%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWW478_1 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:10:27 AM UTC 2026
% Result : Theorem 15.73s 22.05s
% Output : Refutation 16.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 199
% Syntax : Number of formulae : 400 ( 160 unt; 0 typ; 0 def)
% Number of atoms : 913 ( 400 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 6678 ( 162 ~; 14 |; 103 &;6003 @)
% ( 48 <=>; 348 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 10 avg)
% Number of types : 124 ( 123 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 199 ( 197 usr; 63 con; 0-5 aty)
% Number of variables : 1522 ( 0 ^;1493 !; 29 ?;1522 :)
% Comments :
%------------------------------------------------------------------------------
thf(exp_list_char_type,type,
exp_list_char: $tType ).
thf(bool_type,type,
bool: $tType ).
thf(list_char_type,type,
list_char: $tType ).
thf(list_P1999446415t_char_type,type,
list_P1999446415t_char: $tType ).
thf(option_ty_type,type,
option_ty: $tType ).
thf(option_val_type,type,
option_val: $tType ).
thf(ty_type,type,
ty: $tType ).
thf(val_type,type,
val: $tType ).
thf(fun_ex1201926843l_bool_type,type,
fun_ex1201926843l_bool: $tType ).
thf(fun_ex1732109805l_bool_type,type,
fun_ex1732109805l_bool: $tType ).
thf(fun_ex1123147373l_bool_type,type,
fun_ex1123147373l_bool: $tType ).
thf(fun_ex977868519on_val_type,type,
fun_ex977868519on_val: $tType ).
thf(fun_ex1005552999on_val_type,type,
fun_ex1005552999on_val: $tType ).
thf(fun_bool_bool_type,type,
fun_bool_bool: $tType ).
thf(fun_bo1549164019l_bool_type,type,
fun_bo1549164019l_bool: $tType ).
thf(fun_li688206603ion_ty_type,type,
fun_li688206603ion_ty: $tType ).
thf(fun_li1432931796on_val_type,type,
fun_li1432931796on_val: $tType ).
thf(fun_li318226104r_bool_type,type,
fun_li318226104r_bool: $tType ).
thf(fun_na939144002on_val_type,type,
fun_na939144002on_val: $tType ).
thf(fun_fu2122484477l_bool_type,type,
fun_fu2122484477l_bool: $tType ).
thf(fun_fu254083683l_bool_type,type,
fun_fu254083683l_bool: $tType ).
thf(fun_fu1162814663l_bool_type,type,
fun_fu1162814663l_bool: $tType ).
thf(fun_fu1913539015l_bool_type,type,
fun_fu1913539015l_bool: $tType ).
thf(fun_fu1241242885l_bool_type,type,
fun_fu1241242885l_bool: $tType ).
thf(fun_fu676595845l_bool_type,type,
fun_fu676595845l_bool: $tType ).
thf(fun_fu1924376903on_val_type,type,
fun_fu1924376903on_val: $tType ).
thf(fun_fu114905943l_bool_type,type,
fun_fu114905943l_bool: $tType ).
thf(fun_fu2003389793l_bool_type,type,
fun_fu2003389793l_bool: $tType ).
thf(fun_fu1485943649l_bool_type,type,
fun_fu1485943649l_bool: $tType ).
thf(fun_fu781882819l_bool_type,type,
fun_fu781882819l_bool: $tType ).
thf(fun_fu964075521y_bool_type,type,
fun_fu964075521y_bool: $tType ).
thf(fun_fu2075294830l_bool_type,type,
fun_fu2075294830l_bool: $tType ).
thf(fun_fu863769827l_bool_type,type,
fun_fu863769827l_bool: $tType ).
thf(fun_fu1693644106l_bool_type,type,
fun_fu1693644106l_bool: $tType ).
thf(fun_fu1670877422y_bool_type,type,
fun_fu1670877422y_bool: $tType ).
thf(fun_fu1677251708l_bool_type,type,
fun_fu1677251708l_bool: $tType ).
thf(fun_fu905586428l_bool_type,type,
fun_fu905586428l_bool: $tType ).
thf(fun_fu277794946on_val_type,type,
fun_fu277794946on_val: $tType ).
thf(fun_fu1690035458on_val_type,type,
fun_fu1690035458on_val: $tType ).
thf(fun_fu1622757844on_val_type,type,
fun_fu1622757844on_val: $tType ).
thf(fun_fu1246919812l_bool_type,type,
fun_fu1246919812l_bool: $tType ).
thf(fun_fu250820942l_bool_type,type,
fun_fu250820942l_bool: $tType ).
thf(fun_fu570492181l_bool_type,type,
fun_fu570492181l_bool: $tType ).
thf(fun_fu100249073l_bool_type,type,
fun_fu100249073l_bool: $tType ).
thf(fun_fu2141444501y_bool_type,type,
fun_fu2141444501y_bool: $tType ).
thf(fun_fu606696995l_bool_type,type,
fun_fu606696995l_bool: $tType ).
thf(fun_fu110544035l_bool_type,type,
fun_fu110544035l_bool: $tType ).
thf(fun_fu2073188913on_val_type,type,
fun_fu2073188913on_val: $tType ).
thf(fun_fu1639641777on_val_type,type,
fun_fu1639641777on_val: $tType ).
thf(fun_fu1133203323on_val_type,type,
fun_fu1133203323on_val: $tType ).
thf(fun_fu1806184744l_bool_type,type,
fun_fu1806184744l_bool: $tType ).
thf(fun_fu48585473l_bool_type,type,
fun_fu48585473l_bool: $tType ).
thf(fun_fu1590192889l_bool_type,type,
fun_fu1590192889l_bool: $tType ).
thf(fun_fu2083094209l_bool_type,type,
fun_fu2083094209l_bool: $tType ).
thf(fun_fu1640122725l_bool_type,type,
fun_fu1640122725l_bool: $tType ).
thf(fun_fu1176066021l_bool_type,type,
fun_fu1176066021l_bool: $tType ).
thf(fun_fu964448643l_bool_type,type,
fun_fu964448643l_bool: $tType ).
thf(fun_fu1457514859l_bool_type,type,
fun_fu1457514859l_bool: $tType ).
thf(fun_fu1989717467l_bool_type,type,
fun_fu1989717467l_bool: $tType ).
thf(fun_fu1680591819l_bool_type,type,
fun_fu1680591819l_bool: $tType ).
thf(fun_fu459093885l_bool_type,type,
fun_fu459093885l_bool: $tType ).
thf(fun_fu947198233l_bool_type,type,
fun_fu947198233l_bool: $tType ).
thf(fun_fu712248957l_bool_type,type,
fun_fu712248957l_bool: $tType ).
thf(fun_fu1343174525l_bool_type,type,
fun_fu1343174525l_bool: $tType ).
thf(fun_fu1871906941l_bool_type,type,
fun_fu1871906941l_bool: $tType ).
thf(fun_fu1262577777l_bool_type,type,
fun_fu1262577777l_bool: $tType ).
thf(fun_fu192331261on_val_type,type,
fun_fu192331261on_val: $tType ).
thf(fun_fu1722968561l_bool_type,type,
fun_fu1722968561l_bool: $tType ).
thf(fun_fu911981683l_bool_type,type,
fun_fu911981683l_bool: $tType ).
thf(fun_fu442091053on_val_type,type,
fun_fu442091053on_val: $tType ).
thf(fun_fu816125185l_bool_type,type,
fun_fu816125185l_bool: $tType ).
thf(fun_fu938561337l_bool_type,type,
fun_fu938561337l_bool: $tType ).
thf(fun_fu626845499l_bool_type,type,
fun_fu626845499l_bool: $tType ).
thf(fun_fu698854459l_bool_type,type,
fun_fu698854459l_bool: $tType ).
thf(fun_fu1755700589l_bool_type,type,
fun_fu1755700589l_bool: $tType ).
thf(fun_fu1506313313l_bool_type,type,
fun_fu1506313313l_bool: $tType ).
thf(fun_fu1452544581l_bool_type,type,
fun_fu1452544581l_bool: $tType ).
thf(fun_fu470662369l_bool_type,type,
fun_fu470662369l_bool: $tType ).
thf(fun_fu2023535095l_bool_type,type,
fun_fu2023535095l_bool: $tType ).
thf(fun_fu610694927l_bool_type,type,
fun_fu610694927l_bool: $tType ).
thf(fun_fu1104572687l_bool_type,type,
fun_fu1104572687l_bool: $tType ).
thf(fun_fu369322201l_bool_type,type,
fun_fu369322201l_bool: $tType ).
thf(fun_fu1002878233l_bool_type,type,
fun_fu1002878233l_bool: $tType ).
thf(fun_fu983865091l_bool_type,type,
fun_fu983865091l_bool: $tType ).
thf(fun_fu1934636263l_bool_type,type,
fun_fu1934636263l_bool: $tType ).
thf(fun_fu371764249l_bool_type,type,
fun_fu371764249l_bool: $tType ).
thf(fun_fu1562135449l_bool_type,type,
fun_fu1562135449l_bool: $tType ).
thf(fun_fu2138074009l_bool_type,type,
fun_fu2138074009l_bool: $tType ).
thf(fun_fu1176482875l_bool_type,type,
fun_fu1176482875l_bool: $tType ).
thf(fun_fu1753546205on_val_type,type,
fun_fu1753546205on_val: $tType ).
thf(fun_fu151382129l_bool_type,type,
fun_fu151382129l_bool: $tType ).
thf(fun_fu2085256997l_bool_type,type,
fun_fu2085256997l_bool: $tType ).
thf(fun_fu1587641869l_bool_type,type,
fun_fu1587641869l_bool: $tType ).
thf(fun_fu121169625l_bool_type,type,
fun_fu121169625l_bool: $tType ).
thf(fun_fu1929656089l_bool_type,type,
fun_fu1929656089l_bool: $tType ).
thf(fun_fu1802993177l_bool_type,type,
fun_fu1802993177l_bool: $tType ).
thf(fun_fu1319073539l_bool_type,type,
fun_fu1319073539l_bool: $tType ).
thf(fun_fu1929378469l_bool_type,type,
fun_fu1929378469l_bool: $tType ).
thf(fun_fu225006629l_bool_type,type,
fun_fu225006629l_bool: $tType ).
thf(fun_fu169292119l_bool_type,type,
fun_fu169292119l_bool: $tType ).
thf(fun_fu1003774433l_bool_type,type,
fun_fu1003774433l_bool: $tType ).
thf(fun_Pr680585871l_bool_type,type,
fun_Pr680585871l_bool: $tType ).
thf(fun_Pr633696065l_bool_type,type,
fun_Pr633696065l_bool: $tType ).
thf(fun_Pr741412723l_bool_type,type,
fun_Pr741412723l_bool: $tType ).
thf(fun_Pr293514739l_bool_type,type,
fun_Pr293514739l_bool: $tType ).
thf(fun_Pr1719283041on_val_type,type,
fun_Pr1719283041on_val: $tType ).
thf(fun_Pr1391347915on_val_type,type,
fun_Pr1391347915on_val: $tType ).
thf(fun_Pr134674113l_bool_type,type,
fun_Pr134674113l_bool: $tType ).
thf(fun_Pr2087158653on_val_type,type,
fun_Pr2087158653on_val: $tType ).
thf(fun_Pr714818201on_val_type,type,
fun_Pr714818201on_val: $tType ).
thf(fun_Pr1696029455l_bool_type,type,
fun_Pr1696029455l_bool: $tType ).
thf(fun_Pr1793564609l_bool_type,type,
fun_Pr1793564609l_bool: $tType ).
thf(fun_Pr598845249l_bool_type,type,
fun_Pr598845249l_bool: $tType ).
thf(fun_Pr231134077on_val_type,type,
fun_Pr231134077on_val: $tType ).
thf(fun_Pr1833267965on_val_type,type,
fun_Pr1833267965on_val: $tType ).
thf(fun_Pr336360217on_val_type,type,
fun_Pr336360217on_val: $tType ).
thf(fun_Pr691271849l_bool_type,type,
fun_Pr691271849l_bool: $tType ).
thf(fun_Pr650805339l_bool_type,type,
fun_Pr650805339l_bool: $tType ).
thf(fun_Pr1404764635l_bool_type,type,
fun_Pr1404764635l_bool: $tType ).
thf(fun_Pr1727285475on_val_type,type,
fun_Pr1727285475on_val: $tType ).
thf(produc124828825on_val_type,type,
produc124828825on_val: $tType ).
thf(produc12694297on_val_type,type,
produc12694297on_val: $tType ).
thf(produc1102272487on_val_type,type,
produc1102272487on_val: $tType ).
thf(cOMBB_383678192on_val_decl,type,
cOMBB_383678192on_val: fun_fu114905943l_bool ).
thf(cOMBB_672625589on_val_decl,type,
cOMBB_672625589on_val: fun_fu2003389793l_bool ).
thf(cOMBB_338347573on_val_decl,type,
cOMBB_338347573on_val: fun_fu1485943649l_bool ).
thf(cOMBB_1303934920on_val_decl,type,
cOMBB_1303934920on_val: fun_fu781882819l_bool ).
thf(cOMBB_1718333400on_val_decl,type,
cOMBB_1718333400on_val: fun_fu48585473l_bool ).
thf(cOMBB_1522540928on_val_decl,type,
cOMBB_1522540928on_val: fun_fu816125185l_bool ).
thf(cOMBB_1518282696on_val_decl,type,
cOMBB_1518282696on_val: fun_fu938561337l_bool ).
thf(cOMBB_1466889536on_val_decl,type,
cOMBB_1466889536on_val: fun_fu626845499l_bool ).
thf(cOMBB_1153617344on_val_decl,type,
cOMBB_1153617344on_val: fun_fu698854459l_bool ).
thf(cOMBB_1259202826on_val_decl,type,
cOMBB_1259202826on_val: fun_fu1755700589l_bool ).
thf(cOMBB_466903633on_val_decl,type,
cOMBB_466903633on_val: fun_fu1506313313l_bool ).
thf(cOMBB_635947099on_val_decl,type,
cOMBB_635947099on_val: fun_fu1452544581l_bool ).
thf(cOMBB_364363975on_val_decl,type,
cOMBB_364363975on_val: fun_fu470662369l_bool ).
thf(cOMBB_740252943t_char_decl,type,
cOMBB_740252943t_char: fun_fu2023535095l_bool ).
thf(cOMBB_1027621637t_char_decl,type,
cOMBB_1027621637t_char: fun_fu610694927l_bool ).
thf(cOMBB_819439237t_char_decl,type,
cOMBB_819439237t_char: fun_fu1104572687l_bool ).
thf(cOMBB_171276332on_val_decl,type,
cOMBB_171276332on_val: fun_fu369322201l_bool ).
thf(cOMBB_1759207793on_val_decl,type,
cOMBB_1759207793on_val: fun_fu1002878233l_bool ).
thf(cOMBB_1750801836on_val_decl,type,
cOMBB_1750801836on_val: fun_fu121169625l_bool ).
thf(cOMBB_1083177073on_val_decl,type,
cOMBB_1083177073on_val: fun_fu1929656089l_bool ).
thf(cOMBB_877741809on_val_decl,type,
cOMBB_877741809on_val: fun_fu1802993177l_bool ).
thf(cOMBB_1292453606on_val_decl,type,
cOMBB_1292453606on_val: fun_fu169292119l_bool ).
thf(cOMBB_1466662571on_val_decl,type,
cOMBB_1466662571on_val: fun_fu1003774433l_bool ).
thf(cOMBC_832625297y_bool_decl,type,
cOMBC_832625297y_bool: fun_fu2083094209l_bool ).
thf(cOMBC_2027949654l_bool_decl,type,
cOMBC_2027949654l_bool: fun_fu1680591819l_bool ).
thf(cOMBK_1294242658t_char_decl,type,
cOMBK_1294242658t_char: option_ty > fun_li688206603ion_ty ).
thf(cOMBK_1097134891t_char_decl,type,
cOMBK_1097134891t_char: option_val > fun_li1432931796on_val ).
thf(cOMBS_570216337l_bool_decl,type,
cOMBS_570216337l_bool: fun_fu1806184744l_bool > fun_fu100249073l_bool > fun_fu100249073l_bool ).
thf(hconf_97414254t_char_decl,type,
hconf_97414254t_char: list_P1999446415t_char > fun_fu1246919812l_bool ).
thf(lconf_496643946t_char_decl,type,
lconf_496643946t_char: list_P1999446415t_char > fun_fu2141444501y_bool ).
thf(block_list_char_decl,type,
block_list_char: list_char > ty > exp_list_char > exp_list_char ).
thf(lAss_list_char_decl,type,
lAss_list_char: list_char > exp_list_char > exp_list_char ).
thf(seq_list_char_decl,type,
seq_list_char: exp_list_char > exp_list_char > exp_list_char ).
thf(val_list_char_decl,type,
val_list_char: val > exp_list_char ).
thf(fun_up424764369ion_ty_decl,type,
fun_up424764369ion_ty: fun_li688206603ion_ty > list_char > option_ty > fun_li688206603ion_ty ).
thf(fun_up1149430426on_val_decl,type,
fun_up1149430426on_val: fun_li1432931796on_val > list_char > option_val > fun_li1432931796on_val ).
thf(wf_J_mdecl_decl,type,
wf_J_mdecl: fun_li318226104r_bool ).
thf(none_ty_decl,type,
none_ty: option_ty ).
thf(none_val_decl,type,
none_val: option_val ).
thf(some_ty_decl,type,
some_ty: ty > option_ty ).
thf(some_val_decl,type,
some_val: val > option_val ).
thf(produc1259058957on_val_decl,type,
produc1259058957on_val: fun_ex977868519on_val ).
thf(produc899768717on_val_decl,type,
produc899768717on_val: fun_fu1639641777on_val ).
thf(produc1441475159on_val_decl,type,
produc1441475159on_val: fun_Pr1391347915on_val ).
thf(produc399384568l_bool_decl,type,
produc399384568l_bool: fun_fu254083683l_bool ).
thf(produc2128769400l_bool_decl,type,
produc2128769400l_bool: fun_fu947198233l_bool ).
thf(produc1988544340l_bool_decl,type,
produc1988544340l_bool: fun_fu371764249l_bool ).
thf(produc1815960045l_bool_decl,type,
produc1815960045l_bool: fun_fu254083683l_bool ).
thf(produc1275132703l_bool_decl,type,
produc1275132703l_bool: fun_fu1162814663l_bool ).
thf(produc2036005791l_bool_decl,type,
produc2036005791l_bool: fun_fu1913539015l_bool ).
thf(produc1174947465on_val_decl,type,
produc1174947465on_val: fun_fu1924376903on_val ).
thf(produc1958875245l_bool_decl,type,
produc1958875245l_bool: fun_fu947198233l_bool ).
thf(produc334393759l_bool_decl,type,
produc334393759l_bool: fun_fu1343174525l_bool ).
thf(produc121041439l_bool_decl,type,
produc121041439l_bool: fun_fu1871906941l_bool ).
thf(produc901351817on_val_decl,type,
produc901351817on_val: fun_fu192331261on_val ).
thf(produc1148763895on_val_decl,type,
produc1148763895on_val: fun_fu442091053on_val ).
thf(produc1911463199l_bool_decl,type,
produc1911463199l_bool: fun_fu371764249l_bool ).
thf(produc20018513l_bool_decl,type,
produc20018513l_bool: fun_fu1562135449l_bool ).
thf(produc376702929l_bool_decl,type,
produc376702929l_bool: fun_fu2138074009l_bool ).
thf(produc1003071703on_val_decl,type,
produc1003071703on_val: fun_fu1753546205on_val ).
thf(assigned_decl,type,
assigned: list_char > exp_list_char > bool ).
thf(red_decl,type,
red: list_P1999446415t_char > fun_Pr691271849l_bool ).
thf(redp_decl,type,
redp: list_P1999446415t_char > exp_list_char > produc12694297on_val > fun_ex1201926843l_bool ).
thf(hp_decl,type,
hp: produc12694297on_val > fun_na939144002on_val ).
thf(widen_2090681816t_char_decl,type,
widen_2090681816t_char: list_P1999446415t_char > ty > ty > bool ).
thf(typeSa1844245082_sconf_decl,type,
typeSa1844245082_sconf: list_P1999446415t_char > fun_li688206603ion_ty > fun_Pr1696029455l_bool ).
thf(unit_decl,type,
unit: val ).
thf(wf_pro755087577t_char_decl,type,
wf_pro755087577t_char: fun_li318226104r_bool > list_P1999446415t_char > bool ).
thf(wTrt_decl,type,
wTrt: list_P1999446415t_char > fun_na939144002on_val > fun_li688206603ion_ty > exp_list_char > ty > bool ).
thf(fconj_decl,type,
fconj: fun_bo1549164019l_bool ).
thf(hAPP_e1833980889l_bool_decl,type,
hAPP_e1833980889l_bool: fun_ex1201926843l_bool > exp_list_char > fun_Pr1696029455l_bool ).
thf(hAPP_e592495499l_bool_decl,type,
hAPP_e592495499l_bool: fun_ex1732109805l_bool > exp_list_char > fun_Pr1793564609l_bool ).
thf(hAPP_e500528395l_bool_decl,type,
hAPP_e500528395l_bool: fun_ex1123147373l_bool > exp_list_char > fun_Pr598845249l_bool ).
thf(hAPP_e1659493427on_val_decl,type,
hAPP_e1659493427on_val: fun_ex977868519on_val > exp_list_char > fun_Pr231134077on_val ).
thf(hAPP_e108155315on_val_decl,type,
hAPP_e108155315on_val: fun_ex1005552999on_val > exp_list_char > fun_Pr1833267965on_val ).
thf(hAPP_bool_bool_decl,type,
hAPP_bool_bool: fun_bool_bool > bool > bool ).
thf(hAPP_b589554111l_bool_decl,type,
hAPP_b589554111l_bool: fun_bo1549164019l_bool > bool > fun_bool_bool ).
thf(hAPP_l512744617ion_ty_decl,type,
hAPP_l512744617ion_ty: fun_li688206603ion_ty > list_char > option_ty ).
thf(hAPP_l207779698on_val_decl,type,
hAPP_l207779698on_val: fun_li1432931796on_val > list_char > option_val ).
thf(hAPP_f546724245l_bool_decl,type,
hAPP_f546724245l_bool: fun_fu2122484477l_bool > fun_ex1201926843l_bool > fun_ex1201926843l_bool ).
thf(hAPP_f1930574389l_bool_decl,type,
hAPP_f1930574389l_bool: fun_fu254083683l_bool > fun_ex1201926843l_bool > fun_Pr680585871l_bool ).
thf(hAPP_f1760682521l_bool_decl,type,
hAPP_f1760682521l_bool: fun_fu1162814663l_bool > fun_ex1732109805l_bool > fun_Pr633696065l_bool ).
thf(hAPP_f468299289l_bool_decl,type,
hAPP_f468299289l_bool: fun_fu1913539015l_bool > fun_ex1123147373l_bool > fun_Pr134674113l_bool ).
thf(hAPP_f439412817l_bool_decl,type,
hAPP_f439412817l_bool: fun_fu1241242885l_bool > fun_ex977868519on_val > fun_ex1201926843l_bool ).
thf(hAPP_f653692369l_bool_decl,type,
hAPP_f653692369l_bool: fun_fu676595845l_bool > fun_ex1005552999on_val > fun_ex1201926843l_bool ).
thf(hAPP_f1520199827on_val_decl,type,
hAPP_f1520199827on_val: fun_fu1924376903on_val > fun_ex1005552999on_val > fun_Pr2087158653on_val ).
thf(hAPP_f1863694447l_bool_decl,type,
hAPP_f1863694447l_bool: fun_fu114905943l_bool > fun_bool_bool > fun_fu1590192889l_bool ).
thf(hAPP_f1560238713l_bool_decl,type,
hAPP_f1560238713l_bool: fun_fu2003389793l_bool > fun_bool_bool > fun_fu983865091l_bool ).
thf(hAPP_f1308714617l_bool_decl,type,
hAPP_f1308714617l_bool: fun_fu1485943649l_bool > fun_bool_bool > fun_fu1319073539l_bool ).
thf(hAPP_f1977633121l_bool_decl,type,
hAPP_f1977633121l_bool: fun_fu781882819l_bool > fun_bo1549164019l_bool > fun_fu1457514859l_bool ).
thf(hAPP_f1001225811y_bool_decl,type,
hAPP_f1001225811y_bool: fun_fu964075521y_bool > fun_li688206603ion_ty > bool ).
thf(hAPP_f603925568l_bool_decl,type,
hAPP_f603925568l_bool: fun_fu2075294830l_bool > fun_li688206603ion_ty > fun_fu1693644106l_bool ).
thf(hAPP_f550652027l_bool_decl,type,
hAPP_f550652027l_bool: fun_fu863769827l_bool > fun_li688206603ion_ty > fun_fu100249073l_bool ).
thf(hAPP_f1033709212l_bool_decl,type,
hAPP_f1033709212l_bool: fun_fu1693644106l_bool > fun_li1432931796on_val > bool ).
thf(hAPP_f2060496320y_bool_decl,type,
hAPP_f2060496320y_bool: fun_fu1670877422y_bool > fun_li1432931796on_val > fun_fu964075521y_bool ).
thf(hAPP_f2011777102l_bool_decl,type,
hAPP_f2011777102l_bool: fun_fu1677251708l_bool > fun_li1432931796on_val > fun_Pr680585871l_bool ).
thf(hAPP_f396019662l_bool_decl,type,
hAPP_f396019662l_bool: fun_fu905586428l_bool > fun_li1432931796on_val > fun_Pr1696029455l_bool ).
thf(hAPP_f1926378906on_val_decl,type,
hAPP_f1926378906on_val: fun_fu277794946on_val > fun_li1432931796on_val > produc124828825on_val ).
thf(hAPP_f1727192346on_val_decl,type,
hAPP_f1727192346on_val: fun_fu1690035458on_val > fun_li1432931796on_val > produc12694297on_val ).
thf(hAPP_f602593190on_val_decl,type,
hAPP_f602593190on_val: fun_fu1622757844on_val > fun_li1432931796on_val > produc1102272487on_val ).
thf(hAPP_f61040418l_bool_decl,type,
hAPP_f61040418l_bool: fun_fu1246919812l_bool > fun_na939144002on_val > bool ).
thf(hAPP_f1145256474l_bool_decl,type,
hAPP_f1145256474l_bool: fun_fu250820942l_bool > fun_na939144002on_val > fun_bool_bool ).
thf(hAPP_f1617787571l_bool_decl,type,
hAPP_f1617787571l_bool: fun_fu570492181l_bool > fun_na939144002on_val > fun_fu2075294830l_bool ).
thf(hAPP_f1175813647l_bool_decl,type,
hAPP_f1175813647l_bool: fun_fu100249073l_bool > fun_na939144002on_val > fun_fu1693644106l_bool ).
