%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SCT171_2 : TPTP v8.1.2. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n031.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May 19 11:51:00 EDT 2023

% Result   : Theorem 19.17s 5.67s
% Output   : Refutation 20.42s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      : 1442
% Syntax   : Number of formulae    : 2202 ( 388 unt; 684 typ;   0 def)
%            Number of atoms       : 4217 ( 927 equ;   0 cnn)
%            Maximal formula atoms :   22 (   2 avg)
%            Number of connectives : 25629 ( 630   ~;  98   |; 342   &;22300   @)
%                                         ( 179 <=>;2080  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   25 (  10 avg)
%            Number of types       :  253 ( 252 usr)
%            Number of type conns  :  558 ( 558   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  434 ( 432 usr; 138 con; 0-3 aty)
%            Number of variables   : 3558 (   0   ^;3520   !;  38   ?;3558   :)

% Comments : 
%------------------------------------------------------------------------------
thf(arrow_931160158le_alt_type,type,
    arrow_931160158le_alt: $tType ).

thf(arrow_2115524757e_indi_type,type,
    arrow_2115524757e_indi: $tType ).

thf(bool_type,type,
    bool: $tType ).

thf(nat_type,type,
    nat: $tType ).

thf(product_unit_type,type,
    product_unit: $tType ).

thf(fun_Ar1091019988t_bool_type,type,
    fun_Ar1091019988t_bool: $tType ).

thf(fun_Ar1414184139t_bool_type,type,
    fun_Ar1414184139t_bool: $tType ).

thf(fun_Ar1689125069l_bool_type,type,
    fun_Ar1689125069l_bool: $tType ).

thf(fun_Ar1164786343t_bool_type,type,
    fun_Ar1164786343t_bool: $tType ).

thf(fun_Ar2049444117le_alt_type,type,
    fun_Ar2049444117le_alt: $tType ).

thf(fun_Ar2078312923t_bool_type,type,
    fun_Ar2078312923t_bool: $tType ).

thf(fun_Ar421919996t_bool_type,type,
    fun_Ar421919996t_bool: $tType ).

thf(fun_Ar1026121174l_bool_type,type,
    fun_Ar1026121174l_bool: $tType ).

thf(fun_Ar1364097613t_bool_type,type,
    fun_Ar1364097613t_bool: $tType ).

thf(fun_Ar1275715144t_bool_type,type,
    fun_Ar1275715144t_bool: $tType ).

thf(fun_Ar836847646le_alt_type,type,
    fun_Ar836847646le_alt: $tType ).

thf(fun_Ar552120407i_bool_type,type,
    fun_Ar552120407i_bool: $tType ).

thf(fun_Ar1744566822di_nat_type,type,
    fun_Ar1744566822di_nat: $tType ).

thf(fun_Ar1583656131t_bool_type,type,
    fun_Ar1583656131t_bool: $tType ).

thf(fun_Ar698916836t_bool_type,type,
    fun_Ar698916836t_bool: $tType ).

thf(fun_Ar687924991t_bool_type,type,
    fun_Ar687924991t_bool: $tType ).

thf(fun_Ar2045874810t_bool_type,type,
    fun_Ar2045874810t_bool: $tType ).

thf(fun_Ar1380772935l_bool_type,type,
    fun_Ar1380772935l_bool: $tType ).

thf(fun_Ar684516451l_bool_type,type,
    fun_Ar684516451l_bool: $tType ).

thf(fun_Ar1939863823t_bool_type,type,
    fun_Ar1939863823t_bool: $tType ).

thf(fun_Ar1270429299l_bool_type,type,
    fun_Ar1270429299l_bool: $tType ).

thf(fun_Ar1198543961l_bool_type,type,
    fun_Ar1198543961l_bool: $tType ).

thf(fun_Ar1519997101t_bool_type,type,
    fun_Ar1519997101t_bool: $tType ).

thf(fun_Ar1492469401t_bool_type,type,
    fun_Ar1492469401t_bool: $tType ).

thf(fun_Ar500372357t_bool_type,type,
    fun_Ar500372357t_bool: $tType ).

thf(fun_Ar369661729le_alt_type,type,
    fun_Ar369661729le_alt: $tType ).

thf(fun_bool_bool_type,type,
    fun_bool_bool: $tType ).

thf(fun_bool_nat_type,type,
    fun_bool_nat: $tType ).

thf(fun_bo353189547i_bool_type,type,
    fun_bo353189547i_bool: $tType ).

thf(fun_bo266809543t_bool_type,type,
    fun_bo266809543t_bool: $tType ).

thf(fun_bo1549164019l_bool_type,type,
    fun_bo1549164019l_bool: $tType ).

thf(fun_bo1570548802t_bool_type,type,
    fun_bo1570548802t_bool: $tType ).

thf(fun_bo1300789993t_bool_type,type,
    fun_bo1300789993t_bool: $tType ).

thf(fun_bo645734555l_bool_type,type,
    fun_bo645734555l_bool: $tType ).

thf(fun_bo2027801303t_bool_type,type,
    fun_bo2027801303t_bool: $tType ).

thf(fun_bo492988759l_bool_type,type,
    fun_bo492988759l_bool: $tType ).

thf(fun_bo979888811l_bool_type,type,
    fun_bo979888811l_bool: $tType ).

thf(fun_bo96602657l_bool_type,type,
    fun_bo96602657l_bool: $tType ).

thf(fun_bo462718181t_bool_type,type,
    fun_bo462718181t_bool: $tType ).

thf(fun_bo1116297149t_bool_type,type,
    fun_bo1116297149t_bool: $tType ).

thf(fun_bo1479727337le_alt_type,type,
    fun_bo1479727337le_alt: $tType ).

thf(fun_na1392860600e_indi_type,type,
    fun_na1392860600e_indi: $tType ).

thf(fun_nat_bool_type,type,
    fun_nat_bool: $tType ).

thf(fun_nat_nat_type,type,
    fun_nat_nat: $tType ).

thf(fun_nat_Product_unit_type,type,
    fun_nat_Product_unit: $tType ).

thf(fun_na457272970i_bool_type,type,
    fun_na457272970i_bool: $tType ).

thf(fun_na1469252690l_bool_type,type,
    fun_na1469252690l_bool: $tType ).

thf(fun_nat_fun_nat_bool_type,type,
    fun_nat_fun_nat_bool: $tType ).

thf(fun_nat_fun_nat_nat_type,type,
    fun_nat_fun_nat_nat: $tType ).

thf(fun_na1041622088t_bool_type,type,
    fun_na1041622088t_bool: $tType ).

thf(fun_na1436237685l_bool_type,type,
    fun_na1436237685l_bool: $tType ).

thf(fun_Pr1643180309t_bool_type,type,
    fun_Pr1643180309t_bool: $tType ).

thf(fun_Product_unit_nat_type,type,
    fun_Product_unit_nat: $tType ).

thf(fun_Pr321980605t_bool_type,type,
    fun_Pr321980605t_bool: $tType ).

thf(fun_Pr1029464120t_bool_type,type,
    fun_Pr1029464120t_bool: $tType ).

thf(fun_Pr1223320869l_bool_type,type,
    fun_Pr1223320869l_bool: $tType ).

thf(fun_Pr1337256141t_bool_type,type,
    fun_Pr1337256141t_bool: $tType ).

thf(fun_Pr1863373635l_bool_type,type,
    fun_Pr1863373635l_bool: $tType ).

thf(fun_Pr1832937781l_bool_type,type,
    fun_Pr1832937781l_bool: $tType ).

thf(fun_Pr1510236951l_bool_type,type,
    fun_Pr1510236951l_bool: $tType ).

thf(fun_Pr1572389447t_bool_type,type,
    fun_Pr1572389447t_bool: $tType ).

thf(fun_Pr1887046367le_alt_type,type,
    fun_Pr1887046367le_alt: $tType ).

thf(fun_fu853658253l_bool_type,type,
    fun_fu853658253l_bool: $tType ).

thf(fun_fu304639347l_bool_type,type,
    fun_fu304639347l_bool: $tType ).

thf(fun_fu334859135t_bool_type,type,
    fun_fu334859135t_bool: $tType ).

thf(fun_fu960970567l_bool_type,type,
    fun_fu960970567l_bool: $tType ).

thf(fun_fu709917073t_bool_type,type,
    fun_fu709917073t_bool: $tType ).

thf(fun_fu1498496639t_bool_type,type,
    fun_fu1498496639t_bool: $tType ).

thf(fun_fu1476972377l_bool_type,type,
    fun_fu1476972377l_bool: $tType ).

thf(fun_fu1657302605l_bool_type,type,
    fun_fu1657302605l_bool: $tType ).

thf(fun_fu1058839037i_bool_type,type,
    fun_fu1058839037i_bool: $tType ).

thf(fun_fu2115718429t_bool_type,type,
    fun_fu2115718429t_bool: $tType ).

thf(fun_fu1310412861l_bool_type,type,
    fun_fu1310412861l_bool: $tType ).

thf(fun_fu536674321i_bool_type,type,
    fun_fu536674321i_bool: $tType ).

thf(fun_fu192249448t_bool_type,type,
    fun_fu192249448t_bool: $tType ).

thf(fun_fu1845850437t_bool_type,type,
    fun_fu1845850437t_bool: $tType ).

thf(fun_fu85234537l_bool_type,type,
    fun_fu85234537l_bool: $tType ).

thf(fun_fu209106563t_bool_type,type,
    fun_fu209106563t_bool: $tType ).

thf(fun_fu613599045t_bool_type,type,
    fun_fu613599045t_bool: $tType ).

thf(fun_fu1131021301l_bool_type,type,
    fun_fu1131021301l_bool: $tType ).

thf(fun_fu1591782325l_bool_type,type,
    fun_fu1591782325l_bool: $tType ).

thf(fun_fu954933197i_bool_type,type,
    fun_fu954933197i_bool: $tType ).

thf(fun_fu1380565427i_bool_type,type,
    fun_fu1380565427i_bool: $tType ).

thf(fun_fu1944573957l_bool_type,type,
    fun_fu1944573957l_bool: $tType ).

thf(fun_fu1816256693l_bool_type,type,
    fun_fu1816256693l_bool: $tType ).

thf(fun_fu51155629t_bool_type,type,
    fun_fu51155629t_bool: $tType ).

thf(fun_fu2117817733t_bool_type,type,
    fun_fu2117817733t_bool: $tType ).

thf(fun_fu908353023e_indi_type,type,
    fun_fu908353023e_indi: $tType ).

thf(fun_fu775006535l_bool_type,type,
    fun_fu775006535l_bool: $tType ).

thf(fun_fu834038077t_unit_type,type,
    fun_fu834038077t_unit: $tType ).

thf(fun_fu1765260675i_bool_type,type,
    fun_fu1765260675i_bool: $tType ).

thf(fun_fu757621293t_bool_type,type,
    fun_fu757621293t_bool: $tType ).

thf(fun_fu1872020686t_bool_type,type,
    fun_fu1872020686t_bool: $tType ).

thf(fun_fu1471766731l_bool_type,type,
    fun_fu1471766731l_bool: $tType ).

thf(fun_fu587068865t_bool_type,type,
    fun_fu587068865t_bool: $tType ).

thf(fun_fu1291054887l_bool_type,type,
    fun_fu1291054887l_bool: $tType ).

thf(fun_fu787660105l_bool_type,type,
    fun_fu787660105l_bool: $tType ).

thf(fun_fu1595299477t_bool_type,type,
    fun_fu1595299477t_bool: $tType ).

thf(fun_fu2073792791t_bool_type,type,
    fun_fu2073792791t_bool: $tType ).

thf(fun_fu1338365749l_bool_type,type,
    fun_fu1338365749l_bool: $tType ).

thf(fun_fu1255657237l_bool_type,type,
    fun_fu1255657237l_bool: $tType ).

thf(fun_fu701319549l_bool_type,type,
    fun_fu701319549l_bool: $tType ).

thf(fun_fu1393819981l_bool_type,type,
    fun_fu1393819981l_bool: $tType ).

thf(fun_fu1465670113l_bool_type,type,
    fun_fu1465670113l_bool: $tType ).

thf(fun_fu429484960t_bool_type,type,
    fun_fu429484960t_bool: $tType ).

thf(fun_fu1531935961l_bool_type,type,
    fun_fu1531935961l_bool: $tType ).

thf(fun_fu1311768765l_bool_type,type,
    fun_fu1311768765l_bool: $tType ).

thf(fun_fu1395443509l_bool_type,type,
    fun_fu1395443509l_bool: $tType ).

thf(fun_fu497048781l_bool_type,type,
    fun_fu497048781l_bool: $tType ).

thf(fun_fu752049205l_bool_type,type,
    fun_fu752049205l_bool: $tType ).

thf(fun_fu1196098339l_bool_type,type,
    fun_fu1196098339l_bool: $tType ).

thf(fun_fu1337686655l_bool_type,type,
    fun_fu1337686655l_bool: $tType ).

thf(fun_fu572324631l_bool_type,type,
    fun_fu572324631l_bool: $tType ).

thf(fun_fu853181919t_bool_type,type,
    fun_fu853181919t_bool: $tType ).

thf(fun_fu1156700085l_bool_type,type,
    fun_fu1156700085l_bool: $tType ).

thf(fun_fu1470034170i_bool_type,type,
    fun_fu1470034170i_bool: $tType ).

thf(fun_fu1500933005l_bool_type,type,
    fun_fu1500933005l_bool: $tType ).

thf(fun_fu425979586l_bool_type,type,
    fun_fu425979586l_bool: $tType ).

thf(fun_fu1692311659t_bool_type,type,
    fun_fu1692311659t_bool: $tType ).

thf(fun_fu821463397t_bool_type,type,
    fun_fu821463397t_bool: $tType ).

thf(fun_fu2104074051l_bool_type,type,
    fun_fu2104074051l_bool: $tType ).

thf(fun_fu429110920t_bool_type,type,
    fun_fu429110920t_bool: $tType ).

thf(fun_fu1217155507l_bool_type,type,
    fun_fu1217155507l_bool: $tType ).

thf(fun_fu1436348701l_bool_type,type,
    fun_fu1436348701l_bool: $tType ).

thf(fun_fun_nat_nat_bool_type,type,
    fun_fun_nat_nat_bool: $tType ).

thf(fun_fu717290361t_bool_type,type,
    fun_fu717290361t_bool: $tType ).

thf(fun_fu1585362869l_bool_type,type,
    fun_fu1585362869l_bool: $tType ).

thf(fun_fu1988302005l_bool_type,type,
    fun_fu1988302005l_bool: $tType ).

thf(fun_fu1771765432t_bool_type,type,
    fun_fu1771765432t_bool: $tType ).

thf(fun_fu1028680969l_bool_type,type,
    fun_fu1028680969l_bool: $tType ).

thf(fun_fu1733046955t_bool_type,type,
    fun_fu1733046955t_bool: $tType ).

thf(fun_fu522653757at_nat_type,type,
    fun_fu522653757at_nat: $tType ).

thf(fun_fu80187629t_bool_type,type,
    fun_fu80187629t_bool: $tType ).

thf(fun_fu309829899l_bool_type,type,
    fun_fu309829899l_bool: $tType ).

thf(fun_fu391017725t_bool_type,type,
    fun_fu391017725t_bool: $tType ).

thf(fun_fu43485241l_bool_type,type,
    fun_fu43485241l_bool: $tType ).

