fun1419651289t_bool @ cOMBB_963584201e_indi ) @ cOMBS_102864562t_bool ) @ cOMBS_867867294t_bool ) @ ( e @ ( p @ ( arrow_78446834_mktop @ cOMBB_1292070696e_indi ) @ cOMBC_1778077589t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_317992461e_indi ) @ cOMBC_277798809t_bool ) @ ( if_fun1419651289t_bool @ cOMBB_963584201e_indi ) @ cOMBS_102864562t_bool ) @ cOMBS_867867294t_bool ) @ ( f @ hAPP_f695124765t_bool ) @ ( d @ ( c @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(322,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ is_Arr553848933le_alt )
& ( A @ is_Arr553848933le_alt ) )
=> ( ( arrow_1239002508le_Lin @ ( C @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL )
=> ( ( A != B )
=> ( ~ ( C @ ( B @ ( A @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
<=> ( C @ ( A @ ( B @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_notin__Lin__iff) ).
thf(1479,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ is_Arr553848933le_alt )
& ( A @ is_Arr553848933le_alt ) )
=> ( ( arrow_1239002508le_Lin @ ( C @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL )
=> ( ( A != B )
=> ( ( ( C @ ( A @ ( B @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
=> ~ ( C @ ( B @ ( A @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) )
& ( ~ ( C @ ( B @ ( A @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
=> ( C @ ( A @ ( B @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(302,axiom,
f @ ( arrow_467566751nimity @ hAPP_f785543729l_bool ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_u) ).
thf(1347,plain,
f @ ( arrow_467566751nimity @ hAPP_f785543729l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBS_102864562t_bool ) @ hAPP_A1333445289t_bool ) )
= ( C @ ( B @ hAPP_A1374816149t_bool ) @ ( C @ ( A @ hAPP_A869356733t_bool ) @ hAPP_f159424297t_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000_041) ).
thf(325,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBS_102864562t_bool ) @ hAPP_A1333445289t_bool ) )
= ( C @ ( B @ hAPP_A1374816149t_bool ) @ ( C @ ( A @ hAPP_A869356733t_bool ) @ hAPP_f159424297t_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(54,axiom,
lba @ is_fun282293932t_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_v_Lba____) ).
thf(448,plain,
lba @ is_fun282293932t_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(292,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ member1622429502t_bool @ hAPP_f213304539l_bool ) @ hBOOL )
<=> ( A @ ( B @ hAPP_f785543729l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_mem__def) ).
thf(1319,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ hAPP_f785543729l_bool ) @ hBOOL )
=> ( B @ ( A @ member1622429502t_bool @ hAPP_f213304539l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ member1622429502t_bool @ hAPP_f213304539l_bool ) @ hBOOL )
=> ( A @ ( B @ hAPP_f785543729l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(43,axiom,
( top_to1256827021i_bool
= ( fTrue @ ( cOMBK_1157044842e_indi @ hAPP_b1018211123i_bool ) @ collec45183100e_indi ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_UNIV__def) ).
thf(421,plain,
( top_to1256827021i_bool
= ( fTrue @ ( cOMBK_1157044842e_indi @ hAPP_b1018211123i_bool ) @ collec45183100e_indi ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(68,axiom,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f618619045e_indi ) @ is_Arr625519182e_indi ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__O_011) ).
thf(475,plain,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f618619045e_indi ) @ is_Arr625519182e_indi ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(288,axiom,
! [A: $i] :
( ( arrow_1239002508le_Lin @ ( A @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL )
=> ( arrow_413697182e_Prof @ ( A @ ( cOMBK_1152753196e_indi @ hAPP_f1507266205t_bool ) @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_const__Lin__Prof) ).
thf(1302,plain,
! [A: $i] :
( ( arrow_1239002508le_Lin @ ( A @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL )
=> ( arrow_413697182e_Prof @ ( A @ ( cOMBK_1152753196e_indi @ hAPP_f1507266205t_bool ) @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(139,axiom,
! [A: $i] :
~ ( A @ ( top_to40512653l_bool @ ( ord_le1480133609l_bool @ hAPP_f281286919l_bool ) @ hAPP_f213304539l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_not__top__less) ).
thf(646,plain,
! [A: $i] :
~ ( A @ ( top_to40512653l_bool @ ( ord_le1480133609l_bool @ hAPP_f281286919l_bool ) @ hAPP_f213304539l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(220,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_less__imp__neq) ).
thf(1051,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(310,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( C = A )
=> ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_ord__less__eq__trans) ).
thf(1373,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( C = A )
=> ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(51,axiom,
fTrue @ is_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_fTrue) ).
thf(443,plain,
fTrue @ is_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(74,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_1778077589t_bool ) @ hAPP_A1374816149t_bool ) )
= ( B @ ( C @ ( A @ hAPP_A702630576t_bool ) @ hAPP_A619995676t_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000_030) ).
thf(485,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_1778077589t_bool ) @ hAPP_A1374816149t_bool ) )
= ( B @ ( C @ ( A @ hAPP_A702630576t_bool ) @ hAPP_A619995676t_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(173,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ is_Arr553848933le_alt )
& ( C @ is_Arr553848933le_alt )
& ( B @ is_Arr553848933le_alt )
& ( A @ is_Arr553848933le_alt ) )
=> ( ( ( B @ ( A @ produc171383831le_alt ) )
= ( D @ ( C @ produc171383831le_alt ) ) )
<=> ( ( B = D )
& ( A = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_Pair__eq) ).
thf(834,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ is_Arr553848933le_alt )
& ( C @ is_Arr553848933le_alt )
& ( B @ is_Arr553848933le_alt )
& ( A @ is_Arr553848933le_alt ) )
=> ( ( ( ( B = D )
& ( A = C ) )
=> ( ( B @ ( A @ produc171383831le_alt ) )
= ( D @ ( C @ produc171383831le_alt ) ) ) )
& ( ( ( B @ ( A @ produc171383831le_alt ) )
= ( D @ ( C @ produc171383831le_alt ) ) )
=> ( ( B = D )
& ( A = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(313,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( cOMBK_886533338t_bool @ hAPP_f219827985l_bool ) @ ( C @ pi_fun1494794527l_bool ) @ ( B @ member1661336414l_bool @ hAPP_f500145249l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_f1636546729l_bool ) @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_funcset__mem) ).
thf(1383,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( cOMBK_886533338t_bool @ hAPP_f219827985l_bool ) @ ( C @ pi_fun1494794527l_bool ) @ ( B @ member1661336414l_bool @ hAPP_f500145249l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_f1636546729l_bool ) @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(12,axiom,
( top_to2005687013l_bool
= ( fTrue @ ( cOMBK_977355664t_bool @ hAPP_b1965422783l_bool ) @ collec874260222t_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_UNIV__def) ).
thf(348,plain,
( top_to2005687013l_bool
= ( fTrue @ ( cOMBK_977355664t_bool @ hAPP_b1965422783l_bool ) @ collec874260222t_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(109,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun917378774i_bool )
=> ( B @ ( A @ inj_on24934938di_nat ) @ is_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Fun_Oinj__on_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000tc) ).
thf(574,plain,
! [A: $i,B: $i] :
( ( B @ is_fun917378774i_bool )
=> ( B @ ( A @ inj_on24934938di_nat ) @ is_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(256,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_boo71521447t_bool ) @ ( B @ member2081512038t_bool @ hAPP_f1271180905l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_b990649139l_bool ) @ ( A @ ( B @ hAPP_b331122225t_bool ) @ member1622429502t_bool @ hAPP_f213304539l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_Pi__mem) ).
thf(1183,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_boo71521447t_bool ) @ ( B @ member2081512038t_bool @ hAPP_f1271180905l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_b990649139l_bool ) @ ( A @ ( B @ hAPP_b331122225t_bool ) @ member1622429502t_bool @ hAPP_f213304539l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(283,axiom,
top_to1256827021i_bool @ ( h @ inj_on24934938di_nat ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_injh) ).
thf(1283,plain,
top_to1256827021i_bool @ ( h @ inj_on24934938di_nat ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(147,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ is_Arr625519182e_indi )
=> ( ( D @ ( C @ inj_on24934938di_nat ) @ hBOOL )
=> ( ( D @ ( B @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( ( ( B @ ( C @ hAPP_A588601142di_nat ) )
= A )
=> ( ( A @ ( C @ ( D @ hilber1792103167di_nat ) @ hAPP_n385347014e_indi ) )
= B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_inv__into__f__eq) ).
thf(687,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ is_Arr625519182e_indi )
=> ( ( D @ ( C @ inj_on24934938di_nat ) @ hBOOL )
=> ( ( D @ ( B @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( ( ( B @ ( C @ hAPP_A588601142di_nat ) )
= A )
=> ( ( A @ ( C @ ( D @ hilber1792103167di_nat ) @ hAPP_n385347014e_indi ) )
= B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(311,axiom,
! [A: $i,B: $i,C: $i] :
( ( arrow_1239002508le_Lin @ ( C @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ ( B @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_Lin__irrefl) ).
thf(1377,plain,
! [A: $i,B: $i,C: $i] :
( ( arrow_1239002508le_Lin @ ( C @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ ( B @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(148,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL )
=> ~ ( A @ ( B @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_xt1_I9_J) ).
thf(692,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL )
=> ~ ( A @ ( B @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(179,axiom,
! [A: $i] :
~ ( A @ ( top_to1256827021i_bool @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_not__top__less) ).
thf(866,plain,
! [A: $i] :
~ ( A @ ( top_to1256827021i_bool @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(166,axiom,
! [A: $i] : ( top_to2034604131t_bool @ ( A @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_iso__tuple__UNIV__I) ).
thf(774,plain,
! [A: $i] : ( top_to2034604131t_bool @ ( A @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(33,axiom,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_nat_bool ) @ is_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool) ).
thf(396,plain,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_nat_bool ) @ is_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(261,axiom,
! [A: $i] : ( top_to1647826457l_bool @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_iso__tuple__UNIV__I) ).
thf(1201,plain,
! [A: $i] : ( top_to1647826457l_bool @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(176,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( fequal_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
| ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Nat__Onat_T) ).
thf(849,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( fequal_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(265,axiom,
! [A: $i] : ( top_to40512653l_bool @ ( A @ member1622429502t_bool @ hAPP_f213304539l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_UNIV__I) ).
thf(1215,plain,
! [A: $i] : ( top_to40512653l_bool @ ( A @ member1622429502t_bool @ hAPP_f213304539l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(132,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_order__less__trans) ).
thf(634,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(227,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_Arr1511953043t_bool ) @ ( B @ member1833291218t_bool @ hAPP_f204273237l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_A1912483895l_bool ) @ ( A @ ( B @ hAPP_A1594182429t_bool ) @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_Pi__mem) ).
thf(1072,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_Arr1511953043t_bool ) @ ( B @ member1833291218t_bool @ hAPP_f204273237l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_A1912483895l_bool ) @ ( A @ ( B @ hAPP_A1594182429t_bool ) @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(57,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun917378774i_bool )
=> ( B @ ( A @ hAPP_f919661787l_bool ) @ is_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_Mtc_) ).
thf(453,plain,
! [A: $i,B: $i] :
( ( B @ is_fun917378774i_bool )
=> ( B @ ( A @ hAPP_f919661787l_bool ) @ is_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(228,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( cOMBK_1088865252t_bool @ hAPP_f20355883l_bool ) @ ( C @ pi_fun433100839t_bool ) @ ( B @ member1622429502t_bool @ hAPP_f213304539l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_f695124765t_bool ) @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_funcset__mem) ).
thf(1074,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( cOMBK_1088865252t_bool @ hAPP_f20355883l_bool ) @ ( C @ pi_fun433100839t_bool ) @ ( B @ member1622429502t_bool @ hAPP_f213304539l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_f695124765t_bool ) @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(27,axiom,
! [A: $i] :
( ( A @ is_fun631676118l_bool )
=> ( A @ collec1520786044t_bool @ is_fun631676118l_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_OCollect_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____fjewx) ).
thf(380,plain,
! [A: $i] :
( ( A @ is_fun631676118l_bool )
=> ( A @ collec1520786044t_bool @ is_fun631676118l_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(84,axiom,
! [A: $i,B: $i] :
( ( A @ is_fun631676118l_bool )
=> ( ( B @ ( A @ ( cOMBK_1268833122l_bool @ hAPP_f448497509l_bool ) @ hAPP_b990649139l_bool ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel) ).
thf(512,plain,
! [A: $i,B: $i] :
( ( A @ is_fun631676118l_bool )
=> ( ( B @ ( A @ ( cOMBK_1268833122l_bool @ hAPP_f448497509l_bool ) @ hAPP_b990649139l_bool ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(146,axiom,
! [A: $i,B: $i] :
( ( arrow_1239002508le_Lin @ ( cOMBK_1088865252t_bool @ hAPP_f20355883l_bool ) @ ( arrow_413697182e_Prof @ pi_fun433100839t_bool ) @ ( B @ member1622429502t_bool @ hAPP_f213304539l_bool ) @ hBOOL )
=> ( ! [C: $i] :
( ( arrow_413697182e_Prof @ ( C @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL )
=> ! [D: $i,E: $i] :
( ( ( E @ is_Arr553848933le_alt )
& ( D @ is_Arr553848933le_alt ) )
=> ( ( D != E )
=> ( ( A @ ( C @ hAPP_A1374816149t_bool ) @ ( E @ ( D @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
=> ( C @ ( B @ hAPP_f695124765t_bool ) @ ( E @ ( D @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) ) ) )
=> ( A @ ( B @ ( arrow_2061665457ctator @ hAPP_f355113919i_bool ) @ hAPP_A1466488369i_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_dictatorI) ).
thf(678,plain,
! [A: $i,B: $i] :
( ( arrow_1239002508le_Lin @ ( cOMBK_1088865252t_bool @ hAPP_f20355883l_bool ) @ ( arrow_413697182e_Prof @ pi_fun433100839t_bool ) @ ( B @ member1622429502t_bool @ hAPP_f213304539l_bool ) @ hBOOL )
=> ( ! [C: $i] :
( ( arrow_413697182e_Prof @ ( C @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL )
=> ! [D: $i,E: $i] :
( ( ( E @ is_Arr553848933le_alt )
& ( D @ is_Arr553848933le_alt ) )
=> ( ( D != E )
=> ( ( A @ ( C @ hAPP_A1374816149t_bool ) @ ( E @ ( D @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
=> ( C @ ( B @ hAPP_f695124765t_bool ) @ ( E @ ( D @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) ) ) )
=> ( A @ ( B @ ( arrow_2061665457ctator @ hAPP_f355113919i_bool ) @ hAPP_A1466488369i_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(90,axiom,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1279200745l_bool ) @ is_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabell_017) ).
thf(529,plain,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1279200745l_bool ) @ is_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(143,axiom,
! [A: $i] : ( A @ member1056080916le_alt @ is_fun432044380l_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_member_000tc__prod_Itc__Arrow____Order____Mirabelle____fjewxadnqg__Oalt_Mt) ).
thf(661,plain,
! [A: $i] : ( A @ member1056080916le_alt @ is_fun432044380l_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(96,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_317992461e_indi ) @ hAPP_A1922697556t_bool ) )
= ( C @ ( B @ hAPP_A588601142di_nat ) @ ( A @ hAPP_n1699378549t_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_) ).
thf(546,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_317992461e_indi ) @ hAPP_A1922697556t_bool ) )
= ( C @ ( B @ hAPP_A588601142di_nat ) @ ( A @ hAPP_n1699378549t_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(164,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F @ is_Arr553848933le_alt )
& ( E @ is_Arr553848933le_alt )
& ( D @ is_Arr553848933le_alt )
& ( C @ is_Arr553848933le_alt ) )
=> ( ( E != F )
=> ( ( C != D )
=> ( ( E != D )
=> ( ( F != C )
=> ( ( arrow_413697182e_Prof @ ( B @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL )
=> ( ( arrow_413697182e_Prof @ ( A @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL )
=> ( ! [G: $i] :
( ( G @ is_Arr625519182e_indi )
=> ( ( G @ ( B @ hAPP_A1374816149t_bool ) @ ( F @ ( E @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
<=> ( G @ ( A @ hAPP_A1374816149t_bool ) @ ( D @ ( C @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) )
=> ( ( B @ ( f @ hAPP_f695124765t_bool ) @ ( F @ ( E @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
=> ( A @ ( f @ hAPP_f695124765t_bool ) @ ( D @ ( C @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7__C1_C) ).
thf(761,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F @ is_Arr553848933le_alt )
& ( E @ is_Arr553848933le_alt )
& ( D @ is_Arr553848933le_alt )
& ( C @ is_Arr553848933le_alt ) )
=> ( ( E != F )
=> ( ( C != D )
=> ( ( E != D )
=> ( ( F != C )
=> ( ( arrow_413697182e_Prof @ ( B @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL )
=> ( ( arrow_413697182e_Prof @ ( A @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL )
=> ( ! [G: $i] :
( ( G @ is_Arr625519182e_indi )
=> ( ( ( G @ ( A @ hAPP_A1374816149t_bool ) @ ( D @ ( C @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
=> ( G @ ( B @ hAPP_A1374816149t_bool ) @ ( F @ ( E @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) )
& ( ( G @ ( B @ hAPP_A1374816149t_bool ) @ ( F @ ( E @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
=> ( G @ ( A @ hAPP_A1374816149t_bool ) @ ( D @ ( C @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) ) )
=> ( ( B @ ( f @ hAPP_f695124765t_bool ) @ ( F @ ( E @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
=> ( A @ ( f @ hAPP_f695124765t_bool ) @ ( D @ ( C @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(290,axiom,
! [A: $i,B: $i] :
( ( A @ is_bool )
=> ( ( B @ ( A @ ( cOMBK_977355664t_bool @ hAPP_b1965422783l_bool ) @ hAPP_f745298353l_bool ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__prod_Itc__Arrow____Order_) ).
thf(1311,plain,
! [A: $i,B: $i] :
( ( A @ is_bool )
=> ( ( B @ ( A @ ( cOMBK_977355664t_bool @ hAPP_b1965422783l_bool ) @ hAPP_f745298353l_bool ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(225,axiom,
! [A: $i] :
~ ( A @ ( top_to1194196741l_bool @ ( ord_le453141089l_bool @ hAPP_f1760255479l_bool ) @ hAPP_f453661011l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_not__top__less) ).