thf(hAPP_f1213370163y_bool_decl,type,
hAPP_f1213370163y_bool: fun_fu2141444501y_bool > fun_na939144002on_val > fun_fu1670877422y_bool ).
thf(hAPP_f2144092865l_bool_decl,type,
hAPP_f2144092865l_bool: fun_fu606696995l_bool > fun_na939144002on_val > fun_fu1677251708l_bool ).
thf(hAPP_f2135509569l_bool_decl,type,
hAPP_f2135509569l_bool: fun_fu110544035l_bool > fun_na939144002on_val > fun_fu905586428l_bool ).
thf(hAPP_f1840640125on_val_decl,type,
hAPP_f1840640125on_val: fun_fu2073188913on_val > fun_na939144002on_val > fun_fu277794946on_val ).
thf(hAPP_f1849790461on_val_decl,type,
hAPP_f1849790461on_val: fun_fu1639641777on_val > fun_na939144002on_val > fun_fu1690035458on_val ).
thf(hAPP_f600512025on_val_decl,type,
hAPP_f600512025on_val: fun_fu1133203323on_val > fun_na939144002on_val > fun_fu1622757844on_val ).
thf(hAPP_f1492320500l_bool_decl,type,
hAPP_f1492320500l_bool: fun_fu1806184744l_bool > fun_na939144002on_val > fun_fu1590192889l_bool ).
thf(hAPP_f592397849l_bool_decl,type,
hAPP_f592397849l_bool: fun_fu48585473l_bool > fun_fu114905943l_bool > fun_fu1989717467l_bool ).
thf(hAPP_f1074020887l_bool_decl,type,
hAPP_f1074020887l_bool: fun_fu1590192889l_bool > fun_fu1693644106l_bool > fun_fu1693644106l_bool ).
thf(hAPP_f181262431l_bool_decl,type,
hAPP_f181262431l_bool: fun_fu2083094209l_bool > fun_fu1670877422y_bool > fun_fu2075294830l_bool ).
thf(hAPP_f318082871l_bool_decl,type,
hAPP_f318082871l_bool: fun_fu1640122725l_bool > fun_fu277794946on_val > fun_fu1693644106l_bool ).
thf(hAPP_f1008932791l_bool_decl,type,
hAPP_f1008932791l_bool: fun_fu1176066021l_bool > fun_fu1690035458on_val > fun_fu1693644106l_bool ).
thf(hAPP_f524589473l_bool_decl,type,
hAPP_f524589473l_bool: fun_fu964448643l_bool > fun_fu1622757844on_val > fun_fu1693644106l_bool ).
thf(hAPP_f1452292669l_bool_decl,type,
hAPP_f1452292669l_bool: fun_fu1457514859l_bool > fun_fu1246919812l_bool > fun_fu250820942l_bool ).
thf(hAPP_f1523875321l_bool_decl,type,
hAPP_f1523875321l_bool: fun_fu1989717467l_bool > fun_fu250820942l_bool > fun_fu1806184744l_bool ).
thf(hAPP_f838396643l_bool_decl,type,
hAPP_f838396643l_bool: fun_fu1680591819l_bool > fun_fu570492181l_bool > fun_fu863769827l_bool ).
thf(hAPP_f555424277l_bool_decl,type,
hAPP_f555424277l_bool: fun_fu459093885l_bool > fun_fu100249073l_bool > fun_fu100249073l_bool ).
thf(hAPP_f2121594859l_bool_decl,type,
hAPP_f2121594859l_bool: fun_fu947198233l_bool > fun_fu100249073l_bool > fun_Pr1696029455l_bool ).
thf(hAPP_f857351829l_bool_decl,type,
hAPP_f857351829l_bool: fun_fu712248957l_bool > fun_fu2141444501y_bool > fun_fu570492181l_bool ).
thf(hAPP_f833559503l_bool_decl,type,
hAPP_f833559503l_bool: fun_fu1343174525l_bool > fun_fu606696995l_bool > fun_Pr1793564609l_bool ).
thf(hAPP_f1276548047l_bool_decl,type,
hAPP_f1276548047l_bool: fun_fu1871906941l_bool > fun_fu110544035l_bool > fun_Pr598845249l_bool ).
thf(hAPP_f850751421l_bool_decl,type,
hAPP_f850751421l_bool: fun_fu1262577777l_bool > fun_fu2073188913on_val > fun_fu100249073l_bool ).
thf(hAPP_f1309113673on_val_decl,type,
hAPP_f1309113673on_val: fun_fu192331261on_val > fun_fu2073188913on_val > fun_Pr231134077on_val ).
thf(hAPP_f1363667773l_bool_decl,type,
hAPP_f1363667773l_bool: fun_fu1722968561l_bool > fun_fu1639641777on_val > fun_fu100249073l_bool ).
thf(hAPP_f927043595l_bool_decl,type,
hAPP_f927043595l_bool: fun_fu911981683l_bool > fun_fu1133203323on_val > fun_fu100249073l_bool ).
thf(hAPP_f204556415on_val_decl,type,
hAPP_f204556415on_val: fun_fu442091053on_val > fun_fu1133203323on_val > fun_Pr336360217on_val ).
thf(hAPP_f1734879897l_bool_decl,type,
hAPP_f1734879897l_bool: fun_fu816125185l_bool > fun_fu1590192889l_bool > fun_fu459093885l_bool ).
thf(hAPP_f348318673l_bool_decl,type,
hAPP_f348318673l_bool: fun_fu938561337l_bool > fun_fu2083094209l_bool > fun_fu712248957l_bool ).
thf(hAPP_f399538905l_bool_decl,type,
hAPP_f399538905l_bool: fun_fu626845499l_bool > fun_fu1640122725l_bool > fun_fu1262577777l_bool ).
thf(hAPP_f1050935001l_bool_decl,type,
hAPP_f1050935001l_bool: fun_fu698854459l_bool > fun_fu1176066021l_bool > fun_fu1722968561l_bool ).
thf(hAPP_f1043869573l_bool_decl,type,
hAPP_f1043869573l_bool: fun_fu1755700589l_bool > fun_fu964448643l_bool > fun_fu911981683l_bool ).
thf(hAPP_f2032347769l_bool_decl,type,
hAPP_f2032347769l_bool: fun_fu1506313313l_bool > fun_fu983865091l_bool > fun_fu1934636263l_bool ).
thf(hAPP_f1438732387l_bool_decl,type,
hAPP_f1438732387l_bool: fun_fu1452544581l_bool > fun_fu2085256997l_bool > fun_fu1176482875l_bool ).
thf(hAPP_f639265145l_bool_decl,type,
hAPP_f639265145l_bool: fun_fu470662369l_bool > fun_fu1587641869l_bool > fun_fu151382129l_bool ).
thf(hAPP_f917296015l_bool_decl,type,
hAPP_f917296015l_bool: fun_fu2023535095l_bool > fun_fu1319073539l_bool > fun_fu2122484477l_bool ).
thf(hAPP_f1725502637l_bool_decl,type,
hAPP_f1725502637l_bool: fun_fu610694927l_bool > fun_fu1929378469l_bool > fun_fu1241242885l_bool ).
thf(hAPP_f516738477l_bool_decl,type,
hAPP_f516738477l_bool: fun_fu1104572687l_bool > fun_fu225006629l_bool > fun_fu676595845l_bool ).
thf(hAPP_f1233687287l_bool_decl,type,
hAPP_f1233687287l_bool: fun_fu369322201l_bool > fun_Pr680585871l_bool > fun_fu1640122725l_bool ).
thf(hAPP_f10074679l_bool_decl,type,
hAPP_f10074679l_bool: fun_fu1002878233l_bool > fun_Pr680585871l_bool > fun_fu1929378469l_bool ).
thf(hAPP_f926562337l_bool_decl,type,
hAPP_f926562337l_bool: fun_fu983865091l_bool > fun_Pr680585871l_bool > fun_Pr680585871l_bool ).
thf(hAPP_f641257349l_bool_decl,type,
hAPP_f641257349l_bool: fun_fu1934636263l_bool > fun_Pr633696065l_bool > fun_Pr633696065l_bool ).
thf(hAPP_f635218277l_bool_decl,type,
hAPP_f635218277l_bool: fun_fu371764249l_bool > fun_Pr633696065l_bool > fun_Pr691271849l_bool ).
thf(hAPP_f1591648613l_bool_decl,type,
hAPP_f1591648613l_bool: fun_fu1562135449l_bool > fun_Pr741412723l_bool > fun_Pr650805339l_bool ).
thf(hAPP_f444383845l_bool_decl,type,
hAPP_f444383845l_bool: fun_fu2138074009l_bool > fun_Pr293514739l_bool > fun_Pr1404764635l_bool ).
thf(hAPP_f1241216909l_bool_decl,type,
hAPP_f1241216909l_bool: fun_fu1176482875l_bool > fun_Pr1719283041on_val > fun_Pr633696065l_bool ).
thf(hAPP_f394183983on_val_decl,type,
hAPP_f394183983on_val: fun_fu1753546205on_val > fun_Pr1719283041on_val > fun_Pr1727285475on_val ).
thf(hAPP_f1342895119l_bool_decl,type,
hAPP_f1342895119l_bool: fun_fu151382129l_bool > fun_Pr1391347915on_val > fun_Pr633696065l_bool ).
thf(hAPP_f1712766199l_bool_decl,type,
hAPP_f1712766199l_bool: fun_fu2085256997l_bool > fun_Pr2087158653on_val > fun_Pr680585871l_bool ).
thf(hAPP_f204771371l_bool_decl,type,
hAPP_f204771371l_bool: fun_fu1587641869l_bool > fun_Pr714818201on_val > fun_Pr680585871l_bool ).
thf(hAPP_f2057883639l_bool_decl,type,
hAPP_f2057883639l_bool: fun_fu121169625l_bool > fun_Pr1696029455l_bool > fun_fu1176066021l_bool ).
thf(hAPP_f881985847l_bool_decl,type,
hAPP_f881985847l_bool: fun_fu1929656089l_bool > fun_Pr1696029455l_bool > fun_fu2085256997l_bool ).
thf(hAPP_f1825030711l_bool_decl,type,
hAPP_f1825030711l_bool: fun_fu1802993177l_bool > fun_Pr1696029455l_bool > fun_fu225006629l_bool ).
thf(hAPP_f2134824737l_bool_decl,type,
hAPP_f2134824737l_bool: fun_fu1319073539l_bool > fun_Pr1696029455l_bool > fun_Pr1696029455l_bool ).
thf(hAPP_f489055607l_bool_decl,type,
hAPP_f489055607l_bool: fun_fu1929378469l_bool > fun_Pr231134077on_val > fun_Pr1696029455l_bool ).
thf(hAPP_f1301559543l_bool_decl,type,
hAPP_f1301559543l_bool: fun_fu225006629l_bool > fun_Pr1833267965on_val > fun_Pr1696029455l_bool ).
thf(hAPP_f2052660463l_bool_decl,type,
hAPP_f2052660463l_bool: fun_fu169292119l_bool > fun_Pr691271849l_bool > fun_fu964448643l_bool ).
thf(hAPP_f365540729l_bool_decl,type,
hAPP_f365540729l_bool: fun_fu1003774433l_bool > fun_Pr691271849l_bool > fun_fu1587641869l_bool ).
thf(hAPP_P1708370145l_bool_decl,type,
hAPP_P1708370145l_bool: fun_Pr680585871l_bool > produc124828825on_val > bool ).
thf(hAPP_P1116729363l_bool_decl,type,
hAPP_P1116729363l_bool: fun_Pr633696065l_bool > produc124828825on_val > fun_Pr680585871l_bool ).
thf(hAPP_P1953518277l_bool_decl,type,
hAPP_P1953518277l_bool: fun_Pr741412723l_bool > produc124828825on_val > fun_Pr633696065l_bool ).
thf(hAPP_P1134042693l_bool_decl,type,
hAPP_P1134042693l_bool: fun_Pr293514739l_bool > produc124828825on_val > fun_Pr134674113l_bool ).
thf(hAPP_P2083594489on_val_decl,type,
hAPP_P2083594489on_val: fun_Pr1719283041on_val > produc124828825on_val > fun_Pr2087158653on_val ).
thf(hAPP_P1870962205on_val_decl,type,
hAPP_P1870962205on_val: fun_Pr1391347915on_val > produc124828825on_val > fun_Pr714818201on_val ).
thf(hAPP_P595502227l_bool_decl,type,
hAPP_P595502227l_bool: fun_Pr134674113l_bool > produc124828825on_val > fun_Pr1696029455l_bool ).
thf(hAPP_P789556885on_val_decl,type,
hAPP_P789556885on_val: fun_Pr2087158653on_val > produc124828825on_val > produc12694297on_val ).
thf(hAPP_P1886180715on_val_decl,type,
hAPP_P1886180715on_val: fun_Pr714818201on_val > produc124828825on_val > produc1102272487on_val ).
thf(hAPP_P159683425l_bool_decl,type,
hAPP_P159683425l_bool: fun_Pr1696029455l_bool > produc12694297on_val > bool ).
thf(hAPP_P1638898323l_bool_decl,type,
hAPP_P1638898323l_bool: fun_Pr1793564609l_bool > produc12694297on_val > fun_Pr680585871l_bool ).
thf(hAPP_P1988153107l_bool_decl,type,
hAPP_P1988153107l_bool: fun_Pr598845249l_bool > produc12694297on_val > fun_Pr1696029455l_bool ).
thf(hAPP_P604205461on_val_decl,type,
hAPP_P604205461on_val: fun_Pr231134077on_val > produc12694297on_val > produc124828825on_val ).
thf(hAPP_P1776198677on_val_decl,type,
hAPP_P1776198677on_val: fun_Pr1833267965on_val > produc12694297on_val > produc12694297on_val ).
thf(hAPP_P2024243179on_val_decl,type,
hAPP_P2024243179on_val: fun_Pr336360217on_val > produc12694297on_val > produc1102272487on_val ).
thf(hAPP_P282169671l_bool_decl,type,
hAPP_P282169671l_bool: fun_Pr691271849l_bool > produc1102272487on_val > bool ).
thf(hAPP_P678729081l_bool_decl,type,
hAPP_P678729081l_bool: fun_Pr650805339l_bool > produc1102272487on_val > fun_Pr680585871l_bool ).
thf(hAPP_P1826803705l_bool_decl,type,
hAPP_P1826803705l_bool: fun_Pr1404764635l_bool > produc1102272487on_val > fun_Pr1696029455l_bool ).
thf(hAPP_P1760219823on_val_decl,type,
hAPP_P1760219823on_val: fun_Pr1727285475on_val > produc1102272487on_val > produc12694297on_val ).
thf(hBOOL_decl,type,
hBOOL: bool > $o ).
thf(member840932460on_val_decl,type,
member840932460on_val: produc124828825on_val > fun_Pr680585871l_bool > bool ).
thf(member763590124on_val_decl,type,
member763590124on_val: produc12694297on_val > fun_Pr1696029455l_bool > bool ).
thf(member773094996on_val_decl,type,
member773094996on_val: produc1102272487on_val > fun_Pr691271849l_bool > bool ).
thf(e_decl,type,
e: fun_li688206603ion_ty ).
thf(p_decl,type,
p: list_P1999446415t_char ).
thf(t_decl,type,
t: ty ).
thf(t_1_decl,type,
t_1: ty ).
thf(v_1_decl,type,
v_1: list_char ).
thf(e_a_decl,type,
e_a: exp_list_char ).
thf(ea_decl,type,
ea: exp_list_char ).
thf(h_a_decl,type,
h_a: fun_na939144002on_val ).
thf(ha_decl,type,
ha: fun_na939144002on_val ).
thf(l_a_decl,type,
l_a: fun_li1432931796on_val ).
thf(la_decl,type,
la: fun_li1432931796on_val ).
thf(v_2_decl,type,
v_2: val ).
thf(v_decl,type,
v: val ).
thf(180,axiom,
! [A: bool,B: bool] :
( ( B @ hBOOL )
| ~ ( B @ ( A @ ( fconj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
thf(1036,plain,
! [A: bool,B: bool] :
( ( B @ hBOOL )
| ~ ( B @ ( A @ ( fconj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(132,axiom,
! [A: fun_Pr633696065l_bool,B: produc1102272487on_val] :
( ! [C: produc124828825on_val,D: produc124828825on_val] :
( ( B
= ( D @ ( C @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) ) )
=> ( D @ ( C @ ( A @ hAPP_P1116729363l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL ) )
=> ( B @ ( A @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_splitI2) ).
thf(809,plain,
! [A: fun_Pr633696065l_bool,B: produc1102272487on_val] :
( ! [C: produc124828825on_val,D: produc124828825on_val] :
( ( B
= ( D @ ( C @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) ) )
=> ( D @ ( C @ ( A @ hAPP_P1116729363l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL ) )
=> ( B @ ( A @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(91,axiom,
! [A: produc124828825on_val,B: fun_fu606696995l_bool,C: fun_na939144002on_val,D: fun_li1432931796on_val] :
( ( D @ ( C @ ( B @ hAPP_f2144092865l_bool ) @ hAPP_f2011777102l_bool ) @ ( A @ member840932460on_val ) @ hBOOL )
=> ( D @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( B @ ( produc334393759l_bool @ hAPP_f833559503l_bool ) @ hAPP_P1638898323l_bool ) @ ( A @ member840932460on_val ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_mem__splitI) ).
thf(629,plain,
! [A: produc124828825on_val,B: fun_fu606696995l_bool,C: fun_na939144002on_val,D: fun_li1432931796on_val] :
( ( D @ ( C @ ( B @ hAPP_f2144092865l_bool ) @ hAPP_f2011777102l_bool ) @ ( A @ member840932460on_val ) @ hBOOL )
=> ( D @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( B @ ( produc334393759l_bool @ hAPP_f833559503l_bool ) @ hAPP_P1638898323l_bool ) @ ( A @ member840932460on_val ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(60,axiom,
! [A: fun_Pr1696029455l_bool,B: fun_Pr1696029455l_bool] :
( ! [C: fun_na939144002on_val,D: fun_li1432931796on_val] :
( ( B @ ( D @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ member763590124on_val ) @ hBOOL )
<=> ( A @ ( D @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ member763590124on_val ) @ hBOOL ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_pred__equals__eq2) ).
thf(479,plain,
! [A: fun_Pr1696029455l_bool,B: fun_Pr1696029455l_bool] :
( ( ( B = A )
=> ! [C: fun_na939144002on_val,D: fun_li1432931796on_val] :
( ( ( A @ ( D @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ member763590124on_val ) @ hBOOL )
=> ( B @ ( D @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ member763590124on_val ) @ hBOOL ) )
& ( ( B @ ( D @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ member763590124on_val ) @ hBOOL )
=> ( A @ ( D @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ member763590124on_val ) @ hBOOL ) ) ) )
& ( ! [C: fun_na939144002on_val,D: fun_li1432931796on_val] :
( ( ( A @ ( D @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ member763590124on_val ) @ hBOOL )
=> ( B @ ( D @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ member763590124on_val ) @ hBOOL ) )
& ( ( B @ ( D @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ member763590124on_val ) @ hBOOL )
=> ( A @ ( D @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ member763590124on_val ) @ hBOOL ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(160,axiom,
! [A: produc12694297on_val,B: fun_fu110544035l_bool,C: fun_na939144002on_val,D: fun_li1432931796on_val] :
( ( D @ ( C @ ( B @ hAPP_f2135509569l_bool ) @ hAPP_f396019662l_bool ) @ ( A @ member763590124on_val ) @ hBOOL )
=> ( D @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( B @ ( produc121041439l_bool @ hAPP_f1276548047l_bool ) @ hAPP_P1988153107l_bool ) @ ( A @ member763590124on_val ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_mem__splitI) ).
thf(941,plain,
! [A: produc12694297on_val,B: fun_fu110544035l_bool,C: fun_na939144002on_val,D: fun_li1432931796on_val] :
( ( D @ ( C @ ( B @ hAPP_f2135509569l_bool ) @ hAPP_f396019662l_bool ) @ ( A @ member763590124on_val ) @ hBOOL )
=> ( D @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( B @ ( produc121041439l_bool @ hAPP_f1276548047l_bool ) @ hAPP_P1988153107l_bool ) @ ( A @ member763590124on_val ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(30,axiom,
! [A: fun_fu2083094209l_bool,B: fun_fu2141444501y_bool,C: fun_na939144002on_val] :
( ( C @ ( B @ ( A @ ( cOMBB_1518282696on_val @ hAPP_f348318673l_bool ) @ hAPP_f857351829l_bool ) @ hAPP_f1617787571l_bool ) )
= ( C @ ( B @ hAPP_f1213370163y_bool ) @ ( A @ hAPP_f181262431l_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_200) ).
thf(333,plain,
! [A: fun_fu2083094209l_bool,B: fun_fu2141444501y_bool,C: fun_na939144002on_val] :
( ( C @ ( B @ ( A @ ( cOMBB_1518282696on_val @ hAPP_f348318673l_bool ) @ hAPP_f857351829l_bool ) @ hAPP_f1617787571l_bool ) )
= ( C @ ( B @ hAPP_f1213370163y_bool ) @ ( A @ hAPP_f181262431l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(179,axiom,
! [A: produc124828825on_val,B: fun_fu606696995l_bool,C: produc12694297on_val] :
( ! [D: fun_na939144002on_val,E: fun_li1432931796on_val] :
( ( C
= ( E @ ( D @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) ) )
=> ( E @ ( D @ ( B @ hAPP_f2144092865l_bool ) @ hAPP_f2011777102l_bool ) @ ( A @ member840932460on_val ) @ hBOOL ) )
=> ( C @ ( B @ ( produc334393759l_bool @ hAPP_f833559503l_bool ) @ hAPP_P1638898323l_bool ) @ ( A @ member840932460on_val ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_mem__splitI2) ).
thf(1031,plain,
! [A: produc124828825on_val,B: fun_fu606696995l_bool,C: produc12694297on_val] :
( ! [D: fun_na939144002on_val,E: fun_li1432931796on_val] :
( ( C
= ( E @ ( D @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) ) )
=> ( E @ ( D @ ( B @ hAPP_f2144092865l_bool ) @ hAPP_f2011777102l_bool ) @ ( A @ member840932460on_val ) @ hBOOL ) )
=> ( C @ ( B @ ( produc334393759l_bool @ hAPP_f833559503l_bool ) @ hAPP_P1638898323l_bool ) @ ( A @ member840932460on_val ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(190,axiom,
! [A: exp_list_char,B: produc12694297on_val,C: exp_list_char,D: produc12694297on_val] :
( ( ( B @ ( A @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) )
= ( D @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) ) )
<=> ( ( B = D )
& ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_Pair__eq) ).
thf(1068,plain,
! [A: exp_list_char,B: produc12694297on_val,C: exp_list_char,D: produc12694297on_val] :
( ( ( ( B = D )
& ( A = C ) )
=> ( ( B @ ( A @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) )
= ( D @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) ) ) )
& ( ( ( B @ ( A @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) )
= ( D @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(172,axiom,
! [A: list_P1999446415t_char,B: exp_list_char,C: produc12694297on_val,D: exp_list_char,E: produc12694297on_val] :
( ( E @ ( D @ ( C @ ( B @ ( A @ redp ) ) @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
<=> ( A @ red @ ( E @ ( D @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_redp__red__eq) ).
thf(994,plain,
! [A: list_P1999446415t_char,B: exp_list_char,C: produc12694297on_val,D: exp_list_char,E: produc12694297on_val] :
( ( ( A @ red @ ( E @ ( D @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL )
=> ( E @ ( D @ ( C @ ( B @ ( A @ redp ) ) @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ redp ) ) @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
=> ( A @ red @ ( E @ ( D @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(63,axiom,
! [A: produc1102272487on_val,B: fun_Pr691271849l_bool] :
( ( B @ ( A @ member773094996on_val ) @ hBOOL )
<=> ( A @ ( B @ hAPP_P282169671l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_mem__def) ).
thf(511,plain,
! [A: produc1102272487on_val,B: fun_Pr691271849l_bool] :
( ( ( A @ ( B @ hAPP_P282169671l_bool ) @ hBOOL )
=> ( B @ ( A @ member773094996on_val ) @ hBOOL ) )
& ( ( B @ ( A @ member773094996on_val ) @ hBOOL )
=> ( A @ ( B @ hAPP_P282169671l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(182,axiom,
! [A: exp_list_char,B: produc12694297on_val,C: exp_list_char,D: produc12694297on_val] :
( ( ( B @ ( A @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) )
= ( D @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_Pair__inject) ).
thf(1041,plain,
! [A: exp_list_char,B: produc12694297on_val,C: exp_list_char,D: produc12694297on_val] :
( ( ( B @ ( A @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) )
= ( D @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(66,axiom,
! [A: ty,B: list_P1999446415t_char,C: ty,D: ty] :
( ( D @ ( C @ ( B @ widen_2090681816t_char ) ) @ hBOOL )
=> ( ( A @ ( D @ ( B @ widen_2090681816t_char ) ) @ hBOOL )
=> ( A @ ( C @ ( B @ widen_2090681816t_char ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_widen__trans) ).
thf(523,plain,
! [A: ty,B: list_P1999446415t_char,C: ty,D: ty] :
( ( D @ ( C @ ( B @ widen_2090681816t_char ) ) @ hBOOL )
=> ( ( A @ ( D @ ( B @ widen_2090681816t_char ) ) @ hBOOL )
=> ( A @ ( C @ ( B @ widen_2090681816t_char ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(81,axiom,
! [A: bool,B: fun_ex1201926843l_bool,C: produc124828825on_val] :
( ( C @ ( B @ ( A @ ( fconj @ hAPP_b589554111l_bool ) @ ( cOMBB_338347573on_val @ hAPP_f1308714617l_bool ) @ ( cOMBB_740252943t_char @ hAPP_f917296015l_bool ) @ hAPP_f546724245l_bool ) @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL )
<=> ( ( C @ ( B @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL )
& ( A @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_split__part) ).
thf(582,plain,
! [A: bool,B: fun_ex1201926843l_bool,C: produc124828825on_val] :
( ( ( ( C @ ( B @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL )
& ( A @ hBOOL ) )
=> ( C @ ( B @ ( A @ ( fconj @ hAPP_b589554111l_bool ) @ ( cOMBB_338347573on_val @ hAPP_f1308714617l_bool ) @ ( cOMBB_740252943t_char @ hAPP_f917296015l_bool ) @ hAPP_f546724245l_bool ) @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL ) )
& ( ( C @ ( B @ ( A @ ( fconj @ hAPP_b589554111l_bool ) @ ( cOMBB_338347573on_val @ hAPP_f1308714617l_bool ) @ ( cOMBB_740252943t_char @ hAPP_f917296015l_bool ) @ hAPP_f546724245l_bool ) @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL )
=> ( ( C @ ( B @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL )
& ( A @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(3,axiom,
! [A: option_ty,B: list_char] :
( ( B @ ( A @ cOMBK_1294242658t_char @ hAPP_l512744617ion_ty ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__List__Olist_) ).