thf(fun_fu1108851754t_bool_type,type,
    fun_fu1108851754t_bool: $tType ).

thf(fun_fu486305773l_bool_type,type,
    fun_fu486305773l_bool: $tType ).

thf(fun_fu176691123l_bool_type,type,
    fun_fu176691123l_bool: $tType ).

thf(fun_fu166516917l_bool_type,type,
    fun_fu166516917l_bool: $tType ).

thf(fun_fu38582723l_bool_type,type,
    fun_fu38582723l_bool: $tType ).

thf(fun_fu1208702901l_bool_type,type,
    fun_fu1208702901l_bool: $tType ).

thf(fun_fu363747255t_bool_type,type,
    fun_fu363747255t_bool: $tType ).

thf(fun_fu829220361l_bool_type,type,
    fun_fu829220361l_bool: $tType ).

thf(fun_fu1969848875l_bool_type,type,
    fun_fu1969848875l_bool: $tType ).

thf(fun_fu209254101t_bool_type,type,
    fun_fu209254101t_bool: $tType ).

thf(fun_fu662844725l_bool_type,type,
    fun_fu662844725l_bool: $tType ).

thf(fun_fu1737725662l_bool_type,type,
    fun_fu1737725662l_bool: $tType ).

thf(fun_fu1675261879l_bool_type,type,
    fun_fu1675261879l_bool: $tType ).

thf(fun_fu350452167l_bool_type,type,
    fun_fu350452167l_bool: $tType ).

thf(fun_fu887487221i_bool_type,type,
    fun_fu887487221i_bool: $tType ).

thf(fun_fu1227713461l_bool_type,type,
    fun_fu1227713461l_bool: $tType ).

thf(fun_fu614742333l_bool_type,type,
    fun_fu614742333l_bool: $tType ).

thf(fun_fu694861565l_bool_type,type,
    fun_fu694861565l_bool: $tType ).

thf(fun_fu1420978973l_bool_type,type,
    fun_fu1420978973l_bool: $tType ).

thf(fun_fu81176373l_bool_type,type,
    fun_fu81176373l_bool: $tType ).

thf(fun_fu1355931153l_bool_type,type,
    fun_fu1355931153l_bool: $tType ).

thf(fun_fu1386428467t_bool_type,type,
    fun_fu1386428467t_bool: $tType ).

thf(fun_fu1166948533l_bool_type,type,
    fun_fu1166948533l_bool: $tType ).

thf(fun_fu1444789715l_bool_type,type,
    fun_fu1444789715l_bool: $tType ).

thf(fun_fu1596339983e_indi_type,type,
    fun_fu1596339983e_indi: $tType ).

thf(fun_fu1138137687l_bool_type,type,
    fun_fu1138137687l_bool: $tType ).

thf(fun_fu1193945677t_unit_type,type,
    fun_fu1193945677t_unit: $tType ).

thf(fun_fu2127564915i_bool_type,type,
    fun_fu2127564915i_bool: $tType ).

thf(fun_fu1460706235l_bool_type,type,
    fun_fu1460706235l_bool: $tType ).

thf(fun_fu327311537t_bool_type,type,
    fun_fu327311537t_bool: $tType ).

thf(fun_fu446267975l_bool_type,type,
    fun_fu446267975l_bool: $tType ).

thf(fun_fu633681369l_bool_type,type,
    fun_fu633681369l_bool: $tType ).

thf(fun_fu1392295702l_bool_type,type,
    fun_fu1392295702l_bool: $tType ).

thf(fun_fu2017950079l_bool_type,type,
    fun_fu2017950079l_bool: $tType ).

thf(fun_fu2090861455l_bool_type,type,
    fun_fu2090861455l_bool: $tType ).

thf(fun_fu2066072949l_bool_type,type,
    fun_fu2066072949l_bool: $tType ).

thf(fun_fu1023291297l_bool_type,type,
    fun_fu1023291297l_bool: $tType ).

thf(fun_fu1175033968l_bool_type,type,
    fun_fu1175033968l_bool: $tType ).

thf(fun_fu814369080l_bool_type,type,
    fun_fu814369080l_bool: $tType ).

thf(fun_fu1262361717l_bool_type,type,
    fun_fu1262361717l_bool: $tType ).

thf(fun_fu797415470l_bool_type,type,
    fun_fu797415470l_bool: $tType ).

thf(fun_fu599651488l_bool_type,type,
    fun_fu599651488l_bool: $tType ).

thf(fun_fu1804102517l_bool_type,type,
    fun_fu1804102517l_bool: $tType ).

thf(fun_fu79182725l_bool_type,type,
    fun_fu79182725l_bool: $tType ).

thf(fun_fu660051455l_bool_type,type,
    fun_fu660051455l_bool: $tType ).

thf(fun_fu2018671511l_bool_type,type,
    fun_fu2018671511l_bool: $tType ).

thf(fun_fu1936649911l_bool_type,type,
    fun_fu1936649911l_bool: $tType ).

thf(fun_fu117797375l_bool_type,type,
    fun_fu117797375l_bool: $tType ).

thf(fun_fu928599029l_bool_type,type,
    fun_fu928599029l_bool: $tType ).

thf(fun_fu1480005125i_bool_type,type,
    fun_fu1480005125i_bool: $tType ).

thf(fun_fu1739677877l_bool_type,type,
    fun_fu1739677877l_bool: $tType ).

thf(fun_fu1378577485l_bool_type,type,
    fun_fu1378577485l_bool: $tType ).

thf(fun_fu1687768061l_bool_type,type,
    fun_fu1687768061l_bool: $tType ).

thf(fun_fu385975869l_bool_type,type,
    fun_fu385975869l_bool: $tType ).

thf(fun_fu413400117l_bool_type,type,
    fun_fu413400117l_bool: $tType ).

thf(fun_fu829635395t_bool_type,type,
    fun_fu829635395t_bool: $tType ).

thf(fun_fu804386741l_bool_type,type,
    fun_fu804386741l_bool: $tType ).

thf(fun_fu1389232563l_bool_type,type,
    fun_fu1389232563l_bool: $tType ).

thf(fun_fu2038151111l_bool_type,type,
    fun_fu2038151111l_bool: $tType ).

thf(fun_fu211637007l_bool_type,type,
    fun_fu211637007l_bool: $tType ).

thf(fun_fu1106246917l_bool_type,type,
    fun_fu1106246917l_bool: $tType ).

thf(fun_fu1669219279l_bool_type,type,
    fun_fu1669219279l_bool: $tType ).

thf(fun_fu1681173271l_bool_type,type,
    fun_fu1681173271l_bool: $tType ).

thf(fun_fu1656765709l_bool_type,type,
    fun_fu1656765709l_bool: $tType ).

thf(fun_fu976270783l_bool_type,type,
    fun_fu976270783l_bool: $tType ).

thf(fun_fu2088415961l_bool_type,type,
    fun_fu2088415961l_bool: $tType ).

thf(fun_fu790078681i_bool_type,type,
    fun_fu790078681i_bool: $tType ).

thf(fun_fu1041166411l_bool_type,type,
    fun_fu1041166411l_bool: $tType ).

thf(fun_fu705370401l_bool_type,type,
    fun_fu705370401l_bool: $tType ).

thf(fun_fu279877163l_bool_type,type,
    fun_fu279877163l_bool: $tType ).

thf(fun_fu16872987l_bool_type,type,
    fun_fu16872987l_bool: $tType ).

thf(fun_fu830715227l_bool_type,type,
    fun_fu830715227l_bool: $tType ).

thf(fun_fu1216534899l_bool_type,type,
    fun_fu1216534899l_bool: $tType ).

thf(fun_fu1155544867l_bool_type,type,
    fun_fu1155544867l_bool: $tType ).

thf(fun_fu545713175t_bool_type,type,
    fun_fu545713175t_bool: $tType ).

thf(fun_fu978460487l_bool_type,type,
    fun_fu978460487l_bool: $tType ).

thf(fun_fu1916585161l_bool_type,type,
    fun_fu1916585161l_bool: $tType ).

thf(fun_fu675160875l_bool_type,type,
    fun_fu675160875l_bool: $tType ).

thf(fun_fu1697657963l_bool_type,type,
    fun_fu1697657963l_bool: $tType ).

thf(fun_fu1616760087l_bool_type,type,
    fun_fu1616760087l_bool: $tType ).

thf(fun_fu83070487i_bool_type,type,
    fun_fu83070487i_bool: $tType ).

thf(fun_fu1286543157l_bool_type,type,
    fun_fu1286543157l_bool: $tType ).

thf(fun_fu2016509975e_indi_type,type,
    fun_fu2016509975e_indi: $tType ).

thf(fun_fu1015689055l_bool_type,type,
    fun_fu1015689055l_bool: $tType ).

thf(fun_fu603957077t_unit_type,type,
    fun_fu603957077t_unit: $tType ).

thf(fun_fu1540265814t_bool_type,type,
    fun_fu1540265814t_bool: $tType ).

thf(fun_fu157004749t_bool_type,type,
    fun_fu157004749t_bool: $tType ).

thf(fun_fu699199419t_bool_type,type,
    fun_fu699199419t_bool: $tType ).

thf(fun_fu1628463836t_bool_type,type,
    fun_fu1628463836t_bool: $tType ).

thf(fun_fu1766473067i_bool_type,type,
    fun_fu1766473067i_bool: $tType ).

thf(fun_fu1902045723t_bool_type,type,
    fun_fu1902045723t_bool: $tType ).

thf(fun_fu243393031t_bool_type,type,
    fun_fu243393031t_bool: $tType ).

thf(fun_fu44268723l_bool_type,type,
    fun_fu44268723l_bool: $tType ).

thf(fun_fu831091903t_bool_type,type,
    fun_fu831091903t_bool: $tType ).

thf(fun_fu105994665t_bool_type,type,
    fun_fu105994665t_bool: $tType ).

thf(fun_fu1583538011l_bool_type,type,
    fun_fu1583538011l_bool: $tType ).

thf(fun_fu1556412341l_bool_type,type,
    fun_fu1556412341l_bool: $tType ).

thf(fun_fu1515494241l_bool_type,type,
    fun_fu1515494241l_bool: $tType ).

thf(fun_fu1324073361t_bool_type,type,
    fun_fu1324073361t_bool: $tType ).

thf(fun_fu962221693t_bool_type,type,
    fun_fu962221693t_bool: $tType ).

thf(fun_fu1367017557t_bool_type,type,
    fun_fu1367017557t_bool: $tType ).

thf(fun_fu638047541l_bool_type,type,
    fun_fu638047541l_bool: $tType ).

thf(fun_fu528877839t_bool_type,type,
    fun_fu528877839t_bool: $tType ).

thf(fun_Pr1698894881e_indi_type,type,
    fun_Pr1698894881e_indi: $tType ).

thf(fun_Pr1055212137t_bool_type,type,
    fun_Pr1055212137t_bool: $tType ).

thf(fun_Pr215145567t_unit_type,type,
    fun_Pr215145567t_unit: $tType ).

thf(fun_Pr39488737i_bool_type,type,
    fun_Pr39488737i_bool: $tType ).

thf(fun_Pr359894313l_bool_type,type,
    fun_Pr359894313l_bool: $tType ).

thf(fun_Pr1907279903t_bool_type,type,
    fun_Pr1907279903t_bool: $tType ).

thf(fun_Pr1228236907l_bool_type,type,
    fun_Pr1228236907l_bool: $tType ).

thf(produc1840315303le_alt_type,type,
    produc1840315303le_alt: $tType ).

thf(arrow_888693696le_IIA_type,type,
    arrow_888693696le_IIA: fun_fu1138137687l_bool ).

thf(arrow_915577424le_Lin_type,type,
    arrow_915577424le_Lin: fun_fu1015689055l_bool ).

thf(arrow_1190054106e_Prof_type,type,
    arrow_1190054106e_Prof: fun_fu775006535l_bool ).

thf(arrow_1475523868_above_type,type,
    arrow_1475523868_above: fun_fu699199419t_bool ).

thf(arrow_636638768_below_type,type,
    arrow_636638768_below: fun_Pr1055212137t_bool > arrow_931160158le_alt > arrow_931160158le_alt > fun_Pr1055212137t_bool ).

thf(arrow_1472924909ctator_type,type,
    arrow_1472924909ctator: fun_fu2127564915i_bool ).

thf(arrow_592884904_mkbot_type,type,
    arrow_592884904_mkbot: fun_fu1628463836t_bool ).

thf(arrow_741591990_mktop_type,type,
    arrow_741591990_mktop: fun_fu1628463836t_bool ).

thf(arrow_22284131nimity_type,type,
    arrow_22284131nimity: fun_fu1138137687l_bool ).

thf(cOMBB_1015721476ol_nat_type,type,
    cOMBB_1015721476ol_nat: fun_bo1549164019l_bool > fun_fu2104074051l_bool ).

thf(cOMBB_231886989e_indi_type,type,
    cOMBB_231886989e_indi: fun_bo462718181t_bool > fun_fu2115718429t_bool ).

thf(cOMBB_981137617e_indi_type,type,
    cOMBB_981137617e_indi: fun_nat_fun_nat_bool > fun_fu1845850437t_bool ).

thf(cOMBB_800536526ol_nat_type,type,
    cOMBB_800536526ol_nat: fun_nat_fun_nat_bool > fun_fu717290361t_bool ).

thf(cOMBB_1146692694ol_nat_type,type,
    cOMBB_1146692694ol_nat: fun_na1436237685l_bool > fun_fu1585362869l_bool ).

thf(cOMBB_1430402568le_alt_type,type,
    cOMBB_1430402568le_alt: fun_fu709917073t_bool > fun_fu334859135t_bool ).

thf(cOMBB_1605735744le_alt_type,type,
    cOMBB_1605735744le_alt: fun_fu1476972377l_bool > fun_fu960970567l_bool ).

thf(cOMBB_656639247e_indi_type,type,
    cOMBB_656639247e_indi: fun_fu699199419t_bool > fun_fu757621293t_bool ).

thf(cOMBB_117136048e_indi_type,type,
    cOMBB_117136048e_indi: fun_fu1628463836t_bool > fun_fu1872020686t_bool ).

thf(cOMBB_480104238le_alt_type,type,
    cOMBB_480104238le_alt: fun_Pr1228236907l_bool > fun_fu1476972377l_bool ).

thf(cOMBC_571858149l_bool_type,type,
    cOMBC_571858149l_bool: fun_fu709917073t_bool ).

thf(cOMBC_1947566172t_bool_type,type,
    cOMBC_1947566172t_bool: fun_fu1498496639t_bool ).

thf(cOMBC_1505804284t_bool_type,type,
    cOMBC_1505804284t_bool: fun_fu209106563t_bool ).

thf(cOMBC_18834461t_bool_type,type,
    cOMBC_18834461t_bool: fun_fu613599045t_bool ).

thf(cOMBC_922322901t_bool_type,type,
    cOMBC_922322901t_bool: fun_fu954933197i_bool ).

thf(cOMBC_31215906l_bool_type,type,
    cOMBC_31215906l_bool: fun_fu1380565427i_bool ).

thf(cOMBC_1190055014t_bool_type,type,
    cOMBC_1190055014t_bool: fun_fu51155629t_bool ).

thf(cOMBC_1490589522t_bool_type,type,
    cOMBC_1490589522t_bool: fun_fu2117817733t_bool ).

thf(cOMBC_1455277858l_bool_type,type,
    cOMBC_1455277858l_bool: fun_fu1196098339l_bool ).