thf(1067,plain,
! [A: $i] :
~ ( A @ ( top_to1194196741l_bool @ ( ord_le453141089l_bool @ hAPP_f1760255479l_bool ) @ hAPP_f453661011l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(222,axiom,
! [A: $i] :
( ( A @ ( top_to40512653l_bool @ hAPP_f785543729l_bool ) @ hBOOL )
<=> ( top_top_bool @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_top__apply) ).
thf(1057,plain,
! [A: $i] :
( ( ( top_top_bool @ hBOOL )
=> ( A @ ( top_to40512653l_bool @ hAPP_f785543729l_bool ) @ hBOOL ) )
& ( ( A @ ( top_to40512653l_bool @ hAPP_f785543729l_bool ) @ hBOOL )
=> ( top_top_bool @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(278,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_fun1736243859e_indi ) @ ( B @ member1105181906e_indi @ hAPP_f234874197l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_f749892423i_bool ) @ ( A @ ( B @ hAPP_f1818473245e_indi ) @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_PiE) ).
thf(1274,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_fun1736243859e_indi ) @ ( B @ member1105181906e_indi @ hAPP_f234874197l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_f749892423i_bool ) @ ( A @ ( B @ hAPP_f1818473245e_indi ) @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ is_fun959573582l_bool )
=> ( A @ collec1580242420t_bool @ is_fun959573582l_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_OCollect_000tc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__Oi) ).
thf(334,plain,
! [A: $i] :
( ( A @ is_fun959573582l_bool )
=> ( A @ collec1580242420t_bool @ is_fun959573582l_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(235,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_fun1736243859e_indi ) @ ( B @ member1105181906e_indi @ hAPP_f234874197l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_f749892423i_bool ) @ ( A @ ( B @ hAPP_f1818473245e_indi ) @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_Pi__mem) ).
thf(1091,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_fun1736243859e_indi ) @ ( B @ member1105181906e_indi @ hAPP_f234874197l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_f749892423i_bool ) @ ( A @ ( B @ hAPP_f1818473245e_indi ) @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(301,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_order__less__imp__not__eq) ).
thf(1343,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(266,axiom,
f @ ( arrow_1212118780le_IIA @ hAPP_f785543729l_bool ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_assms_I3_J) ).
thf(1217,plain,
f @ ( arrow_1212118780le_IIA @ hAPP_f785543729l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( A @ is_bool )
=> ( ( B @ ( A @ ( cOMBK_2069093696le_alt @ hAPP_b1024867081t_bool ) @ hAPP_P2075002375t_bool ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__prod_Itc__Arrow____Order____Mirabe) ).
thf(392,plain,
! [A: $i,B: $i] :
( ( A @ is_bool )
=> ( ( B @ ( A @ ( cOMBK_2069093696le_alt @ hAPP_b1024867081t_bool ) @ hAPP_P2075002375t_bool ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(46,axiom,
! [A: $i,B: $i] :
( ( A @ is_fun959573582l_bool )
=> ( B @ ( A @ hAPP_f1636546729l_bool ) @ is_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_Mtc__005) ).
thf(429,plain,
! [A: $i,B: $i] :
( ( A @ is_fun959573582l_bool )
=> ( B @ ( A @ hAPP_f1636546729l_bool ) @ is_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(171,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
| ( A = B )
| ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_linorder__less__linear) ).
thf(815,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
| ( A = B )
| ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(159,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_fun433100839t_bool ) @ ( B @ member1622429502t_bool @ hAPP_f213304539l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_f861484971l_bool ) @ ( A @ ( B @ hAPP_f695124765t_bool ) @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_PiE) ).
thf(729,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_fun433100839t_bool ) @ ( B @ member1622429502t_bool @ hAPP_f213304539l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_f861484971l_bool ) @ ( A @ ( B @ hAPP_f695124765t_bool ) @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(38,axiom,
! [A: $i] :
( ( A @ is_bool )
=> ( ( A = fFalse )
| ( A = fTrue ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fTrue_1_1_T) ).
thf(407,plain,
! [A: $i] :
( ( A @ is_bool )
=> ( ( A = fFalse )
| ( A = fTrue ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(131,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_less__imp__neq) ).
thf(630,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(63,axiom,
bool @ ( arrow_1812558424le_alt @ ( arrow_1812558424le_alt @ product_prod ) @ fun ) @ undefi802509179t_bool @ is_fun282293932t_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_HOL_Oundefined_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fj) ).
thf(467,plain,
bool @ ( arrow_1812558424le_alt @ ( arrow_1812558424le_alt @ product_prod ) @ fun ) @ undefi802509179t_bool @ is_fun282293932t_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( cOMBK_1072228194t_bool @ hAPP_f1235573641l_bool ) @ hAPP_f497468491l_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc_036) ).
thf(361,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( cOMBK_1072228194t_bool @ hAPP_f1235573641l_bool ) @ hAPP_f497468491l_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(48,axiom,
! [A: $i,B: $i] :
( ( A @ is_fun917378774i_bool )
=> ( B @ ( A @ pi_Arr688267935t_bool ) @ is_fun959573582l_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000tc_) ).
thf(435,plain,
! [A: $i,B: $i] :
( ( A @ is_fun917378774i_bool )
=> ( B @ ( A @ pi_Arr688267935t_bool ) @ is_fun959573582l_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(87,axiom,
! [A: $i,B: $i] :
( ( B @ is_Arr625519182e_indi )
=> ( B @ ( A @ hAPP_A1374816149t_bool ) @ is_fun282293932t_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000tc__fun_It_003) ).
thf(522,plain,
! [A: $i,B: $i] :
( ( B @ is_Arr625519182e_indi )
=> ( B @ ( A @ hAPP_A1374816149t_bool ) @ is_fun282293932t_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(187,axiom,
arrow_413697182e_Prof @ ( e @ ( p @ ( arrow_2077223396_mkbot @ cOMBB_1292070696e_indi ) @ cOMBC_1778077589t_bool ) @ ( e @ ( c @ ( p @ ( arrow_812378712_above @ cOMBB_69933763e_indi ) @ cOMBC_493523632t_bool ) @ cOMBC_1778077589t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_317992461e_indi ) @ cOMBC_277798809t_bool ) @ ( if_fun1419651289t_bool @ cOMBB_963584201e_indi ) @ cOMBS_102864562t_bool ) @ cOMBS_867867294t_bool ) @ ( e @ ( p @ ( arrow_78446834_mktop @ cOMBB_1292070696e_indi ) @ cOMBC_1778077589t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_317992461e_indi ) @ cOMBC_277798809t_bool ) @ ( if_fun1419651289t_bool @ cOMBB_963584201e_indi ) @ cOMBS_102864562t_bool ) @ cOMBS_867867294t_bool ) @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16__096_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai) ).
thf(889,plain,
arrow_413697182e_Prof @ ( e @ ( p @ ( arrow_2077223396_mkbot @ cOMBB_1292070696e_indi ) @ cOMBC_1778077589t_bool ) @ ( e @ ( c @ ( p @ ( arrow_812378712_above @ cOMBB_69933763e_indi ) @ cOMBC_493523632t_bool ) @ cOMBC_1778077589t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_317992461e_indi ) @ cOMBC_277798809t_bool ) @ ( if_fun1419651289t_bool @ cOMBB_963584201e_indi ) @ cOMBS_102864562t_bool ) @ cOMBS_867867294t_bool ) @ ( e @ ( p @ ( arrow_78446834_mktop @ cOMBB_1292070696e_indi ) @ cOMBC_1778077589t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_317992461e_indi ) @ cOMBC_277798809t_bool ) @ ( if_fun1419651289t_bool @ cOMBB_963584201e_indi ) @ cOMBS_102864562t_bool ) @ cOMBS_867867294t_bool ) @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(77,axiom,
! [A: $i,B: $i] :
( ( A @ is_bool )
=> ( ( B @ ( A @ ( cOMBK_1157044842e_indi @ hAPP_b1018211123i_bool ) @ hAPP_A1466488369i_bool ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Arrow____Order____Mirabelle____fje) ).
thf(493,plain,
! [A: $i,B: $i] :
( ( A @ is_bool )
=> ( ( B @ ( A @ ( cOMBK_1157044842e_indi @ hAPP_b1018211123i_bool ) @ hAPP_A1466488369i_bool ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(259,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( cOMBK_116240846e_indi @ hAPP_f813556705l_bool ) @ ( C @ pi_Arr1511953043t_bool ) @ ( B @ member1833291218t_bool @ hAPP_f204273237l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_A1594182429t_bool ) @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_funcset__mem) ).
thf(1195,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( cOMBK_116240846e_indi @ hAPP_f813556705l_bool ) @ ( C @ pi_Arr1511953043t_bool ) @ ( B @ member1833291218t_bool @ hAPP_f204273237l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_A1594182429t_bool ) @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(282,axiom,
! [A: $i] : ( top_to1194196741l_bool @ ( A @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_UNIV__I) ).
thf(1281,plain,
! [A: $i] : ( top_to1194196741l_bool @ ( A @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(285,axiom,
! [A: $i,B: $i] :
( ( A @ is_Arr625519182e_indi )
=> ( ( top_to1256827021i_bool @ ( B @ inj_on24934938di_nat ) @ hBOOL )
=> ( ( A @ ( B @ hAPP_A588601142di_nat ) @ ( B @ ( top_to1256827021i_bool @ hilber1792103167di_nat ) @ hAPP_n385347014e_indi ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_inv__f__f) ).
thf(1291,plain,
! [A: $i,B: $i] :
( ( A @ is_Arr625519182e_indi )
=> ( ( top_to1256827021i_bool @ ( B @ inj_on24934938di_nat ) @ hBOOL )
=> ( ( A @ ( B @ hAPP_A588601142di_nat ) @ ( B @ ( top_to1256827021i_bool @ hilber1792103167di_nat ) @ hAPP_n385347014e_indi ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(1,conjecture,
p @ ( f @ hAPP_f695124765t_bool ) @ ( d @ ( c @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( p @ ( f @ hAPP_f695124765t_bool ) @ ( d @ ( c @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(324,plain,
~ ( p @ ( f @ hAPP_f695124765t_bool ) @ ( d @ ( c @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(175,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_fun525942951l_bool ) @ ( B @ member387398118l_bool @ hAPP_f1279200745l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_f497468491l_bool ) @ ( A @ ( B @ hAPP_f785543729l_bool ) @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member1622429502t_bool @ hAPP_f213304539l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_PiE) ).
thf(847,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_fun525942951l_bool ) @ ( B @ member387398118l_bool @ hAPP_f1279200745l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_f497468491l_bool ) @ ( A @ ( B @ hAPP_f785543729l_bool ) @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member1622429502t_bool @ hAPP_f213304539l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(73,axiom,
lab @ is_fun282293932t_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_v_Lab____) ).
thf(484,plain,
lab @ is_fun282293932t_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(98,axiom,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1018082273l_bool ) @ is_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__fun_Itc__Arrow____Order____M) ).
thf(551,plain,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1018082273l_bool ) @ is_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(240,axiom,
! [A: $i] :
~ ( A @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_order__less__irrefl) ).
thf(1128,plain,
! [A: $i] :
~ ( A @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(304,axiom,
! [A: $i,B: $i,C: $i] :
( ( B = C )
=> ( ( A @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_ord__eq__less__trans) ).
thf(1350,plain,
! [A: $i,B: $i,C: $i] :
( ( B = C )
=> ( ( A @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(182,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_fun2075749915e_indi ) @ ( B @ member1122398042e_indi @ hAPP_f1766869725l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_f355113919i_bool ) @ ( A @ ( B @ hAPP_f618619045e_indi ) @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member1622429502t_bool @ hAPP_f213304539l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_PiE) ).
thf(874,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_fun2075749915e_indi ) @ ( B @ member1122398042e_indi @ hAPP_f1766869725l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_f355113919i_bool ) @ ( A @ ( B @ hAPP_f618619045e_indi ) @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member1622429502t_bool @ hAPP_f213304539l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(156,axiom,
c @ is_Arr553848933le_alt,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_v_c____) ).
thf(725,plain,
c @ is_Arr553848933le_alt,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun282293932t_bool )
=> ( B @ ( A @ hAPP_f352490559i_bool ) @ is_fun917378774i_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fjewxadnqg___021) ).
thf(403,plain,
! [A: $i,B: $i] :
( ( B @ is_fun282293932t_bool )
=> ( B @ ( A @ hAPP_f352490559i_bool ) @ is_fun917378774i_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(317,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_Arr372473371t_bool ) @ ( B @ member1467476314t_bool @ hAPP_f1012384989l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_A1964572607l_bool ) @ ( A @ ( B @ hAPP_A1062826149t_bool ) @ member1622429502t_bool @ hAPP_f213304539l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_PiE) ).
thf(1425,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_Arr372473371t_bool ) @ ( B @ member1467476314t_bool @ hAPP_f1012384989l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_A1964572607l_bool ) @ ( A @ ( B @ hAPP_A1062826149t_bool ) @ member1622429502t_bool @ hAPP_f213304539l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(180,axiom,
! [A: $i] : ( top_to2005687013l_bool @ ( A @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_UNIV__I) ).
thf(869,plain,
! [A: $i] : ( top_to2005687013l_bool @ ( A @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(242,axiom,
! [A: $i] : ( top_to1647826457l_bool @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_UNIV__I) ).
thf(1138,plain,
! [A: $i] : ( top_to1647826457l_bool @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( A @ is_fun959573582l_bool )
=> ( B @ ( A @ pi_fun433100839t_bool ) @ is_fun631676118l_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_FuncSet_OPi_000tc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__Oin) ).
thf(356,plain,
! [A: $i,B: $i] :
( ( A @ is_fun959573582l_bool )
=> ( B @ ( A @ pi_fun433100839t_bool ) @ is_fun631676118l_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(75,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( cOMBK_1015076504t_bool @ hAPP_f1667233577l_bool ) @ hAPP_f417299659l_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc) ).
thf(488,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( cOMBK_1015076504t_bool @ hAPP_f1667233577l_bool ) @ hAPP_f417299659l_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(93,axiom,
! [A: $i,B: $i] :
( ( A @ is_fun282293932t_bool )
=> ( ( B @ ( A @ ( cOMBK_697786936l_bool @ hAPP_f1520552209t_bool ) @ hAPP_b1024867081t_bool ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fj) ).
thf(537,plain,
! [A: $i,B: $i] :
( ( A @ is_fun282293932t_bool )
=> ( ( B @ ( A @ ( cOMBK_697786936l_bool @ hAPP_f1520552209t_bool ) @ hAPP_b1024867081t_bool ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(136,axiom,
lab @ ( b @ ( a @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096) ).
thf(642,plain,
lab @ ( b @ ( a @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(207,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ~ ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_order__less__asym) ).
thf(970,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ~ ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(316,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL )
<=> ( A @ ( B @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_mem__def) ).
thf(1419,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ hAPP_bool_bool ) @ hBOOL )
=> ( B @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL )
=> ( A @ ( B @ hAPP_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun282293932t_bool )
=> ( ( B @ ( A @ ( fFalse @ ( if_fun1419651289t_bool @ hAPP_b1915039793t_bool ) @ hAPP_f159424297t_bool ) @ hAPP_f1673487381t_bool ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fjewxadn) ).
thf(328,plain,
! [A: $i,B: $i] :
( ( B @ is_fun282293932t_bool )
=> ( ( B @ ( A @ ( fFalse @ ( if_fun1419651289t_bool @ hAPP_b1915039793t_bool ) @ hAPP_f159424297t_bool ) @ hAPP_f1673487381t_bool ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(66,axiom,
arrow_1812558424le_alt @ undefi1301554228le_alt @ is_Arr553848933le_alt,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_HOL_Oundefined_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oalt) ).
thf(471,plain,
arrow_1812558424le_alt @ undefi1301554228le_alt @ is_Arr553848933le_alt,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(184,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_Arr149813489le_alt ) @ ( B @ member859582768le_alt @ hAPP_f483434675l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_A1374816149t_bool ) @ ( A @ ( B @ hAPP_A1736628091le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_Pi__mem) ).
thf(884,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_Arr149813489le_alt ) @ ( B @ member859582768le_alt @ hAPP_f483434675l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_A1374816149t_bool ) @ ( A @ ( B @ hAPP_A1736628091le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(295,axiom,
! [A: $i] :
( ( A @ ( top_to1256827021i_bool @ hAPP_A1466488369i_bool ) @ hBOOL )
<=> ( top_top_bool @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_top__apply) ).
thf(1329,plain,
! [A: $i] :
( ( ( top_top_bool @ hBOOL )
=> ( A @ ( top_to1256827021i_bool @ hAPP_A1466488369i_bool ) @ hBOOL ) )
& ( ( A @ ( top_to1256827021i_bool @ hAPP_A1466488369i_bool ) @ hBOOL )
=> ( top_top_bool @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(214,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_Arr1511953043t_bool ) @ ( B @ member1833291218t_bool @ hAPP_f204273237l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_A1912483895l_bool ) @ ( A @ ( B @ hAPP_A1594182429t_bool ) @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_PiE) ).
thf(1016,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_Arr1511953043t_bool ) @ ( B @ member1833291218t_bool @ hAPP_f204273237l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_A1912483895l_bool ) @ ( A @ ( B @ hAPP_A1594182429t_bool ) @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(264,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ is_Arr625519182e_indi )
& ( A @ is_Arr625519182e_indi ) )
=> ( ( top_to1256827021i_bool @ ( C @ inj_on24934938di_nat ) @ hBOOL )
=> ( ( ( A @ ( C @ hAPP_A588601142di_nat ) )
= ( B @ ( C @ hAPP_A588601142di_nat ) ) )
<=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_inj__eq) ).
thf(1207,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ is_Arr625519182e_indi )
& ( A @ is_Arr625519182e_indi ) )
=> ( ( top_to1256827021i_bool @ ( C @ inj_on24934938di_nat ) @ hBOOL )
=> ( ( ( A = B )
=> ( ( A @ ( C @ hAPP_A588601142di_nat ) )
= ( B @ ( C @ hAPP_A588601142di_nat ) ) ) )
& ( ( ( A @ ( C @ hAPP_A588601142di_nat ) )
= ( B @ ( C @ hAPP_A588601142di_nat ) ) )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(116,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun631676118l_bool )
=> ( B @ ( A @ hAPP_f213304539l_bool ) @ is_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____fjew_016) ).
thf(590,plain,
! [A: $i,B: $i] :
( ( B @ is_fun631676118l_bool )
=> ( B @ ( A @ hAPP_f213304539l_bool ) @ is_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(128,axiom,
! [A: $i] : ( top_to2034604131t_bool @ ( A @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_UNIV__I) ).