thf(202,plain,
! [A: option_ty,B: list_char] :
( ( B @ ( A @ cOMBK_1294242658t_char @ hAPP_l512744617ion_ty ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(85,axiom,
! [A: fun_li1432931796on_val,B: list_char,C: option_val] :
( ( ( C @ ( B @ ( A @ fun_up1149430426on_val ) ) )
= A )
<=> ( ( B @ ( A @ hAPP_l207779698on_val ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_fun__upd__idem__iff) ).
thf(597,plain,
! [A: fun_li1432931796on_val,B: list_char,C: option_val] :
( ( ( ( B @ ( A @ hAPP_l207779698on_val ) )
= C )
=> ( ( C @ ( B @ ( A @ fun_up1149430426on_val ) ) )
= A ) )
& ( ( ( C @ ( B @ ( A @ fun_up1149430426on_val ) ) )
= A )
=> ( ( B @ ( A @ hAPP_l207779698on_val ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(191,axiom,
! [A: fun_fu100249073l_bool,B: fun_Pr1719283041on_val,C: produc1102272487on_val] :
( ( C @ ( B @ ( produc1003071703on_val @ hAPP_f394183983on_val ) @ hAPP_P1760219823on_val ) @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
<=> ( C @ ( B @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ ( cOMBB_1083177073on_val @ hAPP_f881985847l_bool ) @ ( cOMBB_635947099on_val @ hAPP_f1438732387l_bool ) @ hAPP_f1241216909l_bool ) @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_split__twice) ).
thf(1078,plain,
! [A: fun_fu100249073l_bool,B: fun_Pr1719283041on_val,C: produc1102272487on_val] :
( ( ( C @ ( B @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ ( cOMBB_1083177073on_val @ hAPP_f881985847l_bool ) @ ( cOMBB_635947099on_val @ hAPP_f1438732387l_bool ) @ hAPP_f1241216909l_bool ) @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL )
=> ( C @ ( B @ ( produc1003071703on_val @ hAPP_f394183983on_val ) @ hAPP_P1760219823on_val ) @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) )
& ( ( C @ ( B @ ( produc1003071703on_val @ hAPP_f394183983on_val ) @ hAPP_P1760219823on_val ) @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
=> ( C @ ( B @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ ( cOMBB_1083177073on_val @ hAPP_f881985847l_bool ) @ ( cOMBB_635947099on_val @ hAPP_f1438732387l_bool ) @ hAPP_f1241216909l_bool ) @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(133,axiom,
! [A: ty,B: fun_li688206603ion_ty] :
( ( v @ some_val @ ( v_1 @ ( la @ fun_up1149430426on_val ) ) @ ( ha @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( B @ ( p @ typeSa1844245082_sconf ) @ hAPP_P159683425l_bool ) @ hBOOL )
=> ( ( A @ ( ea @ ( B @ ( ha @ ( p @ wTrt ) ) ) ) @ hBOOL )
=> ? [C: ty] :
( ( A @ ( C @ ( p @ widen_2090681816t_char ) ) @ hBOOL )
& ( C @ ( e_a @ ( B @ ( h_a @ ( p @ wTrt ) ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_InitBlockRed_I2_J) ).
thf(814,plain,
! [A: ty,B: fun_li688206603ion_ty] :
( ( v @ some_val @ ( v_1 @ ( la @ fun_up1149430426on_val ) ) @ ( ha @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( B @ ( p @ typeSa1844245082_sconf ) @ hAPP_P159683425l_bool ) @ hBOOL )
=> ( ( A @ ( ea @ ( B @ ( ha @ ( p @ wTrt ) ) ) ) @ hBOOL )
=> ? [C: ty] :
( ( A @ ( C @ ( p @ widen_2090681816t_char ) ) @ hBOOL )
& ( C @ ( e_a @ ( B @ ( h_a @ ( p @ wTrt ) ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(112,axiom,
! [A: produc12694297on_val,B: fun_Pr1696029455l_bool] :
( ( B @ ( A @ member763590124on_val ) @ hBOOL )
<=> ( A @ ( B @ hAPP_P159683425l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_mem__def) ).
thf(698,plain,
! [A: produc12694297on_val,B: fun_Pr1696029455l_bool] :
( ( ( A @ ( B @ hAPP_P159683425l_bool ) @ hBOOL )
=> ( B @ ( A @ member763590124on_val ) @ hBOOL ) )
& ( ( B @ ( A @ member763590124on_val ) @ hBOOL )
=> ( A @ ( B @ hAPP_P159683425l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(104,axiom,
! [A: fun_fu100249073l_bool,B: fun_na939144002on_val,C: fun_li1432931796on_val] :
( ( C @ ( B @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
<=> ( C @ ( B @ ( A @ hAPP_f1175813647l_bool ) @ hAPP_f1033709212l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_prod_Osimps_I2_J) ).
thf(670,plain,
! [A: fun_fu100249073l_bool,B: fun_na939144002on_val,C: fun_li1432931796on_val] :
( ( ( C @ ( B @ ( A @ hAPP_f1175813647l_bool ) @ hAPP_f1033709212l_bool ) @ hBOOL )
=> ( C @ ( B @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) )
& ( ( C @ ( B @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
=> ( C @ ( B @ ( A @ hAPP_f1175813647l_bool ) @ hAPP_f1033709212l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(196,axiom,
! [A: fun_li1432931796on_val,B: option_val,C: list_char,D: list_char] :
( ( C != D )
=> ( ( C @ ( B @ ( D @ ( A @ fun_up1149430426on_val ) ) @ hAPP_l207779698on_val ) )
= ( C @ ( A @ hAPP_l207779698on_val ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_fun__upd__other) ).
thf(1095,plain,
! [A: fun_li1432931796on_val,B: option_val,C: list_char,D: list_char] :
( ( C != D )
=> ( ( C @ ( B @ ( D @ ( A @ fun_up1149430426on_val ) ) @ hAPP_l207779698on_val ) )
= ( C @ ( A @ hAPP_l207779698on_val ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(78,axiom,
! [A: list_P1999446415t_char,B: fun_li688206603ion_ty,C: produc12694297on_val] :
( ( C @ ( B @ ( A @ typeSa1844245082_sconf ) @ hAPP_P159683425l_bool ) @ hBOOL )
<=> ( C @ ( B @ ( A @ lconf_496643946t_char @ ( cOMBC_832625297y_bool @ ( cOMBB_1518282696on_val @ hAPP_f348318673l_bool ) @ hAPP_f857351829l_bool ) @ ( cOMBC_2027949654l_bool @ hAPP_f838396643l_bool ) @ hAPP_f550652027l_bool ) @ ( A @ hconf_97414254t_char @ ( fconj @ ( cOMBB_1303934920on_val @ hAPP_f1977633121l_bool ) @ hAPP_f1452292669l_bool ) @ ( cOMBB_383678192on_val @ ( cOMBB_1718333400on_val @ hAPP_f592397849l_bool ) @ hAPP_f1523875321l_bool ) @ cOMBS_570216337l_bool ) @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_sconf__def) ).
thf(565,plain,
! [A: list_P1999446415t_char,B: fun_li688206603ion_ty,C: produc12694297on_val] :
( ( ( C @ ( B @ ( A @ lconf_496643946t_char @ ( cOMBC_832625297y_bool @ ( cOMBB_1518282696on_val @ hAPP_f348318673l_bool ) @ hAPP_f857351829l_bool ) @ ( cOMBC_2027949654l_bool @ hAPP_f838396643l_bool ) @ hAPP_f550652027l_bool ) @ ( A @ hconf_97414254t_char @ ( fconj @ ( cOMBB_1303934920on_val @ hAPP_f1977633121l_bool ) @ hAPP_f1452292669l_bool ) @ ( cOMBB_383678192on_val @ ( cOMBB_1718333400on_val @ hAPP_f592397849l_bool ) @ hAPP_f1523875321l_bool ) @ cOMBS_570216337l_bool ) @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
=> ( C @ ( B @ ( A @ typeSa1844245082_sconf ) @ hAPP_P159683425l_bool ) @ hBOOL ) )
& ( ( C @ ( B @ ( A @ typeSa1844245082_sconf ) @ hAPP_P159683425l_bool ) @ hBOOL )
=> ( C @ ( B @ ( A @ lconf_496643946t_char @ ( cOMBC_832625297y_bool @ ( cOMBB_1518282696on_val @ hAPP_f348318673l_bool ) @ hAPP_f857351829l_bool ) @ ( cOMBC_2027949654l_bool @ hAPP_f838396643l_bool ) @ hAPP_f550652027l_bool ) @ ( A @ hconf_97414254t_char @ ( fconj @ ( cOMBB_1303934920on_val @ hAPP_f1977633121l_bool ) @ hAPP_f1452292669l_bool ) @ ( cOMBB_383678192on_val @ ( cOMBB_1718333400on_val @ hAPP_f592397849l_bool ) @ hAPP_f1523875321l_bool ) @ cOMBS_570216337l_bool ) @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(16,axiom,
! [A: fun_li688206603ion_ty,B: list_char,C: option_ty] :
( ( ( C @ ( B @ ( A @ fun_up424764369ion_ty ) ) )
= A )
<=> ( ( B @ ( A @ hAPP_l512744617ion_ty ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_fun__upd__idem__iff) ).
thf(257,plain,
! [A: fun_li688206603ion_ty,B: list_char,C: option_ty] :
( ( ( ( B @ ( A @ hAPP_l512744617ion_ty ) )
= C )
=> ( ( C @ ( B @ ( A @ fun_up424764369ion_ty ) ) )
= A ) )
& ( ( ( C @ ( B @ ( A @ fun_up424764369ion_ty ) ) )
= A )
=> ( ( B @ ( A @ hAPP_l512744617ion_ty ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(185,axiom,
! [A: list_P1999446415t_char,B: list_char,C: ty,D: val,E: produc12694297on_val] : ( E @ ( D @ val_list_char @ ( E @ ( D @ val_list_char @ ( C @ ( B @ block_list_char ) ) @ ( A @ redp ) ) @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_redp__redsp_ORedBlock) ).
thf(1055,plain,
! [A: list_P1999446415t_char,B: list_char,C: ty,D: val,E: produc12694297on_val] : ( E @ ( D @ val_list_char @ ( E @ ( D @ val_list_char @ ( C @ ( B @ block_list_char ) ) @ ( A @ redp ) ) @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(40,axiom,
! [A: fun_Pr680585871l_bool,B: fun_fu277794946on_val,C: fun_li1432931796on_val] :
( ( C @ ( B @ ( A @ ( cOMBB_171276332on_val @ hAPP_f1233687287l_bool ) @ hAPP_f318082871l_bool ) @ hAPP_f1033709212l_bool ) )
= ( C @ ( B @ hAPP_f1926378906on_val ) @ ( A @ hAPP_P1708370145l_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__O) ).
thf(372,plain,
! [A: fun_Pr680585871l_bool,B: fun_fu277794946on_val,C: fun_li1432931796on_val] :
( ( C @ ( B @ ( A @ ( cOMBB_171276332on_val @ hAPP_f1233687287l_bool ) @ hAPP_f318082871l_bool ) @ hAPP_f1033709212l_bool ) )
= ( C @ ( B @ hAPP_f1926378906on_val ) @ ( A @ hAPP_P1708370145l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(70,axiom,
! [A: fun_fu1929378469l_bool,B: fun_ex977868519on_val,C: exp_list_char] :
( ( C @ ( B @ ( A @ ( cOMBB_1027621637t_char @ hAPP_f1725502637l_bool ) @ hAPP_f439412817l_bool ) @ hAPP_e1833980889l_bool ) )
= ( C @ ( B @ hAPP_e1659493427on_val ) @ ( A @ hAPP_f489055607l_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__O_207) ).
thf(542,plain,
! [A: fun_fu1929378469l_bool,B: fun_ex977868519on_val,C: exp_list_char] :
( ( C @ ( B @ ( A @ ( cOMBB_1027621637t_char @ hAPP_f1725502637l_bool ) @ hAPP_f439412817l_bool ) @ hAPP_e1833980889l_bool ) )
= ( C @ ( B @ hAPP_e1659493427on_val ) @ ( A @ hAPP_f489055607l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(94,axiom,
! [A: produc12694297on_val,B: fun_Pr293514739l_bool,C: produc124828825on_val,D: produc124828825on_val] :
( ( D @ ( C @ ( B @ hAPP_P1134042693l_bool ) @ hAPP_P595502227l_bool ) @ ( A @ member763590124on_val ) @ hBOOL )
=> ( D @ ( C @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ ( B @ ( produc376702929l_bool @ hAPP_f444383845l_bool ) @ hAPP_P1826803705l_bool ) @ ( A @ member763590124on_val ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_mem__splitI) ).
thf(638,plain,
! [A: produc12694297on_val,B: fun_Pr293514739l_bool,C: produc124828825on_val,D: produc124828825on_val] :
( ( D @ ( C @ ( B @ hAPP_P1134042693l_bool ) @ hAPP_P595502227l_bool ) @ ( A @ member763590124on_val ) @ hBOOL )
=> ( D @ ( C @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ ( B @ ( produc376702929l_bool @ hAPP_f444383845l_bool ) @ hAPP_P1826803705l_bool ) @ ( A @ member763590124on_val ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(51,axiom,
! [A: fun_li688206603ion_ty,B: list_char,C: ty] :
~ ! [D: list_char] :
( ( D @ ( C @ some_ty @ ( B @ ( A @ fun_up424764369ion_ty ) ) @ hAPP_l512744617ion_ty ) )
= none_ty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_map__upd__nonempty) ).
thf(416,plain,
! [A: fun_li688206603ion_ty,B: list_char,C: ty] :
~ ! [D: list_char] :
( ( D @ ( C @ some_ty @ ( B @ ( A @ fun_up424764369ion_ty ) ) @ hAPP_l512744617ion_ty ) )
= none_ty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(21,axiom,
! [A: exp_list_char,B: exp_list_char,C: list_char,D: ty,E: exp_list_char] :
( ( B @ ( A @ seq_list_char ) )
!= ( E @ ( D @ ( C @ block_list_char ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_exp_Osimps_I197_J) ).
thf(289,plain,
! [A: exp_list_char,B: exp_list_char,C: list_char,D: ty,E: exp_list_char] :
( ( B @ ( A @ seq_list_char ) )
!= ( E @ ( D @ ( C @ block_list_char ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(198,axiom,
! [A: list_P1999446415t_char,B: ty] : ( B @ ( B @ ( A @ widen_2090681816t_char ) ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_widen__refl) ).
thf(1100,plain,
! [A: list_P1999446415t_char,B: ty] : ( B @ ( B @ ( A @ widen_2090681816t_char ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(128,axiom,
! [A: fun_Pr680585871l_bool,B: fun_ex1201926843l_bool] :
( ! [C: exp_list_char,D: produc12694297on_val] :
( ( D @ ( C @ ( B @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
<=> ( D @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( A @ hAPP_P1708370145l_bool ) @ hBOOL ) )
=> ( ( B @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_cond__split__eta) ).
thf(789,plain,
! [A: fun_Pr680585871l_bool,B: fun_ex1201926843l_bool] :
( ! [C: exp_list_char,D: produc12694297on_val] :
( ( ( D @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( A @ hAPP_P1708370145l_bool ) @ hBOOL )
=> ( D @ ( C @ ( B @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) )
& ( ( D @ ( C @ ( B @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
=> ( D @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( A @ hAPP_P1708370145l_bool ) @ hBOOL ) ) )
=> ( ( B @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(138,axiom,
! [A: fun_fu100249073l_bool,B: fun_na939144002on_val,C: fun_li1432931796on_val] :
( ( C @ ( B @ ( A @ hAPP_f1175813647l_bool ) @ hAPP_f1033709212l_bool ) @ hBOOL )
=> ( C @ ( B @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_splitI) ).
thf(834,plain,
! [A: fun_fu100249073l_bool,B: fun_na939144002on_val,C: fun_li1432931796on_val] :
( ( C @ ( B @ ( A @ hAPP_f1175813647l_bool ) @ hAPP_f1033709212l_bool ) @ hBOOL )
=> ( C @ ( B @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(80,axiom,
! [A: fun_Pr633696065l_bool,B: produc1102272487on_val,C: produc1102272487on_val] :
( ( B = C )
=> ( ( B @ ( A @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL )
<=> ( C @ ( A @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_split__weak__cong) ).
thf(574,plain,
! [A: fun_Pr633696065l_bool,B: produc1102272487on_val,C: produc1102272487on_val] :
( ( B = C )
=> ( ( ( C @ ( A @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL )
=> ( B @ ( A @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL )
=> ( C @ ( A @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(34,axiom,
! [A: fun_bool_bool,B: fun_Pr1696029455l_bool,C: produc12694297on_val] :
( ( C @ ( B @ ( A @ ( cOMBB_338347573on_val @ hAPP_f1308714617l_bool ) @ hAPP_f2134824737l_bool ) @ hAPP_P159683425l_bool ) )
= ( C @ ( B @ hAPP_P159683425l_bool ) @ ( A @ hAPP_bool_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__prod_Itc__fun_It) ).
thf(353,plain,
! [A: fun_bool_bool,B: fun_Pr1696029455l_bool,C: produc12694297on_val] :
( ( C @ ( B @ ( A @ ( cOMBB_338347573on_val @ hAPP_f1308714617l_bool ) @ hAPP_f2134824737l_bool ) @ hAPP_P159683425l_bool ) )
= ( C @ ( B @ hAPP_P159683425l_bool ) @ ( A @ hAPP_bool_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(165,axiom,
! [A: fun_ex1201926843l_bool,B: exp_list_char,C: produc12694297on_val] :
( ( C @ ( B @ ( A @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
=> ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( A @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_splitI) ).
thf(966,plain,
! [A: fun_ex1201926843l_bool,B: exp_list_char,C: produc12694297on_val] :
( ( C @ ( B @ ( A @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
=> ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( A @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(169,axiom,
! [A: fun_li1432931796on_val,B: list_char,C: val,D: fun_li1432931796on_val,E: val] :
( ( ( C @ some_val @ ( B @ ( A @ fun_up1149430426on_val ) ) )
= ( E @ some_val @ ( B @ ( D @ fun_up1149430426on_val ) ) ) )
=> ( C = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_map__upd__eqD1) ).
thf(981,plain,
! [A: fun_li1432931796on_val,B: list_char,C: val,D: fun_li1432931796on_val,E: val] :
( ( ( C @ some_val @ ( B @ ( A @ fun_up1149430426on_val ) ) )
= ( E @ some_val @ ( B @ ( D @ fun_up1149430426on_val ) ) ) )
=> ( C = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(147,axiom,
! [A: fun_ex1201926843l_bool,B: produc124828825on_val] :
( ( B @ ( A @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL )
=> ~ ! [C: exp_list_char,D: produc12694297on_val] :
( ( B
= ( D @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) ) )
=> ~ ( D @ ( C @ ( A @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_splitE) ).
thf(877,plain,
! [A: fun_ex1201926843l_bool,B: produc124828825on_val] :
( ( B @ ( A @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL )
=> ~ ! [C: exp_list_char,D: produc12694297on_val] :
( ( B
= ( D @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) ) )
=> ~ ( D @ ( C @ ( A @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(22,axiom,
! [A: fun_bo1549164019l_bool,B: fun_fu1246919812l_bool,C: fun_na939144002on_val] :
( ( C @ ( B @ ( A @ ( cOMBB_1303934920on_val @ hAPP_f1977633121l_bool ) @ hAPP_f1452292669l_bool ) @ hAPP_f1145256474l_bool ) )
= ( C @ ( B @ hAPP_f61040418l_bool ) @ ( A @ hAPP_b589554111l_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo) ).
thf(293,plain,
! [A: fun_bo1549164019l_bool,B: fun_fu1246919812l_bool,C: fun_na939144002on_val] :
( ( C @ ( B @ ( A @ ( cOMBB_1303934920on_val @ hAPP_f1977633121l_bool ) @ hAPP_f1452292669l_bool ) @ hAPP_f1145256474l_bool ) )
= ( C @ ( B @ hAPP_f61040418l_bool ) @ ( A @ hAPP_b589554111l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(123,axiom,
! [A: list_char,B: list_P1999446415t_char,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val] :
( ( F @ ( E @ ( D @ ( C @ ( B @ redp ) ) @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
=> ( F @ ( E @ ( A @ lAss_list_char ) @ ( D @ ( C @ ( A @ lAss_list_char ) @ ( B @ redp ) ) @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_redp__redsp_OLAssRed) ).
thf(774,plain,
! [A: list_char,B: list_P1999446415t_char,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val] :
( ( F @ ( E @ ( D @ ( C @ ( B @ redp ) ) @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
=> ( F @ ( E @ ( A @ lAss_list_char ) @ ( D @ ( C @ ( A @ lAss_list_char ) @ ( B @ redp ) ) @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(101,axiom,
! [A: exp_list_char,B: ty,C: list_P1999446415t_char,D: fun_na939144002on_val,E: fun_li688206603ion_ty,F: exp_list_char,G: ty] :
( ( G @ ( F @ ( E @ ( D @ ( C @ wTrt ) ) ) ) @ hBOOL )
=> ( ( B @ ( A @ ( E @ ( D @ ( C @ wTrt ) ) ) ) @ hBOOL )
=> ( B @ ( A @ ( F @ seq_list_char ) @ ( E @ ( D @ ( C @ wTrt ) ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_WTrtSeq) ).
thf(660,plain,
! [A: exp_list_char,B: ty,C: list_P1999446415t_char,D: fun_na939144002on_val,E: fun_li688206603ion_ty,F: exp_list_char,G: ty] :
( ( G @ ( F @ ( E @ ( D @ ( C @ wTrt ) ) ) ) @ hBOOL )
=> ( ( B @ ( A @ ( E @ ( D @ ( C @ wTrt ) ) ) ) @ hBOOL )
=> ( B @ ( A @ ( F @ seq_list_char ) @ ( E @ ( D @ ( C @ wTrt ) ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(54,axiom,
! [A: fun_fu1670877422y_bool,B: fun_li688206603ion_ty,C: fun_li1432931796on_val] :
( ( C @ ( B @ ( A @ ( cOMBC_832625297y_bool @ hAPP_f181262431l_bool ) @ hAPP_f603925568l_bool ) @ hAPP_f1033709212l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f2060496320y_bool ) @ hAPP_f1001225811y_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Optio) ).
thf(428,plain,
! [A: fun_fu1670877422y_bool,B: fun_li688206603ion_ty,C: fun_li1432931796on_val] :
( ( C @ ( B @ ( A @ ( cOMBC_832625297y_bool @ hAPP_f181262431l_bool ) @ hAPP_f603925568l_bool ) @ hAPP_f1033709212l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f2060496320y_bool ) @ hAPP_f1001225811y_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(62,axiom,
! [A: produc12694297on_val] :
~ ! [B: fun_na939144002on_val,C: fun_li1432931796on_val] :
( A
!= ( C @ ( B @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_PairE) ).
thf(507,plain,
! [A: produc12694297on_val] :
~ ! [B: fun_na939144002on_val,C: fun_li1432931796on_val] :
( A
!= ( C @ ( B @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(48,axiom,
! [A: list_char,B: exp_list_char,C: list_char,D: exp_list_char] :
( ( ( B @ ( A @ lAss_list_char ) )
= ( D @ ( C @ lAss_list_char ) ) )
<=> ( ( B = D )
& ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_exp_Osimps_I6_J) ).
thf(397,plain,
! [A: list_char,B: exp_list_char,C: list_char,D: exp_list_char] :
( ( ( ( B = D )
& ( A = C ) )
=> ( ( B @ ( A @ lAss_list_char ) )
= ( D @ ( C @ lAss_list_char ) ) ) )
& ( ( ( B @ ( A @ lAss_list_char ) )
= ( D @ ( C @ lAss_list_char ) ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(108,axiom,
p @ ( wf_J_mdecl @ wf_pro755087577t_char ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_assms) ).
thf(687,plain,
p @ ( wf_J_mdecl @ wf_pro755087577t_char ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(49,axiom,
produc2128769400l_bool = produc1958875245l_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_internal__split__def) ).
thf(411,plain,
produc2128769400l_bool = produc1958875245l_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(171,axiom,
! [A: fun_ex1201926843l_bool,B: exp_list_char,C: produc12694297on_val] :
( ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( A @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL )
<=> ( C @ ( B @ ( A @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_split__conv) ).
thf(988,plain,
! [A: fun_ex1201926843l_bool,B: exp_list_char,C: produc12694297on_val] :
( ( ( C @ ( B @ ( A @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
=> ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( A @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL ) )
& ( ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( A @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL )
=> ( C @ ( B @ ( A @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(17,axiom,
! [A: fun_fu1319073539l_bool,B: fun_ex1201926843l_bool,C: exp_list_char] :
( ( C @ ( B @ ( A @ ( cOMBB_740252943t_char @ hAPP_f917296015l_bool ) @ hAPP_f546724245l_bool ) @ hAPP_e1833980889l_bool ) )
= ( C @ ( B @ hAPP_e1833980889l_bool ) @ ( A @ hAPP_f2134824737l_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__O) ).
thf(265,plain,
! [A: fun_fu1319073539l_bool,B: fun_ex1201926843l_bool,C: exp_list_char] :
( ( C @ ( B @ ( A @ ( cOMBB_740252943t_char @ hAPP_f917296015l_bool ) @ hAPP_f546724245l_bool ) @ hAPP_e1833980889l_bool ) )
= ( C @ ( B @ hAPP_e1833980889l_bool ) @ ( A @ hAPP_f2134824737l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(142,axiom,
! [A: produc12694297on_val,B: fun_Pr293514739l_bool,C: produc1102272487on_val] :
( ! [D: produc124828825on_val,E: produc124828825on_val] :
( ( C
= ( E @ ( D @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) ) )
=> ( E @ ( D @ ( B @ hAPP_P1134042693l_bool ) @ hAPP_P595502227l_bool ) @ ( A @ member763590124on_val ) @ hBOOL ) )
=> ( C @ ( B @ ( produc376702929l_bool @ hAPP_f444383845l_bool ) @ hAPP_P1826803705l_bool ) @ ( A @ member763590124on_val ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_mem__splitI2) ).
thf(849,plain,
! [A: produc12694297on_val,B: fun_Pr293514739l_bool,C: produc1102272487on_val] :
( ! [D: produc124828825on_val,E: produc124828825on_val] :
( ( C
= ( E @ ( D @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) ) )
=> ( E @ ( D @ ( B @ hAPP_P1134042693l_bool ) @ hAPP_P595502227l_bool ) @ ( A @ member763590124on_val ) @ hBOOL ) )
=> ( C @ ( B @ ( produc376702929l_bool @ hAPP_f444383845l_bool ) @ hAPP_P1826803705l_bool ) @ ( A @ member763590124on_val ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(57,axiom,
! [A: fun_fu2085256997l_bool,B: fun_Pr1719283041on_val,C: produc124828825on_val] :
( ( C @ ( B @ ( A @ ( cOMBB_635947099on_val @ hAPP_f1438732387l_bool ) @ hAPP_f1241216909l_bool ) @ hAPP_P1116729363l_bool ) )
= ( C @ ( B @ hAPP_P2083594489on_val ) @ ( A @ hAPP_f1712766199l_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc___210) ).