thf(cOMBC_nat_nat_bool_type,type,
    cOMBC_nat_nat_bool: fun_fu1733046955t_bool ).

thf(cOMBC_nat_nat_nat_type,type,
    cOMBC_nat_nat_nat: fun_fu522653757at_nat ).

thf(cOMBC_226598744l_bool_type,type,
    cOMBC_226598744l_bool: fun_fu80187629t_bool ).

thf(cOMBC_2133163426l_bool_type,type,
    cOMBC_2133163426l_bool: fun_fu363747255t_bool ).

thf(cOMBC_941833506l_bool_type,type,
    cOMBC_941833506l_bool: fun_fu1444789715l_bool ).

thf(cOMBC_1452216610l_bool_type,type,
    cOMBC_1452216610l_bool: fun_fu1389232563l_bool ).

thf(cOMBC_437066390l_bool_type,type,
    cOMBC_437066390l_bool: fun_fu1697657963l_bool ).

thf(cOMBC_697226658l_bool_type,type,
    cOMBC_697226658l_bool: fun_fu528877839t_bool ).

thf(cOMBI_nat_type,type,
    cOMBI_nat: fun_nat_nat ).

thf(cOMBK_1820189998e_indi_type,type,
    cOMBK_1820189998e_indi: fun_bo353189547i_bool ).

thf(cOMBK_bool_nat_type,type,
    cOMBK_bool_nat: fun_bo1570548802t_bool ).

thf(cOMBK_790042732t_unit_type,type,
    cOMBK_790042732t_unit: fun_bo1300789993t_bool ).

thf(cOMBK_670822686t_bool_type,type,
    cOMBK_670822686t_bool: fun_bo645734555l_bool ).

thf(cOMBK_759924014t_bool_type,type,
    cOMBK_759924014t_bool: fun_bo979888811l_bool ).

thf(cOMBK_1216274064t_bool_type,type,
    cOMBK_1216274064t_bool: fun_bo96602657l_bool ).

thf(cOMBK_1566242880le_alt_type,type,
    cOMBK_1566242880le_alt: fun_bo1116297149t_bool ).

thf(cOMBK_854051296t_bool_type,type,
    cOMBK_854051296t_bool: fun_fu536674321i_bool ).

thf(cOMBK_1506144056le_alt_type,type,
    cOMBK_1506144056le_alt: fun_fu1465670113l_bool ).

thf(cOMBK_2091851729e_indi_type,type,
    cOMBK_2091851729e_indi: fun_fu1692311659t_bool ).

thf(cOMBK_583454926ol_nat_type,type,
    cOMBK_583454926ol_nat: fun_fu429110920t_bool ).

thf(cOMBK_2140692976t_bool_type,type,
    cOMBK_2140692976t_bool: fun_fu1355931153l_bool ).

thf(cOMBK_1595020336e_indi_type,type,
    cOMBK_1595020336e_indi: fun_fu279877163l_bool ).

thf(cOMBK_1446432t_bool_type,type,
    cOMBK_1446432t_bool: fun_fu16872987l_bool ).

thf(cOMBK_1522533360e_indi_type,type,
    cOMBK_1522533360e_indi: fun_fu243393031t_bool ).

thf(cOMBK_382434616l_bool_type,type,
    cOMBK_382434616l_bool: fun_fu831091903t_bool ).

thf(cOMBS_811328630t_bool_type,type,
    cOMBS_811328630t_bool: fun_Ar1519997101t_bool > fun_Ar500372357t_bool > fun_Ar1492469401t_bool ).

thf(cOMBS_1921392482t_bool_type,type,
    cOMBS_1921392482t_bool: fun_Ar1492469401t_bool > fun_Ar500372357t_bool > fun_Ar500372357t_bool ).

thf(cOMBS_nat_bool_bool_type,type,
    cOMBS_nat_bool_bool: fun_na1469252690l_bool > fun_nat_bool > fun_nat_bool ).

thf(finite783399747e_indi_type,type,
    finite783399747e_indi: fun_Ar552120407i_bool > nat ).

thf(finite_card_bool_type,type,
    finite_card_bool: fun_bool_bool > nat ).

thf(finite_card_nat_type,type,
    finite_card_nat: fun_nat_bool > nat ).

thf(finite1949902593t_unit_type,type,
    finite1949902593t_unit: fun_Pr1643180309t_bool > nat ).

thf(finite1418900531t_bool_type,type,
    finite1418900531t_bool: fun_fu775006535l_bool > nat ).

thf(finite1445836347t_bool_type,type,
    finite1445836347t_bool: fun_fu1015689055l_bool > nat ).

thf(finite876838485le_alt_type,type,
    finite876838485le_alt: fun_Pr1055212137t_bool > nat ).

thf(finite1350902018e_indi_type,type,
    finite1350902018e_indi: fun_fu1657302605l_bool ).

thf(finite_finite_bool_type,type,
    finite_finite_bool: fun_fu1255657237l_bool ).

thf(finite_finite_nat_type,type,
    finite_finite_nat: fun_fu425979586l_bool ).

thf(finite1217814770t_bool_type,type,
    finite1217814770t_bool: fun_fu614742333l_bool ).

thf(finite775027132t_bool_type,type,
    finite775027132t_bool: fun_fu705370401l_bool ).

thf(finite788329492le_alt_type,type,
    finite788329492le_alt: fun_fu1015689055l_bool ).

thf(in_rel267123714le_alt_type,type,
    in_rel267123714le_alt: fun_Pr1055212137t_bool > arrow_931160158le_alt > arrow_931160158le_alt > bool ).

thf(inj_on886403158di_nat_type,type,
    inj_on886403158di_nat: fun_Ar1744566822di_nat > fun_fu1657302605l_bool ).

thf(inj_on194063285t_bool_type,type,
    inj_on194063285t_bool: fun_Ar500372357t_bool > fun_fu1657302605l_bool ).

thf(inj_on2047198755le_alt_type,type,
    inj_on2047198755le_alt: fun_bo1479727337le_alt > fun_fu1255657237l_bool ).

thf(inj_on_nat_nat_type,type,
    inj_on_nat_nat: fun_nat_nat > fun_fu425979586l_bool ).

thf(inj_on937360581t_bool_type,type,
    inj_on937360581t_bool: fun_fu1595299477t_bool > fun_fu614742333l_bool ).

thf(inj_on1048829645e_indi_type,type,
    inj_on1048829645e_indi: fun_fu2016509975e_indi > fun_fu705370401l_bool ).

thf(inj_on456593853t_bool_type,type,
    inj_on456593853t_bool: fun_fu243393031t_bool > fun_fu705370401l_bool ).

thf(inj_on899118883t_bool_type,type,
    inj_on899118883t_bool: fun_Pr1055212137t_bool > fun_fu1015689055l_bool ).

thf(pi_Arr159321468di_nat_type,type,
    pi_Arr159321468di_nat: fun_Ar552120407i_bool > fun_Ar2045874810t_bool > fun_fu192249448t_bool ).

thf(pi_Arr1376550035t_bool_type,type,
    pi_Arr1376550035t_bool: fun_Ar552120407i_bool > fun_Ar684516451l_bool > fun_fu1131021301l_bool ).

thf(pi_Arr353983907t_bool_type,type,
    pi_Arr353983907t_bool: fun_Ar552120407i_bool > fun_Ar1270429299l_bool > fun_fu1944573957l_bool ).

thf(pi_Arr487970267t_bool_type,type,
    pi_Arr487970267t_bool: fun_Ar552120407i_bool > fun_Ar1198543961l_bool > fun_fu775006535l_bool ).

thf(pi_Arr914482869le_alt_type,type,
    pi_Arr914482869le_alt: fun_Ar552120407i_bool > fun_Ar500372357t_bool > fun_fu2073792791t_bool ).

thf(pi_bool_nat_type,type,
    pi_bool_nat: fun_bool_bool > fun_bo1570548802t_bool > fun_fu429484960t_bool ).

thf(pi_boo573599835t_bool_type,type,
    pi_boo573599835t_bool: fun_bool_bool > fun_bo645734555l_bool > fun_fu1311768765l_bool ).

thf(pi_boo250534251t_bool_type,type,
    pi_boo250534251t_bool: fun_bool_bool > fun_bo979888811l_bool > fun_fu497048781l_bool ).

thf(pi_boo98824211t_bool_type,type,
    pi_boo98824211t_bool: fun_bool_bool > fun_bo96602657l_bool > fun_fu1337686655l_bool ).

thf(pi_boo1374671485le_alt_type,type,
    pi_boo1374671485le_alt: fun_bool_bool > fun_bo1116297149t_bool > fun_fu853181919t_bool ).

thf(pi_nat1905227924e_indi_type,type,
    pi_nat1905227924e_indi: fun_nat_bool > fun_na457272970i_bool > fun_fu1470034170i_bool ).

thf(pi_nat_bool_type,type,
    pi_nat_bool: fun_nat_bool > fun_na1469252690l_bool > fun_fu425979586l_bool ).

thf(pi_nat_nat_type,type,
    pi_nat_nat: fun_nat_bool > fun_nat_fun_nat_bool > fun_fun_nat_nat_bool ).

thf(pi_nat_Product_unit_type,type,
    pi_nat_Product_unit: fun_nat_bool > fun_na1041622088t_bool > fun_fu1771765432t_bool ).

thf(pi_Product_unit_nat_type,type,
    pi_Product_unit_nat: fun_Pr1643180309t_bool > fun_Pr1029464120t_bool > fun_fu1108851754t_bool ).

thf(pi_Pro1008448593t_bool_type,type,
    pi_Pro1008448593t_bool: fun_Pr1643180309t_bool > fun_Pr1223320869l_bool > fun_fu176691123l_bool ).

thf(pi_Pro1014195041t_bool_type,type,
    pi_Pro1014195041t_bool: fun_Pr1643180309t_bool > fun_Pr1832937781l_bool > fun_fu38582723l_bool ).

thf(pi_Pro278326941t_bool_type,type,
    pi_Pro278326941t_bool: fun_Pr1643180309t_bool > fun_Pr1510236951l_bool > fun_fu829220361l_bool ).

thf(pi_Pro1041002611le_alt_type,type,
    pi_Pro1041002611le_alt: fun_Pr1643180309t_bool > fun_Pr1572389447t_bool > fun_fu209254101t_bool ).

thf(pi_fun64467091e_indi_type,type,
    pi_fun64467091e_indi: fun_fu775006535l_bool > fun_fu1765260675i_bool > fun_fu887487221i_bool ).

thf(pi_fun1624909403l_bool_type,type,
    pi_fun1624909403l_bool: fun_fu775006535l_bool > fun_fu1471766731l_bool > fun_fu614742333l_bool ).

thf(pi_fun1455727697t_unit_type,type,
    pi_fun1455727697t_unit: fun_fu775006535l_bool > fun_fu587068865t_bool > fun_fu1386428467t_bool ).

thf(pi_fun530160875t_bool_type,type,
    pi_fun530160875t_bool: fun_fu775006535l_bool > fun_fu787660105l_bool > fun_fu1138137687l_bool ).

thf(pi_fun1073350051e_indi_type,type,
    pi_fun1073350051e_indi: fun_fu1138137687l_bool > fun_fu2127564915i_bool > fun_fu1480005125i_bool ).

thf(pi_fun351900523l_bool_type,type,
    pi_fun351900523l_bool: fun_fu1138137687l_bool > fun_fu1460706235l_bool > fun_fu1378577485l_bool ).

thf(pi_fun1254023521t_unit_type,type,
    pi_fun1254023521t_unit: fun_fu1138137687l_bool > fun_fu327311537t_bool > fun_fu829635395t_bool ).

thf(pi_fun1342736627e_indi_type,type,
    pi_fun1342736627e_indi: fun_fu1015689055l_bool > fun_fu1766473067i_bool > fun_fu790078681i_bool ).

thf(pi_fun1412468411l_bool_type,type,
    pi_fun1412468411l_bool: fun_fu1015689055l_bool > fun_fu44268723l_bool > fun_fu705370401l_bool ).

thf(pi_fun116255921t_unit_type,type,
    pi_fun116255921t_unit: fun_fu1015689055l_bool > fun_fu105994665t_bool > fun_fu545713175t_bool ).

thf(pi_fun49394147t_bool_type,type,
    pi_fun49394147t_bool: fun_fu1015689055l_bool > fun_fu1583538011l_bool > fun_fu1916585161l_bool ).

thf(pi_Pro1592011445e_indi_type,type,
    pi_Pro1592011445e_indi: fun_Pr1055212137t_bool > fun_Pr39488737i_bool > fun_fu83070487i_bool ).

thf(pi_Pro226591613t_bool_type,type,
    pi_Pro226591613t_bool: fun_Pr1055212137t_bool > fun_Pr359894313l_bool > fun_fu1015689055l_bool ).

thf(pi_Pro185129843t_unit_type,type,
    pi_Pro185129843t_unit: fun_Pr1055212137t_bool > fun_Pr1907279903t_bool > fun_fu1367017557t_bool ).

thf(one_one_nat_type,type,
    one_one_nat: nat ).

thf(plus_plus_nat_type,type,
    plus_plus_nat: fun_nat_fun_nat_nat ).

thf(zero_zero_nat_type,type,
    zero_zero_nat: nat ).

thf(hilber506087739di_nat_type,type,
    hilber506087739di_nat: fun_Ar552120407i_bool > fun_Ar1744566822di_nat > fun_na1392860600e_indi ).

thf(hilber195283148at_nat_type,type,
    hilber195283148at_nat: fun_nat_bool > fun_nat_nat > fun_nat_nat ).

thf(if_fun1658569689t_bool_type,type,
    if_fun1658569689t_bool: fun_bo462718181t_bool ).

thf(suc_type,type,
    suc: fun_nat_nat ).

thf(ord_less_bool_type,type,
    ord_less_bool: fun_bo1549164019l_bool ).

thf(ord_less_nat_type,type,
    ord_less_nat: fun_nat_fun_nat_bool ).

thf(ord_le1115695277i_bool_type,type,
    ord_le1115695277i_bool: fun_fu1310412861l_bool ).

thf(ord_le197158773l_bool_type,type,
    ord_le197158773l_bool: fun_fu1393819981l_bool ).

thf(ord_le382113706t_bool_type,type,
    ord_le382113706t_bool: fun_fu1217155507l_bool ).

thf(ord_le1976645739t_bool_type,type,
    ord_le1976645739t_bool: fun_fu43485241l_bool ).

thf(ord_le583255965l_bool_type,type,
    ord_le583255965l_bool: fun_fu1420978973l_bool ).

thf(ord_le1306091181l_bool_type,type,
    ord_le1306091181l_bool: fun_fu385975869l_bool ).

thf(ord_le2104736649l_bool_type,type,
    ord_le2104736649l_bool: fun_fu1216534899l_bool ).

thf(ord_le466311871t_bool_type,type,
    ord_le466311871t_bool: fun_fu1515494241l_bool ).

thf(ord_less_eq_bool_type,type,
    ord_less_eq_bool: fun_bo1549164019l_bool ).

thf(ord_less_eq_nat_type,type,
    ord_less_eq_nat: fun_nat_fun_nat_bool ).

thf(ord_le1254553345t_bool_type,type,
    ord_le1254553345t_bool: fun_fu304639347l_bool ).

thf(ord_le351904673i_bool_type,type,
    ord_le351904673i_bool: fun_fu1310412861l_bool ).