thf(622,plain,
! [A: $i] : ( top_to2034604131t_bool @ ( A @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(287,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ is_Arr625519182e_indi )
=> ( ( top_to1256827021i_bool @ ( C @ inj_on24934938di_nat ) @ hBOOL )
=> ( ( ( A @ ( C @ hAPP_A588601142di_nat ) )
= B )
=> ( ( B @ ( C @ ( top_to1256827021i_bool @ hilber1792103167di_nat ) @ hAPP_n385347014e_indi ) )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_inv__f__eq) ).
thf(1297,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ is_Arr625519182e_indi )
=> ( ( top_to1256827021i_bool @ ( C @ inj_on24934938di_nat ) @ hBOOL )
=> ( ( ( A @ ( C @ hAPP_A588601142di_nat ) )
= B )
=> ( ( B @ ( C @ ( top_to1256827021i_bool @ hilber1792103167di_nat ) @ hAPP_n385347014e_indi ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(241,axiom,
! [A: $i] :
( ( A @ is_fun631676118l_bool )
=> ( ( A != top_to40512653l_bool )
<=> ( top_to40512653l_bool @ ( A @ ( ord_le1480133609l_bool @ hAPP_f281286919l_bool ) @ hAPP_f213304539l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_less__top) ).
thf(1131,plain,
! [A: $i] :
( ( A @ is_fun631676118l_bool )
=> ( ( ( top_to40512653l_bool @ ( A @ ( ord_le1480133609l_bool @ hAPP_f281286919l_bool ) @ hAPP_f213304539l_bool ) @ hBOOL )
=> ( A != top_to40512653l_bool ) )
& ( ( A != top_to40512653l_bool )
=> ( top_to40512653l_bool @ ( A @ ( ord_le1480133609l_bool @ hAPP_f281286919l_bool ) @ hAPP_f213304539l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(258,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A != B )
=> ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_linorder__cases) ).
thf(1192,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A != B )
=> ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(59,axiom,
! [A: $i] :
( ( top_to2005687013l_bool @ ( cOMBK_1158753900e_indi @ hAPP_f1979025587l_bool ) @ ( A @ pi_Arr688267935t_bool ) )
= top_to1194196741l_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_Pi__UNIV) ).
thf(457,plain,
! [A: $i] :
( ( top_to2005687013l_bool @ ( cOMBK_1158753900e_indi @ hAPP_f1979025587l_bool ) @ ( A @ pi_Arr688267935t_bool ) )
= top_to1194196741l_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(196,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ is_Arr553848933le_alt )
& ( D @ is_Arr553848933le_alt )
& ( C @ is_Arr553848933le_alt ) )
=> ( ( D != E )
=> ( ( E != C )
=> ( ( D != C )
=> ( ( arrow_413697182e_Prof @ ( B @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL )
=> ( ( arrow_413697182e_Prof @ ( A @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL )
=> ( ! [F: $i] :
( ( F @ is_Arr625519182e_indi )
=> ( ( F @ ( B @ hAPP_A1374816149t_bool ) @ ( E @ ( D @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
<=> ( F @ ( A @ hAPP_A1374816149t_bool ) @ ( C @ ( E @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) )
=> ( ( B @ ( f @ hAPP_f695124765t_bool ) @ ( E @ ( D @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
<=> ( A @ ( f @ hAPP_f695124765t_bool ) @ ( C @ ( E @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8__C4_C) ).
thf(911,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ is_Arr553848933le_alt )
& ( D @ is_Arr553848933le_alt )
& ( C @ is_Arr553848933le_alt ) )
=> ( ( D != E )
=> ( ( E != C )
=> ( ( D != C )
=> ( ( arrow_413697182e_Prof @ ( B @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL )
=> ( ( arrow_413697182e_Prof @ ( A @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL )
=> ( ! [F: $i] :
( ( F @ is_Arr625519182e_indi )
=> ( ( ( F @ ( A @ hAPP_A1374816149t_bool ) @ ( C @ ( E @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
=> ( F @ ( B @ hAPP_A1374816149t_bool ) @ ( E @ ( D @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) )
& ( ( F @ ( B @ hAPP_A1374816149t_bool ) @ ( E @ ( D @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
=> ( F @ ( A @ hAPP_A1374816149t_bool ) @ ( C @ ( E @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) ) )
=> ( ( ( A @ ( f @ hAPP_f695124765t_bool ) @ ( C @ ( E @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
=> ( B @ ( f @ hAPP_f695124765t_bool ) @ ( E @ ( D @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) )
& ( ( B @ ( f @ hAPP_f695124765t_bool ) @ ( E @ ( D @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
=> ( A @ ( f @ hAPP_f695124765t_bool ) @ ( C @ ( E @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(22,axiom,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f483434675l_bool ) @ is_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__O_014) ).
thf(371,plain,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f483434675l_bool ) @ is_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(121,axiom,
! [A: $i,B: $i] :
( ( A @ is_fun432044380l_bool )
=> ( ( B @ ( A @ ( cOMBK_971068024l_bool @ hAPP_f2135750719l_bool ) @ hAPP_b1965422783l_bool ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe) ).
thf(605,plain,
! [A: $i,B: $i] :
( ( A @ is_fun432044380l_bool )
=> ( ( B @ ( A @ ( cOMBK_971068024l_bool @ hAPP_f2135750719l_bool ) @ hAPP_b1965422783l_bool ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(107,axiom,
! [A: $i,B: $i] :
( ( ( B @ is_Arr625519182e_indi )
& ( A @ is_fun917378774i_bool ) )
=> ( B @ ( A @ hAPP_A1466488369i_bool ) @ is_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000tc__HOL__O) ).
thf(569,plain,
! [A: $i,B: $i] :
( ( ( B @ is_Arr625519182e_indi )
& ( A @ is_fun917378774i_bool ) )
=> ( B @ ( A @ hAPP_A1466488369i_bool ) @ is_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(319,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F @ is_Arr553848933le_alt )
& ( E @ is_Arr553848933le_alt )
& ( D @ is_Arr553848933le_alt )
& ( C @ is_Arr553848933le_alt ) )
=> ( ( E != F )
=> ( ( C != D )
=> ( ( arrow_413697182e_Prof @ ( B @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL )
=> ( ( arrow_413697182e_Prof @ ( A @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL )
=> ( ! [G: $i] :
( ( G @ is_Arr625519182e_indi )
=> ( ( G @ ( B @ hAPP_A1374816149t_bool ) @ ( F @ ( E @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
<=> ( G @ ( A @ hAPP_A1374816149t_bool ) @ ( D @ ( C @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) )
=> ( ( B @ ( f @ hAPP_f695124765t_bool ) @ ( F @ ( E @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
<=> ( A @ ( f @ hAPP_f695124765t_bool ) @ ( D @ ( C @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_pairwise__neutrality) ).
thf(1429,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F @ is_Arr553848933le_alt )
& ( E @ is_Arr553848933le_alt )
& ( D @ is_Arr553848933le_alt )
& ( C @ is_Arr553848933le_alt ) )
=> ( ( E != F )
=> ( ( C != D )
=> ( ( arrow_413697182e_Prof @ ( B @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL )
=> ( ( arrow_413697182e_Prof @ ( A @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL )
=> ( ! [G: $i] :
( ( G @ is_Arr625519182e_indi )
=> ( ( ( G @ ( A @ hAPP_A1374816149t_bool ) @ ( D @ ( C @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
=> ( G @ ( B @ hAPP_A1374816149t_bool ) @ ( F @ ( E @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) )
& ( ( G @ ( B @ hAPP_A1374816149t_bool ) @ ( F @ ( E @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
=> ( G @ ( A @ hAPP_A1374816149t_bool ) @ ( D @ ( C @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) ) )
=> ( ( ( A @ ( f @ hAPP_f695124765t_bool ) @ ( D @ ( C @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
=> ( B @ ( f @ hAPP_f695124765t_bool ) @ ( F @ ( E @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) )
& ( ( B @ ( f @ hAPP_f695124765t_bool ) @ ( F @ ( E @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
=> ( A @ ( f @ hAPP_f695124765t_bool ) @ ( D @ ( C @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(10,axiom,
top_to40512653l_bool @ is_fun631676118l_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Orde) ).
thf(343,plain,
top_to40512653l_bool @ is_fun631676118l_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(270,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( ( A = B )
| ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_not__less__iff__gr__or__eq) ).
thf(1241,plain,
! [A: $i,B: $i] :
( ( ( ( A = B )
| ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A = B )
| ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(82,axiom,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1766869725l_bool ) @ is_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabell) ).
thf(508,plain,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1766869725l_bool ) @ is_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(94,axiom,
! [A: $i,B: $i] :
( ( A @ is_fun631676118l_bool )
=> ( B @ ( A @ hAPP_f785543729l_bool ) @ is_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__O_012) ).
thf(541,plain,
! [A: $i,B: $i] :
( ( A @ is_fun631676118l_bool )
=> ( B @ ( A @ hAPP_f785543729l_bool ) @ is_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(34,axiom,
! [A: $i] :
( ( top_to1647826457l_bool @ ( cOMBK_2008994872le_alt @ hAPP_f1724001331l_bool ) @ ( A @ pi_Pro2135156861t_bool ) )
= top_to2005687013l_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_Pi__UNIV) ).
thf(398,plain,
! [A: $i] :
( ( top_to1647826457l_bool @ ( cOMBK_2008994872le_alt @ hAPP_f1724001331l_bool ) @ ( A @ pi_Pro2135156861t_bool ) )
= top_to2005687013l_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(102,axiom,
! [A: $i,B: $i] :
( ( B @ is_bool )
=> ( B @ ( A @ hAPP_b1024867081t_bool ) @ is_fun282293932t_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabel) ).
thf(558,plain,
! [A: $i,B: $i] :
( ( B @ is_bool )
=> ( B @ ( A @ hAPP_b1024867081t_bool ) @ is_fun282293932t_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(165,axiom,
arrow_1239002508le_Lin @ ( cOMBK_1088865252t_bool @ hAPP_f20355883l_bool ) @ ( arrow_413697182e_Prof @ pi_fun433100839t_bool ) @ ( f @ member1622429502t_bool @ hAPP_f213304539l_bool ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_assms_I1_J) ).
thf(773,plain,
arrow_1239002508le_Lin @ ( cOMBK_1088865252t_bool @ hAPP_f20355883l_bool ) @ ( arrow_413697182e_Prof @ pi_fun433100839t_bool ) @ ( f @ member1622429502t_bool @ hAPP_f213304539l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(201,axiom,
! [A: $i] :
( ( A @ ( top_to2005687013l_bool @ hAPP_f745298353l_bool ) @ hBOOL )
<=> ( top_top_bool @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_top__apply) ).
thf(953,plain,
! [A: $i] :
( ( ( top_top_bool @ hBOOL )
=> ( A @ ( top_to2005687013l_bool @ hAPP_f745298353l_bool ) @ hBOOL ) )
& ( ( A @ ( top_to2005687013l_bool @ hAPP_f745298353l_bool ) @ hBOOL )
=> ( top_top_bool @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(257,axiom,
! [A: $i] :
( ( A @ is_fun959573582l_bool )
=> ( ( A != top_to1194196741l_bool )
<=> ( top_to1194196741l_bool @ ( A @ ( ord_le453141089l_bool @ hAPP_f1760255479l_bool ) @ hAPP_f453661011l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_less__top) ).
thf(1185,plain,
! [A: $i] :
( ( A @ is_fun959573582l_bool )
=> ( ( ( top_to1194196741l_bool @ ( A @ ( ord_le453141089l_bool @ hAPP_f1760255479l_bool ) @ hAPP_f453661011l_bool ) @ hBOOL )
=> ( A != top_to1194196741l_bool ) )
& ( ( A != top_to1194196741l_bool )
=> ( top_to1194196741l_bool @ ( A @ ( ord_le453141089l_bool @ hAPP_f1760255479l_bool ) @ hAPP_f453661011l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(193,axiom,
arrow_1239002508le_Lin @ ( lba @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116__096Lba_A_058_ALin_096) ).
thf(906,plain,
arrow_1239002508le_Lin @ ( lba @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(40,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun282293932t_bool )
=> ( B @ ( A @ hAPP_f1673487381t_bool ) @ is_fun282293932t_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fjewxadnqg___023) ).
thf(412,plain,
! [A: $i,B: $i] :
( ( B @ is_fun282293932t_bool )
=> ( B @ ( A @ hAPP_f1673487381t_bool ) @ is_fun282293932t_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(205,axiom,
! [A: $i] :
~ ( A @ ( top_top_bool @ ( ord_less_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_not__top__less) ).
thf(965,plain,
! [A: $i] :
~ ( A @ ( top_top_bool @ ( ord_less_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(271,axiom,
! [A: $i] :
( ( A @ is_fun432044380l_bool )
=> ( ( A != top_to2005687013l_bool )
<=> ( top_to2005687013l_bool @ ( A @ ( ord_le272605321l_bool @ hAPP_f1669465919l_bool ) @ hAPP_f503012287l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_less__top) ).
thf(1251,plain,
! [A: $i] :
( ( A @ is_fun432044380l_bool )
=> ( ( ( top_to2005687013l_bool @ ( A @ ( ord_le272605321l_bool @ hAPP_f1669465919l_bool ) @ hAPP_f503012287l_bool ) @ hBOOL )
=> ( A != top_to2005687013l_bool ) )
& ( ( A != top_to2005687013l_bool )
=> ( top_to2005687013l_bool @ ( A @ ( ord_le272605321l_bool @ hAPP_f1669465919l_bool ) @ hAPP_f503012287l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(246,axiom,
n @ ( h @ ( top_to1256827021i_bool @ hilber1792103167di_nat ) @ hAPP_n385347014e_indi ) @ ( p @ hAPP_A1374816149t_bool ) @ ( d @ ( c @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12__096c_A_060_092_060_094bsub_062P_A_Iinv_Ah_An_J_092_060_094esub_062_Ad_0) ).
thf(1146,plain,
n @ ( h @ ( top_to1256827021i_bool @ hilber1792103167di_nat ) @ hAPP_n385347014e_indi ) @ ( p @ hAPP_A1374816149t_bool ) @ ( d @ ( c @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(52,axiom,
arrow_2110637339e_indi @ undefi818645567e_indi @ is_Arr625519182e_indi,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_HOL_Oundefined_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi) ).
thf(444,plain,
arrow_2110637339e_indi @ undefi818645567e_indi @ is_Arr625519182e_indi,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(120,axiom,
! [A: $i,B: $i] :
( ( A @ is_fun917378774i_bool )
=> ( ( B @ ( A @ ( cOMBK_454107598t_bool @ hAPP_f681113465i_bool ) @ hAPP_f749892423i_bool ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg___031) ).
thf(601,plain,
! [A: $i,B: $i] :
( ( A @ is_fun917378774i_bool )
=> ( ( B @ ( A @ ( cOMBK_454107598t_bool @ hAPP_f681113465i_bool ) @ hAPP_f749892423i_bool ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(24,axiom,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1012384989l_bool ) @ is_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__O_009) ).
thf(375,plain,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1012384989l_bool ) @ is_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(161,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL )
<=> ( A @ ( B @ hAPP_A1466488369i_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_mem__def) ).
thf(733,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ hAPP_A1466488369i_bool ) @ hBOOL )
=> ( B @ ( A @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( A @ ( B @ hAPP_A1466488369i_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(44,axiom,
! [A: $i,B: $i] :
( ( A @ is_fun432044380l_bool )
=> ( ( B @ ( A @ ( cOMBK_1158753900e_indi @ hAPP_f1979025587l_bool ) @ hAPP_A1944296755l_bool ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_028) ).
thf(423,plain,
! [A: $i,B: $i] :
( ( A @ is_fun432044380l_bool )
=> ( ( B @ ( A @ ( cOMBK_1158753900e_indi @ hAPP_f1979025587l_bool ) @ hAPP_A1944296755l_bool ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(149,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL )
<=> ( A @ ( B @ hAPP_f1636546729l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_mem__def) ).
thf(694,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ hAPP_f1636546729l_bool ) @ hBOOL )
=> ( B @ ( A @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL )
=> ( A @ ( B @ hAPP_f1636546729l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(315,axiom,
! [A: $i] :
( ( A @ ( arrow_1212118780le_IIA @ hAPP_f785543729l_bool ) @ hBOOL )
<=> ! [B: $i] :
( ( arrow_413697182e_Prof @ ( B @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL )
=> ! [C: $i] :
( ( arrow_413697182e_Prof @ ( C @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL )
=> ! [D: $i,E: $i] :
( ( ( E @ is_Arr553848933le_alt )
& ( D @ is_Arr553848933le_alt ) )
=> ( ! [F: $i] :
( ( F @ is_Arr625519182e_indi )
=> ( ( F @ ( B @ hAPP_A1374816149t_bool ) @ ( E @ ( D @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
<=> ( F @ ( C @ hAPP_A1374816149t_bool ) @ ( E @ ( D @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) )
=> ( ( B @ ( A @ hAPP_f695124765t_bool ) @ ( E @ ( D @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
<=> ( C @ ( A @ hAPP_f695124765t_bool ) @ ( E @ ( D @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_IIA__def) ).