thf(452,plain,
! [A: fun_fu2085256997l_bool,B: fun_Pr1719283041on_val,C: produc124828825on_val] :
( ( C @ ( B @ ( A @ ( cOMBB_635947099on_val @ hAPP_f1438732387l_bool ) @ hAPP_f1241216909l_bool ) @ hAPP_P1116729363l_bool ) )
= ( C @ ( B @ hAPP_P2083594489on_val ) @ ( A @ hAPP_f1712766199l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(13,axiom,
! [A: fun_fu1590192889l_bool,B: fun_fu100249073l_bool,C: fun_na939144002on_val] :
( ( C @ ( B @ ( A @ ( cOMBB_1522540928on_val @ hAPP_f1734879897l_bool ) @ hAPP_f555424277l_bool ) @ hAPP_f1175813647l_bool ) )
= ( C @ ( B @ hAPP_f1175813647l_bool ) @ ( A @ hAPP_f1074020887l_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M) ).
thf(248,plain,
! [A: fun_fu1590192889l_bool,B: fun_fu100249073l_bool,C: fun_na939144002on_val] :
( ( C @ ( B @ ( A @ ( cOMBB_1522540928on_val @ hAPP_f1734879897l_bool ) @ hAPP_f555424277l_bool ) @ hAPP_f1175813647l_bool ) )
= ( C @ ( B @ hAPP_f1175813647l_bool ) @ ( A @ hAPP_f1074020887l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(157,axiom,
! [A: produc124828825on_val,B: fun_Pr680585871l_bool] :
( ( B @ ( A @ member840932460on_val ) @ hBOOL )
<=> ( A @ ( B @ hAPP_P1708370145l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_mem__def) ).
thf(925,plain,
! [A: produc124828825on_val,B: fun_Pr680585871l_bool] :
( ( ( A @ ( B @ hAPP_P1708370145l_bool ) @ hBOOL )
=> ( B @ ( A @ member840932460on_val ) @ hBOOL ) )
& ( ( B @ ( A @ member840932460on_val ) @ hBOOL )
=> ( A @ ( B @ hAPP_P1708370145l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(1,conjecture,
p @ red @ ( l_a @ ( h_a @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( e_a @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( v @ some_val @ ( v_1 @ ( la @ fun_up1149430426on_val ) ) @ ( ha @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( ea @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( p @ red @ ( l_a @ ( h_a @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( e_a @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( v @ some_val @ ( v_1 @ ( la @ fun_up1149430426on_val ) ) @ ( ha @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( ea @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(201,plain,
~ ( p @ red @ ( l_a @ ( h_a @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( e_a @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( v @ some_val @ ( v_1 @ ( la @ fun_up1149430426on_val ) ) @ ( ha @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( ea @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(43,axiom,
produc1988544340l_bool = produc1911463199l_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_internal__split__def) ).
thf(381,plain,
produc1988544340l_bool = produc1911463199l_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(38,axiom,
! [A: list_char,B: ty,C: exp_list_char,D: exp_list_char,E: exp_list_char] :
( ( C @ ( B @ ( A @ block_list_char ) ) )
!= ( E @ ( D @ seq_list_char ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_exp_Osimps_I196_J) ).
thf(366,plain,
! [A: list_char,B: ty,C: exp_list_char,D: exp_list_char,E: exp_list_char] :
( ( C @ ( B @ ( A @ block_list_char ) ) )
!= ( E @ ( D @ seq_list_char ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(183,axiom,
! [A: list_char,B: val,C: fun_na939144002on_val,D: fun_li1432931796on_val,E: list_P1999446415t_char] : ( E @ red @ ( B @ some_val @ ( A @ ( D @ fun_up1149430426on_val ) ) @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( unit @ val_list_char @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( D @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( B @ val_list_char @ ( A @ lAss_list_char ) @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_red__reds_ORedLAss) ).
thf(1047,plain,
! [A: list_char,B: val,C: fun_na939144002on_val,D: fun_li1432931796on_val,E: list_P1999446415t_char] : ( E @ red @ ( B @ some_val @ ( A @ ( D @ fun_up1149430426on_val ) ) @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( unit @ val_list_char @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( D @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( B @ val_list_char @ ( A @ lAss_list_char ) @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(186,axiom,
! [A: produc124828825on_val,B: fun_fu606696995l_bool,C: produc12694297on_val] :
( ( C @ ( B @ ( produc334393759l_bool @ hAPP_f833559503l_bool ) @ hAPP_P1638898323l_bool ) @ ( A @ member840932460on_val ) @ hBOOL )
=> ~ ! [D: fun_na939144002on_val,E: fun_li1432931796on_val] :
( ( C
= ( E @ ( D @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) ) )
=> ~ ( E @ ( D @ ( B @ hAPP_f2144092865l_bool ) @ hAPP_f2011777102l_bool ) @ ( A @ member840932460on_val ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_mem__splitE) ).
thf(1057,plain,
! [A: produc124828825on_val,B: fun_fu606696995l_bool,C: produc12694297on_val] :
( ( C @ ( B @ ( produc334393759l_bool @ hAPP_f833559503l_bool ) @ hAPP_P1638898323l_bool ) @ ( A @ member840932460on_val ) @ hBOOL )
=> ~ ! [D: fun_na939144002on_val,E: fun_li1432931796on_val] :
( ( C
= ( E @ ( D @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) ) )
=> ~ ( E @ ( D @ ( B @ hAPP_f2144092865l_bool ) @ hAPP_f2011777102l_bool ) @ ( A @ member840932460on_val ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(154,axiom,
! [A: fun_li688206603ion_ty,B: ty,C: exp_list_char,D: fun_na939144002on_val,E: fun_li1432931796on_val,F: exp_list_char,G: fun_na939144002on_val,H: fun_li1432931796on_val,I: list_P1999446415t_char] :
( ( I @ red @ ( H @ ( G @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( F @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( E @ ( D @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL )
=> ( ( B @ ( C @ ( A @ ( D @ ( I @ wTrt ) ) ) ) @ hBOOL )
=> ( ( D @ ( I @ hconf_97414254t_char @ hAPP_f61040418l_bool ) @ hBOOL )
=> ( G @ ( I @ hconf_97414254t_char @ hAPP_f61040418l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_red__preserves__hconf) ).
thf(910,plain,
! [A: fun_li688206603ion_ty,B: ty,C: exp_list_char,D: fun_na939144002on_val,E: fun_li1432931796on_val,F: exp_list_char,G: fun_na939144002on_val,H: fun_li1432931796on_val,I: list_P1999446415t_char] :
( ( I @ red @ ( H @ ( G @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( F @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( E @ ( D @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL )
=> ( ( B @ ( C @ ( A @ ( D @ ( I @ wTrt ) ) ) ) @ hBOOL )
=> ( ( D @ ( I @ hconf_97414254t_char @ hAPP_f61040418l_bool ) @ hBOOL )
=> ( G @ ( I @ hconf_97414254t_char @ hAPP_f61040418l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(194,axiom,
! [A: fun_li688206603ion_ty,B: ty,C: exp_list_char,D: fun_na939144002on_val,E: fun_li1432931796on_val,F: exp_list_char,G: fun_na939144002on_val,H: fun_li1432931796on_val,I: list_P1999446415t_char] :
( ( I @ red @ ( H @ ( G @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( F @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( E @ ( D @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL )
=> ( ( B @ ( C @ ( A @ ( D @ ( I @ wTrt ) ) ) ) @ hBOOL )
=> ( ( A @ ( E @ ( D @ ( I @ lconf_496643946t_char @ hAPP_f1213370163y_bool ) @ hAPP_f2060496320y_bool ) @ hAPP_f1001225811y_bool ) @ hBOOL )
=> ( A @ ( H @ ( G @ ( I @ lconf_496643946t_char @ hAPP_f1213370163y_bool ) @ hAPP_f2060496320y_bool ) @ hAPP_f1001225811y_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_red__preserves__lconf) ).
thf(1091,plain,
! [A: fun_li688206603ion_ty,B: ty,C: exp_list_char,D: fun_na939144002on_val,E: fun_li1432931796on_val,F: exp_list_char,G: fun_na939144002on_val,H: fun_li1432931796on_val,I: list_P1999446415t_char] :
( ( I @ red @ ( H @ ( G @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( F @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( E @ ( D @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL )
=> ( ( B @ ( C @ ( A @ ( D @ ( I @ wTrt ) ) ) ) @ hBOOL )
=> ( ( A @ ( E @ ( D @ ( I @ lconf_496643946t_char @ hAPP_f1213370163y_bool ) @ hAPP_f2060496320y_bool ) @ hAPP_f1001225811y_bool ) @ hBOOL )
=> ( A @ ( H @ ( G @ ( I @ lconf_496643946t_char @ hAPP_f1213370163y_bool ) @ hAPP_f2060496320y_bool ) @ hAPP_f1001225811y_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(125,axiom,
! [A: produc124828825on_val,B: fun_Pr741412723l_bool,C: produc1102272487on_val] :
( ( C @ ( B @ ( produc20018513l_bool @ hAPP_f1591648613l_bool ) @ hAPP_P678729081l_bool ) @ ( A @ member840932460on_val ) @ hBOOL )
=> ~ ! [D: produc124828825on_val,E: produc124828825on_val] :
( ( C
= ( E @ ( D @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) ) )
=> ~ ( E @ ( D @ ( B @ hAPP_P1953518277l_bool ) @ hAPP_P1116729363l_bool ) @ ( A @ member840932460on_val ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_mem__splitE) ).
thf(778,plain,
! [A: produc124828825on_val,B: fun_Pr741412723l_bool,C: produc1102272487on_val] :
( ( C @ ( B @ ( produc20018513l_bool @ hAPP_f1591648613l_bool ) @ hAPP_P678729081l_bool ) @ ( A @ member840932460on_val ) @ hBOOL )
=> ~ ! [D: produc124828825on_val,E: produc124828825on_val] :
( ( C
= ( E @ ( D @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) ) )
=> ~ ( E @ ( D @ ( B @ hAPP_P1953518277l_bool ) @ hAPP_P1116729363l_bool ) @ ( A @ member840932460on_val ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(25,axiom,
! [A: fun_li688206603ion_ty,B: option_ty,C: option_ty,D: list_char,E: list_char] :
( ( D != E )
=> ( ( C @ ( E @ ( B @ ( D @ ( A @ fun_up424764369ion_ty ) ) @ fun_up424764369ion_ty ) ) )
= ( B @ ( D @ ( C @ ( E @ ( A @ fun_up424764369ion_ty ) ) @ fun_up424764369ion_ty ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_fun__upd__twist) ).
thf(302,plain,
! [A: fun_li688206603ion_ty,B: option_ty,C: option_ty,D: list_char,E: list_char] :
( ( D != E )
=> ( ( C @ ( E @ ( B @ ( D @ ( A @ fun_up424764369ion_ty ) ) @ fun_up424764369ion_ty ) ) )
= ( B @ ( D @ ( C @ ( E @ ( A @ fun_up424764369ion_ty ) ) @ fun_up424764369ion_ty ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(33,axiom,
! [A: list_char,B: exp_list_char,C: exp_list_char,D: exp_list_char] :
( ( B @ ( A @ lAss_list_char ) )
!= ( D @ ( C @ seq_list_char ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_exp_Osimps_I144_J) ).
thf(349,plain,
! [A: list_char,B: exp_list_char,C: exp_list_char,D: exp_list_char] :
( ( B @ ( A @ lAss_list_char ) )
!= ( D @ ( C @ seq_list_char ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(135,axiom,
! [A: fun_Pr1696029455l_bool] :
( ( produc899768717on_val @ ( A @ ( cOMBB_1750801836on_val @ hAPP_f2057883639l_bool ) @ ( cOMBB_1153617344on_val @ hAPP_f1050935001l_bool ) @ hAPP_f1363667773l_bool ) @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_split__eta) ).
thf(820,plain,
! [A: fun_Pr1696029455l_bool] :
( ( produc899768717on_val @ ( A @ ( cOMBB_1750801836on_val @ hAPP_f2057883639l_bool ) @ ( cOMBB_1153617344on_val @ hAPP_f1050935001l_bool ) @ hAPP_f1363667773l_bool ) @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(76,axiom,
! [A: fun_Pr633696065l_bool,B: produc124828825on_val,C: produc124828825on_val] :
( ( C @ ( B @ ( A @ hAPP_P1116729363l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL )
=> ( C @ ( B @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ ( A @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_prod__caseI) ).
thf(561,plain,
! [A: fun_Pr633696065l_bool,B: produc124828825on_val,C: produc124828825on_val] :
( ( C @ ( B @ ( A @ hAPP_P1116729363l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL )
=> ( C @ ( B @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ ( A @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(53,axiom,
! [A: val,B: list_char,C: exp_list_char] :
( ( A @ val_list_char )
!= ( C @ ( B @ lAss_list_char ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_exp_Osimps_I74_J) ).
thf(424,plain,
! [A: val,B: list_char,C: exp_list_char] :
( ( A @ val_list_char )
!= ( C @ ( B @ lAss_list_char ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(20,axiom,
! [A: exp_list_char,B: exp_list_char,C: exp_list_char,D: exp_list_char] :
( ( ( B @ ( A @ seq_list_char ) )
= ( D @ ( C @ seq_list_char ) ) )
<=> ( ( B = D )
& ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_exp_Osimps_I11_J) ).
thf(275,plain,
! [A: exp_list_char,B: exp_list_char,C: exp_list_char,D: exp_list_char] :
( ( ( ( B = D )
& ( A = C ) )
=> ( ( B @ ( A @ seq_list_char ) )
= ( D @ ( C @ seq_list_char ) ) ) )
& ( ( ( B @ ( A @ seq_list_char ) )
= ( D @ ( C @ seq_list_char ) ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(115,axiom,
! [A: fun_Pr1696029455l_bool] :
( ! [B: produc12694297on_val] : ( B @ ( A @ hAPP_P159683425l_bool ) @ hBOOL )
<=> ! [B: fun_na939144002on_val,C: fun_li1432931796on_val] : ( C @ ( B @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( A @ hAPP_P159683425l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_split__paired__All) ).
thf(729,plain,
! [A: fun_Pr1696029455l_bool] :
( ( ! [B: fun_na939144002on_val,C: fun_li1432931796on_val] : ( C @ ( B @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( A @ hAPP_P159683425l_bool ) @ hBOOL )
=> ! [B: produc12694297on_val] : ( B @ ( A @ hAPP_P159683425l_bool ) @ hBOOL ) )
& ( ! [B: produc12694297on_val] : ( B @ ( A @ hAPP_P159683425l_bool ) @ hBOOL )
=> ! [B: fun_na939144002on_val,C: fun_li1432931796on_val] : ( C @ ( B @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( A @ hAPP_P159683425l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(9,axiom,
! [A: fun_Pr1696029455l_bool,B: fun_Pr1833267965on_val,C: produc12694297on_val] :
( ( C @ ( B @ ( A @ ( cOMBB_877741809on_val @ hAPP_f1825030711l_bool ) @ hAPP_f1301559543l_bool ) @ hAPP_P159683425l_bool ) )
= ( C @ ( B @ hAPP_P1776198677on_val ) @ ( A @ hAPP_P159683425l_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It_201) ).
thf(229,plain,
! [A: fun_Pr1696029455l_bool,B: fun_Pr1833267965on_val,C: produc12694297on_val] :
( ( C @ ( B @ ( A @ ( cOMBB_877741809on_val @ hAPP_f1825030711l_bool ) @ hAPP_f1301559543l_bool ) @ hAPP_P159683425l_bool ) )
= ( C @ ( B @ hAPP_P1776198677on_val ) @ ( A @ hAPP_P159683425l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(150,axiom,
! [A: fun_ex1201926843l_bool,B: produc124828825on_val,C: produc124828825on_val] :
( ( B = C )
=> ( ( B @ ( A @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL )
<=> ( C @ ( A @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_split__weak__cong) ).
thf(889,plain,
! [A: fun_ex1201926843l_bool,B: produc124828825on_val,C: produc124828825on_val] :
( ( B = C )
=> ( ( ( C @ ( A @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL )
=> ( B @ ( A @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL )
=> ( C @ ( A @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(121,axiom,
! [A: fun_Pr680585871l_bool] :
( ! [B: produc124828825on_val] : ( B @ ( A @ hAPP_P1708370145l_bool ) @ hBOOL )
<=> ! [B: exp_list_char,C: produc12694297on_val] : ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( A @ hAPP_P1708370145l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_split__paired__All) ).
thf(757,plain,
! [A: fun_Pr680585871l_bool] :
( ( ! [B: exp_list_char,C: produc12694297on_val] : ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( A @ hAPP_P1708370145l_bool ) @ hBOOL )
=> ! [B: produc124828825on_val] : ( B @ ( A @ hAPP_P1708370145l_bool ) @ hBOOL ) )
& ( ! [B: produc124828825on_val] : ( B @ ( A @ hAPP_P1708370145l_bool ) @ hBOOL )
=> ! [B: exp_list_char,C: produc12694297on_val] : ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( A @ hAPP_P1708370145l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(114,axiom,
! [A: fun_li1432931796on_val,B: list_char,C: val,D: list_char,E: val] :
( ( ( D @ ( C @ some_val @ ( B @ ( A @ fun_up1149430426on_val ) ) @ hAPP_l207779698on_val ) )
= ( E @ some_val ) )
<=> ( ( ( ( D @ ( A @ hAPP_l207779698on_val ) )
= ( E @ some_val ) )
& ( D != B ) )
| ( ( C = E )
& ( D = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_map__upd__Some__unfold) ).
thf(710,plain,
! [A: fun_li1432931796on_val,B: list_char,C: val,D: list_char,E: val] :
( ( ( ( ( ( D @ ( A @ hAPP_l207779698on_val ) )
= ( E @ some_val ) )
& ( D != B ) )
| ( ( C = E )
& ( D = B ) ) )
=> ( ( D @ ( C @ some_val @ ( B @ ( A @ fun_up1149430426on_val ) ) @ hAPP_l207779698on_val ) )
= ( E @ some_val ) ) )
& ( ( ( D @ ( C @ some_val @ ( B @ ( A @ fun_up1149430426on_val ) ) @ hAPP_l207779698on_val ) )
= ( E @ some_val ) )
=> ( ( ( ( D @ ( A @ hAPP_l207779698on_val ) )
= ( E @ some_val ) )
& ( D != B ) )
| ( ( C = E )
& ( D = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(27,axiom,
! [A: fun_bool_bool,B: fun_Pr680585871l_bool,C: produc124828825on_val] :
( ( C @ ( B @ ( A @ ( cOMBB_672625589on_val @ hAPP_f1560238713l_bool ) @ hAPP_f926562337l_bool ) @ hAPP_P1708370145l_bool ) )
= ( C @ ( B @ hAPP_P1708370145l_bool ) @ ( A @ hAPP_bool_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__prod_Itc__Expr__) ).
thf(324,plain,
! [A: fun_bool_bool,B: fun_Pr680585871l_bool,C: produc124828825on_val] :
( ( C @ ( B @ ( A @ ( cOMBB_672625589on_val @ hAPP_f1560238713l_bool ) @ hAPP_f926562337l_bool ) @ hAPP_P1708370145l_bool ) )
= ( C @ ( B @ hAPP_P1708370145l_bool ) @ ( A @ hAPP_bool_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(177,axiom,
! [A: val,B: exp_list_char,C: produc12694297on_val,D: list_P1999446415t_char] : ( D @ red @ ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( C @ ( B @ ( A @ val_list_char @ seq_list_char ) @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_red__reds_ORedSeq) ).
thf(1012,plain,
! [A: val,B: exp_list_char,C: produc12694297on_val,D: list_P1999446415t_char] : ( D @ red @ ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( C @ ( B @ ( A @ val_list_char @ seq_list_char ) @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(162,axiom,
! [A: fun_Pr1696029455l_bool] :
( ? [B: produc12694297on_val] : ( B @ ( A @ hAPP_P159683425l_bool ) @ hBOOL )
<=> ? [B: fun_na939144002on_val,C: fun_li1432931796on_val] : ( C @ ( B @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( A @ hAPP_P159683425l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_split__paired__Ex) ).
thf(948,plain,
! [A: fun_Pr1696029455l_bool] :
( ( ? [B: fun_na939144002on_val,C: fun_li1432931796on_val] : ( C @ ( B @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( A @ hAPP_P159683425l_bool ) @ hBOOL )
=> ? [B: produc12694297on_val] : ( B @ ( A @ hAPP_P159683425l_bool ) @ hBOOL ) )
& ( ? [B: produc12694297on_val] : ( B @ ( A @ hAPP_P159683425l_bool ) @ hBOOL )
=> ? [B: fun_na939144002on_val,C: fun_li1432931796on_val] : ( C @ ( B @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( A @ hAPP_P159683425l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(88,axiom,
! [A: bool,B: fun_Pr633696065l_bool,C: produc1102272487on_val] :
( ( C @ ( B @ ( A @ ( fconj @ hAPP_b589554111l_bool ) @ ( cOMBB_672625589on_val @ hAPP_f1560238713l_bool ) @ ( cOMBB_466903633on_val @ hAPP_f2032347769l_bool ) @ hAPP_f641257349l_bool ) @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL )
<=> ( ( C @ ( B @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL )
& ( A @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_split__part) ).
thf(615,plain,
! [A: bool,B: fun_Pr633696065l_bool,C: produc1102272487on_val] :
( ( ( ( C @ ( B @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL )
& ( A @ hBOOL ) )
=> ( C @ ( B @ ( A @ ( fconj @ hAPP_b589554111l_bool ) @ ( cOMBB_672625589on_val @ hAPP_f1560238713l_bool ) @ ( cOMBB_466903633on_val @ hAPP_f2032347769l_bool ) @ hAPP_f641257349l_bool ) @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL ) )
& ( ( C @ ( B @ ( A @ ( fconj @ hAPP_b589554111l_bool ) @ ( cOMBB_672625589on_val @ hAPP_f1560238713l_bool ) @ ( cOMBB_466903633on_val @ hAPP_f2032347769l_bool ) @ hAPP_f641257349l_bool ) @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL )
=> ( ( C @ ( B @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL )
& ( A @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(176,axiom,
! [A: fun_ex1201926843l_bool,B: exp_list_char,C: produc12694297on_val] :
( ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( A @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL )
<=> ( C @ ( B @ ( A @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_prod_Osimps_I2_J) ).
thf(1006,plain,
! [A: fun_ex1201926843l_bool,B: exp_list_char,C: produc12694297on_val] :
( ( ( C @ ( B @ ( A @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
=> ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( A @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL ) )
& ( ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( A @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL )
=> ( C @ ( B @ ( A @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(35,axiom,
! [A: fun_fu983865091l_bool,B: fun_Pr633696065l_bool,C: produc124828825on_val] :
( ( C @ ( B @ ( A @ ( cOMBB_466903633on_val @ hAPP_f2032347769l_bool ) @ hAPP_f641257349l_bool ) @ hAPP_P1116729363l_bool ) )
= ( C @ ( B @ hAPP_P1116729363l_bool ) @ ( A @ hAPP_f926562337l_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__) ).
thf(356,plain,
! [A: fun_fu983865091l_bool,B: fun_Pr633696065l_bool,C: produc124828825on_val] :
( ( C @ ( B @ ( A @ ( cOMBB_466903633on_val @ hAPP_f2032347769l_bool ) @ hAPP_f641257349l_bool ) @ hAPP_P1116729363l_bool ) )
= ( C @ ( B @ hAPP_P1116729363l_bool ) @ ( A @ hAPP_f926562337l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(83,axiom,
t @ ( ea @ ( v @ val_list_char @ ( v_1 @ lAss_list_char ) @ seq_list_char ) @ ( t_1 @ ( v_1 @ block_list_char ) ) @ ( e @ ( ha @ ( p @ wTrt ) ) ) ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_InitBlockRed_I5_J) ).
thf(593,plain,
t @ ( ea @ ( v @ val_list_char @ ( v_1 @ lAss_list_char ) @ seq_list_char ) @ ( t_1 @ ( v_1 @ block_list_char ) ) @ ( e @ ( ha @ ( p @ wTrt ) ) ) ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(87,axiom,
! [A: produc124828825on_val,B: fun_ex1732109805l_bool,C: produc124828825on_val] :
( ( C @ ( B @ ( produc1275132703l_bool @ hAPP_f1760682521l_bool ) @ hAPP_P1116729363l_bool ) @ ( A @ member840932460on_val ) @ hBOOL )
=> ~ ! [D: exp_list_char,E: produc12694297on_val] :
( ( C
= ( E @ ( D @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) ) )
=> ~ ( E @ ( D @ ( B @ hAPP_e592495499l_bool ) @ hAPP_P1638898323l_bool ) @ ( A @ member840932460on_val ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_mem__splitE) ).
thf(610,plain,
! [A: produc124828825on_val,B: fun_ex1732109805l_bool,C: produc124828825on_val] :
( ( C @ ( B @ ( produc1275132703l_bool @ hAPP_f1760682521l_bool ) @ hAPP_P1116729363l_bool ) @ ( A @ member840932460on_val ) @ hBOOL )
=> ~ ! [D: exp_list_char,E: produc12694297on_val] :
( ( C
= ( E @ ( D @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) ) )
=> ~ ( E @ ( D @ ( B @ hAPP_e592495499l_bool ) @ hAPP_P1638898323l_bool ) @ ( A @ member840932460on_val ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(126,axiom,
! [A: bool,B: bool] :
( ( A @ hBOOL )
| ~ ( B @ ( A @ ( fconj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
thf(783,plain,
! [A: bool,B: bool] :
( ( A @ hBOOL )
| ~ ( B @ ( A @ ( fconj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(52,axiom,
! [A: list_char,B: ty,C: exp_list_char,D: val] :
( ( C @ ( B @ ( A @ block_list_char ) ) )
!= ( D @ val_list_char ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_exp_Osimps_I83_J) ).
thf(420,plain,
! [A: list_char,B: ty,C: exp_list_char,D: val] :
( ( C @ ( B @ ( A @ block_list_char ) ) )
!= ( D @ val_list_char ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(8,axiom,
! [A: list_char,B: exp_list_char,C: val] :
( ( B @ ( A @ lAss_list_char ) )
!= ( C @ val_list_char ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_exp_Osimps_I75_J) ).
thf(225,plain,
! [A: list_char,B: exp_list_char,C: val] :
( ( B @ ( A @ lAss_list_char ) )
!= ( C @ val_list_char ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(74,axiom,
! [A: produc1102272487on_val] :
~ ! [B: produc124828825on_val,C: produc124828825on_val] :
( A
!= ( C @ ( B @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_prod_Oexhaust) ).