thf(ord_le742797417l_bool_type,type,
    ord_le742797417l_bool: fun_fu1393819981l_bool ).

thf(ord_le1568362934t_bool_type,type,
    ord_le1568362934t_bool: fun_fu1217155507l_bool ).

thf(ord_le1874503007t_bool_type,type,
    ord_le1874503007t_bool: fun_fu43485241l_bool ).

thf(ord_le1871091345l_bool_type,type,
    ord_le1871091345l_bool: fun_fu1420978973l_bool ).

thf(ord_le161055137l_bool_type,type,
    ord_le161055137l_bool: fun_fu385975869l_bool ).

thf(ord_le1923264405l_bool_type,type,
    ord_le1923264405l_bool: fun_fu1216534899l_bool ).

thf(ord_le565024179t_bool_type,type,
    ord_le565024179t_bool: fun_fu1515494241l_bool ).

thf(top_top_bool_type,type,
    top_top_bool: bool ).

thf(top_to1678393681i_bool_type,type,
    top_to1678393681i_bool: fun_Ar552120407i_bool ).

thf(top_to1647826457l_bool_type,type,
    top_to1647826457l_bool: fun_bool_bool ).

thf(top_top_fun_nat_bool_type,type,
    top_top_fun_nat_bool: fun_nat_bool ).

thf(top_to1257323279t_bool_type,type,
    top_to1257323279t_bool: fun_Pr1643180309t_bool ).

thf(top_to1324311617l_bool_type,type,
    top_to1324311617l_bool: fun_fu775006535l_bool ).

thf(top_to2013953873l_bool_type,type,
    top_to2013953873l_bool: fun_fu1138137687l_bool ).

thf(top_to1690334693l_bool_type,type,
    top_to1690334693l_bool: fun_fu1015689055l_bool ).

thf(top_to126038883t_bool_type,type,
    top_to126038883t_bool: fun_Pr1055212137t_bool ).

thf(produc362059031le_alt_type,type,
    produc362059031le_alt: fun_Ar2049444117le_alt ).

thf(ord_at4362885an_nat_type,type,
    ord_at4362885an_nat: nat > fun_nat_fun_nat_bool ).

thf(collec708328256e_indi_type,type,
    collec708328256e_indi: fun_Ar552120407i_bool > fun_Ar552120407i_bool ).

thf(collect_nat_type,type,
    collect_nat: fun_nat_bool > fun_nat_bool ).

thf(collect_Product_unit_type,type,
    collect_Product_unit: fun_Pr1643180309t_bool > fun_Pr1643180309t_bool ).

thf(collec1461897520t_bool_type,type,
    collec1461897520t_bool: fun_fu775006535l_bool > fun_fu775006535l_bool ).

thf(collec1699798848t_bool_type,type,
    collec1699798848t_bool: fun_fu1138137687l_bool > fun_fu1138137687l_bool ).

thf(collec1113178622t_bool_type,type,
    collec1113178622t_bool: fun_fu1015689055l_bool > fun_fu1015689055l_bool ).

thf(collec1209019986le_alt_type,type,
    collec1209019986le_alt: fun_Pr1055212137t_bool > fun_Pr1055212137t_bool ).

thf(image_391852738di_nat_type,type,
    image_391852738di_nat: fun_Ar1744566822di_nat > fun_Ar552120407i_bool > fun_nat_bool ).

thf(fFalse_type,type,
    fFalse: bool ).

thf(fTrue_type,type,
    fTrue: bool ).

thf(fconj_type,type,
    fconj: fun_bo1549164019l_bool ).

thf(fequal_nat_type,type,
    fequal_nat: fun_nat_fun_nat_bool ).

thf(hAPP_A674791462t_bool_type,type,
    hAPP_A674791462t_bool: fun_Ar1091019988t_bool > arrow_931160158le_alt > bool ).

thf(hAPP_A1858212765t_bool_type,type,
    hAPP_A1858212765t_bool: fun_Ar1414184139t_bool > arrow_931160158le_alt > fun_Ar1091019988t_bool ).

thf(hAPP_A1256181151l_bool_type,type,
    hAPP_A1256181151l_bool: fun_Ar1689125069l_bool > arrow_931160158le_alt > fun_Ar1026121174l_bool ).

thf(hAPP_A501825983t_bool_type,type,
    hAPP_A501825983t_bool: fun_Ar1164786343t_bool > arrow_931160158le_alt > fun_Ar1275715144t_bool ).

thf(hAPP_A1485971815le_alt_type,type,
    hAPP_A1485971815le_alt: fun_Ar2049444117le_alt > arrow_931160158le_alt > fun_Ar836847646le_alt ).

thf(hAPP_A102926893t_bool_type,type,
    hAPP_A102926893t_bool: fun_Ar2078312923t_bool > arrow_931160158le_alt > fun_Ar698916836t_bool ).

thf(hAPP_A658738638t_bool_type,type,
    hAPP_A658738638t_bool: fun_Ar421919996t_bool > arrow_931160158le_alt > fun_Ar500372357t_bool ).

thf(hAPP_A1787768616l_bool_type,type,
    hAPP_A1787768616l_bool: fun_Ar1026121174l_bool > arrow_931160158le_alt > fun_fu1015689055l_bool ).

thf(hAPP_A1770325791t_bool_type,type,
    hAPP_A1770325791t_bool: fun_Ar1364097613t_bool > arrow_931160158le_alt > fun_fu1540265814t_bool ).

thf(hAPP_A606737888t_bool_type,type,
    hAPP_A606737888t_bool: fun_Ar1275715144t_bool > arrow_931160158le_alt > fun_Pr1055212137t_bool ).

thf(hAPP_A1313367280le_alt_type,type,
    hAPP_A1313367280le_alt: fun_Ar836847646le_alt > arrow_931160158le_alt > produc1840315303le_alt ).

thf(hAPP_A1888055029i_bool_type,type,
    hAPP_A1888055029i_bool: fun_Ar552120407i_bool > arrow_2115524757e_indi > bool ).

thf(hAPP_A1450069362di_nat_type,type,
    hAPP_A1450069362di_nat: fun_Ar1744566822di_nat > arrow_2115524757e_indi > nat ).

thf(hAPP_A131904271t_bool_type,type,
    hAPP_A131904271t_bool: fun_Ar1583656131t_bool > arrow_2115524757e_indi > fun_Ar1164786343t_bool ).

thf(hAPP_A1020253872t_bool_type,type,
    hAPP_A1020253872t_bool: fun_Ar698916836t_bool > arrow_2115524757e_indi > fun_Ar1275715144t_bool ).

thf(hAPP_A1458779421t_bool_type,type,
    hAPP_A1458779421t_bool: fun_Ar687924991t_bool > arrow_2115524757e_indi > fun_Ar500372357t_bool ).

thf(hAPP_A981395480t_bool_type,type,
    hAPP_A981395480t_bool: fun_Ar2045874810t_bool > arrow_2115524757e_indi > fun_nat_bool ).

thf(hAPP_A605074405l_bool_type,type,
    hAPP_A605074405l_bool: fun_Ar1380772935l_bool > arrow_2115524757e_indi > fun_fu1657302605l_bool ).

thf(hAPP_A182831535l_bool_type,type,
    hAPP_A182831535l_bool: fun_Ar684516451l_bool > arrow_2115524757e_indi > fun_fu775006535l_bool ).

thf(hAPP_A1044336685t_bool_type,type,
    hAPP_A1044336685t_bool: fun_Ar1939863823t_bool > arrow_2115524757e_indi > fun_fu1595299477t_bool ).

thf(hAPP_A1538515647l_bool_type,type,
    hAPP_A1538515647l_bool: fun_Ar1270429299l_bool > arrow_2115524757e_indi > fun_fu1138137687l_bool ).

thf(hAPP_A1279849719l_bool_type,type,
    hAPP_A1279849719l_bool: fun_Ar1198543961l_bool > arrow_2115524757e_indi > fun_fu1015689055l_bool ).

thf(hAPP_A594708985t_bool_type,type,
    hAPP_A594708985t_bool: fun_Ar1519997101t_bool > arrow_2115524757e_indi > fun_fu1324073361t_bool ).

thf(hAPP_A892860133t_bool_type,type,
    hAPP_A892860133t_bool: fun_Ar1492469401t_bool > arrow_2115524757e_indi > fun_fu962221693t_bool ).

thf(hAPP_A1174518481t_bool_type,type,
    hAPP_A1174518481t_bool: fun_Ar500372357t_bool > arrow_2115524757e_indi > fun_Pr1055212137t_bool ).

thf(hAPP_A353813823le_alt_type,type,
    hAPP_A353813823le_alt: fun_Ar369661729le_alt > arrow_2115524757e_indi > produc1840315303le_alt ).

thf(hAPP_bool_bool_type,type,
    hAPP_bool_bool: fun_bool_bool > bool > bool ).

thf(hAPP_bool_nat_type,type,
    hAPP_bool_nat: fun_bool_nat > bool > nat ).

thf(hAPP_b1439777783i_bool_type,type,
    hAPP_b1439777783i_bool: fun_bo353189547i_bool > bool > fun_Ar552120407i_bool ).

thf(hAPP_b715352037t_bool_type,type,
    hAPP_b715352037t_bool: fun_bo266809543t_bool > bool > fun_Ar500372357t_bool ).

thf(hAPP_b589554111l_bool_type,type,
    hAPP_b589554111l_bool: fun_bo1549164019l_bool > bool > fun_bool_bool ).

thf(hAPP_b1013836512t_bool_type,type,
    hAPP_b1013836512t_bool: fun_bo1570548802t_bool > bool > fun_nat_bool ).

thf(hAPP_b1096750261t_bool_type,type,
    hAPP_b1096750261t_bool: fun_bo1300789993t_bool > bool > fun_Pr1643180309t_bool ).

thf(hAPP_b1849744615l_bool_type,type,
    hAPP_b1849744615l_bool: fun_bo645734555l_bool > bool > fun_fu775006535l_bool ).

thf(hAPP_b510135029t_bool_type,type,
    hAPP_b510135029t_bool: fun_bo2027801303t_bool > bool > fun_fu1595299477t_bool ).

thf(hAPP_b1787118453l_bool_type,type,
    hAPP_b1787118453l_bool: fun_bo492988759l_bool > bool > fun_fu1255657237l_bool ).

thf(hAPP_b816606711l_bool_type,type,
    hAPP_b816606711l_bool: fun_bo979888811l_bool > bool > fun_fu1138137687l_bool ).

thf(hAPP_b1650070463l_bool_type,type,
    hAPP_b1650070463l_bool: fun_bo96602657l_bool > bool > fun_fu1015689055l_bool ).

thf(hAPP_b1061655857t_bool_type,type,
    hAPP_b1061655857t_bool: fun_bo462718181t_bool > bool > fun_fu1324073361t_bool ).

thf(hAPP_b1263785481t_bool_type,type,
    hAPP_b1263785481t_bool: fun_bo1116297149t_bool > bool > fun_Pr1055212137t_bool ).

thf(hAPP_b1314516999le_alt_type,type,
    hAPP_b1314516999le_alt: fun_bo1479727337le_alt > bool > produc1840315303le_alt ).

thf(hAPP_n1048492170e_indi_type,type,
    hAPP_n1048492170e_indi: fun_na1392860600e_indi > nat > arrow_2115524757e_indi ).

thf(hAPP_nat_bool_type,type,
    hAPP_nat_bool: fun_nat_bool > nat > bool ).

thf(hAPP_nat_nat_type,type,
    hAPP_nat_nat: fun_nat_nat > nat > nat ).

thf(hAPP_n633340360t_unit_type,type,
    hAPP_n633340360t_unit: fun_nat_Product_unit > nat > product_unit ).

thf(hAPP_n924210722i_bool_type,type,
    hAPP_n924210722i_bool: fun_na457272970i_bool > nat > fun_Ar552120407i_bool ).

thf(hAPP_n1006566506l_bool_type,type,
    hAPP_n1006566506l_bool: fun_na1469252690l_bool > nat > fun_bool_bool ).

thf(hAPP_n1699378549t_bool_type,type,
    hAPP_n1699378549t_bool: fun_nat_fun_nat_bool > nat > fun_nat_bool ).

thf(hAPP_nat_fun_nat_nat_type,type,
    hAPP_nat_fun_nat_nat: fun_nat_fun_nat_nat > nat > fun_nat_nat ).

thf(hAPP_n454528608t_bool_type,type,
    hAPP_n454528608t_bool: fun_na1041622088t_bool > nat > fun_Pr1643180309t_bool ).

thf(hAPP_n215258509l_bool_type,type,
    hAPP_n215258509l_bool: fun_na1436237685l_bool > nat > fun_fu425979586l_bool ).

thf(hAPP_P1676879539t_bool_type,type,
    hAPP_P1676879539t_bool: fun_Pr1643180309t_bool > product_unit > bool ).

thf(hAPP_P426034740it_nat_type,type,
    hAPP_P426034740it_nat: fun_Product_unit_nat > product_unit > nat ).

thf(hAPP_P1139363291t_bool_type,type,
    hAPP_P1139363291t_bool: fun_Pr321980605t_bool > product_unit > fun_Ar500372357t_bool ).

thf(hAPP_P32877782t_bool_type,type,
    hAPP_P32877782t_bool: fun_Pr1029464120t_bool > product_unit > fun_nat_bool ).

thf(hAPP_P1055953777l_bool_type,type,
    hAPP_P1055953777l_bool: fun_Pr1223320869l_bool > product_unit > fun_fu775006535l_bool ).

thf(hAPP_P1339635435t_bool_type,type,
    hAPP_P1339635435t_bool: fun_Pr1337256141t_bool > product_unit > fun_fu1595299477t_bool ).

thf(hAPP_P607165281l_bool_type,type,
    hAPP_P607165281l_bool: fun_Pr1863373635l_bool > product_unit > fun_fu309829899l_bool ).

thf(hAPP_P1470717569l_bool_type,type,
    hAPP_P1470717569l_bool: fun_Pr1832937781l_bool > product_unit > fun_fu1138137687l_bool ).

thf(hAPP_P1132296885l_bool_type,type,
    hAPP_P1132296885l_bool: fun_Pr1510236951l_bool > product_unit > fun_fu1015689055l_bool ).

thf(hAPP_P902017683t_bool_type,type,
    hAPP_P902017683t_bool: fun_Pr1572389447t_bool > product_unit > fun_Pr1055212137t_bool ).

thf(hAPP_P1763651581le_alt_type,type,
    hAPP_P1763651581le_alt: fun_Pr1887046367le_alt > product_unit > produc1840315303le_alt ).

thf(hAPP_f1733046827l_bool_type,type,
    hAPP_f1733046827l_bool: fun_fu853658253l_bool > fun_Ar1414184139t_bool > bool ).

thf(hAPP_f2062231615l_bool_type,type,
    hAPP_f2062231615l_bool: fun_fu304639347l_bool > fun_Ar1414184139t_bool > fun_fu853658253l_bool ).

thf(hAPP_f1435501085t_bool_type,type,
    hAPP_f1435501085t_bool: fun_fu334859135t_bool > fun_Ar1689125069l_bool > fun_Ar1364097613t_bool ).

thf(hAPP_f1176598245l_bool_type,type,
    hAPP_f1176598245l_bool: fun_fu960970567l_bool > fun_Ar2049444117le_alt > fun_Ar1689125069l_bool ).