thf(1389,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( arrow_413697182e_Prof @ ( B @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL )
=> ! [C: $i] :
( ( arrow_413697182e_Prof @ ( C @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL )
=> ! [D: $i,E: $i] :
( ( ( E @ is_Arr553848933le_alt )
& ( D @ is_Arr553848933le_alt ) )
=> ( ! [F: $i] :
( ( F @ is_Arr625519182e_indi )
=> ( ( ( F @ ( C @ hAPP_A1374816149t_bool ) @ ( E @ ( D @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
=> ( F @ ( B @ hAPP_A1374816149t_bool ) @ ( E @ ( D @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) )
& ( ( F @ ( B @ hAPP_A1374816149t_bool ) @ ( E @ ( D @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
=> ( F @ ( C @ hAPP_A1374816149t_bool ) @ ( E @ ( D @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) ) )
=> ( ( ( C @ ( A @ hAPP_f695124765t_bool ) @ ( E @ ( D @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
=> ( B @ ( A @ hAPP_f695124765t_bool ) @ ( E @ ( D @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ hAPP_f695124765t_bool ) @ ( E @ ( D @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
=> ( C @ ( A @ hAPP_f695124765t_bool ) @ ( E @ ( D @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) ) ) ) ) )
=> ( A @ ( arrow_1212118780le_IIA @ hAPP_f785543729l_bool ) @ hBOOL ) )
& ( ( A @ ( arrow_1212118780le_IIA @ hAPP_f785543729l_bool ) @ hBOOL )
=> ! [B: $i] :
( ( arrow_413697182e_Prof @ ( B @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL )
=> ! [C: $i] :
( ( arrow_413697182e_Prof @ ( C @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL )
=> ! [D: $i,E: $i] :
( ( ( E @ is_Arr553848933le_alt )
& ( D @ is_Arr553848933le_alt ) )
=> ( ! [F: $i] :
( ( F @ is_Arr625519182e_indi )
=> ( ( ( F @ ( C @ hAPP_A1374816149t_bool ) @ ( E @ ( D @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
=> ( F @ ( B @ hAPP_A1374816149t_bool ) @ ( E @ ( D @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) )
& ( ( F @ ( B @ hAPP_A1374816149t_bool ) @ ( E @ ( D @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
=> ( F @ ( C @ hAPP_A1374816149t_bool ) @ ( E @ ( D @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) ) )
=> ( ( ( C @ ( A @ hAPP_f695124765t_bool ) @ ( E @ ( D @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
=> ( B @ ( A @ hAPP_f695124765t_bool ) @ ( E @ ( D @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ hAPP_f695124765t_bool ) @ ( E @ ( D @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
=> ( C @ ( A @ hAPP_f695124765t_bool ) @ ( E @ ( D @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(174,axiom,
! [A: $i,B: $i,C: $i] :
( ( B = C )
=> ( ( C @ ( A @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_xt1_I1_J) ).
thf(843,plain,
! [A: $i,B: $i,C: $i] :
( ( B = C )
=> ( ( C @ ( A @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(112,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_69933763e_indi ) @ hAPP_A460042315t_bool ) )
= ( C @ ( B @ hAPP_A1374816149t_bool ) @ ( A @ hAPP_f1336478923t_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fj_039) ).
thf(579,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_69933763e_indi ) @ hAPP_A460042315t_bool ) )
= ( C @ ( B @ hAPP_A1374816149t_bool ) @ ( A @ hAPP_f1336478923t_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(114,axiom,
! [A: $i] :
( ( A @ is_bool )
=> ( ( A = fFalse )
| ( A = fTrue ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fjewxadn) ).
thf(584,plain,
! [A: $i] :
( ( A @ is_bool )
=> ( ( A = fFalse )
| ( A = fTrue ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(250,axiom,
c != d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__096c_A_126_061_Ad_096) ).
thf(1154,plain,
c != d,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(104,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_493523632t_bool ) @ hAPP_A702630576t_bool ) )
= ( B @ ( C @ ( A @ hAPP_A460042315t_bool ) @ hAPP_A384644407t_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000_033) ).
thf(562,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_493523632t_bool ) @ hAPP_A702630576t_bool ) )
= ( B @ ( C @ ( A @ hAPP_A460042315t_bool ) @ hAPP_A384644407t_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(192,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( cOMBK_971068024l_bool @ hAPP_f2135750719l_bool ) @ ( C @ pi_boo2007389459t_bool ) @ ( B @ member497701034t_bool @ hAPP_f1550037191l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_b1024867081t_bool ) @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_funcset__mem) ).
thf(904,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( cOMBK_971068024l_bool @ hAPP_f2135750719l_bool ) @ ( C @ pi_boo2007389459t_bool ) @ ( B @ member497701034t_bool @ hAPP_f1550037191l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_b1024867081t_bool ) @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(111,axiom,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f861484971l_bool ) @ is_fun432044380l_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_Mtc__007) ).
thf(577,plain,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f861484971l_bool ) @ is_fun432044380l_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(153,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_fun433100839t_bool ) @ ( B @ member1622429502t_bool @ hAPP_f213304539l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_f861484971l_bool ) @ ( A @ ( B @ hAPP_f695124765t_bool ) @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_Pi__mem) ).
thf(711,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_fun433100839t_bool ) @ ( B @ member1622429502t_bool @ hAPP_f213304539l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_f861484971l_bool ) @ ( A @ ( B @ hAPP_f695124765t_bool ) @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(53,axiom,
a != b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193__096a_A_126_061_Ab_096) ).
thf(445,plain,
a != b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( A @ is_fun282293932t_bool )
=> ( ( B @ ( A @ ( fTrue @ ( if_fun1419651289t_bool @ hAPP_b1915039793t_bool ) @ hAPP_f159424297t_bool ) @ hAPP_f1673487381t_bool ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fjewxadn) ).
thf(382,plain,
! [A: $i,B: $i] :
( ( A @ is_fun282293932t_bool )
=> ( ( B @ ( A @ ( fTrue @ ( if_fun1419651289t_bool @ hAPP_b1915039793t_bool ) @ hAPP_f159424297t_bool ) @ hAPP_f1673487381t_bool ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(309,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL )
=> ~ ( A @ ( B @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_order__less__asym) ).
thf(1371,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL )
=> ~ ( A @ ( B @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(154,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_fun525942951l_bool ) @ ( B @ member387398118l_bool @ hAPP_f1279200745l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member1622429502t_bool @ hAPP_f213304539l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_f497468491l_bool ) @ ( A @ ( B @ hAPP_f785543729l_bool ) @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_Pi__mem) ).
thf(713,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_fun525942951l_bool ) @ ( B @ member387398118l_bool @ hAPP_f1279200745l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member1622429502t_bool @ hAPP_f213304539l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_f497468491l_bool ) @ ( A @ ( B @ hAPP_f785543729l_bool ) @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(269,axiom,
! [A: $i] : ( top_to2005687013l_bool @ ( A @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_iso__tuple__UNIV__I) ).
thf(1239,plain,
! [A: $i] : ( top_to2005687013l_bool @ ( A @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(198,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( ( B @ ( C @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( A @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_order__less__imp__triv) ).
thf(947,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( ( B @ ( C @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( A @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(268,axiom,
! [A: $i] :
( ( A @ ( arrow_467566751nimity @ hAPP_f785543729l_bool ) @ hBOOL )
<=> ! [B: $i] :
( ( arrow_413697182e_Prof @ ( B @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL )
=> ! [C: $i,D: $i] :
( ( ( D @ is_Arr553848933le_alt )
& ( C @ is_Arr553848933le_alt ) )
=> ( ! [E: $i] :
( ( E @ is_Arr625519182e_indi )
=> ( E @ ( B @ hAPP_A1374816149t_bool ) @ ( D @ ( C @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) )
=> ( B @ ( A @ hAPP_f695124765t_bool ) @ ( D @ ( C @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_unanimity__def) ).
thf(1224,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( arrow_413697182e_Prof @ ( B @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL )
=> ! [C: $i,D: $i] :
( ( ( D @ is_Arr553848933le_alt )
& ( C @ is_Arr553848933le_alt ) )
=> ( ! [E: $i] :
( ( E @ is_Arr625519182e_indi )
=> ( E @ ( B @ hAPP_A1374816149t_bool ) @ ( D @ ( C @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) )
=> ( B @ ( A @ hAPP_f695124765t_bool ) @ ( D @ ( C @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) ) )
=> ( A @ ( arrow_467566751nimity @ hAPP_f785543729l_bool ) @ hBOOL ) )
& ( ( A @ ( arrow_467566751nimity @ hAPP_f785543729l_bool ) @ hBOOL )
=> ! [B: $i] :
( ( arrow_413697182e_Prof @ ( B @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL )
=> ! [C: $i,D: $i] :
( ( ( D @ is_Arr553848933le_alt )
& ( C @ is_Arr553848933le_alt ) )
=> ( ! [E: $i] :
( ( E @ is_Arr625519182e_indi )
=> ( E @ ( B @ hAPP_A1374816149t_bool ) @ ( D @ ( C @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) )
=> ( B @ ( A @ hAPP_f695124765t_bool ) @ ( D @ ( C @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(13,axiom,
b @ is_Arr553848933le_alt,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_v_b____) ).
thf(350,plain,
b @ is_Arr553848933le_alt,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(272,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_order__less__trans) ).
thf(1258,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(152,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ~ ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_linorder__antisym__conv3) ).
thf(704,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( B = A )
=> ~ ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ~ ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(191,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ is_Arr625519182e_indi )
=> ( ( C @ ( B @ inj_on24934938di_nat ) @ hBOOL )
=> ( ( C @ ( A @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( ( A @ ( B @ hAPP_A588601142di_nat ) @ ( B @ ( C @ hilber1792103167di_nat ) @ hAPP_n385347014e_indi ) )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_inv__into__f__f) ).
thf(900,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ is_Arr625519182e_indi )
=> ( ( C @ ( B @ inj_on24934938di_nat ) @ hBOOL )
=> ( ( C @ ( A @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( ( A @ ( B @ hAPP_A588601142di_nat ) @ ( B @ ( C @ hilber1792103167di_nat ) @ hAPP_n385347014e_indi ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(219,axiom,
! [A: $i] :
~ ( A @ ( A @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_order__less__irrefl) ).
thf(1048,plain,
! [A: $i] :
~ ( A @ ( A @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(245,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( cOMBK_697604314l_bool @ hAPP_f371807573l_bool ) @ ( C @ pi_boo691944735t_bool ) @ ( B @ member1911067358t_bool @ hAPP_f1018082273l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_b833696937t_bool ) @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_funcset__mem) ).
thf(1144,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( cOMBK_697604314l_bool @ hAPP_f371807573l_bool ) @ ( C @ pi_boo691944735t_bool ) @ ( B @ member1911067358t_bool @ hAPP_f1018082273l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_b833696937t_bool ) @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(140,axiom,
! [A: $i] : ( A @ ( top_to1194196741l_bool @ hAPP_f1636546729l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_top1I) ).
thf(649,plain,
! [A: $i] : ( A @ ( top_to1194196741l_bool @ hAPP_f1636546729l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(125,axiom,
e @ is_Arr553848933le_alt,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_v_e____) ).
thf(616,plain,
e @ is_Arr553848933le_alt,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(119,axiom,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_P2024088443e_indi ) @ is_Arr625519182e_indi ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____fjewxadnqg__Oalt_Mtc_) ).
thf(599,plain,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_P2024088443e_indi ) @ is_Arr625519182e_indi ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(25,axiom,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1550037191l_bool ) @ is_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__fun_Itc__prod_Itc__Arrow____) ).
thf(377,plain,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1550037191l_bool ) @ is_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(210,axiom,
! [A: $i,B: $i] :
( ( A @ is_fun1016509681e_indi )
=> ( ( top_to1256827021i_bool @ ( B @ inj_on24934938di_nat ) @ hBOOL )
=> ( ! [C: $i] :
( ( C @ ( A @ hAPP_n385347014e_indi ) @ ( B @ hAPP_A588601142di_nat ) )
= C )
=> ( ( B @ ( top_to1256827021i_bool @ hilber1792103167di_nat ) )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_inj__imp__inv__eq) ).
thf(996,plain,
! [A: $i,B: $i] :
( ( A @ is_fun1016509681e_indi )
=> ( ( top_to1256827021i_bool @ ( B @ inj_on24934938di_nat ) @ hBOOL )
=> ( ! [C: $i] :
( ( C @ ( A @ hAPP_n385347014e_indi ) @ ( B @ hAPP_A588601142di_nat ) )
= C )
=> ( ( B @ ( top_to1256827021i_bool @ hilber1792103167di_nat ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(56,axiom,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_P907763049i_bool ) @ is_fun917378774i_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____fjewxadnqg__Oalt_Mtc__025) ).
thf(451,plain,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_P907763049i_bool ) @ is_fun917378774i_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(106,axiom,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1271180905l_bool ) @ is_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__fun_Itc__fun_Itc__Arrow____O) ).
thf(567,plain,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1271180905l_bool ) @ is_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(188,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_boo1877522301le_alt ) @ ( B @ member42699324le_alt @ hAPP_f1895985727l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_b1024867081t_bool ) @ ( A @ ( B @ hAPP_b1817367815le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_Pi__mem) ).
thf(890,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_boo1877522301le_alt ) @ ( B @ member42699324le_alt @ hAPP_f1895985727l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_b1024867081t_bool ) @ ( A @ ( B @ hAPP_b1817367815le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(69,axiom,
a @ is_Arr553848933le_alt,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_v_a____) ).
thf(477,plain,
a @ is_Arr553848933le_alt,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(231,axiom,
fTrue @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fTrue_1_1_U) ).
thf(1080,plain,
fTrue @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(122,axiom,
! [A: $i,B: $i] :
( ( A @ is_fun282293932t_bool )
=> ( B @ ( A @ pi_Pro2135156861t_bool ) @ is_fun432044380l_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_FuncSet_OPi_000tc__prod_Itc__Arrow____Order____Mirabelle____fjewxadnqg__Oa) ).
thf(609,plain,
! [A: $i,B: $i] :
( ( A @ is_fun282293932t_bool )
=> ( B @ ( A @ pi_Pro2135156861t_bool ) @ is_fun432044380l_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(157,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_fun2075749915e_indi ) @ ( B @ member1122398042e_indi @ hAPP_f1766869725l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member1622429502t_bool @ hAPP_f213304539l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_f355113919i_bool ) @ ( A @ ( B @ hAPP_f618619045e_indi ) @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_Pi__mem) ).
thf(726,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_fun2075749915e_indi ) @ ( B @ member1122398042e_indi @ hAPP_f1766869725l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member1622429502t_bool @ hAPP_f213304539l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_f355113919i_bool ) @ ( A @ ( B @ hAPP_f618619045e_indi ) @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(293,axiom,
! [A: $i] : ( arrow_413697182e_Prof @ ( lba @ ( lab @ ( A @ ( h @ ( ord_less_nat @ cOMBB_317992461e_indi ) @ cOMBC_277798809t_bool ) @ ( if_fun1419651289t_bool @ cOMBB_963584201e_indi ) @ cOMBC_481590946t_bool ) @ cOMBC_437064334t_bool ) @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_PiProf) ).
thf(1325,plain,
! [A: $i] : ( arrow_413697182e_Prof @ ( lba @ ( lab @ ( A @ ( h @ ( ord_less_nat @ cOMBB_317992461e_indi ) @ cOMBC_277798809t_bool ) @ ( if_fun1419651289t_bool @ cOMBB_963584201e_indi ) @ cOMBC_481590946t_bool ) @ cOMBC_437064334t_bool ) @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(130,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_order__less__imp__not__eq2) ).
thf(626,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(253,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_boo71521447t_bool ) @ ( B @ member2081512038t_bool @ hAPP_f1271180905l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_b990649139l_bool ) @ ( A @ ( B @ hAPP_b331122225t_bool ) @ member1622429502t_bool @ hAPP_f213304539l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_PiE) ).
thf(1177,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_boo71521447t_bool ) @ ( B @ member2081512038t_bool @ hAPP_f1271180905l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_b990649139l_bool ) @ ( A @ ( B @ hAPP_b331122225t_bool ) @ member1622429502t_bool @ hAPP_f213304539l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(61,axiom,
! [A: $i,B: $i] :
( ( A @ is_fun282293932t_bool )
=> ( B @ ( A @ hAPP_P2075002375t_bool ) @ is_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____fjewxadnqg__Oalt_Mtc__024) ).
thf(462,plain,
! [A: $i,B: $i] :
( ( A @ is_fun282293932t_bool )
=> ( B @ ( A @ hAPP_P2075002375t_bool ) @ is_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(169,axiom,
! [A: $i,B: $i] :
( ( arrow_1239002508le_Lin @ ( B @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL )
=> ( arrow_1239002508le_Lin @ ( A @ ( B @ ( arrow_2077223396_mkbot @ hAPP_f1290184496t_bool ) @ hAPP_A619995676t_bool ) @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_mkbot__Lin) ).
thf(811,plain,
! [A: $i,B: $i] :
( ( arrow_1239002508le_Lin @ ( B @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL )
=> ( arrow_1239002508le_Lin @ ( A @ ( B @ ( arrow_2077223396_mkbot @ hAPP_f1290184496t_bool ) @ hAPP_A619995676t_bool ) @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_1292070696e_indi ) @ hAPP_A702630576t_bool ) )
= ( C @ ( B @ hAPP_A1374816149t_bool ) @ ( A @ hAPP_f1290184496t_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fj) ).
thf(387,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_1292070696e_indi ) @ hAPP_A702630576t_bool ) )
= ( C @ ( B @ hAPP_A1374816149t_bool ) @ ( A @ hAPP_f1290184496t_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(163,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ is_Arr553848933le_alt )
& ( B @ is_Arr553848933le_alt ) )
=> ( ( B != C )
=> ( ( arrow_1239002508le_Lin @ ( A @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL )
=> ( arrow_1239002508le_Lin @ ( C @ ( B @ ( A @ ( arrow_812378712_above @ hAPP_f1336478923t_bool ) @ hAPP_A384644407t_bool ) @ hAPP_A619995676t_bool ) @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_above__Lin) ).
thf(758,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ is_Arr553848933le_alt )
& ( B @ is_Arr553848933le_alt ) )
=> ( ( B != C )
=> ( ( arrow_1239002508le_Lin @ ( A @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL )
=> ( arrow_1239002508le_Lin @ ( C @ ( B @ ( A @ ( arrow_812378712_above @ hAPP_f1336478923t_bool ) @ hAPP_A384644407t_bool ) @ hAPP_A619995676t_bool ) @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(298,axiom,
d @ is_Arr553848933le_alt,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_v_d____) ).
thf(1339,plain,
d @ is_Arr553848933le_alt,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(150,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL )
=> ~ ( A @ ( B @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_order__less__asym_H) ).
thf(700,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL )
=> ~ ( A @ ( B @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(86,axiom,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f526292585l_bool ) @ is_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabel_018) ).
thf(520,plain,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f526292585l_bool ) @ is_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(202,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_boo1877522301le_alt ) @ ( B @ member42699324le_alt @ hAPP_f1895985727l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_b1024867081t_bool ) @ ( A @ ( B @ hAPP_b1817367815le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_PiE) ).
thf(959,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_boo1877522301le_alt ) @ ( B @ member42699324le_alt @ hAPP_f1895985727l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_b1024867081t_bool ) @ ( A @ ( B @ hAPP_b1817367815le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(58,axiom,
! [A: $i,B: $i] :
( ( B @ is_bool )
=> ( B @ ( A @ hAPP_bool_bool ) @ is_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool) ).
thf(455,plain,
! [A: $i,B: $i] :
( ( B @ is_bool )
=> ( B @ ( A @ hAPP_bool_bool ) @ is_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(211,axiom,
! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( C @ is_Arr625519182e_indi )
& ( B @ is_Arr625519182e_indi ) )
=> ( ( ( B @ ( A @ hAPP_A588601142di_nat ) )
= ( C @ ( A @ hAPP_A588601142di_nat ) ) )
=> ( B = C ) ) )
=> ( top_to1256827021i_bool @ ( A @ inj_on24934938di_nat ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_injI) ).