thf(554,plain,
! [A: produc1102272487on_val] :
~ ! [B: produc124828825on_val,C: produc124828825on_val] :
( A
!= ( C @ ( B @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(153,axiom,
! [A: fun_li1432931796on_val,B: option_val,C: list_char,D: list_char] :
( ( ( C != D )
=> ( ( C @ ( B @ ( D @ ( A @ fun_up1149430426on_val ) ) @ hAPP_l207779698on_val ) )
= ( C @ ( A @ hAPP_l207779698on_val ) ) ) )
& ( ( C = D )
=> ( ( C @ ( B @ ( D @ ( A @ fun_up1149430426on_val ) ) @ hAPP_l207779698on_val ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_fun__upd__apply) ).
thf(901,plain,
! [A: fun_li1432931796on_val,B: option_val,C: list_char,D: list_char] :
( ( ( C != D )
=> ( ( C @ ( B @ ( D @ ( A @ fun_up1149430426on_val ) ) @ hAPP_l207779698on_val ) )
= ( C @ ( A @ hAPP_l207779698on_val ) ) ) )
& ( ( C = D )
=> ( ( C @ ( B @ ( D @ ( A @ fun_up1149430426on_val ) ) @ hAPP_l207779698on_val ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(96,axiom,
! [A: fun_Pr633696065l_bool,B: produc124828825on_val,C: produc124828825on_val] :
( ( C @ ( B @ ( A @ hAPP_P1116729363l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL )
=> ( C @ ( B @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ ( A @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_splitI) ).
thf(642,plain,
! [A: fun_Pr633696065l_bool,B: produc124828825on_val,C: produc124828825on_val] :
( ( C @ ( B @ ( A @ hAPP_P1116729363l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL )
=> ( C @ ( B @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ ( A @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(106,axiom,
! [A: fun_fu100249073l_bool,B: fun_na939144002on_val,C: fun_li1432931796on_val] :
( ( C @ ( B @ ( A @ hAPP_f1175813647l_bool ) @ hAPP_f1033709212l_bool ) @ hBOOL )
=> ( C @ ( B @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_prod__caseI) ).
thf(679,plain,
! [A: fun_fu100249073l_bool,B: fun_na939144002on_val,C: fun_li1432931796on_val] :
( ( C @ ( B @ ( A @ hAPP_f1175813647l_bool ) @ hAPP_f1033709212l_bool ) @ hBOOL )
=> ( C @ ( B @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(72,axiom,
! [A: produc12694297on_val,B: fun_ex1123147373l_bool,C: produc124828825on_val] :
( ! [D: exp_list_char,E: produc12694297on_val] :
( ( C
= ( E @ ( D @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) ) )
=> ( E @ ( D @ ( B @ hAPP_e500528395l_bool ) @ hAPP_P1988153107l_bool ) @ ( A @ member763590124on_val ) @ hBOOL ) )
=> ( C @ ( B @ ( produc2036005791l_bool @ hAPP_f468299289l_bool ) @ hAPP_P595502227l_bool ) @ ( A @ member763590124on_val ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_mem__splitI2) ).
thf(547,plain,
! [A: produc12694297on_val,B: fun_ex1123147373l_bool,C: produc124828825on_val] :
( ! [D: exp_list_char,E: produc12694297on_val] :
( ( C
= ( E @ ( D @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) ) )
=> ( E @ ( D @ ( B @ hAPP_e500528395l_bool ) @ hAPP_P1988153107l_bool ) @ ( A @ member763590124on_val ) @ hBOOL ) )
=> ( C @ ( B @ ( produc2036005791l_bool @ hAPP_f468299289l_bool ) @ hAPP_P595502227l_bool ) @ ( A @ member763590124on_val ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(6,axiom,
! [A: val,B: val] :
( ( ( A @ val_list_char )
= ( B @ val_list_char ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_exp_Osimps_I3_J) ).
thf(212,plain,
! [A: val,B: val] :
( ( ( A = B )
=> ( ( A @ val_list_char )
= ( B @ val_list_char ) ) )
& ( ( ( A @ val_list_char )
= ( B @ val_list_char ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(89,axiom,
! [A: produc1102272487on_val,B: fun_Pr691271849l_bool] :
( ! [C: produc124828825on_val,D: exp_list_char,E: produc12694297on_val] : ( E @ ( D @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( C @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ ( B @ hAPP_P282169671l_bool ) @ hBOOL )
=> ( A @ ( B @ hAPP_P282169671l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_prod__induct3) ).
thf(622,plain,
! [A: produc1102272487on_val,B: fun_Pr691271849l_bool] :
( ! [C: produc124828825on_val,D: exp_list_char,E: produc12694297on_val] : ( E @ ( D @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( C @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ ( B @ hAPP_P282169671l_bool ) @ hBOOL )
=> ( A @ ( B @ hAPP_P282169671l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(47,axiom,
! [A: fun_li688206603ion_ty,B: list_char,C: option_ty] :
( ( ( B @ ( A @ hAPP_l512744617ion_ty ) )
= C )
=> ( ( C @ ( B @ ( A @ fun_up424764369ion_ty ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_fun__upd__idem) ).
thf(393,plain,
! [A: fun_li688206603ion_ty,B: list_char,C: option_ty] :
( ( ( B @ ( A @ hAPP_l512744617ion_ty ) )
= C )
=> ( ( C @ ( B @ ( A @ fun_up424764369ion_ty ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(98,axiom,
! [A: produc12694297on_val,B: fun_Pr293514739l_bool,C: produc1102272487on_val] :
( ( C @ ( B @ ( produc376702929l_bool @ hAPP_f444383845l_bool ) @ hAPP_P1826803705l_bool ) @ ( A @ member763590124on_val ) @ hBOOL )
=> ~ ! [D: produc124828825on_val,E: produc124828825on_val] :
( ( C
= ( E @ ( D @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) ) )
=> ~ ( E @ ( D @ ( B @ hAPP_P1134042693l_bool ) @ hAPP_P595502227l_bool ) @ ( A @ member763590124on_val ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_mem__splitE) ).
thf(647,plain,
! [A: produc12694297on_val,B: fun_Pr293514739l_bool,C: produc1102272487on_val] :
( ( C @ ( B @ ( produc376702929l_bool @ hAPP_f444383845l_bool ) @ hAPP_P1826803705l_bool ) @ ( A @ member763590124on_val ) @ hBOOL )
=> ~ ! [D: produc124828825on_val,E: produc124828825on_val] :
( ( C
= ( E @ ( D @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) ) )
=> ~ ( E @ ( D @ ( B @ hAPP_P1134042693l_bool ) @ hAPP_P595502227l_bool ) @ ( A @ member763590124on_val ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(100,axiom,
! [A: fun_Pr680585871l_bool] :
( ? [B: produc124828825on_val] : ( B @ ( A @ hAPP_P1708370145l_bool ) @ hBOOL )
<=> ? [B: exp_list_char,C: produc12694297on_val] : ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( A @ hAPP_P1708370145l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_split__paired__Ex) ).
thf(654,plain,
! [A: fun_Pr680585871l_bool] :
( ( ? [B: exp_list_char,C: produc12694297on_val] : ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( A @ hAPP_P1708370145l_bool ) @ hBOOL )
=> ? [B: produc124828825on_val] : ( B @ ( A @ hAPP_P1708370145l_bool ) @ hBOOL ) )
& ( ? [B: produc124828825on_val] : ( B @ ( A @ hAPP_P1708370145l_bool ) @ hBOOL )
=> ? [B: exp_list_char,C: produc12694297on_val] : ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( A @ hAPP_P1708370145l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(170,axiom,
! [A: produc1102272487on_val] :
~ ! [B: produc124828825on_val,C: exp_list_char,D: fun_na939144002on_val,E: fun_li1432931796on_val] :
( A
!= ( E @ ( D @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( B @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_prod__cases4) ).
thf(984,plain,
! [A: produc1102272487on_val] :
~ ! [B: produc124828825on_val,C: exp_list_char,D: fun_na939144002on_val,E: fun_li1432931796on_val] :
( A
!= ( E @ ( D @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( B @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(174,axiom,
la @ ( ha @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( e @ ( p @ typeSa1844245082_sconf ) @ hAPP_P159683425l_bool ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_InitBlockRed_I4_J) ).
thf(1002,plain,
la @ ( ha @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( e @ ( p @ typeSa1844245082_sconf ) @ hAPP_P159683425l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(86,axiom,
! [A: fun_ex1201926843l_bool,B: produc124828825on_val] :
( ! [C: exp_list_char,D: produc12694297on_val] :
( ( B
= ( D @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) ) )
=> ( D @ ( C @ ( A @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) )
=> ( B @ ( A @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_splitI2) ).
thf(605,plain,
! [A: fun_ex1201926843l_bool,B: produc124828825on_val] :
( ! [C: exp_list_char,D: produc12694297on_val] :
( ( B
= ( D @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) ) )
=> ( D @ ( C @ ( A @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) )
=> ( B @ ( A @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(193,axiom,
! [A: fun_bool_bool,B: fun_Pr633696065l_bool,C: produc1102272487on_val] :
( ( C @ ( B @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ ( A @ hAPP_bool_bool ) @ hBOOL )
=> ~ ! [D: produc124828825on_val,E: produc124828825on_val] :
( ( C
= ( E @ ( D @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) ) )
=> ~ ( E @ ( D @ ( B @ hAPP_P1116729363l_bool ) @ hAPP_P1708370145l_bool ) @ ( A @ hAPP_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_splitE2) ).
thf(1086,plain,
! [A: fun_bool_bool,B: fun_Pr633696065l_bool,C: produc1102272487on_val] :
( ( C @ ( B @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ ( A @ hAPP_bool_bool ) @ hBOOL )
=> ~ ! [D: produc124828825on_val,E: produc124828825on_val] :
( ( C
= ( E @ ( D @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) ) )
=> ~ ( E @ ( D @ ( B @ hAPP_P1116729363l_bool ) @ hAPP_P1708370145l_bool ) @ ( A @ hAPP_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(4,axiom,
! [A: list_char,B: list_char] :
( ( B @ ( none_ty @ ( A @ ( none_ty @ cOMBK_1294242658t_char @ fun_up424764369ion_ty ) ) @ hAPP_l512744617ion_ty ) )
= none_ty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_empty__upd__none) ).
thf(205,plain,
! [A: list_char,B: list_char] :
( ( B @ ( none_ty @ ( A @ ( none_ty @ cOMBK_1294242658t_char @ fun_up424764369ion_ty ) ) @ hAPP_l512744617ion_ty ) )
= none_ty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(75,axiom,
! [A: ty,B: val,C: exp_list_char,D: fun_na939144002on_val,E: fun_li1432931796on_val,F: list_char,G: exp_list_char,H: fun_na939144002on_val,I: fun_li1432931796on_val,J: list_P1999446415t_char] :
( ( J @ red @ ( I @ ( H @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( G @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( none_val @ ( F @ ( E @ fun_up1149430426on_val ) ) @ ( D @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL )
=> ( ( ( F @ ( I @ hAPP_l207779698on_val ) )
= ( B @ some_val ) )
=> ( ~ ( C @ ( F @ assigned ) @ hBOOL )
=> ( J @ red @ ( F @ ( E @ hAPP_l207779698on_val ) @ ( F @ ( I @ fun_up1149430426on_val ) ) @ ( H @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( G @ ( B @ val_list_char @ ( F @ lAss_list_char ) @ seq_list_char ) @ ( A @ ( F @ block_list_char ) ) @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( E @ ( D @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( C @ ( A @ ( F @ block_list_char ) ) @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_red__reds_OBlockRedSome) ).
thf(558,plain,
! [A: ty,B: val,C: exp_list_char,D: fun_na939144002on_val,E: fun_li1432931796on_val,F: list_char,G: exp_list_char,H: fun_na939144002on_val,I: fun_li1432931796on_val,J: list_P1999446415t_char] :
( ( J @ red @ ( I @ ( H @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( G @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( none_val @ ( F @ ( E @ fun_up1149430426on_val ) ) @ ( D @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL )
=> ( ( ( F @ ( I @ hAPP_l207779698on_val ) )
= ( B @ some_val ) )
=> ( ~ ( C @ ( F @ assigned ) @ hBOOL )
=> ( J @ red @ ( F @ ( E @ hAPP_l207779698on_val ) @ ( F @ ( I @ fun_up1149430426on_val ) ) @ ( H @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( G @ ( B @ val_list_char @ ( F @ lAss_list_char ) @ seq_list_char ) @ ( A @ ( F @ block_list_char ) ) @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( E @ ( D @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( C @ ( A @ ( F @ block_list_char ) ) @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(23,axiom,
! [A: fun_li688206603ion_ty,B: list_char,C: option_ty,D: option_ty] :
( ( D @ ( B @ ( C @ ( B @ ( A @ fun_up424764369ion_ty ) ) @ fun_up424764369ion_ty ) ) )
= ( D @ ( B @ ( A @ fun_up424764369ion_ty ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_fun__upd__upd) ).
thf(296,plain,
! [A: fun_li688206603ion_ty,B: list_char,C: option_ty,D: option_ty] :
( ( D @ ( B @ ( C @ ( B @ ( A @ fun_up424764369ion_ty ) ) @ fun_up424764369ion_ty ) ) )
= ( D @ ( B @ ( A @ fun_up424764369ion_ty ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(41,axiom,
! [A: fun_fu225006629l_bool,B: fun_ex1005552999on_val,C: exp_list_char] :
( ( C @ ( B @ ( A @ ( cOMBB_819439237t_char @ hAPP_f516738477l_bool ) @ hAPP_f653692369l_bool ) @ hAPP_e1833980889l_bool ) )
= ( C @ ( B @ hAPP_e108155315on_val ) @ ( A @ hAPP_f1301559543l_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__O_206) ).
thf(375,plain,
! [A: fun_fu225006629l_bool,B: fun_ex1005552999on_val,C: exp_list_char] :
( ( C @ ( B @ ( A @ ( cOMBB_819439237t_char @ hAPP_f516738477l_bool ) @ hAPP_f653692369l_bool ) @ hAPP_e1833980889l_bool ) )
= ( C @ ( B @ hAPP_e108155315on_val ) @ ( A @ hAPP_f1301559543l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(111,axiom,
! [A: produc12694297on_val] :
~ ! [B: fun_na939144002on_val,C: fun_li1432931796on_val] :
( A
!= ( C @ ( B @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_prod_Oexhaust) ).
thf(694,plain,
! [A: produc12694297on_val] :
~ ! [B: fun_na939144002on_val,C: fun_li1432931796on_val] :
( A
!= ( C @ ( B @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(118,axiom,
! [A: fun_fu100249073l_bool,B: produc12694297on_val] :
( ( B @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
=> ~ ! [C: fun_na939144002on_val,D: fun_li1432931796on_val] :
( ( B
= ( D @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) ) )
=> ~ ( D @ ( C @ ( A @ hAPP_f1175813647l_bool ) @ hAPP_f1033709212l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_splitE) ).
thf(743,plain,
! [A: fun_fu100249073l_bool,B: produc12694297on_val] :
( ( B @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
=> ~ ! [C: fun_na939144002on_val,D: fun_li1432931796on_val] :
( ( B
= ( D @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) ) )
=> ~ ( D @ ( C @ ( A @ hAPP_f1175813647l_bool ) @ hAPP_f1033709212l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(71,axiom,
! [A: list_char,B: ty,C: val,D: val,E: produc12694297on_val,F: list_P1999446415t_char] : ( F @ red @ ( E @ ( D @ val_list_char @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( E @ ( D @ val_list_char @ ( C @ val_list_char @ ( A @ lAss_list_char ) @ seq_list_char ) @ ( B @ ( A @ block_list_char ) ) @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_red__reds_ORedInitBlock) ).
thf(545,plain,
! [A: list_char,B: ty,C: val,D: val,E: produc12694297on_val,F: list_P1999446415t_char] : ( F @ red @ ( E @ ( D @ val_list_char @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( E @ ( D @ val_list_char @ ( C @ val_list_char @ ( A @ lAss_list_char ) @ seq_list_char ) @ ( B @ ( A @ block_list_char ) ) @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(50,axiom,
! [A: fun_bool_bool,B: fun_fu1693644106l_bool,C: fun_li1432931796on_val] :
( ( C @ ( B @ ( A @ ( cOMBB_383678192on_val @ hAPP_f1863694447l_bool ) @ hAPP_f1074020887l_bool ) @ hAPP_f1033709212l_bool ) )
= ( C @ ( B @ hAPP_f1033709212l_bool ) @ ( A @ hAPP_bool_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__List__O) ).
thf(413,plain,
! [A: fun_bool_bool,B: fun_fu1693644106l_bool,C: fun_li1432931796on_val] :
( ( C @ ( B @ ( A @ ( cOMBB_383678192on_val @ hAPP_f1863694447l_bool ) @ hAPP_f1074020887l_bool ) @ hAPP_f1033709212l_bool ) )
= ( C @ ( B @ hAPP_f1033709212l_bool ) @ ( A @ hAPP_bool_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(11,axiom,
! [A: fun_li688206603ion_ty,B: list_char,C: option_ty] :
( ( B @ ( C @ ( B @ ( A @ fun_up424764369ion_ty ) ) @ hAPP_l512744617ion_ty ) )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_fun__upd__same) ).
thf(236,plain,
! [A: fun_li688206603ion_ty,B: list_char,C: option_ty] :
( ( B @ ( C @ ( B @ ( A @ fun_up424764369ion_ty ) ) @ hAPP_l512744617ion_ty ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(130,axiom,
! [A: fun_fu1176066021l_bool,B: fun_fu1639641777on_val,C: fun_na939144002on_val] :
( ( C @ ( B @ ( A @ ( cOMBB_1153617344on_val @ hAPP_f1050935001l_bool ) @ hAPP_f1363667773l_bool ) @ hAPP_f1175813647l_bool ) )
= ( C @ ( B @ hAPP_f1849790461on_val ) @ ( A @ hAPP_f1008932791l_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_204) ).
thf(804,plain,
! [A: fun_fu1176066021l_bool,B: fun_fu1639641777on_val,C: fun_na939144002on_val] :
( ( C @ ( B @ ( A @ ( cOMBB_1153617344on_val @ hAPP_f1050935001l_bool ) @ hAPP_f1363667773l_bool ) @ hAPP_f1175813647l_bool ) )
= ( C @ ( B @ hAPP_f1849790461on_val ) @ ( A @ hAPP_f1008932791l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(113,axiom,
! [A: produc124828825on_val,B: produc124828825on_val,C: produc124828825on_val,D: produc124828825on_val] :
( ( ( B @ ( A @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) )
= ( D @ ( C @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_Pair__inject) ).
thf(704,plain,
! [A: produc124828825on_val,B: produc124828825on_val,C: produc124828825on_val,D: produc124828825on_val] :
( ( ( B @ ( A @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) )
= ( D @ ( C @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(168,axiom,
( ( v_1 @ ( l_a @ hAPP_l207779698on_val ) )
= ( v_2 @ some_val ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_InitBlockRed_I3_J) ).
thf(979,plain,
( ( v_1 @ ( l_a @ hAPP_l207779698on_val ) )
= ( v_2 @ some_val ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(107,axiom,
! [A: fun_na939144002on_val,B: fun_li1432931796on_val,C: fun_na939144002on_val,D: fun_li1432931796on_val] :
( ( ( B @ ( A @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) )
= ( D @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_Pair__inject) ).
thf(681,plain,
! [A: fun_na939144002on_val,B: fun_li1432931796on_val,C: fun_na939144002on_val,D: fun_li1432931796on_val] :
( ( ( B @ ( A @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) )
= ( D @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(117,axiom,
! [A: fun_Pr691271849l_bool] :
( ! [B: produc1102272487on_val] : ( B @ ( A @ hAPP_P282169671l_bool ) @ hBOOL )
<=> ! [B: produc124828825on_val,C: produc124828825on_val] : ( C @ ( B @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ ( A @ hAPP_P282169671l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_split__paired__All) ).
thf(737,plain,
! [A: fun_Pr691271849l_bool] :
( ( ! [B: produc124828825on_val,C: produc124828825on_val] : ( C @ ( B @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ ( A @ hAPP_P282169671l_bool ) @ hBOOL )
=> ! [B: produc1102272487on_val] : ( B @ ( A @ hAPP_P282169671l_bool ) @ hBOOL ) )
& ( ! [B: produc1102272487on_val] : ( B @ ( A @ hAPP_P282169671l_bool ) @ hBOOL )
=> ! [B: produc124828825on_val,C: produc124828825on_val] : ( C @ ( B @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ ( A @ hAPP_P282169671l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(56,axiom,
! [A: list_char,B: ty,C: exp_list_char,D: list_char,E: ty,F: exp_list_char] :
( ( ( C @ ( B @ ( A @ block_list_char ) ) )
= ( F @ ( E @ ( D @ block_list_char ) ) ) )
<=> ( ( C = F )
& ( B = E )
& ( A = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_exp_Osimps_I10_J) ).
thf(434,plain,
! [A: list_char,B: ty,C: exp_list_char,D: list_char,E: ty,F: exp_list_char] :
( ( ( ( C = F )
& ( B = E )
& ( A = D ) )
=> ( ( C @ ( B @ ( A @ block_list_char ) ) )
= ( F @ ( E @ ( D @ block_list_char ) ) ) ) )
& ( ( ( C @ ( B @ ( A @ block_list_char ) ) )
= ( F @ ( E @ ( D @ block_list_char ) ) ) )
=> ( ( C = F )
& ( B = E )
& ( A = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(19,axiom,
! [A: exp_list_char,B: exp_list_char,C: val] :
( ( B @ ( A @ seq_list_char ) )
!= ( C @ val_list_char ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_exp_Osimps_I85_J) ).
thf(271,plain,
! [A: exp_list_char,B: exp_list_char,C: val] :
( ( B @ ( A @ seq_list_char ) )
!= ( C @ val_list_char ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(5,axiom,
! [A: val,B: list_char,C: ty,D: exp_list_char] :
( ( A @ val_list_char )
!= ( D @ ( C @ ( B @ block_list_char ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_exp_Osimps_I82_J) ).
thf(208,plain,
! [A: val,B: list_char,C: ty,D: exp_list_char] :
( ( A @ val_list_char )
!= ( D @ ( C @ ( B @ block_list_char ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(92,axiom,
! [A: produc12694297on_val,B: fun_ex1123147373l_bool,C: produc124828825on_val] :
( ( C @ ( B @ ( produc2036005791l_bool @ hAPP_f468299289l_bool ) @ hAPP_P595502227l_bool ) @ ( A @ member763590124on_val ) @ hBOOL )
=> ~ ! [D: exp_list_char,E: produc12694297on_val] :
( ( C
= ( E @ ( D @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) ) )
=> ~ ( E @ ( D @ ( B @ hAPP_e500528395l_bool ) @ hAPP_P1988153107l_bool ) @ ( A @ member763590124on_val ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_mem__splitE) ).
thf(631,plain,
! [A: produc12694297on_val,B: fun_ex1123147373l_bool,C: produc124828825on_val] :
( ( C @ ( B @ ( produc2036005791l_bool @ hAPP_f468299289l_bool ) @ hAPP_P595502227l_bool ) @ ( A @ member763590124on_val ) @ hBOOL )
=> ~ ! [D: exp_list_char,E: produc12694297on_val] :
( ( C
= ( E @ ( D @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) ) )
=> ~ ( E @ ( D @ ( B @ hAPP_e500528395l_bool ) @ hAPP_P1988153107l_bool ) @ ( A @ member763590124on_val ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(84,axiom,
! [A: fun_li1432931796on_val,B: list_char,C: val] :
( ( ( B @ ( A @ hAPP_l207779698on_val ) )
= ( C @ some_val ) )
=> ( ( C @ some_val @ ( B @ ( A @ fun_up1149430426on_val ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_map__upd__triv) ).
thf(594,plain,
! [A: fun_li1432931796on_val,B: list_char,C: val] :
( ( ( B @ ( A @ hAPP_l207779698on_val ) )
= ( C @ some_val ) )
=> ( ( C @ some_val @ ( B @ ( A @ fun_up1149430426on_val ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(14,axiom,
! [A: fun_fu1806184744l_bool,B: fun_fu100249073l_bool,C: fun_na939144002on_val] :
( ( C @ ( B @ ( A @ cOMBS_570216337l_bool ) @ hAPP_f1175813647l_bool ) )
= ( C @ ( B @ hAPP_f1175813647l_bool ) @ ( C @ ( A @ hAPP_f1492320500l_bool ) @ hAPP_f1074020887l_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It) ).
thf(251,plain,
! [A: fun_fu1806184744l_bool,B: fun_fu100249073l_bool,C: fun_na939144002on_val] :
( ( C @ ( B @ ( A @ cOMBS_570216337l_bool ) @ hAPP_f1175813647l_bool ) )
= ( C @ ( B @ hAPP_f1175813647l_bool ) @ ( C @ ( A @ hAPP_f1492320500l_bool ) @ hAPP_f1074020887l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(156,axiom,
! [A: produc124828825on_val,B: produc124828825on_val,C: produc124828825on_val,D: produc124828825on_val] :
( ( ( B @ ( A @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) )
= ( D @ ( C @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) ) )
<=> ( ( B = D )
& ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_Pair__eq) ).
thf(915,plain,
! [A: produc124828825on_val,B: produc124828825on_val,C: produc124828825on_val,D: produc124828825on_val] :
( ( ( ( B = D )
& ( A = C ) )
=> ( ( B @ ( A @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) )
= ( D @ ( C @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) ) ) )
& ( ( ( B @ ( A @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) )
= ( D @ ( C @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(161,axiom,
! [A: fun_bool_bool,B: fun_fu100249073l_bool,C: produc12694297on_val] :
( ( C @ ( B @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ ( A @ hAPP_bool_bool ) @ hBOOL )
=> ~ ! [D: fun_na939144002on_val,E: fun_li1432931796on_val] :
( ( C
= ( E @ ( D @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) ) )
=> ~ ( E @ ( D @ ( B @ hAPP_f1175813647l_bool ) @ hAPP_f1033709212l_bool ) @ ( A @ hAPP_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_splitE2) ).
thf(943,plain,
! [A: fun_bool_bool,B: fun_fu100249073l_bool,C: produc12694297on_val] :
( ( C @ ( B @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ ( A @ hAPP_bool_bool ) @ hBOOL )
=> ~ ! [D: fun_na939144002on_val,E: fun_li1432931796on_val] :
( ( C
= ( E @ ( D @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) ) )
=> ~ ( E @ ( D @ ( B @ hAPP_f1175813647l_bool ) @ hAPP_f1033709212l_bool ) @ ( A @ hAPP_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(29,axiom,
! [A: fun_fu114905943l_bool,B: fun_fu250820942l_bool,C: fun_na939144002on_val] :
( ( C @ ( B @ ( A @ ( cOMBB_1718333400on_val @ hAPP_f592397849l_bool ) @ hAPP_f1523875321l_bool ) @ hAPP_f1492320500l_bool ) )
= ( C @ ( B @ hAPP_f1145256474l_bool ) @ ( A @ hAPP_f1863694447l_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc) ).