thf(hAPP_f2087965871t_bool_type,type,
    hAPP_f2087965871t_bool: fun_fu709917073t_bool > fun_Ar1026121174l_bool > fun_fu1540265814t_bool ).

thf(hAPP_f15758621t_bool_type,type,
    hAPP_f15758621t_bool: fun_fu1498496639t_bool > fun_Ar1364097613t_bool > fun_fu157004749t_bool ).

thf(hAPP_f1395387255l_bool_type,type,
    hAPP_f1395387255l_bool: fun_fu1476972377l_bool > fun_Ar836847646le_alt > fun_Ar1026121174l_bool ).

thf(hAPP_f1397511071l_bool_type,type,
    hAPP_f1397511071l_bool: fun_fu1657302605l_bool > fun_Ar552120407i_bool > bool ).

thf(hAPP_f1282576021i_bool_type,type,
    hAPP_f1282576021i_bool: fun_fu1058839037i_bool > fun_Ar552120407i_bool > fun_Ar552120407i_bool ).

thf(hAPP_f509814255t_bool_type,type,
    hAPP_f509814255t_bool: fun_fu2115718429t_bool > fun_Ar552120407i_bool > fun_Ar1519997101t_bool ).

thf(hAPP_f1938592399l_bool_type,type,
    hAPP_f1938592399l_bool: fun_fu1310412861l_bool > fun_Ar552120407i_bool > fun_fu1657302605l_bool ).

thf(hAPP_f676424105i_bool_type,type,
    hAPP_f676424105i_bool: fun_fu536674321i_bool > fun_Ar552120407i_bool > fun_fu1766473067i_bool ).

thf(hAPP_f1381130897t_bool_type,type,
    hAPP_f1381130897t_bool: fun_fu1845850437t_bool > fun_Ar1744566822di_nat > fun_Ar2045874810t_bool ).

thf(hAPP_f516936199l_bool_type,type,
    hAPP_f516936199l_bool: fun_fu85234537l_bool > fun_Ar1744566822di_nat > fun_fu1737725662l_bool ).

thf(hAPP_f141075873t_bool_type,type,
    hAPP_f141075873t_bool: fun_fu209106563t_bool > fun_Ar1583656131t_bool > fun_Ar2078312923t_bool ).

thf(hAPP_f293545699t_bool_type,type,
    hAPP_f293545699t_bool: fun_fu613599045t_bool > fun_Ar698916836t_bool > fun_Ar421919996t_bool ).

thf(hAPP_f162243405l_bool_type,type,
    hAPP_f162243405l_bool: fun_fu1591782325l_bool > fun_Ar687924991t_bool > fun_fu1675261879l_bool ).

thf(hAPP_f62620517i_bool_type,type,
    hAPP_f62620517i_bool: fun_fu954933197i_bool > fun_Ar2045874810t_bool > fun_na457272970i_bool ).

thf(hAPP_f833264203i_bool_type,type,
    hAPP_f833264203i_bool: fun_fu1380565427i_bool > fun_Ar1380772935l_bool > fun_fu1058839037i_bool ).

thf(hAPP_f467714381l_bool_type,type,
    hAPP_f467714381l_bool: fun_fu1816256693l_bool > fun_Ar1939863823t_bool > fun_fu350452167l_bool ).

thf(hAPP_f1328803787t_bool_type,type,
    hAPP_f1328803787t_bool: fun_fu51155629t_bool > fun_Ar1519997101t_bool > fun_fu1902045723t_bool ).

thf(hAPP_f1302245795t_bool_type,type,
    hAPP_f1302245795t_bool: fun_fu2117817733t_bool > fun_Ar1492469401t_bool > fun_fu243393031t_bool ).

thf(hAPP_f146696477e_indi_type,type,
    hAPP_f146696477e_indi: fun_fu908353023e_indi > fun_Ar500372357t_bool > arrow_2115524757e_indi ).

thf(hAPP_f1766661605l_bool_type,type,
    hAPP_f1766661605l_bool: fun_fu775006535l_bool > fun_Ar500372357t_bool > bool ).

thf(hAPP_f1586642395t_unit_type,type,
    hAPP_f1586642395t_unit: fun_fu834038077t_unit > fun_Ar500372357t_bool > product_unit ).

thf(hAPP_f109229519i_bool_type,type,
    hAPP_f109229519i_bool: fun_fu1765260675i_bool > fun_Ar500372357t_bool > fun_Ar552120407i_bool ).

thf(hAPP_f576849227t_bool_type,type,
    hAPP_f576849227t_bool: fun_fu757621293t_bool > fun_Ar500372357t_bool > fun_Ar1583656131t_bool ).

thf(hAPP_f842954860t_bool_type,type,
    hAPP_f842954860t_bool: fun_fu1872020686t_bool > fun_Ar500372357t_bool > fun_Ar698916836t_bool ).

thf(hAPP_f84039575l_bool_type,type,
    hAPP_f84039575l_bool: fun_fu1471766731l_bool > fun_Ar500372357t_bool > fun_bool_bool ).

thf(hAPP_f290914957t_bool_type,type,
    hAPP_f290914957t_bool: fun_fu587068865t_bool > fun_Ar500372357t_bool > fun_Pr1643180309t_bool ).

thf(hAPP_f2029708741l_bool_type,type,
    hAPP_f2029708741l_bool: fun_fu1291054887l_bool > fun_Ar500372357t_bool > fun_fu614742333l_bool ).

thf(hAPP_f1498158055l_bool_type,type,
    hAPP_f1498158055l_bool: fun_fu787660105l_bool > fun_Ar500372357t_bool > fun_fu1015689055l_bool ).

thf(hAPP_f792184801t_bool_type,type,
    hAPP_f792184801t_bool: fun_fu1595299477t_bool > fun_Ar500372357t_bool > fun_Pr1055212137t_bool ).

thf(hAPP_f1269190349l_bool_type,type,
    hAPP_f1269190349l_bool: fun_fu1338365749l_bool > fun_Ar369661729le_alt > fun_fu633681369l_bool ).

thf(hAPP_f387058535l_bool_type,type,
    hAPP_f387058535l_bool: fun_fu1255657237l_bool > fun_bool_bool > bool ).

thf(hAPP_f961197973l_bool_type,type,
    hAPP_f961197973l_bool: fun_fu701319549l_bool > fun_bool_bool > fun_bool_bool ).

thf(hAPP_f612708895l_bool_type,type,
    hAPP_f612708895l_bool: fun_fu1393819981l_bool > fun_bool_bool > fun_fu1255657237l_bool ).

thf(hAPP_f1426772275l_bool_type,type,
    hAPP_f1426772275l_bool: fun_fu1465670113l_bool > fun_bool_bool > fun_Pr359894313l_bool ).

thf(hAPP_f144393719l_bool_type,type,
    hAPP_f144393719l_bool: fun_fu1531935961l_bool > fun_bool_nat > fun_fu1392295702l_bool ).

thf(hAPP_f621492301l_bool_type,type,
    hAPP_f621492301l_bool: fun_fu1395443509l_bool > fun_bo266809543t_bool > fun_fu2017950079l_bool ).

thf(hAPP_f674575949l_bool_type,type,
    hAPP_f674575949l_bool: fun_fu752049205l_bool > fun_bo2027801303t_bool > fun_fu2090861455l_bool ).

thf(hAPP_f1996228283l_bool_type,type,
    hAPP_f1996228283l_bool: fun_fu1196098339l_bool > fun_bo492988759l_bool > fun_fu701319549l_bool ).

thf(hAPP_f134102069l_bool_type,type,
    hAPP_f134102069l_bool: fun_fu572324631l_bool > fun_bo1116297149t_bool > fun_fu2066072949l_bool ).

thf(hAPP_f1862158541l_bool_type,type,
    hAPP_f1862158541l_bool: fun_fu1156700085l_bool > fun_bo1479727337le_alt > fun_fu1023291297l_bool ).

thf(hAPP_f138236715l_bool_type,type,
    hAPP_f138236715l_bool: fun_fu1500933005l_bool > fun_na1392860600e_indi > fun_fu1175033968l_bool ).

thf(hAPP_f54304608l_bool_type,type,
    hAPP_f54304608l_bool: fun_fu425979586l_bool > fun_nat_bool > bool ).

thf(hAPP_f426535095t_bool_type,type,
    hAPP_f426535095t_bool: fun_fu1692311659t_bool > fun_nat_bool > fun_Ar2045874810t_bool ).

thf(hAPP_f800510211t_bool_type,type,
    hAPP_f800510211t_bool: fun_fu821463397t_bool > fun_nat_bool > fun_nat_bool ).

thf(hAPP_f1146629647l_bool_type,type,
    hAPP_f1146629647l_bool: fun_fu2104074051l_bool > fun_nat_bool > fun_na1469252690l_bool ).

thf(hAPP_f1570313510t_bool_type,type,
    hAPP_f1570313510t_bool: fun_fu429110920t_bool > fun_nat_bool > fun_nat_fun_nat_bool ).

thf(hAPP_f103356543l_bool_type,type,
    hAPP_f103356543l_bool: fun_fu1217155507l_bool > fun_nat_bool > fun_fu425979586l_bool ).

thf(hAPP_f1951378235l_bool_type,type,
    hAPP_f1951378235l_bool: fun_fu1436348701l_bool > fun_nat_bool > fun_fu814369080l_bool ).

thf(hAPP_f618557131t_bool_type,type,
    hAPP_f618557131t_bool: fun_fu717290361t_bool > fun_nat_nat > fun_nat_fun_nat_bool ).

thf(hAPP_f66927821l_bool_type,type,
    hAPP_f66927821l_bool: fun_fu1585362869l_bool > fun_nat_nat > fun_na1436237685l_bool ).

thf(hAPP_f2040535501l_bool_type,type,
    hAPP_f2040535501l_bool: fun_fu1988302005l_bool > fun_nat_nat > fun_fu1262361717l_bool ).

thf(hAPP_f1598887207l_bool_type,type,
    hAPP_f1598887207l_bool: fun_fu1028680969l_bool > fun_nat_Product_unit > fun_fu797415470l_bool ).

thf(hAPP_f229349961t_bool_type,type,
    hAPP_f229349961t_bool: fun_fu1733046955t_bool > fun_nat_fun_nat_bool > fun_nat_fun_nat_bool ).

thf(hAPP_f416620757at_nat_type,type,
    hAPP_f416620757at_nat: fun_fu522653757at_nat > fun_nat_fun_nat_nat > fun_nat_fun_nat_nat ).

thf(hAPP_f1722879237t_bool_type,type,
    hAPP_f1722879237t_bool: fun_fu80187629t_bool > fun_na1436237685l_bool > fun_fu821463397t_bool ).

thf(hAPP_f2028818269l_bool_type,type,
    hAPP_f2028818269l_bool: fun_fu309829899l_bool > fun_Pr1643180309t_bool > bool ).

thf(hAPP_f427533077t_bool_type,type,
    hAPP_f427533077t_bool: fun_fu391017725t_bool > fun_Pr1643180309t_bool > fun_Pr1643180309t_bool ).

thf(hAPP_f272527115l_bool_type,type,
    hAPP_f272527115l_bool: fun_fu43485241l_bool > fun_Pr1643180309t_bool > fun_fu309829899l_bool ).

thf(hAPP_f1950626059l_bool_type,type,
    hAPP_f1950626059l_bool: fun_fu486305773l_bool > fun_Product_unit_nat > fun_fu599651488l_bool ).

thf(hAPP_f1119259085l_bool_type,type,
    hAPP_f1119259085l_bool: fun_fu166516917l_bool > fun_Pr321980605t_bool > fun_fu1804102517l_bool ).

thf(hAPP_f1960079821l_bool_type,type,
    hAPP_f1960079821l_bool: fun_fu1208702901l_bool > fun_Pr1337256141t_bool > fun_fu79182725l_bool ).

thf(hAPP_f1458726223t_bool_type,type,
    hAPP_f1458726223t_bool: fun_fu363747255t_bool > fun_Pr1863373635l_bool > fun_fu391017725t_bool ).

thf(hAPP_f2046606153l_bool_type,type,
    hAPP_f2046606153l_bool: fun_fu1969848875l_bool > fun_Pr1572389447t_bool > fun_fu660051455l_bool ).

thf(hAPP_f1413342797l_bool_type,type,
    hAPP_f1413342797l_bool: fun_fu662844725l_bool > fun_Pr1887046367le_alt > fun_fu2018671511l_bool ).

thf(hAPP_f1290810160l_bool_type,type,
    hAPP_f1290810160l_bool: fun_fu1737725662l_bool > fun_fu192249448t_bool > bool ).

thf(hAPP_f1037107797l_bool_type,type,
    hAPP_f1037107797l_bool: fun_fu1675261879l_bool > fun_fu1131021301l_bool > bool ).

thf(hAPP_f2076228197l_bool_type,type,
    hAPP_f2076228197l_bool: fun_fu350452167l_bool > fun_fu1944573957l_bool > bool ).

thf(hAPP_f1690559309l_bool_type,type,
    hAPP_f1690559309l_bool: fun_fu1227713461l_bool > fun_fu908353023e_indi > fun_fu1936649911l_bool ).

thf(hAPP_f1465510031l_bool_type,type,
    hAPP_f1465510031l_bool: fun_fu614742333l_bool > fun_fu775006535l_bool > bool ).

thf(hAPP_f626396309l_bool_type,type,
    hAPP_f626396309l_bool: fun_fu694861565l_bool > fun_fu775006535l_bool > fun_fu775006535l_bool ).

thf(hAPP_f95487087l_bool_type,type,
    hAPP_f95487087l_bool: fun_fu1420978973l_bool > fun_fu775006535l_bool > fun_fu614742333l_bool ).

thf(hAPP_f120150093l_bool_type,type,
    hAPP_f120150093l_bool: fun_fu81176373l_bool > fun_fu775006535l_bool > fun_fu117797375l_bool ).

thf(hAPP_f1197023401l_bool_type,type,
    hAPP_f1197023401l_bool: fun_fu1355931153l_bool > fun_fu775006535l_bool > fun_fu1583538011l_bool ).

thf(hAPP_f1505765837l_bool_type,type,
    hAPP_f1505765837l_bool: fun_fu1166948533l_bool > fun_fu834038077t_unit > fun_fu928599029l_bool ).

thf(hAPP_f228579435l_bool_type,type,
    hAPP_f228579435l_bool: fun_fu1444789715l_bool > fun_fu1291054887l_bool > fun_fu694861565l_bool ).

thf(hAPP_f1763702829e_indi_type,type,
    hAPP_f1763702829e_indi: fun_fu1596339983e_indi > fun_fu1595299477t_bool > arrow_2115524757e_indi ).

thf(hAPP_f611501301l_bool_type,type,
    hAPP_f611501301l_bool: fun_fu1138137687l_bool > fun_fu1595299477t_bool > bool ).

thf(hAPP_f1579463915t_unit_type,type,
    hAPP_f1579463915t_unit: fun_fu1193945677t_unit > fun_fu1595299477t_bool > product_unit ).

thf(hAPP_f740807359i_bool_type,type,
    hAPP_f740807359i_bool: fun_fu2127564915i_bool > fun_fu1595299477t_bool > fun_Ar552120407i_bool ).

thf(hAPP_f352672903l_bool_type,type,
    hAPP_f352672903l_bool: fun_fu1460706235l_bool > fun_fu1595299477t_bool > fun_bool_bool ).