thf(1000,plain,
! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( C @ is_Arr625519182e_indi )
& ( B @ is_Arr625519182e_indi ) )
=> ( ( ( B @ ( A @ hAPP_A588601142di_nat ) )
= ( C @ ( A @ hAPP_A588601142di_nat ) ) )
=> ( B = C ) ) )
=> ( top_to1256827021i_bool @ ( A @ inj_on24934938di_nat ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(321,axiom,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f695124765t_bool ) @ is_fun282293932t_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_Mtc__008) ).
thf(1477,plain,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f695124765t_bool ) @ is_fun282293932t_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(49,axiom,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f592909149l_bool ) @ is_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabel) ).
thf(438,plain,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f592909149l_bool ) @ is_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(142,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ is_Arr625519182e_indi )
& ( A @ is_Arr625519182e_indi ) )
=> ( ( D @ ( C @ inj_on24934938di_nat ) @ hBOOL )
=> ( ( D @ ( B @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( ( D @ ( A @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( ( ( B @ ( C @ hAPP_A588601142di_nat ) )
= ( A @ ( C @ hAPP_A588601142di_nat ) ) )
<=> ( B = A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_inj__on__iff) ).
thf(653,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ is_Arr625519182e_indi )
& ( A @ is_Arr625519182e_indi ) )
=> ( ( D @ ( C @ inj_on24934938di_nat ) @ hBOOL )
=> ( ( D @ ( B @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( ( D @ ( A @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( ( ( B = A )
=> ( ( B @ ( C @ hAPP_A588601142di_nat ) )
= ( A @ ( C @ hAPP_A588601142di_nat ) ) ) )
& ( ( ( B @ ( C @ hAPP_A588601142di_nat ) )
= ( A @ ( C @ hAPP_A588601142di_nat ) ) )
=> ( B = A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(133,axiom,
! [A: $i,B: $i] :
( ( A != B )
=> ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_linorder__neqE) ).
thf(636,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(217,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( C @ ( A @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_xt1_I10_J) ).
thf(1044,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( C @ ( A @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(229,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( cOMBK_1372975190t_bool @ hAPP_f1677452273i_bool ) @ ( C @ pi_fun2075749915e_indi ) @ ( B @ member1122398042e_indi @ hAPP_f1766869725l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member1622429502t_bool @ hAPP_f213304539l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_f618619045e_indi ) @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_funcset__mem) ).
thf(1076,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( cOMBK_1372975190t_bool @ hAPP_f1677452273i_bool ) @ ( C @ pi_fun2075749915e_indi ) @ ( B @ member1122398042e_indi @ hAPP_f1766869725l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member1622429502t_bool @ hAPP_f213304539l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_f618619045e_indi ) @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(289,axiom,
! [A: $i] :
( ( A @ is_fun282293932t_bool )
=> ( ( A != top_to2034604131t_bool )
<=> ( top_to2034604131t_bool @ ( A @ ( ord_le227393471t_bool @ hAPP_f2056167603l_bool ) @ hAPP_f745298353l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_less__top) ).
thf(1304,plain,
! [A: $i] :
( ( A @ is_fun282293932t_bool )
=> ( ( ( top_to2034604131t_bool @ ( A @ ( ord_le227393471t_bool @ hAPP_f2056167603l_bool ) @ hAPP_f745298353l_bool ) @ hBOOL )
=> ( A != top_to2034604131t_bool ) )
& ( ( A != top_to2034604131t_bool )
=> ( top_to2034604131t_bool @ ( A @ ( ord_le227393471t_bool @ hAPP_f2056167603l_bool ) @ hAPP_f745298353l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(262,axiom,
! [A: $i,B: $i] :
( ( ( B @ is_fun282293932t_bool )
& ( A @ is_fun432044380l_bool ) )
=> ( B @ ( A @ hAPP_f745298353l_bool ) @ is_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fjewxadnqg___020) ).
thf(1203,plain,
! [A: $i,B: $i] :
( ( ( B @ is_fun282293932t_bool )
& ( A @ is_fun432044380l_bool ) )
=> ( B @ ( A @ hAPP_f745298353l_bool ) @ is_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(91,axiom,
! [A: $i,B: $i] :
( ( B @ is_Arr553848933le_alt )
=> ( B @ ( A @ hAPP_A619995676t_bool ) @ is_fun282293932t_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oalt_000tc__fun_Itc) ).
thf(531,plain,
! [A: $i,B: $i] :
( ( B @ is_Arr553848933le_alt )
=> ( B @ ( A @ hAPP_A619995676t_bool ) @ is_fun282293932t_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(144,axiom,
! [A: $i] :
( ~ ( ( A @ hBOOL )
<=> ( top_top_bool @ hBOOL ) )
<=> ( top_top_bool @ ( A @ ( ord_less_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_less__top) ).
thf(663,plain,
! [A: $i] :
( ( ( top_top_bool @ ( A @ ( ord_less_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ~ ( ( ( top_top_bool @ hBOOL )
=> ( A @ hBOOL ) )
& ( ( A @ hBOOL )
=> ( top_top_bool @ hBOOL ) ) ) )
& ( ~ ( ( ( top_top_bool @ hBOOL )
=> ( A @ hBOOL ) )
& ( ( A @ hBOOL )
=> ( top_top_bool @ hBOOL ) ) )
=> ( top_top_bool @ ( A @ ( ord_less_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(197,axiom,
! [A: $i,B: $i] :
( ( ( B @ is_fun282293932t_bool )
& ( A @ is_fun282293932t_bool ) )
=> ( ! [C: $i,D: $i] :
( ( ( D @ is_Arr553848933le_alt )
& ( C @ is_Arr553848933le_alt ) )
=> ( ( B @ ( D @ ( C @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
<=> ( A @ ( D @ ( C @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_pred__equals__eq2) ).
thf(927,plain,
! [A: $i,B: $i] :
( ( ( B @ is_fun282293932t_bool )
& ( A @ is_fun282293932t_bool ) )
=> ( ( ( B = A )
=> ! [C: $i,D: $i] :
( ( ( D @ is_Arr553848933le_alt )
& ( C @ is_Arr553848933le_alt ) )
=> ( ( ( A @ ( D @ ( C @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
=> ( B @ ( D @ ( C @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) )
& ( ( B @ ( D @ ( C @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
=> ( A @ ( D @ ( C @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) ) ) )
& ( ! [C: $i,D: $i] :
( ( ( D @ is_Arr553848933le_alt )
& ( C @ is_Arr553848933le_alt ) )
=> ( ( ( A @ ( D @ ( C @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
=> ( B @ ( D @ ( C @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) )
& ( ( B @ ( D @ ( C @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
=> ( A @ ( D @ ( C @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(280,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_fun972956463e_indi ) @ ( B @ member329987264e_indi @ hAPP_f592909149l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_f352490559i_bool ) @ ( A @ ( B @ hAPP_f1659504677e_indi ) @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_Pi__mem) ).
thf(1277,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_fun972956463e_indi ) @ ( B @ member329987264e_indi @ hAPP_f592909149l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_f352490559i_bool ) @ ( A @ ( B @ hAPP_f1659504677e_indi ) @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(232,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( cOMBK_1152753196e_indi @ hAPP_f1507266205t_bool ) @ ( C @ pi_Arr149813489le_alt ) @ ( B @ member859582768le_alt @ hAPP_f483434675l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_A1736628091le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_funcset__mem) ).
thf(1081,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( cOMBK_1152753196e_indi @ hAPP_f1507266205t_bool ) @ ( C @ pi_Arr149813489le_alt ) @ ( B @ member859582768le_alt @ hAPP_f483434675l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_A1736628091le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(299,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( cOMBK_454107598t_bool @ hAPP_f681113465i_bool ) @ ( C @ pi_fun1736243859e_indi ) @ ( B @ member1105181906e_indi @ hAPP_f234874197l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_f1818473245e_indi ) @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_funcset__mem) ).
thf(1340,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( cOMBK_454107598t_bool @ hAPP_f681113465i_bool ) @ ( C @ pi_fun1736243859e_indi ) @ ( B @ member1105181906e_indi @ hAPP_f234874197l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_f1818473245e_indi ) @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(215,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ is_Arr553848933le_alt )
& ( B @ is_Arr553848933le_alt )
& ( A @ is_Arr553848933le_alt ) )
=> ( ( D @ ( C @ ( arrow_78446834_mktop @ hAPP_f1290184496t_bool ) @ hAPP_A619995676t_bool ) @ ( B @ ( A @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
<=> ( ( ( B != D )
=> ( C @ ( B @ ( A @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) )
& ( ( B = D )
=> ( A != B ) )
& ( A != D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_in__mktop) ).
thf(1018,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ is_Arr553848933le_alt )
& ( B @ is_Arr553848933le_alt )
& ( A @ is_Arr553848933le_alt ) )
=> ( ( ( ( ( B != D )
=> ( C @ ( B @ ( A @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) )
& ( ( B = D )
=> ( A != B ) )
& ( A != D ) )
=> ( D @ ( C @ ( arrow_78446834_mktop @ hAPP_f1290184496t_bool ) @ hAPP_A619995676t_bool ) @ ( B @ ( A @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) )
& ( ( D @ ( C @ ( arrow_78446834_mktop @ hAPP_f1290184496t_bool ) @ hAPP_A619995676t_bool ) @ ( B @ ( A @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
=> ( ( ( B != D )
=> ( C @ ( B @ ( A @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) )
& ( ( B = D )
=> ( A != B ) )
& ( A != D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(99,axiom,
! [A: $i,B: $i] :
( ( B @ is_bool )
=> ( B @ ( A @ hAPP_b990649139l_bool ) @ is_fun631676118l_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order___) ).
thf(553,plain,
! [A: $i,B: $i] :
( ( B @ is_bool )
=> ( B @ ( A @ hAPP_b990649139l_bool ) @ is_fun631676118l_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(126,axiom,
! [A: $i,B: $i] :
( ( B @ is_Arr625519182e_indi )
=> ( B @ ( A @ hAPP_A1964572607l_bool ) @ is_fun631676118l_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000tc__fun_It_001) ).
thf(617,plain,
! [A: $i,B: $i] :
( ( B @ is_Arr625519182e_indi )
=> ( B @ ( A @ hAPP_A1964572607l_bool ) @ is_fun631676118l_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(85,axiom,
! [A: $i,B: $i] :
( ( A @ is_fun432044380l_bool )
=> ( ( B @ ( A @ ( cOMBK_1088865252t_bool @ hAPP_f20355883l_bool ) @ hAPP_f861484971l_bool ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_035) ).
thf(516,plain,
! [A: $i,B: $i] :
( ( A @ is_fun432044380l_bool )
=> ( ( B @ ( A @ ( cOMBK_1088865252t_bool @ hAPP_f20355883l_bool ) @ hAPP_f861484971l_bool ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(206,axiom,
! [A: $i] : ( A @ ( top_to1256827021i_bool @ hAPP_A1466488369i_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_top1I) ).
thf(968,plain,
! [A: $i] : ( A @ ( top_to1256827021i_bool @ hAPP_A1466488369i_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(255,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_fun1727820731l_bool ) @ ( B @ member1033316428l_bool @ hAPP_f526292585l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_f417299659l_bool ) @ ( A @ ( B @ hAPP_f745298353l_bool ) @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_PiE) ).
thf(1181,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_fun1727820731l_bool ) @ ( B @ member1033316428l_bool @ hAPP_f526292585l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_f417299659l_bool ) @ ( A @ ( B @ hAPP_f745298353l_bool ) @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(167,axiom,
! [A: $i] :
( ( ( ~ ( n @ ( A @ ( h @ hAPP_A588601142di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( ( A @ ( h @ hAPP_A588601142di_nat ) )
!= n )
=> ( e @ ( A @ ( p @ hAPP_A1374816149t_bool ) @ ( arrow_2077223396_mkbot @ hAPP_f1290184496t_bool ) @ hAPP_A619995676t_bool ) @ ( d @ ( e @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) )
& ( ( ( A @ ( h @ hAPP_A588601142di_nat ) )
= n )
=> ( e @ ( c @ ( A @ ( p @ hAPP_A1374816149t_bool ) @ ( arrow_812378712_above @ hAPP_f1336478923t_bool ) @ hAPP_A384644407t_bool ) @ hAPP_A619995676t_bool ) @ ( d @ ( e @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) ) )
& ( ( n @ ( A @ ( h @ hAPP_A588601142di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( e @ ( A @ ( p @ hAPP_A1374816149t_bool ) @ ( arrow_78446834_mktop @ hAPP_f1290184496t_bool ) @ hAPP_A619995676t_bool ) @ ( d @ ( e @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) )
<=> ( ( ~ ( n @ ( A @ ( h @ hAPP_A588601142di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( lba @ ( a @ ( b @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) )
& ( ( n @ ( A @ ( h @ hAPP_A588601142di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( lab @ ( a @ ( b @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Am) ).
thf(776,plain,
! [A: $i] :
( ( ( ( ~ ( n @ ( A @ ( h @ hAPP_A588601142di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( lba @ ( a @ ( b @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) )
& ( ( n @ ( A @ ( h @ hAPP_A588601142di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( lab @ ( a @ ( b @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) )
=> ( ( ~ ( n @ ( A @ ( h @ hAPP_A588601142di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( ( A @ ( h @ hAPP_A588601142di_nat ) )
!= n )
=> ( e @ ( A @ ( p @ hAPP_A1374816149t_bool ) @ ( arrow_2077223396_mkbot @ hAPP_f1290184496t_bool ) @ hAPP_A619995676t_bool ) @ ( d @ ( e @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) )
& ( ( ( A @ ( h @ hAPP_A588601142di_nat ) )
= n )
=> ( e @ ( c @ ( A @ ( p @ hAPP_A1374816149t_bool ) @ ( arrow_812378712_above @ hAPP_f1336478923t_bool ) @ hAPP_A384644407t_bool ) @ hAPP_A619995676t_bool ) @ ( d @ ( e @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) ) )
& ( ( n @ ( A @ ( h @ hAPP_A588601142di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( e @ ( A @ ( p @ hAPP_A1374816149t_bool ) @ ( arrow_78446834_mktop @ hAPP_f1290184496t_bool ) @ hAPP_A619995676t_bool ) @ ( d @ ( e @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) ) )
& ( ( ( ~ ( n @ ( A @ ( h @ hAPP_A588601142di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( ( A @ ( h @ hAPP_A588601142di_nat ) )
!= n )
=> ( e @ ( A @ ( p @ hAPP_A1374816149t_bool ) @ ( arrow_2077223396_mkbot @ hAPP_f1290184496t_bool ) @ hAPP_A619995676t_bool ) @ ( d @ ( e @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) )
& ( ( ( A @ ( h @ hAPP_A588601142di_nat ) )
= n )
=> ( e @ ( c @ ( A @ ( p @ hAPP_A1374816149t_bool ) @ ( arrow_812378712_above @ hAPP_f1336478923t_bool ) @ hAPP_A384644407t_bool ) @ hAPP_A619995676t_bool ) @ ( d @ ( e @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) ) )
& ( ( n @ ( A @ ( h @ hAPP_A588601142di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( e @ ( A @ ( p @ hAPP_A1374816149t_bool ) @ ( arrow_78446834_mktop @ hAPP_f1290184496t_bool ) @ hAPP_A619995676t_bool ) @ ( d @ ( e @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) )
=> ( ( ~ ( n @ ( A @ ( h @ hAPP_A588601142di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( lba @ ( a @ ( b @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) )
& ( ( n @ ( A @ ( h @ hAPP_A588601142di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( lab @ ( a @ ( b @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(89,axiom,
! [A: $i,B: $i] :
( ( A @ is_bool )
=> ( ( B @ ( A @ ( cOMBK_789167586t_bool @ hAPP_b1719629739l_bool ) @ hAPP_f1636546729l_bool ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabel) ).
thf(525,plain,
! [A: $i,B: $i] :
( ( A @ is_bool )
=> ( ( B @ ( A @ ( cOMBK_789167586t_bool @ hAPP_b1719629739l_bool ) @ hAPP_f1636546729l_bool ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(101,axiom,
arrow_1212118780le_IIA @ is_fun631676118l_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Arrow__Order__Mirabelle__fjewxadnqg_OIIA) ).
thf(557,plain,
arrow_1212118780le_IIA @ is_fun631676118l_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(178,axiom,
! [A: $i,B: $i] :
( ( A != B )
<=> ( ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
| ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_linorder__neq__iff) ).
thf(855,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
| ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( A != B ) )
& ( ( A != B )
=> ( ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
| ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(135,axiom,
! [A: $i] : ( top_to1256827021i_bool @ ( A @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_UNIV__I) ).
thf(640,plain,
! [A: $i] : ( top_to1256827021i_bool @ ( A @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(226,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ~ ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_xt1_I9_J) ).
thf(1070,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ~ ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(186,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_Pro2135156861t_bool ) @ ( B @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_P2127852789l_bool ) @ ( A @ ( B @ hAPP_P2075002375t_bool ) @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_Pi__mem) ).
thf(887,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_Pro2135156861t_bool ) @ ( B @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_P2127852789l_bool ) @ ( A @ ( B @ hAPP_P2075002375t_bool ) @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ( A @ is_fun917378774i_bool )
=> ( B @ ( A @ hilber1792103167di_nat ) @ is_fun1016509681e_indi ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Hilbert__Choice_Oinv__into_000tc__Arrow____Order____Mirabelle____fjewxadnq) ).
thf(414,plain,
! [A: $i,B: $i] :
( ( A @ is_fun917378774i_bool )
=> ( B @ ( A @ hilber1792103167di_nat ) @ is_fun1016509681e_indi ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(162,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ inj_on24934938di_nat ) @ hBOOL )
<=> ! [C: $i] :
( ( C @ is_Arr625519182e_indi )
=> ( ( B @ ( C @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL )
=> ! [D: $i] :
( ( D @ is_Arr625519182e_indi )
=> ( ( B @ ( D @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( ( ( C @ ( A @ hAPP_A588601142di_nat ) )
= ( D @ ( A @ hAPP_A588601142di_nat ) ) )
=> ( C = D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_inj__on__def) ).