thf(330,plain,
! [A: fun_fu114905943l_bool,B: fun_fu250820942l_bool,C: fun_na939144002on_val] :
( ( C @ ( B @ ( A @ ( cOMBB_1718333400on_val @ hAPP_f592397849l_bool ) @ hAPP_f1523875321l_bool ) @ hAPP_f1492320500l_bool ) )
= ( C @ ( B @ hAPP_f1145256474l_bool ) @ ( A @ hAPP_f1863694447l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(59,axiom,
! [A: fun_Pr691271849l_bool,B: fun_Pr691271849l_bool] :
( ! [C: produc124828825on_val,D: produc124828825on_val] :
( ( B @ ( D @ ( C @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL )
<=> ( A @ ( D @ ( C @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_pred__equals__eq2) ).
thf(462,plain,
! [A: fun_Pr691271849l_bool,B: fun_Pr691271849l_bool] :
( ( ( B = A )
=> ! [C: produc124828825on_val,D: produc124828825on_val] :
( ( ( A @ ( D @ ( C @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL )
=> ( B @ ( D @ ( C @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL ) )
& ( ( B @ ( D @ ( C @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL )
=> ( A @ ( D @ ( C @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL ) ) ) )
& ( ! [C: produc124828825on_val,D: produc124828825on_val] :
( ( ( A @ ( D @ ( C @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL )
=> ( B @ ( D @ ( C @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL ) )
& ( ( B @ ( D @ ( C @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL )
=> ( A @ ( D @ ( C @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(32,axiom,
! [A: val,B: exp_list_char,C: exp_list_char] :
( ( A @ val_list_char )
!= ( C @ ( B @ seq_list_char ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_exp_Osimps_I84_J) ).
thf(345,plain,
! [A: val,B: exp_list_char,C: exp_list_char] :
( ( A @ val_list_char )
!= ( C @ ( B @ seq_list_char ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(73,axiom,
! [A: fun_ex1201926843l_bool,B: exp_list_char,C: produc12694297on_val] :
( ( C @ ( B @ ( A @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
=> ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( A @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_prod__caseI) ).
thf(552,plain,
! [A: fun_ex1201926843l_bool,B: exp_list_char,C: produc12694297on_val] :
( ( C @ ( B @ ( A @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
=> ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( A @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(93,axiom,
! [A: fun_Pr633696065l_bool,B: produc124828825on_val,C: produc124828825on_val] :
( ( C @ ( B @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ ( A @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL )
=> ( C @ ( B @ ( A @ hAPP_P1116729363l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_splitD) ).
thf(636,plain,
! [A: fun_Pr633696065l_bool,B: produc124828825on_val,C: produc124828825on_val] :
( ( C @ ( B @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ ( A @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL )
=> ( C @ ( B @ ( A @ hAPP_P1116729363l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(189,axiom,
! [A: bool,B: bool] :
( ( A @ ( B @ ( fconj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
| ~ ( A @ hBOOL )
| ~ ( B @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
thf(1066,plain,
! [A: bool,B: bool] :
( ( A @ ( B @ ( fconj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
| ~ ( A @ hBOOL )
| ~ ( B @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(58,axiom,
! [A: bool,B: fun_fu100249073l_bool,C: produc12694297on_val] :
( ( C @ ( B @ ( A @ ( fconj @ hAPP_b589554111l_bool ) @ ( cOMBB_383678192on_val @ hAPP_f1863694447l_bool ) @ ( cOMBB_1522540928on_val @ hAPP_f1734879897l_bool ) @ hAPP_f555424277l_bool ) @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
<=> ( ( C @ ( B @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
& ( A @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_split__part) ).
thf(455,plain,
! [A: bool,B: fun_fu100249073l_bool,C: produc12694297on_val] :
( ( ( ( C @ ( B @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
& ( A @ hBOOL ) )
=> ( C @ ( B @ ( A @ ( fconj @ hAPP_b589554111l_bool ) @ ( cOMBB_383678192on_val @ hAPP_f1863694447l_bool ) @ ( cOMBB_1522540928on_val @ hAPP_f1734879897l_bool ) @ hAPP_f555424277l_bool ) @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) )
& ( ( C @ ( B @ ( A @ ( fconj @ hAPP_b589554111l_bool ) @ ( cOMBB_383678192on_val @ hAPP_f1863694447l_bool ) @ ( cOMBB_1522540928on_val @ hAPP_f1734879897l_bool ) @ hAPP_f555424277l_bool ) @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
=> ( ( C @ ( B @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
& ( A @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(77,axiom,
! [A: produc124828825on_val,B: fun_Pr741412723l_bool,C: produc124828825on_val,D: produc124828825on_val] :
( ( D @ ( C @ ( B @ hAPP_P1953518277l_bool ) @ hAPP_P1116729363l_bool ) @ ( A @ member840932460on_val ) @ hBOOL )
=> ( D @ ( C @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ ( B @ ( produc20018513l_bool @ hAPP_f1591648613l_bool ) @ hAPP_P678729081l_bool ) @ ( A @ member840932460on_val ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_mem__splitI) ).
thf(563,plain,
! [A: produc124828825on_val,B: fun_Pr741412723l_bool,C: produc124828825on_val,D: produc124828825on_val] :
( ( D @ ( C @ ( B @ hAPP_P1953518277l_bool ) @ hAPP_P1116729363l_bool ) @ ( A @ member840932460on_val ) @ hBOOL )
=> ( D @ ( C @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ ( B @ ( produc20018513l_bool @ hAPP_f1591648613l_bool ) @ hAPP_P678729081l_bool ) @ ( A @ member840932460on_val ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(173,axiom,
! [A: produc124828825on_val,B: fun_Pr680585871l_bool] :
( ! [C: exp_list_char,D: fun_na939144002on_val,E: fun_li1432931796on_val] : ( E @ ( D @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( B @ hAPP_P1708370145l_bool ) @ hBOOL )
=> ( A @ ( B @ hAPP_P1708370145l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_prod__induct3) ).
thf(1000,plain,
! [A: produc124828825on_val,B: fun_Pr680585871l_bool] :
( ! [C: exp_list_char,D: fun_na939144002on_val,E: fun_li1432931796on_val] : ( E @ ( D @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( B @ hAPP_P1708370145l_bool ) @ hBOOL )
=> ( A @ ( B @ hAPP_P1708370145l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(24,axiom,
! [A: fun_li688206603ion_ty,B: list_char,C: ty,D: fun_li688206603ion_ty,E: ty] :
( ( ( C @ some_ty @ ( B @ ( A @ fun_up424764369ion_ty ) ) )
= ( E @ some_ty @ ( B @ ( D @ fun_up424764369ion_ty ) ) ) )
=> ( C = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_map__upd__eqD1) ).
thf(299,plain,
! [A: fun_li688206603ion_ty,B: list_char,C: ty,D: fun_li688206603ion_ty,E: ty] :
( ( ( C @ some_ty @ ( B @ ( A @ fun_up424764369ion_ty ) ) )
= ( E @ some_ty @ ( B @ ( D @ fun_up424764369ion_ty ) ) ) )
=> ( C = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(199,axiom,
! [A: fun_ex1201926843l_bool,B: fun_fu2073188913on_val,C: produc12694297on_val] :
( ( C @ ( B @ ( produc901351817on_val @ hAPP_f1309113673on_val ) @ hAPP_P604205461on_val ) @ ( A @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL )
<=> ( C @ ( B @ ( A @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ ( cOMBB_171276332on_val @ hAPP_f1233687287l_bool ) @ ( cOMBB_1466889536on_val @ hAPP_f399538905l_bool ) @ hAPP_f850751421l_bool ) @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_split__twice) ).
thf(1102,plain,
! [A: fun_ex1201926843l_bool,B: fun_fu2073188913on_val,C: produc12694297on_val] :
( ( ( C @ ( B @ ( A @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ ( cOMBB_171276332on_val @ hAPP_f1233687287l_bool ) @ ( cOMBB_1466889536on_val @ hAPP_f399538905l_bool ) @ hAPP_f850751421l_bool ) @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
=> ( C @ ( B @ ( produc901351817on_val @ hAPP_f1309113673on_val ) @ hAPP_P604205461on_val ) @ ( A @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL ) )
& ( ( C @ ( B @ ( produc901351817on_val @ hAPP_f1309113673on_val ) @ hAPP_P604205461on_val ) @ ( A @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL )
=> ( C @ ( B @ ( A @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ ( cOMBB_171276332on_val @ hAPP_f1233687287l_bool ) @ ( cOMBB_1466889536on_val @ hAPP_f399538905l_bool ) @ hAPP_f850751421l_bool ) @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(55,axiom,
! [A: fun_fu570492181l_bool,B: fun_li688206603ion_ty,C: fun_na939144002on_val] :
( ( C @ ( B @ ( A @ ( cOMBC_2027949654l_bool @ hAPP_f838396643l_bool ) @ hAPP_f550652027l_bool ) @ hAPP_f1175813647l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f1617787571l_bool ) @ hAPP_f603925568l_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It) ).
thf(431,plain,
! [A: fun_fu570492181l_bool,B: fun_li688206603ion_ty,C: fun_na939144002on_val] :
( ( C @ ( B @ ( A @ ( cOMBC_2027949654l_bool @ hAPP_f838396643l_bool ) @ hAPP_f550652027l_bool ) @ hAPP_f1175813647l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f1617787571l_bool ) @ hAPP_f603925568l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(155,axiom,
! [A: fun_li1432931796on_val,B: list_char,C: option_val] :
( ( B @ ( C @ ( B @ ( A @ fun_up1149430426on_val ) ) @ hAPP_l207779698on_val ) )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_fun__upd__same) ).
thf(912,plain,
! [A: fun_li1432931796on_val,B: list_char,C: option_val] :
( ( B @ ( C @ ( B @ ( A @ fun_up1149430426on_val ) ) @ hAPP_l207779698on_val ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(65,axiom,
! [A: fun_fu100249073l_bool,B: fun_na939144002on_val,C: fun_li1432931796on_val] :
( ( C @ ( B @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
=> ( C @ ( B @ ( A @ hAPP_f1175813647l_bool ) @ hAPP_f1033709212l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_splitD) ).
thf(521,plain,
! [A: fun_fu100249073l_bool,B: fun_na939144002on_val,C: fun_li1432931796on_val] :
( ( C @ ( B @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
=> ( C @ ( B @ ( A @ hAPP_f1175813647l_bool ) @ hAPP_f1033709212l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(82,axiom,
! [A: fun_li1432931796on_val,B: list_char,C: val] :
~ ! [D: list_char] :
( ( D @ ( C @ some_val @ ( B @ ( A @ fun_up1149430426on_val ) ) @ hAPP_l207779698on_val ) )
= none_val ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_map__upd__nonempty) ).
thf(589,plain,
! [A: fun_li1432931796on_val,B: list_char,C: val] :
~ ! [D: list_char] :
( ( D @ ( C @ some_val @ ( B @ ( A @ fun_up1149430426on_val ) ) @ hAPP_l207779698on_val ) )
= none_val ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(102,axiom,
! [A: produc1102272487on_val] :
~ ! [B: produc124828825on_val,C: exp_list_char,D: produc12694297on_val] :
( A
!= ( D @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( B @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_prod__cases3) ).
thf(663,plain,
! [A: produc1102272487on_val] :
~ ! [B: produc124828825on_val,C: exp_list_char,D: produc12694297on_val] :
( A
!= ( D @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( B @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(139,axiom,
! [A: fun_Pr691271849l_bool] :
( ( produc1441475159on_val @ ( A @ ( cOMBB_1466662571on_val @ hAPP_f365540729l_bool ) @ ( cOMBB_364363975on_val @ hAPP_f639265145l_bool ) @ hAPP_f1342895119l_bool ) @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_split__eta) ).
thf(836,plain,
! [A: fun_Pr691271849l_bool] :
( ( produc1441475159on_val @ ( A @ ( cOMBB_1466662571on_val @ hAPP_f365540729l_bool ) @ ( cOMBB_364363975on_val @ hAPP_f639265145l_bool ) @ hAPP_f1342895119l_bool ) @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(184,axiom,
! [A: fun_Pr633696065l_bool,B: fun_fu1133203323on_val,C: produc12694297on_val] :
( ( C @ ( B @ ( produc1148763895on_val @ hAPP_f204556415on_val ) @ hAPP_P2024243179on_val ) @ ( A @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL )
<=> ( C @ ( B @ ( A @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ ( cOMBB_1292453606on_val @ hAPP_f2052660463l_bool ) @ ( cOMBB_1259202826on_val @ hAPP_f1043869573l_bool ) @ hAPP_f927043595l_bool ) @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_split__twice) ).
thf(1049,plain,
! [A: fun_Pr633696065l_bool,B: fun_fu1133203323on_val,C: produc12694297on_val] :
( ( ( C @ ( B @ ( A @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ ( cOMBB_1292453606on_val @ hAPP_f2052660463l_bool ) @ ( cOMBB_1259202826on_val @ hAPP_f1043869573l_bool ) @ hAPP_f927043595l_bool ) @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
=> ( C @ ( B @ ( produc1148763895on_val @ hAPP_f204556415on_val ) @ hAPP_P2024243179on_val ) @ ( A @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL ) )
& ( ( C @ ( B @ ( produc1148763895on_val @ hAPP_f204556415on_val ) @ hAPP_P2024243179on_val ) @ ( A @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL )
=> ( C @ ( B @ ( A @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ ( cOMBB_1292453606on_val @ hAPP_f2052660463l_bool ) @ ( cOMBB_1259202826on_val @ hAPP_f1043869573l_bool ) @ hAPP_f927043595l_bool ) @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(166,axiom,
! [A: fun_fu100249073l_bool,B: produc12694297on_val,C: produc12694297on_val] :
( ( B = C )
=> ( ( B @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
<=> ( C @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_split__weak__cong) ).
thf(968,plain,
! [A: fun_fu100249073l_bool,B: produc12694297on_val,C: produc12694297on_val] :
( ( B = C )
=> ( ( ( C @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
=> ( B @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
=> ( C @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(136,axiom,
! [A: fun_Pr633696065l_bool,B: produc1102272487on_val] :
( ( B @ ( A @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL )
=> ~ ! [C: produc124828825on_val,D: produc124828825on_val] :
( ( B
= ( D @ ( C @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) ) )
=> ~ ( D @ ( C @ ( A @ hAPP_P1116729363l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_splitE) ).
thf(823,plain,
! [A: fun_Pr633696065l_bool,B: produc1102272487on_val] :
( ( B @ ( A @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL )
=> ~ ! [C: produc124828825on_val,D: produc124828825on_val] :
( ( B
= ( D @ ( C @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) ) )
=> ~ ( D @ ( C @ ( A @ hAPP_P1116729363l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(124,axiom,
! [A: produc12694297on_val,B: fun_ex1123147373l_bool,C: exp_list_char,D: produc12694297on_val] :
( ( D @ ( C @ ( B @ hAPP_e500528395l_bool ) @ hAPP_P1988153107l_bool ) @ ( A @ member763590124on_val ) @ hBOOL )
=> ( D @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( B @ ( produc2036005791l_bool @ hAPP_f468299289l_bool ) @ hAPP_P595502227l_bool ) @ ( A @ member763590124on_val ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_mem__splitI) ).
thf(776,plain,
! [A: produc12694297on_val,B: fun_ex1123147373l_bool,C: exp_list_char,D: produc12694297on_val] :
( ( D @ ( C @ ( B @ hAPP_e500528395l_bool ) @ hAPP_P1988153107l_bool ) @ ( A @ member763590124on_val ) @ hBOOL )
=> ( D @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( B @ ( produc2036005791l_bool @ hAPP_f468299289l_bool ) @ hAPP_P595502227l_bool ) @ ( A @ member763590124on_val ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(67,axiom,
! [A: fun_Pr691271849l_bool,B: fun_Pr714818201on_val,C: produc124828825on_val] :
( ( C @ ( B @ ( A @ ( cOMBB_1466662571on_val @ hAPP_f365540729l_bool ) @ hAPP_f204771371l_bool ) @ hAPP_P1708370145l_bool ) )
= ( C @ ( B @ hAPP_P1886180715on_val ) @ ( A @ hAPP_P282169671l_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__208) ).
thf(525,plain,
! [A: fun_Pr691271849l_bool,B: fun_Pr714818201on_val,C: produc124828825on_val] :
( ( C @ ( B @ ( A @ ( cOMBB_1466662571on_val @ hAPP_f365540729l_bool ) @ hAPP_f204771371l_bool ) @ hAPP_P1708370145l_bool ) )
= ( C @ ( B @ hAPP_P1886180715on_val ) @ ( A @ hAPP_P282169671l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(175,axiom,
! [A: ty,B: val,C: exp_list_char,D: fun_na939144002on_val,E: fun_li1432931796on_val,F: list_char,G: val,H: exp_list_char,I: fun_na939144002on_val,J: fun_li1432931796on_val,K: list_P1999446415t_char] :
( ( K @ red @ ( J @ ( I @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( H @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( G @ some_val @ ( F @ ( E @ fun_up1149430426on_val ) ) @ ( D @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL )
=> ( ( ( F @ ( J @ hAPP_l207779698on_val ) )
= ( B @ some_val ) )
=> ( K @ red @ ( F @ ( E @ hAPP_l207779698on_val ) @ ( F @ ( J @ fun_up1149430426on_val ) ) @ ( I @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( H @ ( B @ val_list_char @ ( F @ lAss_list_char ) @ seq_list_char ) @ ( A @ ( F @ block_list_char ) ) @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( E @ ( D @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( C @ ( G @ val_list_char @ ( F @ lAss_list_char ) @ seq_list_char ) @ ( A @ ( F @ block_list_char ) ) @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_red__reds_OInitBlockRed) ).
thf(1003,plain,
! [A: ty,B: val,C: exp_list_char,D: fun_na939144002on_val,E: fun_li1432931796on_val,F: list_char,G: val,H: exp_list_char,I: fun_na939144002on_val,J: fun_li1432931796on_val,K: list_P1999446415t_char] :
( ( K @ red @ ( J @ ( I @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( H @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( G @ some_val @ ( F @ ( E @ fun_up1149430426on_val ) ) @ ( D @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL )
=> ( ( ( F @ ( J @ hAPP_l207779698on_val ) )
= ( B @ some_val ) )
=> ( K @ red @ ( F @ ( E @ hAPP_l207779698on_val ) @ ( F @ ( J @ fun_up1149430426on_val ) ) @ ( I @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( H @ ( B @ val_list_char @ ( F @ lAss_list_char ) @ seq_list_char ) @ ( A @ ( F @ block_list_char ) ) @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( E @ ( D @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( C @ ( G @ val_list_char @ ( F @ lAss_list_char ) @ seq_list_char ) @ ( A @ ( F @ block_list_char ) ) @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(95,axiom,
! [A: fun_li688206603ion_ty,B: ty,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val,G: list_P1999446415t_char] :
( ( G @ red @ ( F @ ( E @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( D @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL )
=> ( ( B @ ( C @ ( A @ ( D @ hp @ ( G @ wTrt ) ) ) ) @ hBOOL )
=> ( ( D @ ( A @ ( G @ typeSa1844245082_sconf ) @ hAPP_P159683425l_bool ) @ hBOOL )
=> ( F @ ( A @ ( G @ typeSa1844245082_sconf ) @ hAPP_P159683425l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_red__preserves__sconf) ).
thf(640,plain,
! [A: fun_li688206603ion_ty,B: ty,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val,G: list_P1999446415t_char] :
( ( G @ red @ ( F @ ( E @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( D @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL )
=> ( ( B @ ( C @ ( A @ ( D @ hp @ ( G @ wTrt ) ) ) ) @ hBOOL )
=> ( ( D @ ( A @ ( G @ typeSa1844245082_sconf ) @ hAPP_P159683425l_bool ) @ hBOOL )
=> ( F @ ( A @ ( G @ typeSa1844245082_sconf ) @ hAPP_P159683425l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(149,axiom,
! [A: produc1102272487on_val,B: fun_Pr691271849l_bool] :
( ! [C: produc124828825on_val,D: exp_list_char,E: fun_na939144002on_val,F: fun_li1432931796on_val] : ( F @ ( E @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( D @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( C @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ ( B @ hAPP_P282169671l_bool ) @ hBOOL )
=> ( A @ ( B @ hAPP_P282169671l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_prod__induct4) ).
thf(887,plain,
! [A: produc1102272487on_val,B: fun_Pr691271849l_bool] :
( ! [C: produc124828825on_val,D: exp_list_char,E: fun_na939144002on_val,F: fun_li1432931796on_val] : ( F @ ( E @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( D @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( C @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ ( B @ hAPP_P282169671l_bool ) @ hBOOL )
=> ( A @ ( B @ hAPP_P282169671l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(28,axiom,
! [A: option_val,B: list_char] :
( ( B @ ( A @ cOMBK_1097134891t_char @ hAPP_l207779698on_val ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__Option__Ooption_Itc__Value__Oval_J_000tc__List__Olis) ).
thf(327,plain,
! [A: option_val,B: list_char] :
( ( B @ ( A @ cOMBK_1097134891t_char @ hAPP_l207779698on_val ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(163,axiom,
! [A: fun_li1432931796on_val,B: option_val,C: list_char,D: list_char] :
( ( ( D != C )
=> ( ( D @ ( B @ ( C @ ( A @ fun_up1149430426on_val ) ) @ hAPP_l207779698on_val ) )
= ( D @ ( A @ hAPP_l207779698on_val ) ) ) )
& ( ( D = C )
=> ( ( D @ ( B @ ( C @ ( A @ fun_up1149430426on_val ) ) @ hAPP_l207779698on_val ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_fun__upd__def) ).
thf(954,plain,
! [A: fun_li1432931796on_val,B: option_val,C: list_char,D: list_char] :
( ( ( D != C )
=> ( ( D @ ( B @ ( C @ ( A @ fun_up1149430426on_val ) ) @ hAPP_l207779698on_val ) )
= ( D @ ( A @ hAPP_l207779698on_val ) ) ) )
& ( ( D = C )
=> ( ( D @ ( B @ ( C @ ( A @ fun_up1149430426on_val ) ) @ hAPP_l207779698on_val ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(197,axiom,
! [A: produc124828825on_val,B: fun_ex1732109805l_bool,C: exp_list_char,D: produc12694297on_val] :
( ( D @ ( C @ ( B @ hAPP_e592495499l_bool ) @ hAPP_P1638898323l_bool ) @ ( A @ member840932460on_val ) @ hBOOL )
=> ( D @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( B @ ( produc1275132703l_bool @ hAPP_f1760682521l_bool ) @ hAPP_P1116729363l_bool ) @ ( A @ member840932460on_val ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_mem__splitI) ).
thf(1098,plain,
! [A: produc124828825on_val,B: fun_ex1732109805l_bool,C: exp_list_char,D: produc12694297on_val] :
( ( D @ ( C @ ( B @ hAPP_e592495499l_bool ) @ hAPP_P1638898323l_bool ) @ ( A @ member840932460on_val ) @ hBOOL )
=> ( D @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( B @ ( produc1275132703l_bool @ hAPP_f1760682521l_bool ) @ hAPP_P1116729363l_bool ) @ ( A @ member840932460on_val ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(36,axiom,
! [A: list_char,B: ty,C: exp_list_char,D: list_char,E: exp_list_char] :
( ( C @ ( B @ ( A @ block_list_char ) ) )
!= ( E @ ( D @ lAss_list_char ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_exp_Osimps_I143_J) ).
thf(359,plain,
! [A: list_char,B: ty,C: exp_list_char,D: list_char,E: exp_list_char] :
( ( C @ ( B @ ( A @ block_list_char ) ) )
!= ( E @ ( D @ lAss_list_char ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(181,axiom,
! [A: fun_li1432931796on_val,B: list_char,C: option_val,D: option_val] :
( ( D @ ( B @ ( C @ ( B @ ( A @ fun_up1149430426on_val ) ) @ fun_up1149430426on_val ) ) )
= ( D @ ( B @ ( A @ fun_up1149430426on_val ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_fun__upd__upd) ).
thf(1038,plain,
! [A: fun_li1432931796on_val,B: list_char,C: option_val,D: option_val] :
( ( D @ ( B @ ( C @ ( B @ ( A @ fun_up1149430426on_val ) ) @ fun_up1149430426on_val ) ) )
= ( D @ ( B @ ( A @ fun_up1149430426on_val ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(39,axiom,
produc399384568l_bool = produc1815960045l_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_internal__split__def) ).
thf(370,plain,
produc399384568l_bool = produc1815960045l_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(31,axiom,
! [A: fun_li688206603ion_ty,B: option_ty,C: list_char,D: list_char] :
( ( ( C != D )
=> ( ( C @ ( B @ ( D @ ( A @ fun_up424764369ion_ty ) ) @ hAPP_l512744617ion_ty ) )
= ( C @ ( A @ hAPP_l512744617ion_ty ) ) ) )
& ( ( C = D )
=> ( ( C @ ( B @ ( D @ ( A @ fun_up424764369ion_ty ) ) @ hAPP_l512744617ion_ty ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_fun__upd__apply) ).
thf(336,plain,
! [A: fun_li688206603ion_ty,B: option_ty,C: list_char,D: list_char] :
( ( ( C != D )
=> ( ( C @ ( B @ ( D @ ( A @ fun_up424764369ion_ty ) ) @ hAPP_l512744617ion_ty ) )
= ( C @ ( A @ hAPP_l512744617ion_ty ) ) ) )
& ( ( C = D )
=> ( ( C @ ( B @ ( D @ ( A @ fun_up424764369ion_ty ) ) @ hAPP_l512744617ion_ty ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(45,axiom,
! [A: exp_list_char,B: exp_list_char,C: list_char,D: exp_list_char] :
( ( B @ ( A @ seq_list_char ) )
!= ( D @ ( C @ lAss_list_char ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_exp_Osimps_I145_J) ).
thf(386,plain,
! [A: exp_list_char,B: exp_list_char,C: list_char,D: exp_list_char] :
( ( B @ ( A @ seq_list_char ) )
!= ( D @ ( C @ lAss_list_char ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(79,axiom,
! [A: fun_li1432931796on_val,B: list_char] :
( ( B @ ( A @ hAPP_l207779698on_val ) @ ( B @ ( A @ fun_up1149430426on_val ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_fun__upd__triv) ).
thf(571,plain,
! [A: fun_li1432931796on_val,B: list_char] :
( ( B @ ( A @ hAPP_l207779698on_val ) @ ( B @ ( A @ fun_up1149430426on_val ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(192,axiom,
! [A: exp_list_char,B: list_P1999446415t_char,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val] :
( ( F @ ( E @ ( D @ ( C @ ( B @ redp ) ) @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
=> ( F @ ( A @ ( E @ seq_list_char ) @ ( D @ ( A @ ( C @ seq_list_char ) @ ( B @ redp ) ) @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_redp__redsp_OSeqRed) ).