thf(hAPP_f1483290493t_bool_type,type,
    hAPP_f1483290493t_bool: fun_fu327311537t_bool > fun_fu1595299477t_bool > fun_Pr1643180309t_bool ).

thf(hAPP_f1709225957l_bool_type,type,
    hAPP_f1709225957l_bool: fun_fu446267975l_bool > fun_fu1595299477t_bool > fun_fu1378577485l_bool ).

thf(hAPP_f1625336439l_bool_type,type,
    hAPP_f1625336439l_bool: fun_fu633681369l_bool > fun_fu2073792791t_bool > bool ).

thf(hAPP_f67777128l_bool_type,type,
    hAPP_f67777128l_bool: fun_fu1392295702l_bool > fun_fu429484960t_bool > bool ).

thf(hAPP_f976121117l_bool_type,type,
    hAPP_f976121117l_bool: fun_fu2017950079l_bool > fun_fu1311768765l_bool > bool ).

thf(hAPP_f1812901165l_bool_type,type,
    hAPP_f1812901165l_bool: fun_fu2090861455l_bool > fun_fu497048781l_bool > bool ).

thf(hAPP_f2041629639l_bool_type,type,
    hAPP_f2041629639l_bool: fun_fu2066072949l_bool > fun_fu1337686655l_bool > bool ).

thf(hAPP_f1339624767l_bool_type,type,
    hAPP_f1339624767l_bool: fun_fu1023291297l_bool > fun_fu853181919t_bool > bool ).

thf(hAPP_f728118466l_bool_type,type,
    hAPP_f728118466l_bool: fun_fu1175033968l_bool > fun_fu1470034170i_bool > bool ).

thf(hAPP_f1637334154l_bool_type,type,
    hAPP_f1637334154l_bool: fun_fu814369080l_bool > fun_fu425979586l_bool > bool ).

thf(hAPP_f1426445843l_bool_type,type,
    hAPP_f1426445843l_bool: fun_fu1262361717l_bool > fun_fun_nat_nat_bool > bool ).

thf(hAPP_f537623936l_bool_type,type,
    hAPP_f537623936l_bool: fun_fu797415470l_bool > fun_fu1771765432t_bool > bool ).

thf(hAPP_f339859954l_bool_type,type,
    hAPP_f339859954l_bool: fun_fu599651488l_bool > fun_fu1108851754t_bool > bool ).

thf(hAPP_f1221487891l_bool_type,type,
    hAPP_f1221487891l_bool: fun_fu1804102517l_bool > fun_fu176691123l_bool > bool ).

thf(hAPP_f522449699l_bool_type,type,
    hAPP_f522449699l_bool: fun_fu79182725l_bool > fun_fu38582723l_bool > bool ).

thf(hAPP_f922750545l_bool_type,type,
    hAPP_f922750545l_bool: fun_fu660051455l_bool > fun_fu829220361l_bool > bool ).

thf(hAPP_f403597109l_bool_type,type,
    hAPP_f403597109l_bool: fun_fu2018671511l_bool > fun_fu209254101t_bool > bool ).

thf(hAPP_f1298495829l_bool_type,type,
    hAPP_f1298495829l_bool: fun_fu1936649911l_bool > fun_fu887487221i_bool > bool ).

thf(hAPP_f1223452061l_bool_type,type,
    hAPP_f1223452061l_bool: fun_fu117797375l_bool > fun_fu614742333l_bool > bool ).

thf(hAPP_f345984403l_bool_type,type,
    hAPP_f345984403l_bool: fun_fu928599029l_bool > fun_fu1386428467t_bool > bool ).

thf(hAPP_f1536115021l_bool_type,type,
    hAPP_f1536115021l_bool: fun_fu1739677877l_bool > fun_fu1596339983e_indi > fun_fu2038151111l_bool ).

thf(hAPP_f361555359l_bool_type,type,
    hAPP_f361555359l_bool: fun_fu1378577485l_bool > fun_fu1138137687l_bool > bool ).

thf(hAPP_f1077478037l_bool_type,type,
    hAPP_f1077478037l_bool: fun_fu1687768061l_bool > fun_fu1138137687l_bool > fun_fu1138137687l_bool ).

thf(hAPP_f173704847l_bool_type,type,
    hAPP_f173704847l_bool: fun_fu385975869l_bool > fun_fu1138137687l_bool > fun_fu1378577485l_bool ).

thf(hAPP_f481662541l_bool_type,type,
    hAPP_f481662541l_bool: fun_fu413400117l_bool > fun_fu1138137687l_bool > fun_fu211637007l_bool ).

thf(hAPP_f1065603533l_bool_type,type,
    hAPP_f1065603533l_bool: fun_fu804386741l_bool > fun_fu1193945677t_unit > fun_fu1106246917l_bool ).

thf(hAPP_f230252107l_bool_type,type,
    hAPP_f230252107l_bool: fun_fu1389232563l_bool > fun_fu446267975l_bool > fun_fu1687768061l_bool ).

thf(hAPP_f1616443493l_bool_type,type,
    hAPP_f1616443493l_bool: fun_fu2038151111l_bool > fun_fu1480005125i_bool > bool ).

thf(hAPP_f2081160365l_bool_type,type,
    hAPP_f2081160365l_bool: fun_fu211637007l_bool > fun_fu1378577485l_bool > bool ).

thf(hAPP_f1549513891l_bool_type,type,
    hAPP_f1549513891l_bool: fun_fu1106246917l_bool > fun_fu829635395t_bool > bool ).

thf(hAPP_f372503329l_bool_type,type,
    hAPP_f372503329l_bool: fun_fu1669219279l_bool > fun_fu790078681i_bool > bool ).

thf(hAPP_f1656729961l_bool_type,type,
    hAPP_f1656729961l_bool: fun_fu1681173271l_bool > fun_fu705370401l_bool > bool ).

thf(hAPP_f1919464799l_bool_type,type,
    hAPP_f1919464799l_bool: fun_fu1656765709l_bool > fun_fu545713175t_bool > bool ).

thf(hAPP_f2106732305l_bool_type,type,
    hAPP_f2106732305l_bool: fun_fu976270783l_bool > fun_fu1916585161l_bool > bool ).

thf(hAPP_f932587383l_bool_type,type,
    hAPP_f932587383l_bool: fun_fu2088415961l_bool > fun_fu83070487i_bool > bool ).

thf(hAPP_f43388905l_bool_type,type,
    hAPP_f43388905l_bool: fun_fu1041166411l_bool > fun_fu2016509975e_indi > fun_fu1669219279l_bool ).

thf(hAPP_f1021703871l_bool_type,type,
    hAPP_f1021703871l_bool: fun_fu705370401l_bool > fun_fu1015689055l_bool > bool ).

thf(hAPP_f1793492343l_bool_type,type,
    hAPP_f1793492343l_bool: fun_fu279877163l_bool > fun_fu1015689055l_bool > fun_Ar1198543961l_bool ).

thf(hAPP_f422714471l_bool_type,type,
    hAPP_f422714471l_bool: fun_fu16872987l_bool > fun_fu1015689055l_bool > fun_fu787660105l_bool ).

thf(hAPP_f717334393l_bool_type,type,
    hAPP_f717334393l_bool: fun_fu830715227l_bool > fun_fu1015689055l_bool > fun_fu1681173271l_bool ).

thf(hAPP_f868566847l_bool_type,type,
    hAPP_f868566847l_bool: fun_fu1216534899l_bool > fun_fu1015689055l_bool > fun_fu705370401l_bool ).

thf(hAPP_f1050277569l_bool_type,type,
    hAPP_f1050277569l_bool: fun_fu1155544867l_bool > fun_fu1015689055l_bool > fun_fu1015689055l_bool ).

thf(hAPP_f803471205l_bool_type,type,
    hAPP_f803471205l_bool: fun_fu978460487l_bool > fun_fu603957077t_unit > fun_fu1656765709l_bool ).

thf(hAPP_f2071392713l_bool_type,type,
    hAPP_f2071392713l_bool: fun_fu675160875l_bool > fun_fu243393031t_bool > fun_fu976270783l_bool ).

thf(hAPP_f639477379l_bool_type,type,
    hAPP_f639477379l_bool: fun_fu1697657963l_bool > fun_fu1556412341l_bool > fun_fu1155544867l_bool ).

thf(hAPP_f1685685l_bool_type,type,
    hAPP_f1685685l_bool: fun_fu1616760087l_bool > fun_fu1367017557t_bool > bool ).

thf(hAPP_f1165889229l_bool_type,type,
    hAPP_f1165889229l_bool: fun_fu1286543157l_bool > fun_Pr1698894881e_indi > fun_fu2088415961l_bool ).

thf(hAPP_f2029284841e_indi_type,type,
    hAPP_f2029284841e_indi: fun_fu2016509975e_indi > fun_Pr1055212137t_bool > arrow_2115524757e_indi ).

thf(hAPP_f429946033l_bool_type,type,
    hAPP_f429946033l_bool: fun_fu1015689055l_bool > fun_Pr1055212137t_bool > bool ).

thf(hAPP_f739946663t_unit_type,type,
    hAPP_f739946663t_unit: fun_fu603957077t_unit > fun_Pr1055212137t_bool > product_unit ).

thf(hAPP_f1099651112t_bool_type,type,
    hAPP_f1099651112t_bool: fun_fu1540265814t_bool > fun_Pr1055212137t_bool > fun_Ar1091019988t_bool ).

thf(hAPP_f1810968607t_bool_type,type,
    hAPP_f1810968607t_bool: fun_fu157004749t_bool > fun_Pr1055212137t_bool > fun_Ar1414184139t_bool ).

thf(hAPP_f1909595219t_bool_type,type,
    hAPP_f1909595219t_bool: fun_fu699199419t_bool > fun_Pr1055212137t_bool > fun_Ar1164786343t_bool ).

thf(hAPP_f786530292t_bool_type,type,
    hAPP_f786530292t_bool: fun_fu1628463836t_bool > fun_Pr1055212137t_bool > fun_Ar1275715144t_bool ).

thf(hAPP_f1957024259i_bool_type,type,
    hAPP_f1957024259i_bool: fun_fu1766473067i_bool > fun_Pr1055212137t_bool > fun_Ar552120407i_bool ).

thf(hAPP_f1755759597t_bool_type,type,
    hAPP_f1755759597t_bool: fun_fu1902045723t_bool > fun_Pr1055212137t_bool > fun_Ar1492469401t_bool ).

thf(hAPP_f311418073t_bool_type,type,
    hAPP_f311418073t_bool: fun_fu243393031t_bool > fun_Pr1055212137t_bool > fun_Ar500372357t_bool ).

thf(hAPP_f269590987l_bool_type,type,
    hAPP_f269590987l_bool: fun_fu44268723l_bool > fun_Pr1055212137t_bool > fun_bool_bool ).

thf(hAPP_f414777105t_bool_type,type,
    hAPP_f414777105t_bool: fun_fu831091903t_bool > fun_Pr1055212137t_bool > fun_bo1116297149t_bool ).

thf(hAPP_f862859457t_bool_type,type,
    hAPP_f862859457t_bool: fun_fu105994665t_bool > fun_Pr1055212137t_bool > fun_Pr1643180309t_bool ).

thf(hAPP_f1410143987l_bool_type,type,
    hAPP_f1410143987l_bool: fun_fu1583538011l_bool > fun_Pr1055212137t_bool > fun_fu775006535l_bool ).

thf(hAPP_f1370368205l_bool_type,type,
    hAPP_f1370368205l_bool: fun_fu1556412341l_bool > fun_Pr1055212137t_bool > fun_fu705370401l_bool ).

thf(hAPP_f314169011l_bool_type,type,
    hAPP_f314169011l_bool: fun_fu1515494241l_bool > fun_Pr1055212137t_bool > fun_fu1015689055l_bool ).

thf(hAPP_f1409483817t_bool_type,type,
    hAPP_f1409483817t_bool: fun_fu1324073361t_bool > fun_Pr1055212137t_bool > fun_fu962221693t_bool ).

thf(hAPP_f70231061t_bool_type,type,
    hAPP_f70231061t_bool: fun_fu962221693t_bool > fun_Pr1055212137t_bool > fun_Pr1055212137t_bool ).

thf(hAPP_f106186317l_bool_type,type,
    hAPP_f106186317l_bool: fun_fu638047541l_bool > fun_Pr215145567t_unit > fun_fu1616760087l_bool ).

thf(hAPP_f46399911t_bool_type,type,
    hAPP_f46399911t_bool: fun_fu528877839t_bool > fun_Pr1228236907l_bool > fun_fu962221693t_bool ).

thf(hAPP_P1031342399e_indi_type,type,
    hAPP_P1031342399e_indi: fun_Pr1698894881e_indi > produc1840315303le_alt > arrow_2115524757e_indi ).

thf(hAPP_P166437127t_bool_type,type,
    hAPP_P166437127t_bool: fun_Pr1055212137t_bool > produc1840315303le_alt > bool ).

thf(hAPP_P907778813t_unit_type,type,
    hAPP_P907778813t_unit: fun_Pr215145567t_unit > produc1840315303le_alt > product_unit ).

thf(hAPP_P1326783277i_bool_type,type,
    hAPP_P1326783277i_bool: fun_Pr39488737i_bool > produc1840315303le_alt > fun_Ar552120407i_bool ).

thf(hAPP_P1830623733l_bool_type,type,
    hAPP_P1830623733l_bool: fun_Pr359894313l_bool > produc1840315303le_alt > fun_bool_bool ).

thf(hAPP_P728132331t_bool_type,type,
    hAPP_P728132331t_bool: fun_Pr1907279903t_bool > produc1840315303le_alt > fun_Pr1643180309t_bool ).

thf(hAPP_P840149257l_bool_type,type,
    hAPP_P840149257l_bool: fun_Pr1228236907l_bool > produc1840315303le_alt > fun_fu1015689055l_bool ).

thf(hBOOL_type,type,
    hBOOL: bool > $o ).

thf(member590466050e_indi_type,type,
    member590466050e_indi: fun_Ar1380772935l_bool ).

thf(member_bool_type,type,
    member_bool: fun_bo492988759l_bool ).

thf(member_nat_type,type,
    member_nat: fun_na1436237685l_bool ).

thf(member_Product_unit_type,type,
    member_Product_unit: fun_Pr1863373635l_bool ).

thf(member428554515di_nat_type,type,
    member428554515di_nat: fun_fu85234537l_bool ).

thf(member1188420050t_bool_type,type,
    member1188420050t_bool: fun_fu1591782325l_bool ).

thf(member291481314t_bool_type,type,
    member291481314t_bool: fun_fu1816256693l_bool ).

thf(member1159072754t_bool_type,type,
    member1159072754t_bool: fun_fu1291054887l_bool ).

thf(member418553588le_alt_type,type,
    member418553588le_alt: fun_fu1338365749l_bool ).

thf(member_fun_bool_nat_type,type,
    member_fun_bool_nat: fun_fu1531935961l_bool ).

thf(member1283254298t_bool_type,type,
    member1283254298t_bool: fun_fu1395443509l_bool ).

thf(member1103019306t_bool_type,type,
    member1103019306t_bool: fun_fu752049205l_bool ).

thf(member818572202t_bool_type,type,
    member818572202t_bool: fun_fu572324631l_bool ).

thf(member481633596le_alt_type,type,
    member481633596le_alt: fun_fu1156700085l_bool ).

thf(member76848293e_indi_type,type,
    member76848293e_indi: fun_fu1500933005l_bool ).