thf(739,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( C @ is_Arr625519182e_indi )
=> ( ( B @ ( C @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL )
=> ! [D: $i] :
( ( D @ is_Arr625519182e_indi )
=> ( ( B @ ( D @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( ( ( C @ ( A @ hAPP_A588601142di_nat ) )
= ( D @ ( A @ hAPP_A588601142di_nat ) ) )
=> ( C = D ) ) ) ) ) )
=> ( B @ ( A @ inj_on24934938di_nat ) @ hBOOL ) )
& ( ( B @ ( A @ inj_on24934938di_nat ) @ hBOOL )
=> ! [C: $i] :
( ( C @ is_Arr625519182e_indi )
=> ( ( B @ ( C @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL )
=> ! [D: $i] :
( ( D @ is_Arr625519182e_indi )
=> ( ( B @ ( D @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( ( ( C @ ( A @ hAPP_A588601142di_nat ) )
= ( D @ ( A @ hAPP_A588601142di_nat ) ) )
=> ( C = D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_481590946t_bool ) @ hAPP_A1333445289t_bool ) )
= ( B @ ( C @ ( A @ hAPP_A869356733t_bool ) @ hAPP_f159424297t_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000_040) ).
thf(331,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_481590946t_bool ) @ hAPP_A1333445289t_bool ) )
= ( B @ ( C @ ( A @ hAPP_A869356733t_bool ) @ hAPP_f159424297t_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(274,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_Arr688267935t_bool ) @ ( B @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_A1944296755l_bool ) @ ( A @ ( B @ hAPP_A1374816149t_bool ) @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_Pi__mem) ).
thf(1262,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_Arr688267935t_bool ) @ ( B @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_A1944296755l_bool ) @ ( A @ ( B @ hAPP_A1374816149t_bool ) @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(200,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( cOMBK_1015076504t_bool @ hAPP_f1667233577l_bool ) @ ( C @ pi_fun1727820731l_bool ) @ ( B @ member1033316428l_bool @ hAPP_f526292585l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_f745298353l_bool ) @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_funcset__mem) ).
thf(951,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( cOMBK_1015076504t_bool @ hAPP_f1667233577l_bool ) @ ( C @ pi_fun1727820731l_bool ) @ ( B @ member1033316428l_bool @ hAPP_f526292585l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_f745298353l_bool ) @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(17,axiom,
( top_to40512653l_bool
= ( fTrue @ ( cOMBK_580911210t_bool @ hAPP_b990649139l_bool ) @ collec1520786044t_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_UNIV__def) ).
thf(359,plain,
( top_to40512653l_bool
= ( fTrue @ ( cOMBK_580911210t_bool @ hAPP_b990649139l_bool ) @ collec1520786044t_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(267,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL )
<=> ( A @ ( B @ hAPP_f745298353l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_mem__def) ).
thf(1218,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ hAPP_f745298353l_bool ) @ hBOOL )
=> ( B @ ( A @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL )
=> ( A @ ( B @ hAPP_f745298353l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(137,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_Pro437273841e_indi ) @ ( B @ member765089840e_indi @ hAPP_f460310451l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_P907763049i_bool ) @ ( A @ ( B @ hAPP_P2024088443e_indi ) @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_Pi__mem) ).
thf(643,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_Pro437273841e_indi ) @ ( B @ member765089840e_indi @ hAPP_f460310451l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_P907763049i_bool ) @ ( A @ ( B @ hAPP_P2024088443e_indi ) @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(216,axiom,
! [A: $i] :
( ( A @ ( top_to2034604131t_bool @ hAPP_P2075002375t_bool ) @ hBOOL )
<=> ( top_top_bool @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_top__apply) ).
thf(1038,plain,
! [A: $i] :
( ( ( top_top_bool @ hBOOL )
=> ( A @ ( top_to2034604131t_bool @ hAPP_P2075002375t_bool ) @ hBOOL ) )
& ( ( A @ ( top_to2034604131t_bool @ hAPP_P2075002375t_bool ) @ hBOOL )
=> ( top_top_bool @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(21,axiom,
top_to2034604131t_bool @ is_fun282293932t_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__prod_Itc__Arrow____Order____Mir) ).
thf(370,plain,
top_to2034604131t_bool @ is_fun282293932t_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(234,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ is_Arr553848933le_alt )
& ( C @ is_Arr553848933le_alt )
& ( B @ is_Arr553848933le_alt )
& ( A @ is_Arr553848933le_alt ) )
=> ( ( ( B @ ( A @ produc171383831le_alt ) )
= ( D @ ( C @ produc171383831le_alt ) ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_Pair__inject) ).
thf(1085,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ is_Arr553848933le_alt )
& ( C @ is_Arr553848933le_alt )
& ( B @ is_Arr553848933le_alt )
& ( A @ is_Arr553848933le_alt ) )
=> ( ( ( B @ ( A @ produc171383831le_alt ) )
= ( D @ ( C @ produc171383831le_alt ) ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(65,axiom,
arrow_467566751nimity @ is_fun631676118l_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Arrow__Order__Mirabelle__fjewxadnqg_Ounanimity) ).
thf(470,plain,
arrow_467566751nimity @ is_fun631676118l_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(110,axiom,
top_top_bool @ is_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Orderings_Otop__class_Otop_000tc__HOL__Obool) ).
thf(576,plain,
top_top_bool @ is_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(95,axiom,
! [A: $i] :
( ( A @ is_fun432044380l_bool )
=> ( A @ collec874260222t_bool @ is_fun432044380l_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_OCollect_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fjew) ).
thf(544,plain,
! [A: $i] :
( ( A @ is_fun432044380l_bool )
=> ( A @ collec874260222t_bool @ is_fun432044380l_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(194,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_boo2007389459t_bool ) @ ( B @ member497701034t_bool @ hAPP_f1550037191l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_b1965422783l_bool ) @ ( A @ ( B @ hAPP_b1024867081t_bool ) @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_Pi__mem) ).
thf(907,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_boo2007389459t_bool ) @ ( B @ member497701034t_bool @ hAPP_f1550037191l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_b1965422783l_bool ) @ ( A @ ( B @ hAPP_b1024867081t_bool ) @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( A @ is_fun282293932t_bool )
=> ( ( B @ ( A @ ( cOMBK_1152753196e_indi @ hAPP_f1507266205t_bool ) @ hAPP_A1374816149t_bool ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fj_026) ).
thf(336,plain,
! [A: $i,B: $i] :
( ( A @ is_fun282293932t_bool )
=> ( ( B @ ( A @ ( cOMBK_1152753196e_indi @ hAPP_f1507266205t_bool ) @ hAPP_A1374816149t_bool ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(284,axiom,
! [A: $i] :
( ( A @ is_fun917378774i_bool )
=> ( ( A != top_to1256827021i_bool )
<=> ( top_to1256827021i_bool @ ( A @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_less__top) ).
thf(1284,plain,
! [A: $i] :
( ( A @ is_fun917378774i_bool )
=> ( ( ( top_to1256827021i_bool @ ( A @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( A != top_to1256827021i_bool ) )
& ( ( A != top_to1256827021i_bool )
=> ( top_to1256827021i_bool @ ( A @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(318,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_boo691944735t_bool ) @ ( B @ member1911067358t_bool @ hAPP_f1018082273l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_b1719629739l_bool ) @ ( A @ ( B @ hAPP_b833696937t_bool ) @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_PiE) ).
thf(1427,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_boo691944735t_bool ) @ ( B @ member1911067358t_bool @ hAPP_f1018082273l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_b1719629739l_bool ) @ ( A @ ( B @ hAPP_b833696937t_bool ) @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(212,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ~ ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_order__less__imp__not__less) ).
thf(1008,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ~ ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(108,axiom,
! [A: $i] :
( ( A @ is_fun917378774i_bool )
=> ( ( A @ collec45183100e_indi )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_Collect__def) ).
thf(571,plain,
! [A: $i] :
( ( A @ is_fun917378774i_bool )
=> ( ( A @ collec45183100e_indi )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(243,axiom,
! [A: $i] : ( top_to1256827021i_bool @ ( A @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_iso__tuple__UNIV__I) ).
thf(1140,plain,
! [A: $i] : ( top_to1256827021i_bool @ ( A @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(29,axiom,
arrow_1239002508le_Lin @ is_fun432044380l_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Arrow__Order__Mirabelle__fjewxadnqg_OLin) ).
thf(386,plain,
arrow_1239002508le_Lin @ is_fun432044380l_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(277,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_Pro2135156861t_bool ) @ ( B @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_P2127852789l_bool ) @ ( A @ ( B @ hAPP_P2075002375t_bool ) @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_PiE) ).
thf(1272,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_Pro2135156861t_bool ) @ ( B @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_P2127852789l_bool ) @ ( A @ ( B @ hAPP_P2075002375t_bool ) @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(123,axiom,
( top_to1194196741l_bool
= ( fTrue @ ( cOMBK_789167586t_bool @ hAPP_b1719629739l_bool ) @ collec1580242420t_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_UNIV__def) ).
thf(612,plain,
( top_to1194196741l_bool
= ( fTrue @ ( cOMBK_789167586t_bool @ hAPP_b1719629739l_bool ) @ collec1580242420t_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(78,axiom,
! [A: $i,B: $i] :
( ( A @ is_fun1016509681e_indi )
=> ( B @ ( A @ hAPP_n385347014e_indi ) @ is_Arr625519182e_indi ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oi) ).
thf(497,plain,
! [A: $i,B: $i] :
( ( A @ is_fun1016509681e_indi )
=> ( B @ ( A @ hAPP_n385347014e_indi ) @ is_Arr625519182e_indi ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(183,axiom,
! [A: $i,B: $i] :
( ( ( B @ is_Arr553848933le_alt )
& ( A @ is_Arr553848933le_alt ) )
=> ( ( A != B )
=> ? [C: $i] :
( ( C @ ( B @ ( A @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
& ( arrow_1239002508le_Lin @ ( C @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL )
& ( C @ is_fun282293932t_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_complete__Lin) ).
thf(876,plain,
! [A: $i,B: $i] :
( ( ( B @ is_Arr553848933le_alt )
& ( A @ is_Arr553848933le_alt ) )
=> ( ( A != B )
=> ? [C: $i] :
( ( C @ ( B @ ( A @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
& ( arrow_1239002508le_Lin @ ( C @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL )
& ( C @ is_fun282293932t_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(62,axiom,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1895985727l_bool ) @ is_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__prod_Itc__Arrow____Order____) ).
thf(465,plain,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1895985727l_bool ) @ is_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(72,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun282293932t_bool )
=> ( B @ ( A @ hAPP_f2056167603l_bool ) @ is_fun432044380l_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fjewxadnqg___022) ).
thf(482,plain,
! [A: $i,B: $i] :
( ( B @ is_fun282293932t_bool )
=> ( B @ ( A @ hAPP_f2056167603l_bool ) @ is_fun432044380l_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(251,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ is_Arr553848933le_alt )
& ( C @ is_Arr553848933le_alt ) )
=> ( ( C != D )
=> ( ( arrow_413697182e_Prof @ ( B @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL )
=> ( ( arrow_413697182e_Prof @ ( A @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL )
=> ( ! [E: $i] :
( ( E @ is_Arr625519182e_indi )
=> ( ( E @ ( B @ hAPP_A1374816149t_bool ) @ ( D @ ( C @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
<=> ( E @ ( A @ hAPP_A1374816149t_bool ) @ ( C @ ( D @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) )
=> ( ( B @ ( f @ hAPP_f695124765t_bool ) @ ( D @ ( C @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
<=> ( A @ ( f @ hAPP_f695124765t_bool ) @ ( C @ ( D @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10__C3_C) ).
thf(1157,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ is_Arr553848933le_alt )
& ( C @ is_Arr553848933le_alt ) )
=> ( ( C != D )
=> ( ( arrow_413697182e_Prof @ ( B @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL )
=> ( ( arrow_413697182e_Prof @ ( A @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL )
=> ( ! [E: $i] :
( ( E @ is_Arr625519182e_indi )
=> ( ( ( E @ ( A @ hAPP_A1374816149t_bool ) @ ( C @ ( D @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
=> ( E @ ( B @ hAPP_A1374816149t_bool ) @ ( D @ ( C @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) )
& ( ( E @ ( B @ hAPP_A1374816149t_bool ) @ ( D @ ( C @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
=> ( E @ ( A @ hAPP_A1374816149t_bool ) @ ( C @ ( D @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) ) )
=> ( ( ( A @ ( f @ hAPP_f695124765t_bool ) @ ( C @ ( D @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
=> ( B @ ( f @ hAPP_f695124765t_bool ) @ ( D @ ( C @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) )
& ( ( B @ ( f @ hAPP_f695124765t_bool ) @ ( D @ ( C @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
=> ( A @ ( f @ hAPP_f695124765t_bool ) @ ( C @ ( D @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(88,axiom,
fFalse @ is_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_fFalse) ).
thf(524,plain,
fFalse @ is_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(239,axiom,
~ ( lab @ ( a @ ( b @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197__096_Ib_M_Aa_J_A_126_058_ALab_096) ).
thf(1126,plain,
~ ( lab @ ( a @ ( b @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(213,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
<=> ( A @ ( B @ hAPP_P2075002375t_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_mem__def) ).
thf(1010,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ hAPP_P2075002375t_bool ) @ hBOOL )
=> ( B @ ( A @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
=> ( A @ ( B @ hAPP_P2075002375t_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun959573582l_bool )
=> ( B @ ( A @ hAPP_f453661011l_bool ) @ is_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__O_010) ).
thf(368,plain,
! [A: $i,B: $i] :
( ( B @ is_fun959573582l_bool )
=> ( B @ ( A @ hAPP_f453661011l_bool ) @ is_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(279,axiom,
top_to1256827021i_bool @ finite120254591e_indi @ ( n @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_n_I1_J) ).
thf(1276,plain,
top_to1256827021i_bool @ finite120254591e_indi @ ( n @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(204,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( cOMBK_2076140708t_bool @ hAPP_f1903519657i_bool ) @ ( C @ pi_fun972956463e_indi ) @ ( B @ member329987264e_indi @ hAPP_f592909149l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_f1659504677e_indi ) @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_funcset__mem) ).
thf(963,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( cOMBK_2076140708t_bool @ hAPP_f1903519657i_bool ) @ ( C @ pi_fun972956463e_indi ) @ ( B @ member329987264e_indi @ hAPP_f592909149l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_f1659504677e_indi ) @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(190,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_order__less__imp__not__eq2) ).
thf(896,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(14,axiom,
arrow_413697182e_Prof @ is_fun959573582l_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Arrow__Order__Mirabelle__fjewxadnqg_OProf) ).
thf(351,plain,
arrow_413697182e_Prof @ is_fun959573582l_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(31,axiom,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f234874197l_bool ) @ is_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____fjew) ).
thf(390,plain,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f234874197l_bool ) @ is_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(35,axiom,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f749892423i_bool ) @ is_fun917378774i_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_Mtc__006) ).
thf(401,plain,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f749892423i_bool ) @ is_fun917378774i_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(160,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( cOMBK_697786936l_bool @ hAPP_f1520552209t_bool ) @ ( C @ pi_boo1877522301le_alt ) @ ( B @ member42699324le_alt @ hAPP_f1895985727l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_b1817367815le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_funcset__mem) ).
thf(731,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( cOMBK_697786936l_bool @ hAPP_f1520552209t_bool ) @ ( C @ pi_boo1877522301le_alt ) @ ( B @ member42699324le_alt @ hAPP_f1895985727l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_b1817367815le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(203,axiom,
! [A: $i] : ( A @ ( top_to40512653l_bool @ hAPP_f785543729l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_top1I) ).
thf(961,plain,
! [A: $i] : ( A @ ( top_to40512653l_bool @ hAPP_f785543729l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(170,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL )
=> ~ ( A @ ( B @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_order__less__imp__not__less) ).
thf(813,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL )
=> ~ ( A @ ( B @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(314,axiom,
( ( p @ ( f @ hAPP_f695124765t_bool ) @ ( d @ ( c @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
<=> ( e @ ( p @ ( arrow_2077223396_mkbot @ cOMBB_1292070696e_indi ) @ cOMBC_1778077589t_bool ) @ ( e @ ( c @ ( p @ ( arrow_812378712_above @ cOMBB_69933763e_indi ) @ cOMBC_493523632t_bool ) @ cOMBC_1778077589t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_317992461e_indi ) @ cOMBC_277798809t_bool ) @ ( if_fun1419651289t_bool @ cOMBB_963584201e_indi ) @ cOMBS_102864562t_bool ) @ cOMBS_867867294t_bool ) @ ( e @ ( p @ ( arrow_78446834_mktop @ cOMBB_1292070696e_indi ) @ cOMBC_1778077589t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_317992461e_indi ) @ cOMBC_277798809t_bool ) @ ( if_fun1419651289t_bool @ cOMBB_963584201e_indi ) @ cOMBS_102864562t_bool ) @ cOMBS_867867294t_bool ) @ ( f @ hAPP_f695124765t_bool ) @ ( d @ ( c @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_PW) ).
thf(1385,plain,
( ( ( e @ ( p @ ( arrow_2077223396_mkbot @ cOMBB_1292070696e_indi ) @ cOMBC_1778077589t_bool ) @ ( e @ ( c @ ( p @ ( arrow_812378712_above @ cOMBB_69933763e_indi ) @ cOMBC_493523632t_bool ) @ cOMBC_1778077589t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_317992461e_indi ) @ cOMBC_277798809t_bool ) @ ( if_fun1419651289t_bool @ cOMBB_963584201e_indi ) @ cOMBS_102864562t_bool ) @ cOMBS_867867294t_bool ) @ ( e @ ( p @ ( arrow_78446834_mktop @ cOMBB_1292070696e_indi ) @ cOMBC_1778077589t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_317992461e_indi ) @ cOMBC_277798809t_bool ) @ ( if_fun1419651289t_bool @ cOMBB_963584201e_indi ) @ cOMBS_102864562t_bool ) @ cOMBS_867867294t_bool ) @ ( f @ hAPP_f695124765t_bool ) @ ( d @ ( c @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
=> ( p @ ( f @ hAPP_f695124765t_bool ) @ ( d @ ( c @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) )
& ( ( p @ ( f @ hAPP_f695124765t_bool ) @ ( d @ ( c @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
=> ( e @ ( p @ ( arrow_2077223396_mkbot @ cOMBB_1292070696e_indi ) @ cOMBC_1778077589t_bool ) @ ( e @ ( c @ ( p @ ( arrow_812378712_above @ cOMBB_69933763e_indi ) @ cOMBC_493523632t_bool ) @ cOMBC_1778077589t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_317992461e_indi ) @ cOMBC_277798809t_bool ) @ ( if_fun1419651289t_bool @ cOMBB_963584201e_indi ) @ cOMBS_102864562t_bool ) @ cOMBS_867867294t_bool ) @ ( e @ ( p @ ( arrow_78446834_mktop @ cOMBB_1292070696e_indi ) @ cOMBC_1778077589t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_317992461e_indi ) @ cOMBC_277798809t_bool ) @ ( if_fun1419651289t_bool @ cOMBB_963584201e_indi ) @ cOMBS_102864562t_bool ) @ cOMBS_867867294t_bool ) @ ( f @ hAPP_f695124765t_bool ) @ ( d @ ( c @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(83,axiom,
( arrow_413697182e_Prof
= ( arrow_1239002508le_Lin @ ( cOMBK_1158753900e_indi @ hAPP_f1979025587l_bool ) @ ( top_to1256827021i_bool @ pi_Arr688267935t_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_Prof__def) ).