thf(1084,plain,
! [A: exp_list_char,B: list_P1999446415t_char,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val] :
( ( F @ ( E @ ( D @ ( C @ ( B @ redp ) ) @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
=> ( F @ ( A @ ( E @ seq_list_char ) @ ( D @ ( A @ ( C @ seq_list_char ) @ ( B @ redp ) ) @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(37,axiom,
! [A: fun_li688206603ion_ty,B: list_char,C: ty] :
( ( ( B @ ( A @ hAPP_l512744617ion_ty ) )
= ( C @ some_ty ) )
=> ( ( C @ some_ty @ ( B @ ( A @ fun_up424764369ion_ty ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_map__upd__triv) ).
thf(363,plain,
! [A: fun_li688206603ion_ty,B: list_char,C: ty] :
( ( ( B @ ( A @ hAPP_l512744617ion_ty ) )
= ( C @ some_ty ) )
=> ( ( C @ some_ty @ ( B @ ( A @ fun_up424764369ion_ty ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(158,axiom,
! [A: produc124828825on_val] :
~ ! [B: exp_list_char,C: produc12694297on_val] :
( A
!= ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_PairE) ).
thf(931,plain,
! [A: produc124828825on_val] :
~ ! [B: exp_list_char,C: produc12694297on_val] :
( A
!= ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(141,axiom,
! [A: produc124828825on_val,B: fun_Pr741412723l_bool,C: produc1102272487on_val] :
( ! [D: produc124828825on_val,E: produc124828825on_val] :
( ( C
= ( E @ ( D @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) ) )
=> ( E @ ( D @ ( B @ hAPP_P1953518277l_bool ) @ hAPP_P1116729363l_bool ) @ ( A @ member840932460on_val ) @ hBOOL ) )
=> ( C @ ( B @ ( produc20018513l_bool @ hAPP_f1591648613l_bool ) @ hAPP_P678729081l_bool ) @ ( A @ member840932460on_val ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_mem__splitI2) ).
thf(844,plain,
! [A: produc124828825on_val,B: fun_Pr741412723l_bool,C: produc1102272487on_val] :
( ! [D: produc124828825on_val,E: produc124828825on_val] :
( ( C
= ( E @ ( D @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) ) )
=> ( E @ ( D @ ( B @ hAPP_P1953518277l_bool ) @ hAPP_P1116729363l_bool ) @ ( A @ member840932460on_val ) @ hBOOL ) )
=> ( C @ ( B @ ( produc20018513l_bool @ hAPP_f1591648613l_bool ) @ hAPP_P678729081l_bool ) @ ( A @ member840932460on_val ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(200,axiom,
! [A: fun_fu100249073l_bool,B: fun_na939144002on_val,C: fun_li1432931796on_val] :
( ( C @ ( B @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
<=> ( C @ ( B @ ( A @ hAPP_f1175813647l_bool ) @ hAPP_f1033709212l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_split__conv) ).
thf(1108,plain,
! [A: fun_fu100249073l_bool,B: fun_na939144002on_val,C: fun_li1432931796on_val] :
( ( ( C @ ( B @ ( A @ hAPP_f1175813647l_bool ) @ hAPP_f1033709212l_bool ) @ hBOOL )
=> ( C @ ( B @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) )
& ( ( C @ ( B @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
=> ( C @ ( B @ ( A @ hAPP_f1175813647l_bool ) @ hAPP_f1033709212l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(167,axiom,
! [A: fun_Pr680585871l_bool] :
( ( produc1259058957on_val @ ( A @ ( cOMBB_1759207793on_val @ hAPP_f10074679l_bool ) @ ( cOMBB_1027621637t_char @ hAPP_f1725502637l_bool ) @ hAPP_f439412817l_bool ) @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_split__eta) ).
thf(976,plain,
! [A: fun_Pr680585871l_bool] :
( ( produc1259058957on_val @ ( A @ ( cOMBB_1759207793on_val @ hAPP_f10074679l_bool ) @ ( cOMBB_1027621637t_char @ hAPP_f1725502637l_bool ) @ hAPP_f439412817l_bool ) @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(109,axiom,
! [A: fun_fu1587641869l_bool,B: fun_Pr1391347915on_val,C: produc124828825on_val] :
( ( C @ ( B @ ( A @ ( cOMBB_364363975on_val @ hAPP_f639265145l_bool ) @ hAPP_f1342895119l_bool ) @ hAPP_P1116729363l_bool ) )
= ( C @ ( B @ hAPP_P1870962205on_val ) @ ( A @ hAPP_f204771371l_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc___211) ).
thf(688,plain,
! [A: fun_fu1587641869l_bool,B: fun_Pr1391347915on_val,C: produc124828825on_val] :
( ( C @ ( B @ ( A @ ( cOMBB_364363975on_val @ hAPP_f639265145l_bool ) @ hAPP_f1342895119l_bool ) @ hAPP_P1116729363l_bool ) )
= ( C @ ( B @ hAPP_P1870962205on_val ) @ ( A @ hAPP_f204771371l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(119,axiom,
! [A: produc1102272487on_val] :
~ ! [B: produc124828825on_val,C: produc124828825on_val] :
( A
!= ( C @ ( B @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_PairE) ).
thf(748,plain,
! [A: produc1102272487on_val] :
~ ! [B: produc124828825on_val,C: produc124828825on_val] :
( A
!= ( C @ ( B @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(187,axiom,
! [A: fun_Pr680585871l_bool,B: fun_Pr231134077on_val,C: produc12694297on_val] :
( ( C @ ( B @ ( A @ ( cOMBB_1759207793on_val @ hAPP_f10074679l_bool ) @ hAPP_f489055607l_bool ) @ hAPP_P159683425l_bool ) )
= ( C @ ( B @ hAPP_P604205461on_val ) @ ( A @ hAPP_P1708370145l_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__O_202) ).
thf(1062,plain,
! [A: fun_Pr680585871l_bool,B: fun_Pr231134077on_val,C: produc12694297on_val] :
( ( C @ ( B @ ( A @ ( cOMBB_1759207793on_val @ hAPP_f10074679l_bool ) @ hAPP_f489055607l_bool ) @ hAPP_P159683425l_bool ) )
= ( C @ ( B @ hAPP_P604205461on_val ) @ ( A @ hAPP_P1708370145l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(99,axiom,
! [A: exp_list_char,B: exp_list_char,C: produc12694297on_val,D: exp_list_char,E: produc12694297on_val,F: list_P1999446415t_char] :
( ( F @ red @ ( E @ ( D @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL )
=> ( F @ red @ ( E @ ( A @ ( D @ seq_list_char ) @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( C @ ( A @ ( B @ seq_list_char ) @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_red__reds_OSeqRed) ).
thf(652,plain,
! [A: exp_list_char,B: exp_list_char,C: produc12694297on_val,D: exp_list_char,E: produc12694297on_val,F: list_P1999446415t_char] :
( ( F @ red @ ( E @ ( D @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL )
=> ( F @ red @ ( E @ ( A @ ( D @ seq_list_char ) @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( C @ ( A @ ( B @ seq_list_char ) @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(46,axiom,
! [A: fun_fu1640122725l_bool,B: fun_fu2073188913on_val,C: fun_na939144002on_val] :
( ( C @ ( B @ ( A @ ( cOMBB_1466889536on_val @ hAPP_f399538905l_bool ) @ hAPP_f850751421l_bool ) @ hAPP_f1175813647l_bool ) )
= ( C @ ( B @ hAPP_f1840640125on_val ) @ ( A @ hAPP_f318082871l_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_205) ).
thf(390,plain,
! [A: fun_fu1640122725l_bool,B: fun_fu2073188913on_val,C: fun_na939144002on_val] :
( ( C @ ( B @ ( A @ ( cOMBB_1466889536on_val @ hAPP_f399538905l_bool ) @ hAPP_f850751421l_bool ) @ hAPP_f1175813647l_bool ) )
= ( C @ ( B @ hAPP_f1840640125on_val ) @ ( A @ hAPP_f318082871l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(127,axiom,
! [A: ty,B: list_P1999446415t_char,C: exp_list_char,D: fun_na939144002on_val,E: fun_li1432931796on_val,F: list_char,G: exp_list_char,H: fun_na939144002on_val,I: fun_li1432931796on_val] :
( ( I @ ( H @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( G @ ( none_val @ ( F @ ( E @ fun_up1149430426on_val ) ) @ ( D @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( C @ ( B @ redp ) ) @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
=> ( ( ( F @ ( I @ hAPP_l207779698on_val ) )
= none_val )
=> ( ~ ( C @ ( F @ assigned ) @ hBOOL )
=> ( F @ ( E @ hAPP_l207779698on_val ) @ ( F @ ( I @ fun_up1149430426on_val ) ) @ ( H @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( G @ ( A @ ( F @ block_list_char ) ) @ ( E @ ( D @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( C @ ( A @ ( F @ block_list_char ) ) @ ( B @ redp ) ) @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_redp__redsp_OBlockRedNone) ).
thf(786,plain,
! [A: ty,B: list_P1999446415t_char,C: exp_list_char,D: fun_na939144002on_val,E: fun_li1432931796on_val,F: list_char,G: exp_list_char,H: fun_na939144002on_val,I: fun_li1432931796on_val] :
( ( I @ ( H @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( G @ ( none_val @ ( F @ ( E @ fun_up1149430426on_val ) ) @ ( D @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( C @ ( B @ redp ) ) @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
=> ( ( ( F @ ( I @ hAPP_l207779698on_val ) )
= none_val )
=> ( ~ ( C @ ( F @ assigned ) @ hBOOL )
=> ( F @ ( E @ hAPP_l207779698on_val ) @ ( F @ ( I @ fun_up1149430426on_val ) ) @ ( H @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( G @ ( A @ ( F @ block_list_char ) ) @ ( E @ ( D @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( C @ ( A @ ( F @ block_list_char ) ) @ ( B @ redp ) ) @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(164,axiom,
! [A: fun_Pr1696029455l_bool,B: fun_fu1690035458on_val,C: fun_li1432931796on_val] :
( ( C @ ( B @ ( A @ ( cOMBB_1750801836on_val @ hAPP_f2057883639l_bool ) @ hAPP_f1008932791l_bool ) @ hAPP_f1033709212l_bool ) )
= ( C @ ( B @ hAPP_f1727192346on_val ) @ ( A @ hAPP_P159683425l_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It) ).
thf(963,plain,
! [A: fun_Pr1696029455l_bool,B: fun_fu1690035458on_val,C: fun_li1432931796on_val] :
( ( C @ ( B @ ( A @ ( cOMBB_1750801836on_val @ hAPP_f2057883639l_bool ) @ hAPP_f1008932791l_bool ) @ hAPP_f1033709212l_bool ) )
= ( C @ ( B @ hAPP_f1727192346on_val ) @ ( A @ hAPP_P159683425l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(64,axiom,
! [A: fun_li1432931796on_val,B: list_char,C: option_val] :
( ( ( B @ ( A @ hAPP_l207779698on_val ) )
= C )
=> ( ( C @ ( B @ ( A @ fun_up1149430426on_val ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_fun__upd__idem) ).
thf(517,plain,
! [A: fun_li1432931796on_val,B: list_char,C: option_val] :
( ( ( B @ ( A @ hAPP_l207779698on_val ) )
= C )
=> ( ( C @ ( B @ ( A @ fun_up1149430426on_val ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(42,axiom,
! [A: fun_Pr691271849l_bool,B: fun_fu1622757844on_val,C: fun_li1432931796on_val] :
( ( C @ ( B @ ( A @ ( cOMBB_1292453606on_val @ hAPP_f2052660463l_bool ) @ hAPP_f524589473l_bool ) @ hAPP_f1033709212l_bool ) )
= ( C @ ( B @ hAPP_f602593190on_val ) @ ( A @ hAPP_P282169671l_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc_) ).
thf(378,plain,
! [A: fun_Pr691271849l_bool,B: fun_fu1622757844on_val,C: fun_li1432931796on_val] :
( ( C @ ( B @ ( A @ ( cOMBB_1292453606on_val @ hAPP_f2052660463l_bool ) @ hAPP_f524589473l_bool ) @ hAPP_f1033709212l_bool ) )
= ( C @ ( B @ hAPP_f602593190on_val ) @ ( A @ hAPP_P282169671l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(103,axiom,
! [A: list_char,B: list_char] :
( ( B @ ( none_val @ ( A @ ( none_val @ cOMBK_1097134891t_char @ fun_up1149430426on_val ) ) @ hAPP_l207779698on_val ) )
= none_val ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_empty__upd__none) ).
thf(667,plain,
! [A: list_char,B: list_char] :
( ( B @ ( none_val @ ( A @ ( none_val @ cOMBK_1097134891t_char @ fun_up1149430426on_val ) ) @ hAPP_l207779698on_val ) )
= none_val ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(122,axiom,
! [A: fun_Pr1696029455l_bool,B: fun_fu100249073l_bool] :
( ! [C: fun_na939144002on_val,D: fun_li1432931796on_val] :
( ( D @ ( C @ ( B @ hAPP_f1175813647l_bool ) @ hAPP_f1033709212l_bool ) @ hBOOL )
<=> ( D @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( A @ hAPP_P159683425l_bool ) @ hBOOL ) )
=> ( ( B @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_cond__split__eta) ).
thf(763,plain,
! [A: fun_Pr1696029455l_bool,B: fun_fu100249073l_bool] :
( ! [C: fun_na939144002on_val,D: fun_li1432931796on_val] :
( ( ( D @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( A @ hAPP_P159683425l_bool ) @ hBOOL )
=> ( D @ ( C @ ( B @ hAPP_f1175813647l_bool ) @ hAPP_f1033709212l_bool ) @ hBOOL ) )
& ( ( D @ ( C @ ( B @ hAPP_f1175813647l_bool ) @ hAPP_f1033709212l_bool ) @ hBOOL )
=> ( D @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( A @ hAPP_P159683425l_bool ) @ hBOOL ) ) )
=> ( ( B @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(44,axiom,
! [A: fun_fu964448643l_bool,B: fun_fu1133203323on_val,C: fun_na939144002on_val] :
( ( C @ ( B @ ( A @ ( cOMBB_1259202826on_val @ hAPP_f1043869573l_bool ) @ hAPP_f927043595l_bool ) @ hAPP_f1175813647l_bool ) )
= ( C @ ( B @ hAPP_f600512025on_val ) @ ( A @ hAPP_f524589473l_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_209) ).
thf(383,plain,
! [A: fun_fu964448643l_bool,B: fun_fu1133203323on_val,C: fun_na939144002on_val] :
( ( C @ ( B @ ( A @ ( cOMBB_1259202826on_val @ hAPP_f1043869573l_bool ) @ hAPP_f927043595l_bool ) @ hAPP_f1175813647l_bool ) )
= ( C @ ( B @ hAPP_f600512025on_val ) @ ( A @ hAPP_f524589473l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(152,axiom,
! [A: list_P1999446415t_char,B: fun_na939144002on_val,C: fun_li688206603ion_ty,D: list_char,E: ty,F: exp_list_char,G: ty] :
( ( G @ ( F @ ( E @ some_ty @ ( D @ ( C @ fun_up424764369ion_ty ) ) @ ( B @ ( A @ wTrt ) ) ) ) @ hBOOL )
=> ( G @ ( F @ ( E @ ( D @ block_list_char ) ) @ ( C @ ( B @ ( A @ wTrt ) ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_WTrtBlock) ).
thf(899,plain,
! [A: list_P1999446415t_char,B: fun_na939144002on_val,C: fun_li688206603ion_ty,D: list_char,E: ty,F: exp_list_char,G: ty] :
( ( G @ ( F @ ( E @ some_ty @ ( D @ ( C @ fun_up424764369ion_ty ) ) @ ( B @ ( A @ wTrt ) ) ) ) @ hBOOL )
=> ( G @ ( F @ ( E @ ( D @ block_list_char ) ) @ ( C @ ( B @ ( A @ wTrt ) ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(129,axiom,
! [A: produc124828825on_val] :
~ ! [B: exp_list_char,C: produc12694297on_val] :
( A
!= ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_prod_Oexhaust) ).
thf(800,plain,
! [A: produc124828825on_val] :
~ ! [B: exp_list_char,C: produc12694297on_val] :
( A
!= ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(120,axiom,
! [A: fun_fu100249073l_bool,B: produc12694297on_val] :
( ! [C: fun_na939144002on_val,D: fun_li1432931796on_val] :
( ( B
= ( D @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) ) )
=> ( D @ ( C @ ( A @ hAPP_f1175813647l_bool ) @ hAPP_f1033709212l_bool ) @ hBOOL ) )
=> ( B @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_splitI2) ).
thf(752,plain,
! [A: fun_fu100249073l_bool,B: produc12694297on_val] :
( ! [C: fun_na939144002on_val,D: fun_li1432931796on_val] :
( ( B
= ( D @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) ) )
=> ( D @ ( C @ ( A @ hAPP_f1175813647l_bool ) @ hAPP_f1033709212l_bool ) @ hBOOL ) )
=> ( B @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(134,axiom,
! [A: list_P1999446415t_char,B: val,C: exp_list_char,D: produc12694297on_val] : ( D @ ( C @ ( D @ ( C @ ( B @ val_list_char @ seq_list_char ) @ ( A @ redp ) ) @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_redp__redsp_ORedSeq) ).
thf(818,plain,
! [A: list_P1999446415t_char,B: val,C: exp_list_char,D: produc12694297on_val] : ( D @ ( C @ ( D @ ( C @ ( B @ val_list_char @ seq_list_char ) @ ( A @ redp ) ) @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(143,axiom,
! [A: fun_Pr633696065l_bool,B: produc124828825on_val,C: produc124828825on_val] :
( ( C @ ( B @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ ( A @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL )
<=> ( C @ ( B @ ( A @ hAPP_P1116729363l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_prod_Osimps_I2_J) ).
thf(854,plain,
! [A: fun_Pr633696065l_bool,B: produc124828825on_val,C: produc124828825on_val] :
( ( ( C @ ( B @ ( A @ hAPP_P1116729363l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL )
=> ( C @ ( B @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ ( A @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL ) )
& ( ( C @ ( B @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ ( A @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL )
=> ( C @ ( B @ ( A @ hAPP_P1116729363l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(145,axiom,
! [A: fun_Pr691271849l_bool] :
( ? [B: produc1102272487on_val] : ( B @ ( A @ hAPP_P282169671l_bool ) @ hBOOL )
<=> ? [B: produc124828825on_val,C: produc124828825on_val] : ( C @ ( B @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ ( A @ hAPP_P282169671l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_split__paired__Ex) ).
thf(865,plain,
! [A: fun_Pr691271849l_bool] :
( ( ? [B: produc124828825on_val,C: produc124828825on_val] : ( C @ ( B @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ ( A @ hAPP_P282169671l_bool ) @ hBOOL )
=> ? [B: produc1102272487on_val] : ( B @ ( A @ hAPP_P282169671l_bool ) @ hBOOL ) )
& ( ? [B: produc1102272487on_val] : ( B @ ( A @ hAPP_P282169671l_bool ) @ hBOOL )
=> ? [B: produc124828825on_val,C: produc124828825on_val] : ( C @ ( B @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ ( A @ hAPP_P282169671l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(116,axiom,
! [A: fun_ex1201926843l_bool,B: exp_list_char,C: produc12694297on_val] :
( ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( A @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL )
=> ( C @ ( B @ ( A @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_splitD) ).
thf(735,plain,
! [A: fun_ex1201926843l_bool,B: exp_list_char,C: produc12694297on_val] :
( ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( A @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL )
=> ( C @ ( B @ ( A @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(26,axiom,
! [A: fun_li688206603ion_ty,B: list_char,C: ty,D: list_char,E: ty] :
( ( ( D @ ( C @ some_ty @ ( B @ ( A @ fun_up424764369ion_ty ) ) @ hAPP_l512744617ion_ty ) )
= ( E @ some_ty ) )
<=> ( ( ( ( D @ ( A @ hAPP_l512744617ion_ty ) )
= ( E @ some_ty ) )
& ( D != B ) )
| ( ( C = E )
& ( D = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_map__upd__Some__unfold) ).
thf(305,plain,
! [A: fun_li688206603ion_ty,B: list_char,C: ty,D: list_char,E: ty] :
( ( ( ( ( ( D @ ( A @ hAPP_l512744617ion_ty ) )
= ( E @ some_ty ) )
& ( D != B ) )
| ( ( C = E )
& ( D = B ) ) )
=> ( ( D @ ( C @ some_ty @ ( B @ ( A @ fun_up424764369ion_ty ) ) @ hAPP_l512744617ion_ty ) )
= ( E @ some_ty ) ) )
& ( ( ( D @ ( C @ some_ty @ ( B @ ( A @ fun_up424764369ion_ty ) ) @ hAPP_l512744617ion_ty ) )
= ( E @ some_ty ) )
=> ( ( ( ( D @ ( A @ hAPP_l512744617ion_ty ) )
= ( E @ some_ty ) )
& ( D != B ) )
| ( ( C = E )
& ( D = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(12,axiom,
! [A: fun_li688206603ion_ty,B: option_ty,C: list_char,D: list_char] :
( ( ( D != C )
=> ( ( D @ ( B @ ( C @ ( A @ fun_up424764369ion_ty ) ) @ hAPP_l512744617ion_ty ) )
= ( D @ ( A @ hAPP_l512744617ion_ty ) ) ) )
& ( ( D = C )
=> ( ( D @ ( B @ ( C @ ( A @ fun_up424764369ion_ty ) ) @ hAPP_l512744617ion_ty ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_fun__upd__def) ).
thf(239,plain,
! [A: fun_li688206603ion_ty,B: option_ty,C: list_char,D: list_char] :
( ( ( D != C )
=> ( ( D @ ( B @ ( C @ ( A @ fun_up424764369ion_ty ) ) @ hAPP_l512744617ion_ty ) )
= ( D @ ( A @ hAPP_l512744617ion_ty ) ) ) )
& ( ( D = C )
=> ( ( D @ ( B @ ( C @ ( A @ fun_up424764369ion_ty ) ) @ hAPP_l512744617ion_ty ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(18,axiom,
! [A: fun_li688206603ion_ty,B: list_char] :
( ( B @ ( A @ hAPP_l512744617ion_ty ) @ ( B @ ( A @ fun_up424764369ion_ty ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_fun__upd__triv) ).
thf(268,plain,
! [A: fun_li688206603ion_ty,B: list_char] :
( ( B @ ( A @ hAPP_l512744617ion_ty ) @ ( B @ ( A @ fun_up424764369ion_ty ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(131,axiom,
! [A: list_char,B: exp_list_char,C: produc12694297on_val,D: exp_list_char,E: produc12694297on_val,F: list_P1999446415t_char] :
( ( F @ red @ ( E @ ( D @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL )
=> ( F @ red @ ( E @ ( D @ ( A @ lAss_list_char ) @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( C @ ( B @ ( A @ lAss_list_char ) @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_red__reds_OLAssRed) ).
thf(807,plain,
! [A: list_char,B: exp_list_char,C: produc12694297on_val,D: exp_list_char,E: produc12694297on_val,F: list_P1999446415t_char] :
( ( F @ red @ ( E @ ( D @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( C @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL )
=> ( F @ red @ ( E @ ( D @ ( A @ lAss_list_char ) @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( C @ ( B @ ( A @ lAss_list_char ) @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(151,axiom,
! [A: list_char,B: ty,C: val,D: produc12694297on_val,E: list_P1999446415t_char] : ( E @ red @ ( D @ ( C @ val_list_char @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( D @ ( C @ val_list_char @ ( B @ ( A @ block_list_char ) ) @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_red__reds_ORedBlock) ).
thf(897,plain,
! [A: list_char,B: ty,C: val,D: produc12694297on_val,E: list_P1999446415t_char] : ( E @ red @ ( D @ ( C @ val_list_char @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( D @ ( C @ val_list_char @ ( B @ ( A @ block_list_char ) ) @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(137,axiom,
! [A: fun_fu100249073l_bool,B: fun_ex1005552999on_val,C: produc124828825on_val] :
( ( C @ ( B @ ( produc1174947465on_val @ hAPP_f1520199827on_val ) @ hAPP_P789556885on_val ) @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
<=> ( C @ ( B @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ ( cOMBB_877741809on_val @ hAPP_f1825030711l_bool ) @ ( cOMBB_819439237t_char @ hAPP_f516738477l_bool ) @ hAPP_f653692369l_bool ) @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_split__twice) ).
thf(828,plain,
! [A: fun_fu100249073l_bool,B: fun_ex1005552999on_val,C: produc124828825on_val] :
( ( ( C @ ( B @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ ( cOMBB_877741809on_val @ hAPP_f1825030711l_bool ) @ ( cOMBB_819439237t_char @ hAPP_f516738477l_bool ) @ hAPP_f653692369l_bool ) @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL )
=> ( C @ ( B @ ( produc1174947465on_val @ hAPP_f1520199827on_val ) @ hAPP_P789556885on_val ) @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) )
& ( ( C @ ( B @ ( produc1174947465on_val @ hAPP_f1520199827on_val ) @ hAPP_P789556885on_val ) @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
=> ( C @ ( B @ ( A @ ( produc1958875245l_bool @ hAPP_f2121594859l_bool ) @ ( cOMBB_877741809on_val @ hAPP_f1825030711l_bool ) @ ( cOMBB_819439237t_char @ hAPP_f516738477l_bool ) @ hAPP_f653692369l_bool ) @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(69,axiom,
! [A: fun_na939144002on_val,B: fun_li1432931796on_val,C: fun_na939144002on_val,D: fun_li1432931796on_val] :
( ( ( B @ ( A @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) )
= ( D @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) ) )
<=> ( ( B = D )
& ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_Pair__eq) ).
thf(532,plain,
! [A: fun_na939144002on_val,B: fun_li1432931796on_val,C: fun_na939144002on_val,D: fun_li1432931796on_val] :
( ( ( ( B = D )
& ( A = C ) )
=> ( ( B @ ( A @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) )
= ( D @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) ) ) )
& ( ( ( B @ ( A @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) )
= ( D @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(188,axiom,
p @ red @ ( l_a @ ( h_a @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( e_a @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( v @ some_val @ ( v_1 @ ( la @ fun_up1149430426on_val ) ) @ ( ha @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( ea @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_InitBlockRed_I1_J) ).
thf(1065,plain,
p @ red @ ( l_a @ ( h_a @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( e_a @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( v @ some_val @ ( v_1 @ ( la @ fun_up1149430426on_val ) ) @ ( ha @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( ea @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ member773094996on_val ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(144,axiom,
! [A: fun_bool_bool,B: fun_ex1201926843l_bool,C: produc124828825on_val] :
( ( C @ ( B @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ ( A @ hAPP_bool_bool ) @ hBOOL )
=> ~ ! [D: exp_list_char,E: produc12694297on_val] :
( ( C
= ( E @ ( D @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) ) )
=> ~ ( E @ ( D @ ( B @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ ( A @ hAPP_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_splitE2) ).