thf(member_fun_nat_bool_type,type,
    member_fun_nat_bool: fun_fu1436348701l_bool ).

thf(member_fun_nat_nat_type,type,
    member_fun_nat_nat: fun_fu1988302005l_bool ).

thf(member1024687843t_unit_type,type,
    member1024687843t_unit: fun_fu1028680969l_bool ).

thf(member87760213it_nat_type,type,
    member87760213it_nat: fun_fu486305773l_bool ).

thf(member1302538000t_bool_type,type,
    member1302538000t_bool: fun_fu166516917l_bool ).

thf(member1948336672t_bool_type,type,
    member1948336672t_bool: fun_fu1208702901l_bool ).

thf(member488877876t_bool_type,type,
    member488877876t_bool: fun_fu1969848875l_bool ).

thf(member666484274le_alt_type,type,
    member666484274le_alt: fun_fu662844725l_bool ).

thf(member1408848082e_indi_type,type,
    member1408848082e_indi: fun_fu1227713461l_bool ).

thf(member1791451290l_bool_type,type,
    member1791451290l_bool: fun_fu81176373l_bool ).

thf(member1814595472t_unit_type,type,
    member1814595472t_unit: fun_fu1166948533l_bool ).

thf(member1801442306t_bool_type,type,
    member1801442306t_bool: fun_fu446267975l_bool ).

thf(member2095441122e_indi_type,type,
    member2095441122e_indi: fun_fu1739677877l_bool ).

thf(member213355690l_bool_type,type,
    member213355690l_bool: fun_fu413400117l_bool ).

thf(member1805026208t_unit_type,type,
    member1805026208t_unit: fun_fu804386741l_bool ).

thf(member527726724e_indi_type,type,
    member527726724e_indi: fun_fu1041166411l_bool ).

thf(member717964108l_bool_type,type,
    member717964108l_bool: fun_fu830715227l_bool ).

thf(member1667929154t_unit_type,type,
    member1667929154t_unit: fun_fu978460487l_bool ).

thf(member449535860t_bool_type,type,
    member449535860t_bool: fun_fu675160875l_bool ).

thf(member1747786740e_indi_type,type,
    member1747786740e_indi: fun_fu1286543157l_bool ).

thf(member57118396t_bool_type,type,
    member57118396t_bool: fun_fu1556412341l_bool ).

thf(member1142067122t_unit_type,type,
    member1142067122t_unit: fun_fu638047541l_bool ).

thf(member553230100le_alt_type,type,
    member553230100le_alt: fun_Pr1228236907l_bool ).

thf(f_type,type,
    f: fun_fu1595299477t_bool ).

thf(lab_type,type,
    lab: fun_Pr1055212137t_bool ).

thf(lba_type,type,
    lba: fun_Pr1055212137t_bool ).

thf(p_type,type,
    p: fun_Ar500372357t_bool ).

thf(a_type,type,
    a: arrow_931160158le_alt ).

thf(b_type,type,
    b: arrow_931160158le_alt ).

thf(c_type,type,
    c: arrow_931160158le_alt ).

thf(d_type,type,
    d: arrow_931160158le_alt ).

thf(e_type,type,
    e: arrow_931160158le_alt ).

thf(h_type,type,
    h: fun_Ar1744566822di_nat ).

thf(n_type,type,
    n: nat ).

thf(390,axiom,
    ! [A: product_unit,B: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ A ) @ B ) )
    <=> ( hBOOL @ ( hAPP_P1676879539t_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_mem__def) ).

thf(2199,plain,
    ! [A: product_unit,B: fun_Pr1643180309t_bool] :
      ( ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_P1676879539t_bool @ B @ A ) ) )
      & ( ( hBOOL @ ( hAPP_P1676879539t_bool @ B @ A ) )
       => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(356,axiom,
    ! [A: nat,B: nat] :
      ( ( A != B )
     => ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_529_linorder__neqE__nat) ).

thf(2094,plain,
    ! [A: nat,B: nat] :
      ( ( A != B )
     => ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(83,axiom,
    ! [A: bool,B: product_unit] :
      ( ( hAPP_P1676879539t_bool @ ( hAPP_b1096750261t_bool @ cOMBK_790042732t_unit @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Product____Type__Ounit_U) ).

thf(1024,plain,
    ! [A: bool,B: product_unit] :
      ( ( hAPP_P1676879539t_bool @ ( hAPP_b1096750261t_bool @ cOMBK_790042732t_unit @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(105,axiom,
    ! [A: nat] :
      ( ( hAPP_nat_nat @ suc @ A )
     != zero_zero_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_673_Suc__neq__Zero) ).

thf(1105,plain,
    ! [A: nat] :
      ( ( hAPP_nat_nat @ suc @ A )
     != zero_zero_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(714,axiom,
    ! [A: arrow_2115524757e_indi] : ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ A ) @ top_to1678393681i_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_UNIV__I) ).

thf(3477,plain,
    ! [A: arrow_2115524757e_indi] : ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ A ) @ top_to1678393681i_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).

thf(696,axiom,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( ( A != B )
     => ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ B ) @ A ) )
       => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_xt1_I12_J) ).

thf(3397,plain,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( ( A != B )
     => ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ B ) @ A ) )
       => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).

thf(741,axiom,
    ! [A: fun_nat_bool] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ top_top_fun_nat_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_345_top__greatest) ).

thf(3581,plain,
    ! [A: fun_nat_bool] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ top_top_fun_nat_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).

thf(163,axiom,
    ! [A: nat,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ B @ A ) )
       => ( hBOOL @ ( hAPP_nat_bool @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_479_predicate1D) ).

thf(1315,plain,
    ! [A: nat,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ B @ A ) )
       => ( hBOOL @ ( hAPP_nat_bool @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(416,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( A != B )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_xt1_I12_J) ).

thf(2331,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( A != B )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).

thf(226,axiom,
    ! [A: nat,B: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_561_le__add1) ).

thf(1549,plain,
    ! [A: nat,B: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(239,axiom,
    ! [A: fun_nat_fun_nat_bool,B: fun_nat_nat,C: nat] :
      ( ( hAPP_n1699378549t_bool @ ( hAPP_f618557131t_bool @ ( cOMBB_800536526ol_nat @ A ) @ B ) @ C )
      = ( hAPP_n1699378549t_bool @ A @ ( hAPP_nat_nat @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_) ).

thf(1586,plain,
    ! [A: fun_nat_fun_nat_bool,B: fun_nat_nat,C: nat] :
      ( ( hAPP_n1699378549t_bool @ ( hAPP_f618557131t_bool @ ( cOMBB_800536526ol_nat @ A ) @ B ) @ C )
      = ( hAPP_n1699378549t_bool @ A @ ( hAPP_nat_nat @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(441,axiom,
    ! [A: fun_fu1595299477t_bool] : ( hBOOL @ ( hAPP_f611501301l_bool @ top_to2013953873l_bool @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_top1I) ).

thf(2452,plain,
    ! [A: fun_fu1595299477t_bool] : ( hBOOL @ ( hAPP_f611501301l_bool @ top_to2013953873l_bool @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).

thf(566,axiom,
    ! [A: fun_bool_bool,B: bool,C: fun_bool_bool] :
      ( ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_f612708895l_bool @ ord_le742797417l_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_471_set__rev__mp) ).

thf(2889,plain,
    ! [A: fun_bool_bool,B: bool,C: fun_bool_bool] :
      ( ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_f612708895l_bool @ ord_le742797417l_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).

thf(131,axiom,
    ! [A: fun_fu787660105l_bool,B: fun_fu787660105l_bool,C: fun_fu775006535l_bool] :
      ( ! [D: fun_Ar500372357t_bool] :
          ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ D ) @ C ) )
         => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f868566847l_bool @ ord_le1923264405l_bool @ ( hAPP_f1498158055l_bool @ A @ D ) ) @ ( hAPP_f1498158055l_bool @ B @ D ) ) ) )
     => ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f173704847l_bool @ ord_le161055137l_bool @ ( pi_fun530160875t_bool @ C @ A ) ) @ ( pi_fun530160875t_bool @ C @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_503_Pi__mono) ).

thf(1190,plain,
    ! [A: fun_fu787660105l_bool,B: fun_fu787660105l_bool,C: fun_fu775006535l_bool] :
      ( ! [D: fun_Ar500372357t_bool] :
          ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ D ) @ C ) )
         => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f868566847l_bool @ ord_le1923264405l_bool @ ( hAPP_f1498158055l_bool @ A @ D ) ) @ ( hAPP_f1498158055l_bool @ B @ D ) ) ) )
     => ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f173704847l_bool @ ord_le161055137l_bool @ ( pi_fun530160875t_bool @ C @ A ) ) @ ( pi_fun530160875t_bool @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(610,axiom,
    ! [A: fun_Pr1643180309t_bool] : ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ A ) @ top_to1257323279t_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_411_subset__UNIV) ).

thf(3053,plain,
    ! [A: fun_Pr1643180309t_bool] : ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ A ) @ top_to1257323279t_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).

thf(1,conjecture,
    hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ c ) @ d ) ) @ ( hAPP_f792184801t_bool @ f @ p ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

thf(2,negated_conjecture,
    ~ ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ c ) @ d ) ) @ ( hAPP_f792184801t_bool @ f @ p ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(760,plain,
    ~ ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ c ) @ d ) ) @ ( hAPP_f792184801t_bool @ f @ p ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(418,axiom,
    ! [A: fun_fu1138137687l_bool] : ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f173704847l_bool @ ord_le161055137l_bool @ A ) @ top_to2013953873l_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_407_subset__UNIV) ).

thf(2336,plain,
    ! [A: fun_fu1138137687l_bool] : ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f173704847l_bool @ ord_le161055137l_bool @ A ) @ top_to2013953873l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

thf(366,axiom,
    ! [A: fun_fu1015689055l_bool] :
      ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f868566847l_bool @ ord_le1923264405l_bool @ top_to1690334693l_bool ) @ A ) )
     => ( A = top_to1690334693l_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_357_top__le) ).

thf(2131,plain,
    ! [A: fun_fu1015689055l_bool] :
      ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f868566847l_bool @ ord_le1923264405l_bool @ top_to1690334693l_bool ) @ A ) )
     => ( A = top_to1690334693l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(449,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( B != A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_531_less__not__refl2) ).

thf(2480,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( B != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).

thf(66,axiom,
    ! [A: nat,B: nat] :
      ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) )
      = ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_644_add__Suc__right) ).

thf(962,plain,
    ! [A: nat,B: nat] :
      ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) )
      = ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(295,axiom,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ B ) )
    <=> ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ A ) @ B ) )
        & ~ ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_400_less__fun__def) ).

thf(1818,plain,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ B ) )
       => ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ A ) @ B ) )
          & ~ ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ B ) @ A ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ A ) @ B ) )
          & ~ ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ B ) @ A ) ) )
       => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(157,axiom,
    ! [A: fun_Pr1055212137t_bool] :
      ( ( pi_Pro226591613t_bool @ A @ ( hAPP_f1426772275l_bool @ cOMBK_1506144056le_alt @ top_to1647826457l_bool ) )
      = top_to1690334693l_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_Pi__UNIV) ).

thf(1295,plain,
    ! [A: fun_Pr1055212137t_bool] :
      ( ( pi_Pro226591613t_bool @ A @ ( hAPP_f1426772275l_bool @ cOMBK_1506144056le_alt @ top_to1647826457l_bool ) )
      = top_to1690334693l_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(726,axiom,
    ! [A: fun_fu1595299477t_bool,B: arrow_2115524757e_indi] :
      ( ( hBOOL @ ( hAPP_A1888055029i_bool @ ( hAPP_f740807359i_bool @ arrow_1472924909ctator @ A ) @ B ) )
    <=> ! [C: fun_Ar500372357t_bool] :
          ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ C ) @ arrow_1190054106e_Prof ) )
         => ( ( hAPP_f792184801t_bool @ A @ C )
            = ( hAPP_A1174518481t_bool @ C @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_380_dictator__def) ).

thf(3534,plain,
    ! [A: fun_fu1595299477t_bool,B: arrow_2115524757e_indi] :
      ( ( ( hBOOL @ ( hAPP_A1888055029i_bool @ ( hAPP_f740807359i_bool @ arrow_1472924909ctator @ A ) @ B ) )
       => ! [C: fun_Ar500372357t_bool] :
            ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ C ) @ arrow_1190054106e_Prof ) )
           => ( ( hAPP_f792184801t_bool @ A @ C )
              = ( hAPP_A1174518481t_bool @ C @ B ) ) ) )
      & ( ! [C: fun_Ar500372357t_bool] :
            ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ C ) @ arrow_1190054106e_Prof ) )
           => ( ( hAPP_f792184801t_bool @ A @ C )
              = ( hAPP_A1174518481t_bool @ C @ B ) ) )
       => ( hBOOL @ ( hAPP_A1888055029i_bool @ ( hAPP_f740807359i_bool @ arrow_1472924909ctator @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).

thf(669,axiom,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ A ) @ B ) )
     => ( ( A != B )
       => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_order__le__neq__trans) ).

thf(3317,plain,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ A ) @ B ) )
     => ( ( A != B )
       => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).

thf(315,axiom,
    ! [A: fun_fu787660105l_bool,B: fun_fu775006535l_bool,C: fun_fu775006535l_bool] :
      ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f95487087l_bool @ ord_le1871091345l_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f173704847l_bool @ ord_le161055137l_bool @ ( pi_fun530160875t_bool @ C @ A ) ) @ ( pi_fun530160875t_bool @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_404_Pi__anti__mono) ).

thf(1882,plain,
    ! [A: fun_fu787660105l_bool,B: fun_fu775006535l_bool,C: fun_fu775006535l_bool] :
      ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f95487087l_bool @ ord_le1871091345l_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f173704847l_bool @ ord_le161055137l_bool @ ( pi_fun530160875t_bool @ C @ A ) ) @ ( pi_fun530160875t_bool @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(400,axiom,
    ! [A: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ top_to1678393681i_bool ) @ A ) )
     => ( A = top_to1678393681i_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_363_top__le) ).

thf(2231,plain,
    ! [A: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ top_to1678393681i_bool ) @ A ) )
     => ( A = top_to1678393681i_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).

thf(217,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ? [C: nat] :
          ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ C ) )
          & ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C )
            = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_627_less__imp__add__positive) ).