thf(510,plain,
( arrow_413697182e_Prof
= ( arrow_1239002508le_Lin @ ( cOMBK_1158753900e_indi @ hAPP_f1979025587l_bool ) @ ( top_to1256827021i_bool @ pi_Arr688267935t_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(70,axiom,
top_to2005687013l_bool @ is_fun432044380l_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Ord) ).
thf(478,plain,
top_to2005687013l_bool @ is_fun432044380l_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(97,axiom,
( top_to2034604131t_bool
= ( fTrue @ ( cOMBK_2069093696le_alt @ hAPP_b1024867081t_bool ) @ collec1711870802le_alt ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_UNIV__def) ).
thf(549,plain,
( top_to2034604131t_bool
= ( fTrue @ ( cOMBK_2069093696le_alt @ hAPP_b1024867081t_bool ) @ collec1711870802le_alt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(303,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_fun972956463e_indi ) @ ( B @ member329987264e_indi @ hAPP_f592909149l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_f352490559i_bool ) @ ( A @ ( B @ hAPP_f1659504677e_indi ) @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_PiE) ).
thf(1348,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_fun972956463e_indi ) @ ( B @ member329987264e_indi @ hAPP_f592909149l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_f352490559i_bool ) @ ( A @ ( B @ hAPP_f1659504677e_indi ) @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(47,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_277798809t_bool ) @ hAPP_A1466488369i_bool ) )
= ( B @ ( C @ ( A @ hAPP_A1922697556t_bool ) @ hAPP_nat_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000) ).
thf(432,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBC_277798809t_bool ) @ hAPP_A1466488369i_bool ) )
= ( B @ ( C @ ( A @ hAPP_A1922697556t_bool ) @ hAPP_nat_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(39,axiom,
! [A: $i] :
( ( A @ is_fun917378774i_bool )
=> ( A @ collec45183100e_indi @ is_fun917378774i_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_OCollect_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi) ).
thf(410,plain,
! [A: $i] :
( ( A @ is_fun917378774i_bool )
=> ( A @ collec45183100e_indi @ is_fun917378774i_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(172,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F @ is_Arr553848933le_alt )
& ( E @ is_Arr553848933le_alt )
& ( D @ is_Arr553848933le_alt )
& ( C @ is_Arr553848933le_alt ) )
=> ( ( E != F )
=> ( ( C != D )
=> ( ( E != D )
=> ( ( F != C )
=> ( ( arrow_413697182e_Prof @ ( B @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL )
=> ( ( arrow_413697182e_Prof @ ( A @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL )
=> ( ! [G: $i] :
( ( G @ is_Arr625519182e_indi )
=> ( ( G @ ( B @ hAPP_A1374816149t_bool ) @ ( F @ ( E @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
<=> ( G @ ( A @ hAPP_A1374816149t_bool ) @ ( D @ ( C @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) )
=> ( ( B @ ( f @ hAPP_f695124765t_bool ) @ ( F @ ( E @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
<=> ( A @ ( f @ hAPP_f695124765t_bool ) @ ( D @ ( C @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6__C2_C) ).
thf(818,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F @ is_Arr553848933le_alt )
& ( E @ is_Arr553848933le_alt )
& ( D @ is_Arr553848933le_alt )
& ( C @ is_Arr553848933le_alt ) )
=> ( ( E != F )
=> ( ( C != D )
=> ( ( E != D )
=> ( ( F != C )
=> ( ( arrow_413697182e_Prof @ ( B @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL )
=> ( ( arrow_413697182e_Prof @ ( A @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL )
=> ( ! [G: $i] :
( ( G @ is_Arr625519182e_indi )
=> ( ( ( G @ ( A @ hAPP_A1374816149t_bool ) @ ( D @ ( C @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
=> ( G @ ( B @ hAPP_A1374816149t_bool ) @ ( F @ ( E @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) )
& ( ( G @ ( B @ hAPP_A1374816149t_bool ) @ ( F @ ( E @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
=> ( G @ ( A @ hAPP_A1374816149t_bool ) @ ( D @ ( C @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) ) )
=> ( ( ( A @ ( f @ hAPP_f695124765t_bool ) @ ( D @ ( C @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
=> ( B @ ( f @ hAPP_f695124765t_bool ) @ ( F @ ( E @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) )
& ( ( B @ ( f @ hAPP_f695124765t_bool ) @ ( F @ ( E @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
=> ( A @ ( f @ hAPP_f695124765t_bool ) @ ( D @ ( C @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( B @ is_bool )
=> ( B @ ( A @ hAPP_b1965422783l_bool ) @ is_fun432044380l_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order__) ).
thf(405,plain,
! [A: $i,B: $i] :
( ( B @ is_bool )
=> ( B @ ( A @ hAPP_b1965422783l_bool ) @ is_fun432044380l_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(248,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B = A )
=> ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_xt1_I2_J) ).
thf(1148,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B = A )
=> ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( B @ is_fun432044380l_bool )
=> ( B @ ( A @ hAPP_f503012287l_bool ) @ is_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fje_019) ).
thf(373,plain,
! [A: $i,B: $i] :
( ( B @ is_fun432044380l_bool )
=> ( B @ ( A @ hAPP_f503012287l_bool ) @ is_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(9,axiom,
! [A: $i,B: $i] : ( B @ ( A @ cOMBC_277798809t_bool ) @ is_fun917378774i_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_COMBC_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000tc__Nat__) ).
thf(341,plain,
! [A: $i,B: $i] : ( B @ ( A @ cOMBC_277798809t_bool ) @ is_fun917378774i_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(81,axiom,
! [A: $i,B: $i] :
( ( B @ is_Arr625519182e_indi )
=> ( B @ ( A @ hAPP_A1944296755l_bool ) @ is_fun432044380l_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000tc__fun_It_002) ).
thf(506,plain,
! [A: $i,B: $i] :
( ( B @ is_Arr625519182e_indi )
=> ( B @ ( A @ hAPP_A1944296755l_bool ) @ is_fun432044380l_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(168,axiom,
( ( e @ ( p @ ( arrow_2077223396_mkbot @ cOMBB_1292070696e_indi ) @ cOMBC_1778077589t_bool ) @ ( e @ ( c @ ( p @ ( arrow_812378712_above @ cOMBB_69933763e_indi ) @ cOMBC_493523632t_bool ) @ cOMBC_1778077589t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_317992461e_indi ) @ cOMBC_277798809t_bool ) @ ( if_fun1419651289t_bool @ cOMBB_963584201e_indi ) @ cOMBS_102864562t_bool ) @ cOMBS_867867294t_bool ) @ ( e @ ( p @ ( arrow_78446834_mktop @ cOMBB_1292070696e_indi ) @ cOMBC_1778077589t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_317992461e_indi ) @ cOMBC_277798809t_bool ) @ ( if_fun1419651289t_bool @ cOMBB_963584201e_indi ) @ cOMBS_102864562t_bool ) @ cOMBS_867867294t_bool ) @ ( f @ hAPP_f695124765t_bool ) @ ( d @ ( e @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
<=> ( lba @ ( lab @ ( n @ ( h @ ( ord_less_nat @ cOMBB_317992461e_indi ) @ cOMBC_277798809t_bool ) @ ( if_fun1419651289t_bool @ cOMBB_963584201e_indi ) @ cOMBC_481590946t_bool ) @ cOMBC_437064334t_bool ) @ ( f @ hAPP_f695124765t_bool ) @ ( a @ ( b @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191__096_Ie_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Am) ).
thf(807,plain,
( ( ( lba @ ( lab @ ( n @ ( h @ ( ord_less_nat @ cOMBB_317992461e_indi ) @ cOMBC_277798809t_bool ) @ ( if_fun1419651289t_bool @ cOMBB_963584201e_indi ) @ cOMBC_481590946t_bool ) @ cOMBC_437064334t_bool ) @ ( f @ hAPP_f695124765t_bool ) @ ( a @ ( b @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
=> ( e @ ( p @ ( arrow_2077223396_mkbot @ cOMBB_1292070696e_indi ) @ cOMBC_1778077589t_bool ) @ ( e @ ( c @ ( p @ ( arrow_812378712_above @ cOMBB_69933763e_indi ) @ cOMBC_493523632t_bool ) @ cOMBC_1778077589t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_317992461e_indi ) @ cOMBC_277798809t_bool ) @ ( if_fun1419651289t_bool @ cOMBB_963584201e_indi ) @ cOMBS_102864562t_bool ) @ cOMBS_867867294t_bool ) @ ( e @ ( p @ ( arrow_78446834_mktop @ cOMBB_1292070696e_indi ) @ cOMBC_1778077589t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_317992461e_indi ) @ cOMBC_277798809t_bool ) @ ( if_fun1419651289t_bool @ cOMBB_963584201e_indi ) @ cOMBS_102864562t_bool ) @ cOMBS_867867294t_bool ) @ ( f @ hAPP_f695124765t_bool ) @ ( d @ ( e @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) )
& ( ( e @ ( p @ ( arrow_2077223396_mkbot @ cOMBB_1292070696e_indi ) @ cOMBC_1778077589t_bool ) @ ( e @ ( c @ ( p @ ( arrow_812378712_above @ cOMBB_69933763e_indi ) @ cOMBC_493523632t_bool ) @ cOMBC_1778077589t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_317992461e_indi ) @ cOMBC_277798809t_bool ) @ ( if_fun1419651289t_bool @ cOMBB_963584201e_indi ) @ cOMBS_102864562t_bool ) @ cOMBS_867867294t_bool ) @ ( e @ ( p @ ( arrow_78446834_mktop @ cOMBB_1292070696e_indi ) @ cOMBC_1778077589t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_317992461e_indi ) @ cOMBC_277798809t_bool ) @ ( if_fun1419651289t_bool @ cOMBB_963584201e_indi ) @ cOMBS_102864562t_bool ) @ cOMBS_867867294t_bool ) @ ( f @ hAPP_f695124765t_bool ) @ ( d @ ( e @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
=> ( lba @ ( lab @ ( n @ ( h @ ( ord_less_nat @ cOMBB_317992461e_indi ) @ cOMBC_277798809t_bool ) @ ( if_fun1419651289t_bool @ cOMBB_963584201e_indi ) @ cOMBC_481590946t_bool ) @ cOMBC_437064334t_bool ) @ ( f @ hAPP_f695124765t_bool ) @ ( a @ ( b @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(296,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_Arr149813489le_alt ) @ ( B @ member859582768le_alt @ hAPP_f483434675l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_A1374816149t_bool ) @ ( A @ ( B @ hAPP_A1736628091le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_PiE) ).
thf(1335,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_Arr149813489le_alt ) @ ( B @ member859582768le_alt @ hAPP_f483434675l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_A1374816149t_bool ) @ ( A @ ( B @ hAPP_A1736628091le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(260,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ is_Arr625519182e_indi )
& ( A @ is_Arr625519182e_indi ) )
=> ( ( top_to1256827021i_bool @ ( C @ inj_on24934938di_nat ) @ hBOOL )
=> ( ( ( A @ ( C @ hAPP_A588601142di_nat ) )
= ( B @ ( C @ hAPP_A588601142di_nat ) ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_injD) ).
thf(1197,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ is_Arr625519182e_indi )
& ( A @ is_Arr625519182e_indi ) )
=> ( ( top_to1256827021i_bool @ ( C @ inj_on24934938di_nat ) @ hBOOL )
=> ( ( ( A @ ( C @ hAPP_A588601142di_nat ) )
= ( B @ ( C @ hAPP_A588601142di_nat ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(224,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_fun1727820731l_bool ) @ ( B @ member1033316428l_bool @ hAPP_f526292585l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_f417299659l_bool ) @ ( A @ ( B @ hAPP_f745298353l_bool ) @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_Pi__mem) ).
thf(1065,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_fun1727820731l_bool ) @ ( B @ member1033316428l_bool @ hAPP_f526292585l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member1965683644t_bool @ hAPP_f503012287l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_f417299659l_bool ) @ ( A @ ( B @ hAPP_f745298353l_bool ) @ member_bool @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(185,axiom,
arrow_413697182e_Prof @ ( p @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3__096P_A_058_AProf_096) ).
thf(886,plain,
arrow_413697182e_Prof @ ( p @ member1277417654t_bool @ hAPP_f453661011l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(158,axiom,
lba @ ( a @ ( b @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096) ).
thf(728,plain,
lba @ ( a @ ( b @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(276,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ is_Arr625519182e_indi )
& ( A @ is_Arr625519182e_indi ) )
=> ( ( D @ ( C @ inj_on24934938di_nat ) @ hBOOL )
=> ( ( A != B )
=> ( ( D @ ( A @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( ( D @ ( B @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( ( A @ ( C @ hAPP_A588601142di_nat ) )
!= ( B @ ( C @ hAPP_A588601142di_nat ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_inj__on__contraD) ).
thf(1268,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ is_Arr625519182e_indi )
& ( A @ is_Arr625519182e_indi ) )
=> ( ( D @ ( C @ inj_on24934938di_nat ) @ hBOOL )
=> ( ( A != B )
=> ( ( D @ ( A @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( ( D @ ( B @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( ( A @ ( C @ hAPP_A588601142di_nat ) )
!= ( B @ ( C @ hAPP_A588601142di_nat ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(118,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBS_867867294t_bool ) @ hAPP_A1374816149t_bool ) )
= ( C @ ( B @ hAPP_A1374816149t_bool ) @ ( C @ ( A @ hAPP_A1333445289t_bool ) @ hAPP_f1673487381t_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000) ).
thf(596,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBS_867867294t_bool ) @ hAPP_A1374816149t_bool ) )
= ( C @ ( B @ hAPP_A1374816149t_bool ) @ ( C @ ( A @ hAPP_A1333445289t_bool ) @ hAPP_f1673487381t_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(306,axiom,
! [A: $i] : ( A @ ( top_to2034604131t_bool @ hAPP_P2075002375t_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_top1I) ).
thf(1357,plain,
! [A: $i] : ( A @ ( top_to2034604131t_bool @ hAPP_P2075002375t_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(209,axiom,
! [A: $i,B: $i,C: $i] :
( ( B = C )
=> ( ( A @ ( C @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_ord__eq__less__trans) ).
thf(992,plain,
! [A: $i,B: $i,C: $i] :
( ( B = C )
=> ( ( A @ ( C @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_le694128617i_bool @ hAPP_f1710416135l_bool ) @ hAPP_f919661787l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(181,axiom,
! [A: $i,B: $i] :
( ( A = B )
| ~ ( B @ ( A @ ( fequal_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Nat__Onat_T) ).
thf(871,plain,
! [A: $i,B: $i] :
( ( A = B )
| ~ ( B @ ( A @ ( fequal_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(238,axiom,
! [A: $i] :
( ( A @ ( top_to1194196741l_bool @ hAPP_f1636546729l_bool ) @ hBOOL )
<=> ( top_top_bool @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_top__apply) ).
thf(1120,plain,
! [A: $i] :
( ( ( top_top_bool @ hBOOL )
=> ( A @ ( top_to1194196741l_bool @ hAPP_f1636546729l_bool ) @ hBOOL ) )
& ( ( A @ ( top_to1194196741l_bool @ hAPP_f1636546729l_bool ) @ hBOOL )
=> ( top_top_bool @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(236,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_Arr372473371t_bool ) @ ( B @ member1467476314t_bool @ hAPP_f1012384989l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_A1964572607l_bool ) @ ( A @ ( B @ hAPP_A1062826149t_bool ) @ member1622429502t_bool @ hAPP_f213304539l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_Pi__mem) ).
thf(1093,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_Arr372473371t_bool ) @ ( B @ member1467476314t_bool @ hAPP_f1012384989l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL )
=> ( A @ ( D @ hAPP_A1964572607l_bool ) @ ( A @ ( B @ hAPP_A1062826149t_bool ) @ member1622429502t_bool @ hAPP_f213304539l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(129,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ~ ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_order__less__asym_H) ).
thf(624,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ~ ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(249,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( cOMBK_100791596le_alt @ hAPP_f1970593179i_bool ) @ ( C @ pi_Pro437273841e_indi ) @ ( B @ member765089840e_indi @ hAPP_f460310451l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_P2024088443e_indi ) @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_funcset__mem) ).
thf(1152,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( cOMBK_100791596le_alt @ hAPP_f1970593179i_bool ) @ ( C @ pi_Pro437273841e_indi ) @ ( B @ member765089840e_indi @ hAPP_f460310451l_bool ) @ hBOOL )
=> ( ( C @ ( A @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
=> ( D @ ( A @ ( B @ hAPP_P2024088443e_indi ) @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(45,axiom,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f387058535l_bool ) @ is_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__HOL__Obool) ).
thf(427,plain,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f387058535l_bool ) @ is_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(103,axiom,
! [A: $i] :
( ( A @ is_fun282293932t_bool )
=> ( A @ collec1711870802le_alt @ is_fun282293932t_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_OCollect_000tc__prod_Itc__Arrow____Order____Mirabelle____fjewxadnqg__O) ).
thf(560,plain,
! [A: $i] :
( ( A @ is_fun282293932t_bool )
=> ( A @ collec1711870802le_alt @ is_fun282293932t_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(134,axiom,
e @ ( p @ ( arrow_2077223396_mkbot @ cOMBB_1292070696e_indi ) @ cOMBC_1778077589t_bool ) @ ( e @ ( c @ ( p @ ( arrow_812378712_above @ cOMBB_69933763e_indi ) @ cOMBC_493523632t_bool ) @ cOMBC_1778077589t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_317992461e_indi ) @ cOMBC_277798809t_bool ) @ ( if_fun1419651289t_bool @ cOMBB_963584201e_indi ) @ cOMBS_102864562t_bool ) @ cOMBS_867867294t_bool ) @ ( e @ ( p @ ( arrow_78446834_mktop @ cOMBB_1292070696e_indi ) @ cOMBC_1778077589t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_317992461e_indi ) @ cOMBC_277798809t_bool ) @ ( if_fun1419651289t_bool @ cOMBB_963584201e_indi ) @ cOMBS_102864562t_bool ) @ cOMBS_867867294t_bool ) @ ( f @ hAPP_f695124765t_bool ) @ ( d @ ( e @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18__096e_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto) ).