thf(860,plain,
! [A: fun_bool_bool,B: fun_ex1201926843l_bool,C: produc124828825on_val] :
( ( C @ ( B @ ( produc1815960045l_bool @ hAPP_f1930574389l_bool ) @ hAPP_P1708370145l_bool ) @ ( A @ hAPP_bool_bool ) @ hBOOL )
=> ~ ! [D: exp_list_char,E: produc12694297on_val] :
( ( C
= ( E @ ( D @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) ) )
=> ~ ( E @ ( D @ ( B @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ ( A @ hAPP_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(68,axiom,
! [A: produc124828825on_val] :
~ ! [B: exp_list_char,C: fun_na939144002on_val,D: fun_li1432931796on_val] :
( A
!= ( D @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_prod__cases3) ).
thf(528,plain,
! [A: produc124828825on_val] :
~ ! [B: exp_list_char,C: fun_na939144002on_val,D: fun_li1432931796on_val] :
( A
!= ( D @ ( C @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( B @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(97,axiom,
! [A: fun_li1432931796on_val,B: option_val,C: option_val,D: list_char,E: list_char] :
( ( D != E )
=> ( ( C @ ( E @ ( B @ ( D @ ( A @ fun_up1149430426on_val ) ) @ fun_up1149430426on_val ) ) )
= ( B @ ( D @ ( C @ ( E @ ( A @ fun_up1149430426on_val ) ) @ fun_up1149430426on_val ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_fun__upd__twist) ).
thf(644,plain,
! [A: fun_li1432931796on_val,B: option_val,C: option_val,D: list_char,E: list_char] :
( ( D != E )
=> ( ( C @ ( E @ ( B @ ( D @ ( A @ fun_up1149430426on_val ) ) @ fun_up1149430426on_val ) ) )
= ( B @ ( D @ ( C @ ( E @ ( A @ fun_up1149430426on_val ) ) @ fun_up1149430426on_val ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(110,axiom,
! [A: ty,B: val,C: list_P1999446415t_char,D: exp_list_char,E: fun_na939144002on_val,F: fun_li1432931796on_val,G: list_char,H: exp_list_char,I: fun_na939144002on_val,J: fun_li1432931796on_val] :
( ( J @ ( I @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( H @ ( none_val @ ( G @ ( F @ fun_up1149430426on_val ) ) @ ( E @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( D @ ( C @ redp ) ) @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
=> ( ( ( G @ ( J @ hAPP_l207779698on_val ) )
= ( B @ some_val ) )
=> ( ~ ( D @ ( G @ assigned ) @ hBOOL )
=> ( G @ ( F @ hAPP_l207779698on_val ) @ ( G @ ( J @ fun_up1149430426on_val ) ) @ ( I @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( H @ ( B @ val_list_char @ ( G @ lAss_list_char ) @ seq_list_char ) @ ( A @ ( G @ block_list_char ) ) @ ( F @ ( E @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( D @ ( A @ ( G @ block_list_char ) ) @ ( C @ redp ) ) @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_redp__redsp_OBlockRedSome) ).
thf(691,plain,
! [A: ty,B: val,C: list_P1999446415t_char,D: exp_list_char,E: fun_na939144002on_val,F: fun_li1432931796on_val,G: list_char,H: exp_list_char,I: fun_na939144002on_val,J: fun_li1432931796on_val] :
( ( J @ ( I @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( H @ ( none_val @ ( G @ ( F @ fun_up1149430426on_val ) ) @ ( E @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( D @ ( C @ redp ) ) @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
=> ( ( ( G @ ( J @ hAPP_l207779698on_val ) )
= ( B @ some_val ) )
=> ( ~ ( D @ ( G @ assigned ) @ hBOOL )
=> ( G @ ( F @ hAPP_l207779698on_val ) @ ( G @ ( J @ fun_up1149430426on_val ) ) @ ( I @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( H @ ( B @ val_list_char @ ( G @ lAss_list_char ) @ seq_list_char ) @ ( A @ ( G @ block_list_char ) ) @ ( F @ ( E @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( D @ ( A @ ( G @ block_list_char ) ) @ ( C @ redp ) ) @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(146,axiom,
! [A: fun_fu100249073l_bool,B: fun_na939144002on_val,C: fun_li1432931796on_val] :
( ( C @ ( B @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( A @ ( produc2128769400l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
<=> ( C @ ( B @ ( A @ hAPP_f1175813647l_bool ) @ hAPP_f1033709212l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_internal__split__conv) ).
thf(871,plain,
! [A: fun_fu100249073l_bool,B: fun_na939144002on_val,C: fun_li1432931796on_val] :
( ( ( C @ ( B @ ( A @ hAPP_f1175813647l_bool ) @ hAPP_f1033709212l_bool ) @ hBOOL )
=> ( C @ ( B @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( A @ ( produc2128769400l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) )
& ( ( C @ ( B @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( A @ ( produc2128769400l_bool @ hAPP_f2121594859l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
=> ( C @ ( B @ ( A @ hAPP_f1175813647l_bool ) @ hAPP_f1033709212l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(195,axiom,
! [A: list_P1999446415t_char,B: list_char,C: ty,D: val,E: val,F: produc12694297on_val] : ( F @ ( E @ val_list_char @ ( F @ ( E @ val_list_char @ ( D @ val_list_char @ ( B @ lAss_list_char ) @ seq_list_char ) @ ( C @ ( B @ block_list_char ) ) @ ( A @ redp ) ) @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_redp__redsp_ORedInitBlock) ).
thf(1093,plain,
! [A: list_P1999446415t_char,B: list_char,C: ty,D: val,E: val,F: produc12694297on_val] : ( F @ ( E @ val_list_char @ ( F @ ( E @ val_list_char @ ( D @ val_list_char @ ( B @ lAss_list_char ) @ seq_list_char ) @ ( C @ ( B @ block_list_char ) ) @ ( A @ redp ) ) @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(90,axiom,
! [A: produc12694297on_val,B: fun_fu110544035l_bool,C: produc12694297on_val] :
( ( C @ ( B @ ( produc121041439l_bool @ hAPP_f1276548047l_bool ) @ hAPP_P1988153107l_bool ) @ ( A @ member763590124on_val ) @ hBOOL )
=> ~ ! [D: fun_na939144002on_val,E: fun_li1432931796on_val] :
( ( C
= ( E @ ( D @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) ) )
=> ~ ( E @ ( D @ ( B @ hAPP_f2135509569l_bool ) @ hAPP_f396019662l_bool ) @ ( A @ member763590124on_val ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_mem__splitE) ).
thf(624,plain,
! [A: produc12694297on_val,B: fun_fu110544035l_bool,C: produc12694297on_val] :
( ( C @ ( B @ ( produc121041439l_bool @ hAPP_f1276548047l_bool ) @ hAPP_P1988153107l_bool ) @ ( A @ member763590124on_val ) @ hBOOL )
=> ~ ! [D: fun_na939144002on_val,E: fun_li1432931796on_val] :
( ( C
= ( E @ ( D @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) ) )
=> ~ ( E @ ( D @ ( B @ hAPP_f2135509569l_bool ) @ hAPP_f396019662l_bool ) @ ( A @ member763590124on_val ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(140,axiom,
! [A: produc12694297on_val,B: fun_fu110544035l_bool,C: produc12694297on_val] :
( ! [D: fun_na939144002on_val,E: fun_li1432931796on_val] :
( ( C
= ( E @ ( D @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) ) )
=> ( E @ ( D @ ( B @ hAPP_f2135509569l_bool ) @ hAPP_f396019662l_bool ) @ ( A @ member763590124on_val ) @ hBOOL ) )
=> ( C @ ( B @ ( produc121041439l_bool @ hAPP_f1276548047l_bool ) @ hAPP_P1988153107l_bool ) @ ( A @ member763590124on_val ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_mem__splitI2) ).
thf(839,plain,
! [A: produc12694297on_val,B: fun_fu110544035l_bool,C: produc12694297on_val] :
( ! [D: fun_na939144002on_val,E: fun_li1432931796on_val] :
( ( C
= ( E @ ( D @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) ) )
=> ( E @ ( D @ ( B @ hAPP_f2135509569l_bool ) @ hAPP_f396019662l_bool ) @ ( A @ member763590124on_val ) @ hBOOL ) )
=> ( C @ ( B @ ( produc121041439l_bool @ hAPP_f1276548047l_bool ) @ hAPP_P1988153107l_bool ) @ ( A @ member763590124on_val ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(15,axiom,
! [A: fun_Pr1696029455l_bool,B: fun_Pr2087158653on_val,C: produc124828825on_val] :
( ( C @ ( B @ ( A @ ( cOMBB_1083177073on_val @ hAPP_f881985847l_bool ) @ hAPP_f1712766199l_bool ) @ hAPP_P1708370145l_bool ) )
= ( C @ ( B @ hAPP_P789556885on_val ) @ ( A @ hAPP_P159683425l_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It_203) ).
thf(254,plain,
! [A: fun_Pr1696029455l_bool,B: fun_Pr2087158653on_val,C: produc124828825on_val] :
( ( C @ ( B @ ( A @ ( cOMBB_1083177073on_val @ hAPP_f881985847l_bool ) @ hAPP_f1712766199l_bool ) @ hAPP_P1708370145l_bool ) )
= ( C @ ( B @ hAPP_P789556885on_val ) @ ( A @ hAPP_P159683425l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(159,axiom,
! [A: fun_Pr633696065l_bool,B: produc124828825on_val,C: produc124828825on_val] :
( ( C @ ( B @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ ( A @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL )
<=> ( C @ ( B @ ( A @ hAPP_P1116729363l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_split__conv) ).
thf(935,plain,
! [A: fun_Pr633696065l_bool,B: produc124828825on_val,C: produc124828825on_val] :
( ( ( C @ ( B @ ( A @ hAPP_P1116729363l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL )
=> ( C @ ( B @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ ( A @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL ) )
& ( ( C @ ( B @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ ( A @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) @ hAPP_P282169671l_bool ) @ hBOOL )
=> ( C @ ( B @ ( A @ hAPP_P1116729363l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(105,axiom,
! [A: ty,B: val,C: list_P1999446415t_char,D: exp_list_char,E: fun_na939144002on_val,F: fun_li1432931796on_val,G: list_char,H: val,I: exp_list_char,J: fun_na939144002on_val,K: fun_li1432931796on_val] :
( ( K @ ( J @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( I @ ( H @ some_val @ ( G @ ( F @ fun_up1149430426on_val ) ) @ ( E @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( D @ ( C @ redp ) ) @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
=> ( ( ( G @ ( K @ hAPP_l207779698on_val ) )
= ( B @ some_val ) )
=> ( G @ ( F @ hAPP_l207779698on_val ) @ ( G @ ( K @ fun_up1149430426on_val ) ) @ ( J @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( I @ ( B @ val_list_char @ ( G @ lAss_list_char ) @ seq_list_char ) @ ( A @ ( G @ block_list_char ) ) @ ( F @ ( E @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( D @ ( H @ val_list_char @ ( G @ lAss_list_char ) @ seq_list_char ) @ ( A @ ( G @ block_list_char ) ) @ ( C @ redp ) ) @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_redp__redsp_OInitBlockRed) ).
thf(676,plain,
! [A: ty,B: val,C: list_P1999446415t_char,D: exp_list_char,E: fun_na939144002on_val,F: fun_li1432931796on_val,G: list_char,H: val,I: exp_list_char,J: fun_na939144002on_val,K: fun_li1432931796on_val] :
( ( K @ ( J @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( I @ ( H @ some_val @ ( G @ ( F @ fun_up1149430426on_val ) ) @ ( E @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( D @ ( C @ redp ) ) @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL )
=> ( ( ( G @ ( K @ hAPP_l207779698on_val ) )
= ( B @ some_val ) )
=> ( G @ ( F @ hAPP_l207779698on_val ) @ ( G @ ( K @ fun_up1149430426on_val ) ) @ ( J @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( I @ ( B @ val_list_char @ ( G @ lAss_list_char ) @ seq_list_char ) @ ( A @ ( G @ block_list_char ) ) @ ( F @ ( E @ ( produc899768717on_val @ hAPP_f1849790461on_val ) @ hAPP_f1727192346on_val ) @ ( D @ ( H @ val_list_char @ ( G @ lAss_list_char ) @ seq_list_char ) @ ( A @ ( G @ block_list_char ) ) @ ( C @ redp ) ) @ hAPP_e1833980889l_bool ) @ hAPP_P159683425l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(7,axiom,
! [A: fun_li688206603ion_ty,B: option_ty,C: list_char,D: list_char] :
( ( C != D )
=> ( ( C @ ( B @ ( D @ ( A @ fun_up424764369ion_ty ) ) @ hAPP_l512744617ion_ty ) )
= ( C @ ( A @ hAPP_l512744617ion_ty ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_fun__upd__other) ).
thf(222,plain,
! [A: fun_li688206603ion_ty,B: option_ty,C: list_char,D: list_char] :
( ( C != D )
=> ( ( C @ ( B @ ( D @ ( A @ fun_up424764369ion_ty ) ) @ hAPP_l512744617ion_ty ) )
= ( C @ ( A @ hAPP_l512744617ion_ty ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(61,axiom,
! [A: fun_Pr691271849l_bool,B: fun_Pr633696065l_bool] :
( ! [C: produc124828825on_val,D: produc124828825on_val] :
( ( D @ ( C @ ( B @ hAPP_P1116729363l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL )
<=> ( D @ ( C @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ ( A @ hAPP_P282169671l_bool ) @ hBOOL ) )
=> ( ( B @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_cond__split__eta) ).
thf(496,plain,
! [A: fun_Pr691271849l_bool,B: fun_Pr633696065l_bool] :
( ! [C: produc124828825on_val,D: produc124828825on_val] :
( ( ( D @ ( C @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ ( A @ hAPP_P282169671l_bool ) @ hBOOL )
=> ( D @ ( C @ ( B @ hAPP_P1116729363l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL ) )
& ( ( D @ ( C @ ( B @ hAPP_P1116729363l_bool ) @ hAPP_P1708370145l_bool ) @ hBOOL )
=> ( D @ ( C @ ( produc1441475159on_val @ hAPP_P1870962205on_val ) @ hAPP_P1886180715on_val ) @ ( A @ hAPP_P282169671l_bool ) @ hBOOL ) ) )
=> ( ( B @ ( produc1911463199l_bool @ hAPP_f635218277l_bool ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(10,axiom,
! [A: list_char,B: exp_list_char,C: list_char,D: ty,E: exp_list_char] :
( ( B @ ( A @ lAss_list_char ) )
!= ( E @ ( D @ ( C @ block_list_char ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_exp_Osimps_I142_J) ).
thf(232,plain,
! [A: list_char,B: exp_list_char,C: list_char,D: ty,E: exp_list_char] :
( ( B @ ( A @ lAss_list_char ) )
!= ( E @ ( D @ ( C @ block_list_char ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(148,axiom,
! [A: produc124828825on_val,B: fun_ex1732109805l_bool,C: produc124828825on_val] :
( ! [D: exp_list_char,E: produc12694297on_val] :
( ( C
= ( E @ ( D @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) ) )
=> ( E @ ( D @ ( B @ hAPP_e592495499l_bool ) @ hAPP_P1638898323l_bool ) @ ( A @ member840932460on_val ) @ hBOOL ) )
=> ( C @ ( B @ ( produc1275132703l_bool @ hAPP_f1760682521l_bool ) @ hAPP_P1116729363l_bool ) @ ( A @ member840932460on_val ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_mem__splitI2) ).
thf(882,plain,
! [A: produc124828825on_val,B: fun_ex1732109805l_bool,C: produc124828825on_val] :
( ! [D: exp_list_char,E: produc12694297on_val] :
( ( C
= ( E @ ( D @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) ) )
=> ( E @ ( D @ ( B @ hAPP_e592495499l_bool ) @ hAPP_P1638898323l_bool ) @ ( A @ member840932460on_val ) @ hBOOL ) )
=> ( C @ ( B @ ( produc1275132703l_bool @ hAPP_f1760682521l_bool ) @ hAPP_P1116729363l_bool ) @ ( A @ member840932460on_val ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(178,axiom,
! [A: fun_Pr680585871l_bool,B: fun_Pr680585871l_bool] :
( ! [C: exp_list_char,D: produc12694297on_val] :
( ( B @ ( D @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ member840932460on_val ) @ hBOOL )
<=> ( A @ ( D @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ member840932460on_val ) @ hBOOL ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_pred__equals__eq2) ).
thf(1014,plain,
! [A: fun_Pr680585871l_bool,B: fun_Pr680585871l_bool] :
( ( ( B = A )
=> ! [C: exp_list_char,D: produc12694297on_val] :
( ( ( A @ ( D @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ member840932460on_val ) @ hBOOL )
=> ( B @ ( D @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ member840932460on_val ) @ hBOOL ) )
& ( ( B @ ( D @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ member840932460on_val ) @ hBOOL )
=> ( A @ ( D @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ member840932460on_val ) @ hBOOL ) ) ) )
& ( ! [C: exp_list_char,D: produc12694297on_val] :
( ( ( A @ ( D @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ member840932460on_val ) @ hBOOL )
=> ( B @ ( D @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ member840932460on_val ) @ hBOOL ) )
& ( ( B @ ( D @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ member840932460on_val ) @ hBOOL )
=> ( A @ ( D @ ( C @ ( produc1259058957on_val @ hAPP_e1659493427on_val ) @ hAPP_P604205461on_val ) @ member840932460on_val ) @ hBOOL ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(1117,plain,
$false,
inference(e,[status(thm)],[1036,809,629,479,941,333,1031,1068,994,511,1041,523,582,202,597,1078,814,698,670,1095,565,257,1055,372,542,638,416,289,1100,789,834,574,353,966,981,877,293,774,660,428,507,397,687,411,988,265,849,452,248,925,201,381,366,1047,1057,910,1091,778,302,349,820,561,424,275,729,229,889,757,710,324,1012,948,615,1006,356,593,610,783,420,225,554,901,642,679,547,212,622,393,647,654,984,1002,605,1086,205,558,296,375,694,743,545,413,236,804,704,979,681,737,434,271,208,631,594,251,915,943,330,462,345,552,636,1066,455,563,1000,299,1102,431,912,521,589,663,836,1049,968,823,776,525,1003,640,887,327,954,1098,359,1038,370,336,386,571,1084,363,931,844,1108,976,688,748,1062,652,390,786,963,517,378,667,763,383,899,800,752,818,854,865,735,305,239,268,807,897,828,532,1065,860,528,644,691,871,1093,624,839,254,935,676,222,496,232,882,1014]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW478_1 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.14/15.44 % Computer : n006.cluster.edu
% 0.14/15.44 % Model : x86_64 x86_64
% 0.14/15.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/15.44 % Memory : 8046.5625MB
% 0.14/15.44 % OS : Linux 6.8.0-71-generic
% 0.14/15.44 % CPULimit : 300
% 0.14/15.44 % WCLimit : 300
% 0.14/15.44 % DateTime : Sat Sep 26 16:07:44 UTC 2026
% 0.14/15.44 % CPUTime :
% 0.14/15.44 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.95/16.06 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.21/16.66 % [INFO] Parsing done (592ms).
% 2.21/16.68 % [INFO] Running in sequential loop mode.
% 3.33/17.26 % [INFO] eprover registered as external prover.
% 3.33/17.27 % [INFO] Scanning for conjecture ...
% 4.01/17.61 % [INFO] Found a conjecture (or negated_conjecture) and 198 axioms. Running axiom selection ...
% 4.55/17.86 % [INFO] Axiom selection finished. Selected 198 axioms (removed 0 axioms).
% 5.79/18.39 % [INFO] Problem is typed first-order (TPTP TFF).
% 5.98/18.42 % [INFO] Type checking passed.
% 5.98/18.43 % [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 ...
% 15.19/22.04 % External prover 'e' found a proof!
% 15.19/22.04 % [INFO] Killing All external provers ...
% 15.19/22.04 % Time passed: 6450ms (effective reasoning time: 5348ms)
% 15.19/22.04 % 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)>
% 15.73/22.05 % Axioms used in derivation (198): fact_129_cond__split__eta, fact_100_splitE, fact_111_red__reds_OSeqRed, fact_4_assms, help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_204, fact_69_splitI, help_COMBB_1_1_COMBB_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc, fact_24_fun__upd__def, fact_17_Pair__inject, fact_145_exp_Osimps_I85_J, fact_63_sconf__def, fact_65_prod__caseI, fact_116_mem__splitE, fact_19_Pair__eq, fact_134_exp_Osimps_I143_J, fact_98_splitI2, help_fconj_3_1_U, fact_25_fun__upd__def, fact_5_map__upd__Some__unfold, fact_166_redp__redsp_ORedInitBlock, fact_60_PairE, fact_109_mem__splitI, fact_136_exp_Osimps_I3_J, fact_105_mem__splitI, fact_6_map__upd__Some__unfold, fact_67_splitI, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__prod_Itc__Expr__, fact_78_internal__split__def, fact_104_mem__splitI, fact_86_prod_Osimps_I2_J, fact_57_split__paired__Ex, fact_7_map__upd__triv, fact_11_InitBlockRed_I2_J, fact_32_fun__upd__apply, fact_139_mem__def, fact_27_fun__upd__idem, fact_54_widen__trans, fact_0_InitBlockRed_I3_J, help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It, fact_23_split__paired__All, fact_2_fun__upd__triv, fact_148_exp_Osimps_I83_J, fact_91_split__conv, fact_42_red__preserves__lconf, fact_117_mem__splitE, fact_158_redp__redsp_ORedSeq, fact_33_fun__upd__apply, fact_76_internal__split__def, help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_200, fact_114_red__reds_ORedBlock, fact_26_fun__upd__idem, help_COMBB_1_1_COMBB_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__O_202, fact_130_cond__split__eta, fact_140_mem__def, fact_125_mem__splitI2, fact_137_exp_Osimps_I11_J, fact_102_splitE, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__O, fact_39_fun__upd__idem__iff, fact_93_split__eta, fact_66_prod__caseI, fact_46_prod__induct3, fact_28_fun__upd__other, fact_12_prod__induct4, fact_132_splitE2, fact_30_fun__upd__twist, fact_94_split__eta, fact_123_mem__splitI2, help_COMBB_1_1_COMBB_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc_, help_COMBK_1_1_COMBK_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__List__Olist_, fact_53_prod_Oexhaust, fact_152_exp_Osimps_I142_J, help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_209, fact_151_exp_Osimps_I197_J, fact_126_mem__splitI2, fact_52_prod_Oexhaust, fact_71_splitD, fact_64_prod__caseI, fact_59_PairE, fact_164_redp__redsp_OBlockRedSome, fact_22_split__paired__All, fact_106_mem__splitI, fact_34_fun__upd__same, fact_144_exp_Osimps_I74_J, help_COMBB_1_1_COMBB_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__208, fact_61_PairE, fact_89_split__conv, fact_142_exp_Osimps_I10_J, help_fconj_2_1_U, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc___211, fact_9_map__upd__eqD1, fact_103_WTrtBlock, fact_83_split__part, fact_95_red__reds_OInitBlockRed, fact_45_prod__induct3, fact_41_red__preserves__hconf, fact_38_fun__upd__idem__iff, fact_20_Pair__eq, fact_113_red__reds_ORedSeq, fact_118_mem__splitE, fact_13_prod__cases4, fact_121_mem__splitI2, fact_50_pred__equals__eq2, fact_37_fun__upd__upd, fact_138_exp_Osimps_I6_J, fact_56_split__paired__Ex, fact_157_redp__redsp_OBlockRedNone, help_COMBB_1_1_COMBB_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It_201, help_COMBB_1_1_COMBB_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__O, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__O_206, fact_84_split__part, fact_131_splitE2, help_COMBK_1_1_COMBK_000tc__Option__Ooption_Itc__Value__Oval_J_000tc__List__Olis, fact_29_fun__upd__other, fact_141_mem__def, fact_10_map__upd__eqD1, fact_68_splitI, fact_101_splitE, fact_15_Pair__inject, fact_156_redp__redsp_OLAssRed, fact_143_exp_Osimps_I84_J, fact_35_fun__upd__same, fact_55_InitBlockRed_I5_J, fact_127_red__reds_ORedLAss, fact_110_WTrtSeq, fact_36_fun__upd__upd, fact_154_red__reds_OBlockRedSome, fact_124_mem__splitI2, fact_107_mem__splitI, fact_48_pred__equals__eq2, help_COMBC_1_1_COMBC_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Optio, fact_161_redp__redsp_ORedBlock, help_COMBS_1_1_COMBS_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It, fact_88_prod_Osimps_I2_J, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__, fact_155_redp__redsp_OSeqRed, fact_40_widen__refl, fact_92_split__eta, fact_82_split__twice, fact_162_empty__upd__none, fact_51_prod_Oexhaust, fact_43_prod__cases3, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc___210, fact_16_Pair__inject, fact_165_redp__red__eq, fact_62_internal__split__conv, help_fconj_1_1_U, fact_85_split__part, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__prod_Itc__fun_It, fact_149_exp_Osimps_I145_J, fact_159_map__upd__nonempty, fact_122_mem__splitI2, fact_163_empty__upd__none, fact_8_map__upd__triv, help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_205, fact_72_splitD, fact_74_split__weak__cong, fact_18_Pair__eq, fact_99_splitI2, fact_160_map__upd__nonempty, fact_3_fun__upd__triv, fact_1_InitBlockRed_I1_J, help_COMBB_1_1_COMBB_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It_203, fact_58_split__paired__Ex, fact_147_exp_Osimps_I82_J, fact_70_splitD, fact_75_split__weak__cong, help_COMBB_1_1_COMBB_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It, fact_120_mem__splitE, help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M, fact_49_pred__equals__eq2, fact_119_mem__splitE, fact_21_split__paired__All, fact_44_prod__cases3, fact_150_exp_Osimps_I144_J, fact_81_split__twice, fact_47_red__preserves__sconf, fact_146_exp_Osimps_I75_J, fact_96_red__reds_ORedInitBlock, fact_87_prod_Osimps_I2_J, fact_128_cond__split__eta, fact_97_splitI2, fact_79_split__twice, fact_90_split__conv, fact_133_splitE2, fact_77_internal__split__def, fact_115_mem__splitE, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__O_207, fact_112_red__reds_OLAssRed, fact_73_split__weak__cong, fact_80_split__twice, fact_135_exp_Osimps_I196_J, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__List__O, fact_153_redp__redsp_OInitBlockRed, fact_14_InitBlockRed_I4_J, fact_108_mem__splitI, fact_31_fun__upd__twist
% 15.73/22.05 % No. of inferences in proof: 400
% 15.73/22.05 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 6450 ms resp. 5348 ms w/o parsing
% 16.59/22.45 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 16.59/22.47 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------