thf(639,plain,
e @ ( p @ ( arrow_2077223396_mkbot @ cOMBB_1292070696e_indi ) @ cOMBC_1778077589t_bool ) @ ( e @ ( c @ ( p @ ( arrow_812378712_above @ cOMBB_69933763e_indi ) @ cOMBC_493523632t_bool ) @ cOMBC_1778077589t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_317992461e_indi ) @ cOMBC_277798809t_bool ) @ ( if_fun1419651289t_bool @ cOMBB_963584201e_indi ) @ cOMBS_102864562t_bool ) @ cOMBS_867867294t_bool ) @ ( e @ ( p @ ( arrow_78446834_mktop @ cOMBB_1292070696e_indi ) @ cOMBC_1778077589t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_317992461e_indi ) @ cOMBC_277798809t_bool ) @ ( if_fun1419651289t_bool @ cOMBB_963584201e_indi ) @ cOMBS_102864562t_bool ) @ cOMBS_867867294t_bool ) @ ( f @ hAPP_f695124765t_bool ) @ ( d @ ( e @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(145,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_Pro437273841e_indi ) @ ( B @ member765089840e_indi @ hAPP_f460310451l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_P907763049i_bool ) @ ( A @ ( B @ hAPP_P2024088443e_indi ) @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_PiE) ).
thf(676,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ pi_Pro437273841e_indi ) @ ( B @ member765089840e_indi @ hAPP_f460310451l_bool ) @ hBOOL )
=> ( ~ ( A @ ( D @ hAPP_P907763049i_bool ) @ ( A @ ( B @ hAPP_P2024088443e_indi ) @ member2074804542e_indi @ hAPP_f919661787l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(76,axiom,
! [A: $i,B: $i] :
( ( B @ is_bool )
=> ( B @ ( A @ hAPP_b1719629739l_bool ) @ is_fun959573582l_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabell) ).
thf(491,plain,
! [A: $i,B: $i] :
( ( B @ is_bool )
=> ( B @ ( A @ hAPP_b1719629739l_bool ) @ is_fun959573582l_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(117,axiom,
! [A: $i,B: $i] :
( ( A @ is_fun959573582l_bool )
=> ( ( B @ ( A @ ( cOMBK_116240846e_indi @ hAPP_f813556705l_bool ) @ hAPP_A1912483895l_bool ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____fje_032) ).
thf(592,plain,
! [A: $i,B: $i] :
( ( A @ is_fun959573582l_bool )
=> ( ( B @ ( A @ ( cOMBK_116240846e_indi @ hAPP_f813556705l_bool ) @ hAPP_A1912483895l_bool ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( A @ is_fun917378774i_bool )
=> ( ( B @ ( A @ ( cOMBK_2076140708t_bool @ hAPP_f1903519657i_bool ) @ hAPP_f352490559i_bool ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg___027) ).
thf(364,plain,
! [A: $i,B: $i] :
( ( A @ is_fun917378774i_bool )
=> ( ( B @ ( A @ ( cOMBK_2076140708t_bool @ hAPP_f1903519657i_bool ) @ hAPP_f352490559i_bool ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(208,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ is_Arr553848933le_alt )
& ( B @ is_Arr553848933le_alt )
& ( A @ is_Arr553848933le_alt ) )
=> ( ( D @ ( C @ ( arrow_2077223396_mkbot @ hAPP_f1290184496t_bool ) @ hAPP_A619995676t_bool ) @ ( B @ ( A @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
<=> ( ( ( A != D )
=> ( C @ ( B @ ( A @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) )
& ( ( A = D )
=> ( A != B ) )
& ( B != D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_in__mkbot) ).
thf(972,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ is_Arr553848933le_alt )
& ( B @ is_Arr553848933le_alt )
& ( A @ is_Arr553848933le_alt ) )
=> ( ( ( ( ( A != D )
=> ( C @ ( B @ ( A @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) )
& ( ( A = D )
=> ( A != B ) )
& ( B != D ) )
=> ( D @ ( C @ ( arrow_2077223396_mkbot @ hAPP_f1290184496t_bool ) @ hAPP_A619995676t_bool ) @ ( B @ ( A @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) )
& ( ( D @ ( C @ ( arrow_2077223396_mkbot @ hAPP_f1290184496t_bool ) @ hAPP_A619995676t_bool ) @ ( B @ ( A @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL )
=> ( ( ( A != D )
=> ( C @ ( B @ ( A @ produc171383831le_alt ) @ member1056080916le_alt @ hAPP_f745298353l_bool ) @ hBOOL ) )
& ( ( A = D )
=> ( A != B ) )
& ( B != D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(1489,plain,
$false,
inference(e,[status(thm)],[1337,1369,479,909,1315,1179,555,1295,352,645,892,1083,468,582,440,614,1205,449,1142,379,1173,1486,1078,533,500,715,472,1327,1260,1342,1354,1063,340,1095,1441,417,1046,1359,565,651,1055,504,1264,702,344,1279,949,460,587,619,853,1379,1147,1479,1347,325,448,1319,421,475,1302,646,1051,1373,443,485,834,1383,348,574,1183,1283,687,1377,692,866,774,396,1201,849,1215,634,1072,453,1074,380,512,678,529,661,546,761,1311,1067,1057,1274,334,1091,1343,1217,392,429,815,729,407,630,467,361,435,522,889,493,1195,1281,1291,324,847,484,551,1128,1350,874,725,403,1425,869,1138,356,488,537,642,970,1419,328,471,884,1329,1016,1207,590,622,1297,1131,1192,457,911,371,605,569,1429,343,1241,508,541,398,558,773,953,1185,906,412,965,1251,1146,444,601,375,733,423,694,1389,843,579,584,1154,562,904,577,711,445,382,1371,713,1239,947,1224,350,1258,704,900,1048,1144,649,616,599,377,996,451,567,890,477,1080,609,726,1325,626,1177,462,811,387,758,1339,700,520,959,455,1000,1477,438,653,636,1044,1076,1304,1203,531,663,927,1277,1081,1340,1018,553,617,516,968,1181,776,525,557,855,640,1070,887,414,739,331,1262,951,359,1218,643,1038,370,1085,470,576,544,907,336,1284,1427,1008,571,1140,386,1272,612,497,876,465,482,1157,524,1126,1010,368,1276,963,896,351,390,401,731,961,813,1385,510,478,549,1348,432,410,818,405,1148,373,341,506,807,1335,1197,1065,886,728,1268,596,1357,992,871,1120,1093,624,1152,427,560,639,676,491,592,364,972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT171+1 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.13/0.39 % Computer : n011.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sat Sep 26 06:37:43 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.89/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.98/1.33 % [INFO] Parsing done (345ms).
% 1.98/1.35 % [INFO] Running in sequential loop mode.
% 2.89/1.75 % [INFO] eprover registered as external prover.
% 2.89/1.76 % [INFO] Scanning for conjecture ...
% 3.40/1.94 % [INFO] Found a conjecture (or negated_conjecture) and 321 axioms. Running axiom selection ...
% 4.26/2.16 % [INFO] Axiom selection finished. Selected 321 axioms (removed 0 axioms).
% 5.26/2.46 % [INFO] Problem is first-order (TPTP FOF).
% 5.26/2.49 % [INFO] Type checking passed.
% 5.26/2.50 % [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 ...
% 16.02/5.00 % External prover 'e' found a proof!
% 16.02/5.00 % [INFO] Killing All external provers ...
% 16.02/5.00 % Time passed: 4461ms (effective reasoning time: 3644ms)
% 16.02/5.00 % 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)>
% 16.02/5.01 % Axioms used in derivation (321): fact_115_assms_I1_J, fact_132_dictatorI, gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabell, fact_113_inj__imp__inv__eq, fact_25_top1I, gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__O_009, gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000tc__fun_It_001, gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_Mtc__007, fact_45_top__apply, fact_65_xt1_I1_J, gsy_c_Fun_Oinj__on_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000tc, gsy_v_Lab____, fact_31_UNIV__I, fact_83_less__imp__neq, fact_101_less__top, fact_195__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096, gsy_c_FuncSet_OPi_000tc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__Oin, fact_112_injD, gsy_c_Set_OCollect_000tc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__Oi, help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel, fact_127_mktop__Lin, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fj_039, help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__, help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc_036, fact_152_Pi__mem, fact_97_less__top, fact_179_funcset__mem, gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Orde, fact_141_PiE, help_fequal_2_1_fequal_000tc__Nat__Onat_T, fact_92_UNIV__def, fact_63_ord__less__eq__trans, gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__O_012, fact_185_funcset__mem, help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000, gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fje, fact_136_PiE, fact_187_dictator__def, fact_58_order__less__trans, gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__Arrow____Order____Mirabelle____, fact_87_not__less__iff__gr__or__eq, fact_68_xt1_I9_J, gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oalt_000tc__fun_Itc, fact_172_funcset__mem, fact_191__096_Ie_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Am, fact_6__C2_C, fact_142_PiE, fact_67_ord__eq__less__trans, gsy_c_Set_OCollect_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi, help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabel, fact_22_Pair__eq, fact_79_order__less__imp__not__less, gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____fjew, gsy_v_Lba____, help_fTrue_1_1_T, fact_0_assms_I3_J, help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel_038, gsy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000tc_, gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____fjew_015, gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__fun_Itc__prod_Itc__Arrow____, gsy_v_b____, gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000tc__fun_It, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fj, fact_64_xt1_I1_J, fact_77_order__less__imp__not__eq, gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order__, fact_41_iso__tuple__UNIV__I, fact_106_inv__into__f__eq, fact_128_mkbot__Lin, help_If_2_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fjewxadn, fact_55_order__less__asym, help_If_3_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fjewxadn, fact_148_PiE, gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____fjewxadnqg__Oalt_Mtc__024, gsy_v_d____, fact_18__096e_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto, fact_3__096P_A_058_AProf_096, gsy_c_fFalse, fact_161_Pi__mem, fact_75_order__less__imp__not__eq2, gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__O_011, fact_89_order__less__irrefl, gsy_c_FuncSet_OPi_000tc__prod_Itc__Arrow____Order____Mirabelle____fjewxadnqg__Oa, fact_43_top__apply, fact_182_funcset__mem, help_fTrue_1_1_U, fact_29_top1I, gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabel, gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_Mtc__004, gsy_c_fTrue, fact_40_iso__tuple__UNIV__I, fact_180_funcset__mem, gsy_c_Set_OCollect_000tc__prod_Itc__Arrow____Order____Mirabelle____fjewxadnqg__O, fact_109_inj__on__contraD, help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000_034, gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____fjew_016, fact_175_funcset__mem, fact_166_Pi__mem, help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_035, fact_30_UNIV__I, fact_28_top1I, fact_38_iso__tuple__UNIV__I, fact_21_Pair__inject, fact_121_mem__def, gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____fjewxadnqg__Oalt_Mtc_, fact_44_top__apply, gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__prod_Itc__Arrow____Order____, gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_Mtc_, fact_125_mem__def, fact_165_Pi__mem, fact_20_injh, gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000tc__HOL__O, gsy_c_member_000tc__prod_Itc__Arrow____Order____Mirabelle____fjewxadnqg__Oalt_Mt, fact_178_funcset__mem, fact_131_in__above, help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000_030, fact_107_inj__eq, fact_105_inv__into__f__f, fact_86_linorder__less__linear, fact_103_inv__f__eq, help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__prod_It, fact_133_PiE, fact_196__096_Ia_M_Ab_J_A_126_058_ALba_096, fact_168_Pi__mem, fact_160_Pi__mem, gsy_v_c____, fact_177_funcset__mem, fact_183_funcset__mem, fact_153_Pi__mem, fact_23_IIA__def, fact_164_Pi__mem, gsy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool, fact_74_order__less__imp__not__eq2, fact_184_funcset__mem, fact_130_const__Lin__Prof, fact_47_not__top__less, fact_150_complete__Lin, help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc_029, help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg___027, help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fj_026, fact_88_linorder__neq__iff, fact_181_funcset__mem, help_fequal_1_1_fequal_000tc__Nat__Onat_T, help_COMBS_1_1_COMBS_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000_041, gsy_v_e____, fact_111_inj__onD, fact_140_PiE, fact_32_UNIV__I, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow_, fact_70_order__less__asym_H, fact_37_iso__tuple__UNIV__I, fact_82_less__imp__neq, gsy_c_Set_OCollect_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____fjewx, gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabelle____fjew, fact_120_mem__def, fact_116__096Lba_A_058_ALin_096, fact_59_order__less__trans, fact_69_xt1_I9_J, help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__prod_Itc__Arrow____Order____Mirabe, gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000tc__fun_It_002, fact_100_less__top, fact_56_xt1_I10_J, fact_138_PiE, fact_110_inj__on__iff, fact_194__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096, help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000_040, fact_46_top__apply, gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__fun_Itc__fun_Itc__Arrow____O, help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000_033, help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Arrow____Order____Mirabelle____fje, gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__prod_Itc__Arrow____Order____Mir, fact_124_mem__def, gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fjewxadnqg___021, fact_162_Pi__mem, gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000tc__fun_It_003, fact_85_linorder__antisym__conv3, gsy_c_Arrow__Order__Mirabelle__fjewxadnqg_OIIA, fact_186_funcset__mem, fact_149_PiE, gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fjewxadnqg__, gsy_c_Arrow__Order__Mirabelle__fjewxadnqg_OProf, gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_Mtc__005, gsy_c_Hilbert__Choice_Oinv__into_000tc__Arrow____Order____Mirabelle____fjewxadnq, fact_72_order__less__imp__triv, help_If_1_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fjewxadn, fact_192__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Am, help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____fje, fact_119_notin__Lin__iff, gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__O_010, fact_91_UNIV__def, fact_11__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ad_J, fact_52_not__top__less, fact_71_order__less__asym_H, fact_2__096c_A_126_061_Ad_096, fact_26_top1I, gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order___, fact_4_in__mkbot, gsy_c_Arrow__Order__Mirabelle__fjewxadnqg_OLin, help_COMBS_1_1_COMBS_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000, fact_96_pred__equals__eq2, fact_163_Pi__mem, fact_8__C4_C, fact_50_not__top__less, gsy_c_hAPP_000tc__Nat__Onat_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oi, fact_66_ord__eq__less__trans, fact_98_less__top, help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg___037, fact_134_PiE, fact_171_funcset__mem, fact_57_xt1_I10_J, gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Ord, gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabell_017, fact_35_UNIV__I, fact_189_Pi__UNIV, fact_99_less__top, fact_36_iso__tuple__UNIV__I, gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabel, fact_49_not__top__less, help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Arrow____Order__, fact_154_Pi__mem, gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__O, gsy_c_HOL_Oundefined_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi, fact_143_PiE, fact_151_PiProf, gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__fun_Itc__Arrow____Order____Mira, gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fjewxadnqg___022, fact_93_UNIV__def, gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_Mtc__006, fact_78_order__less__imp__not__less, gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_Mtc__008, fact_156_Pi__mem, fact_24_unanimity__def, fact_90_order__less__irrefl, gsy_c_Set_OCollect_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fjew, fact_1_u, fact_9_pairwise__neutrality, fact_51_not__top__less, fact_33_UNIV__I, fact_176_funcset__mem, fact_60_xt1_I2_J, fact_14_PW, help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____fje_032, fact_27_top1I, gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabel_018, fact_188_Pi__UNIV, fact_193__096a_A_126_061_Ab_096, fact_144_PiE, fact_39_iso__tuple__UNIV__I, fact_169_Prof__def, fact_118_Lin__irrefl, fact_155_Pi__mem, gsy_c_Orderings_Otop__class_Otop_000tc__HOL__Obool, fact_81_order__less__not__sym, fact_15_split__paired__All, fact_129_above__Lin, fact_126_Collect__def, fact_102_less__top, help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_028, help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg___031, gsy_c_HOL_Oundefined_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fj, fact_5_in__mktop, gsy_c_HOL_Oundefined_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oalt, fact_76_order__less__imp__not__eq, fact_7__C1_C, gsy_c_COMBC_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000tc__Nat__, fact_147_PiE, fact_19_n_I1_J, fact_159_Pi__mem, gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabell, help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc, fact_62_ord__less__eq__trans, gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__O_013, help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__prod_Itc__Arrow____Order_, fact_117__096Lab_A_058_ALin_096, fact_104_inv__f__f, help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fj, fact_95_UNIV__def, fact_61_xt1_I2_J, fact_73_order__less__imp__triv, gsy_c_Arrow__Order__Mirabelle__fjewxadnqg_Ounanimity, gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__O_014, fact_48_not__top__less, fact_84_linorder__neqE, gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fje_019, fact_16__096_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai, fact_17__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto, gsy_v_a____, fact_108_inj__on__def, fact_158_Pi__mem, fact_10__C3_C, fact_139_PiE, fact_173_funcset__mem, gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fjewxadnqg___023, fact_53_linorder__cases, fact_135_PiE, fact_34_UNIV__I, help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe, fact_123_mem__def, gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool, fact_157_Pi__mem, fact_146_PiE, fact_54_order__less__asym, gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____fjewxadnqg__Oalt_Mtc__025, help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_, fact_42_top__apply, fact_80_order__less__not__sym, fact_190_Pi__UNIV, gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__fun_Itc__Arrow____Order____M, fact_174_funcset__mem, gsy_c_hAPP_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__HOL__Obool, fact_94_UNIV__def, fact_145_PiE, fact_197__096_Ib_M_Aa_J_A_126_058_ALab_096, fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto, fact_114_injI, fact_137_PiE, fact_122_mem__def, fact_12__096c_A_060_092_060_094bsub_062P_A_Iinv_Ah_An_J_092_060_094esub_062_Ad_0, gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fjewxadnqg___020, fact_170_funcset__mem, fact_167_Pi__mem
% 16.02/5.01 % No. of inferences in proof: 646
% 16.02/5.01 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4461 ms resp. 3644 ms w/o parsing
% 17.20/5.30 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 17.63/5.30 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------