thf(1522,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ? [C: nat] :
          ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ C ) )
          & ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C )
            = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(729,axiom,
    ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ c ) @ d ) ) @ ( hAPP_f792184801t_bool @ f @ p ) ) )
  <=> ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ c ) @ d ) ) @ ( hAPP_f792184801t_bool @ f @ ( cOMBS_1921392482t_bool @ ( cOMBS_811328630t_bool @ ( hAPP_f509814255t_bool @ ( cOMBB_231886989e_indi @ if_fun1658569689t_bool ) @ ( hAPP_n924210722i_bool @ ( hAPP_f62620517i_bool @ cOMBC_922322901t_bool @ ( hAPP_f1381130897t_bool @ ( cOMBB_981137617e_indi @ ord_less_nat ) @ h ) ) @ n ) ) @ ( hAPP_A658738638t_bool @ ( hAPP_f293545699t_bool @ cOMBC_18834461t_bool @ ( hAPP_f842954860t_bool @ ( cOMBB_117136048e_indi @ arrow_741591990_mktop ) @ p ) ) @ e ) ) @ ( cOMBS_1921392482t_bool @ ( cOMBS_811328630t_bool @ ( hAPP_f509814255t_bool @ ( cOMBB_231886989e_indi @ if_fun1658569689t_bool ) @ ( hAPP_n924210722i_bool @ ( hAPP_f62620517i_bool @ cOMBC_922322901t_bool @ ( hAPP_f1381130897t_bool @ ( cOMBB_981137617e_indi @ fequal_nat ) @ h ) ) @ n ) ) @ ( hAPP_A658738638t_bool @ ( hAPP_f293545699t_bool @ cOMBC_18834461t_bool @ ( hAPP_A102926893t_bool @ ( hAPP_f141075873t_bool @ cOMBC_1505804284t_bool @ ( hAPP_f576849227t_bool @ ( cOMBB_656639247e_indi @ arrow_1475523868_above ) @ p ) ) @ c ) ) @ e ) ) @ ( hAPP_A658738638t_bool @ ( hAPP_f293545699t_bool @ cOMBC_18834461t_bool @ ( hAPP_f842954860t_bool @ ( cOMBB_117136048e_indi @ arrow_592884904_mkbot ) @ p ) ) @ e ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_PW) ).

thf(3549,plain,
    ( ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ c ) @ d ) ) @ ( hAPP_f792184801t_bool @ f @ p ) ) )
     => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ c ) @ d ) ) @ ( hAPP_f792184801t_bool @ f @ ( cOMBS_1921392482t_bool @ ( cOMBS_811328630t_bool @ ( hAPP_f509814255t_bool @ ( cOMBB_231886989e_indi @ if_fun1658569689t_bool ) @ ( hAPP_n924210722i_bool @ ( hAPP_f62620517i_bool @ cOMBC_922322901t_bool @ ( hAPP_f1381130897t_bool @ ( cOMBB_981137617e_indi @ ord_less_nat ) @ h ) ) @ n ) ) @ ( hAPP_A658738638t_bool @ ( hAPP_f293545699t_bool @ cOMBC_18834461t_bool @ ( hAPP_f842954860t_bool @ ( cOMBB_117136048e_indi @ arrow_741591990_mktop ) @ p ) ) @ e ) ) @ ( cOMBS_1921392482t_bool @ ( cOMBS_811328630t_bool @ ( hAPP_f509814255t_bool @ ( cOMBB_231886989e_indi @ if_fun1658569689t_bool ) @ ( hAPP_n924210722i_bool @ ( hAPP_f62620517i_bool @ cOMBC_922322901t_bool @ ( hAPP_f1381130897t_bool @ ( cOMBB_981137617e_indi @ fequal_nat ) @ h ) ) @ n ) ) @ ( hAPP_A658738638t_bool @ ( hAPP_f293545699t_bool @ cOMBC_18834461t_bool @ ( hAPP_A102926893t_bool @ ( hAPP_f141075873t_bool @ cOMBC_1505804284t_bool @ ( hAPP_f576849227t_bool @ ( cOMBB_656639247e_indi @ arrow_1475523868_above ) @ p ) ) @ c ) ) @ e ) ) @ ( hAPP_A658738638t_bool @ ( hAPP_f293545699t_bool @ cOMBC_18834461t_bool @ ( hAPP_f842954860t_bool @ ( cOMBB_117136048e_indi @ arrow_592884904_mkbot ) @ p ) ) @ e ) ) ) ) ) ) )
    & ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ c ) @ d ) ) @ ( hAPP_f792184801t_bool @ f @ ( cOMBS_1921392482t_bool @ ( cOMBS_811328630t_bool @ ( hAPP_f509814255t_bool @ ( cOMBB_231886989e_indi @ if_fun1658569689t_bool ) @ ( hAPP_n924210722i_bool @ ( hAPP_f62620517i_bool @ cOMBC_922322901t_bool @ ( hAPP_f1381130897t_bool @ ( cOMBB_981137617e_indi @ ord_less_nat ) @ h ) ) @ n ) ) @ ( hAPP_A658738638t_bool @ ( hAPP_f293545699t_bool @ cOMBC_18834461t_bool @ ( hAPP_f842954860t_bool @ ( cOMBB_117136048e_indi @ arrow_741591990_mktop ) @ p ) ) @ e ) ) @ ( cOMBS_1921392482t_bool @ ( cOMBS_811328630t_bool @ ( hAPP_f509814255t_bool @ ( cOMBB_231886989e_indi @ if_fun1658569689t_bool ) @ ( hAPP_n924210722i_bool @ ( hAPP_f62620517i_bool @ cOMBC_922322901t_bool @ ( hAPP_f1381130897t_bool @ ( cOMBB_981137617e_indi @ fequal_nat ) @ h ) ) @ n ) ) @ ( hAPP_A658738638t_bool @ ( hAPP_f293545699t_bool @ cOMBC_18834461t_bool @ ( hAPP_A102926893t_bool @ ( hAPP_f141075873t_bool @ cOMBC_1505804284t_bool @ ( hAPP_f576849227t_bool @ ( cOMBB_656639247e_indi @ arrow_1475523868_above ) @ p ) ) @ c ) ) @ e ) ) @ ( hAPP_A658738638t_bool @ ( hAPP_f293545699t_bool @ cOMBC_18834461t_bool @ ( hAPP_f842954860t_bool @ ( cOMBB_117136048e_indi @ arrow_592884904_mkbot ) @ p ) ) @ e ) ) ) ) ) )
     => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ c ) @ d ) ) @ ( hAPP_f792184801t_bool @ f @ p ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).

thf(529,axiom,
    ! [A: fun_Ar500372357t_bool,B: fun_Ar500372357t_bool,C: arrow_931160158le_alt,D: arrow_931160158le_alt,E: arrow_931160158le_alt,F: arrow_931160158le_alt] :
      ( ( E != F )
     => ( ( C != D )
       => ( ( E != D )
         => ( ( F != C )
           => ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ B ) @ arrow_1190054106e_Prof ) )
             => ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ A ) @ arrow_1190054106e_Prof ) )
               => ( ! [G: arrow_2115524757e_indi] :
                      ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ E ) @ F ) ) @ ( hAPP_A1174518481t_bool @ B @ G ) ) )
                    <=> ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ C ) @ D ) ) @ ( hAPP_A1174518481t_bool @ A @ G ) ) ) )
                 => ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ E ) @ F ) ) @ ( hAPP_f792184801t_bool @ f @ B ) ) )
                   => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ C ) @ D ) ) @ ( hAPP_f792184801t_bool @ f @ A ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7__C1_C) ).

thf(2776,plain,
    ! [A: fun_Ar500372357t_bool,B: fun_Ar500372357t_bool,C: arrow_931160158le_alt,D: arrow_931160158le_alt,E: arrow_931160158le_alt,F: arrow_931160158le_alt] :
      ( ( E != F )
     => ( ( C != D )
       => ( ( E != D )
         => ( ( F != C )
           => ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ B ) @ arrow_1190054106e_Prof ) )
             => ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ A ) @ arrow_1190054106e_Prof ) )
               => ( ! [G: arrow_2115524757e_indi] :
                      ( ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ E ) @ F ) ) @ ( hAPP_A1174518481t_bool @ B @ G ) ) )
                       => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ C ) @ D ) ) @ ( hAPP_A1174518481t_bool @ A @ G ) ) ) )
                      & ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ C ) @ D ) ) @ ( hAPP_A1174518481t_bool @ A @ G ) ) )
                       => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ E ) @ F ) ) @ ( hAPP_A1174518481t_bool @ B @ G ) ) ) ) )
                 => ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ E ) @ F ) ) @ ( hAPP_f792184801t_bool @ f @ B ) ) )
                   => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ C ) @ D ) ) @ ( hAPP_f792184801t_bool @ f @ A ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).

thf(688,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_520_psubset__trans) ).

thf(3377,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).

thf(483,axiom,
    ! [A: fun_fu1595299477t_bool,B: fun_fu243393031t_bool,C: fun_fu1015689055l_bool,D: fun_fu775006535l_bool] :
      ( ( hBOOL @ ( hAPP_f2106732305l_bool @ ( hAPP_f2071392713l_bool @ member449535860t_bool @ B ) @ ( pi_fun49394147t_bool @ C @ ( hAPP_f1197023401l_bool @ cOMBK_2140692976t_bool @ D ) ) ) )
     => ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( inj_on456593853t_bool @ B ) @ C ) )
       => ( ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ A ) @ ( pi_fun530160875t_bool @ D @ ( hAPP_f422714471l_bool @ cOMBK_1446432t_bool @ C ) ) ) )
         => ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( inj_on937360581t_bool @ A ) @ D ) )
           => ( ( hBOOL @ ( hAPP_f1021703871l_bool @ finite775027132t_bool @ C ) )
             => ( ( hBOOL @ ( hAPP_f1465510031l_bool @ finite1217814770t_bool @ D ) )
               => ( ( finite1445836347t_bool @ C )
                  = ( finite1418900531t_bool @ D ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_597_card__bij) ).

thf(2590,plain,
    ! [A: fun_fu1595299477t_bool,B: fun_fu243393031t_bool,C: fun_fu1015689055l_bool,D: fun_fu775006535l_bool] :
      ( ( hBOOL @ ( hAPP_f2106732305l_bool @ ( hAPP_f2071392713l_bool @ member449535860t_bool @ B ) @ ( pi_fun49394147t_bool @ C @ ( hAPP_f1197023401l_bool @ cOMBK_2140692976t_bool @ D ) ) ) )
     => ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( inj_on456593853t_bool @ B ) @ C ) )
       => ( ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ A ) @ ( pi_fun530160875t_bool @ D @ ( hAPP_f422714471l_bool @ cOMBK_1446432t_bool @ C ) ) ) )
         => ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( inj_on937360581t_bool @ A ) @ D ) )
           => ( ( hBOOL @ ( hAPP_f1021703871l_bool @ finite775027132t_bool @ C ) )
             => ( ( hBOOL @ ( hAPP_f1465510031l_bool @ finite1217814770t_bool @ D ) )
               => ( ( finite1445836347t_bool @ C )
                  = ( finite1418900531t_bool @ D ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).

thf(614,axiom,
    ! [A: produc1840315303le_alt,B: fun_Pr1698894881e_indi,C: fun_Pr1055212137t_bool,D: fun_Pr39488737i_bool] :
      ( ( hBOOL @ ( hAPP_f932587383l_bool @ ( hAPP_f1165889229l_bool @ member1747786740e_indi @ B ) @ ( pi_Pro1592011445e_indi @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ ( hAPP_P1031342399e_indi @ B @ A ) ) @ ( hAPP_P1326783277i_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_PiE) ).

thf(3098,plain,
    ! [A: produc1840315303le_alt,B: fun_Pr1698894881e_indi,C: fun_Pr1055212137t_bool,D: fun_Pr39488737i_bool] :
      ( ( hBOOL @ ( hAPP_f932587383l_bool @ ( hAPP_f1165889229l_bool @ member1747786740e_indi @ B ) @ ( pi_Pro1592011445e_indi @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ ( hAPP_P1031342399e_indi @ B @ A ) ) @ ( hAPP_P1326783277i_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).

thf(343,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( A = B )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_488_equalityD2) ).

thf(2014,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( A = B )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(135,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ D ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ D ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_396_add__le__less__mono) ).

thf(1205,plain,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ D ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ D ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(119,axiom,
    ! [A: fun_bo1549164019l_bool,B: fun_nat_bool,C: nat] :
      ( ( hAPP_n1006566506l_bool @ ( hAPP_f1146629647l_bool @ ( cOMBB_1015721476ol_nat @ A ) @ B ) @ C )
      = ( hAPP_b589554111l_bool @ A @ ( hAPP_nat_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo) ).

thf(1142,plain,
    ! [A: fun_bo1549164019l_bool,B: fun_nat_bool,C: nat] :
      ( ( hAPP_n1006566506l_bool @ ( hAPP_f1146629647l_bool @ ( cOMBB_1015721476ol_nat @ A ) @ B ) @ C )
      = ( hAPP_b589554111l_bool @ A @ ( hAPP_nat_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(721,axiom,
    ! [A: arrow_931160158le_alt,B: arrow_931160158le_alt,C: fun_Pr1055212137t_bool,D: arrow_931160158le_alt] :
      ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ A ) @ B ) ) @ ( hAPP_A606737888t_bool @ ( hAPP_f786530292t_bool @ arrow_741591990_mktop @ C ) @ D ) ) )
    <=> ( ( A != D )
        & ( ( B = D )
         => ( A != B ) )
        & ( ( B != D )
         => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ A ) @ B ) ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_in__mktop) ).

thf(3498,plain,
    ! [A: arrow_931160158le_alt,B: arrow_931160158le_alt,C: fun_Pr1055212137t_bool,D: arrow_931160158le_alt] :
      ( ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ A ) @ B ) ) @ ( hAPP_A606737888t_bool @ ( hAPP_f786530292t_bool @ arrow_741591990_mktop @ C ) @ D ) ) )
       => ( ( A != D )
          & ( ( B = D )
           => ( A != B ) )
          & ( ( B != D )
           => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ A ) @ B ) ) @ C ) ) ) ) )
      & ( ( ( A != D )
          & ( ( B = D )
           => ( A != B ) )
          & ( ( B != D )
           => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ A ) @ B ) ) @ C ) ) ) )
       => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ A ) @ B ) ) @ ( hAPP_A606737888t_bool @ ( hAPP_f786530292t_bool @ arrow_741591990_mktop @ C ) @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).

thf(552,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_452_psubset__imp__subset) ).

thf(2854,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).

thf(34,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
      | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_linorder__le__less__linear) ).

thf(861,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
      | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(638,axiom,
    hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ a ) @ b ) ) @ ( hAPP_f792184801t_bool @ f @ ( hAPP_f311418073t_bool @ ( hAPP_f1302245795t_bool @ cOMBC_1490589522t_bool @ ( hAPP_f1755759597t_bool @ ( hAPP_f1328803787t_bool @ cOMBC_1190055014t_bool @ ( hAPP_f509814255t_bool @ ( cOMBB_231886989e_indi @ if_fun1658569689t_bool ) @ ( hAPP_n924210722i_bool @ ( hAPP_f62620517i_bool @ cOMBC_922322901t_bool @ ( hAPP_f1381130897t_bool @ ( cOMBB_981137617e_indi @ ord_less_nat ) @ h ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ n ) @ one_one_nat ) ) ) ) @ lab ) ) @ lba ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_n_I3_J) ).

thf(3185,plain,
    hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ a ) @ b ) ) @ ( hAPP_f792184801t_bool @ f @ ( hAPP_f311418073t_bool @ ( hAPP_f1302245795t_bool @ cOMBC_1490589522t_bool @ ( hAPP_f1755759597t_bool @ ( hAPP_f1328803787t_bool @ cOMBC_1190055014t_bool @ ( hAPP_f509814255t_bool @ ( cOMBB_231886989e_indi @ if_fun1658569689t_bool ) @ ( hAPP_n924210722i_bool @ ( hAPP_f62620517i_bool @ cOMBC_922322901t_bool @ ( hAPP_f1381130897t_bool @ ( cOMBB_981137617e_indi @ ord_less_nat ) @ h ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ n ) @ one_one_nat ) ) ) ) @ lab ) ) @ lba ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).

thf(72,axiom,
    ! [A: nat,B: nat] :
      ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) )
      <=> ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_648_not__less__less__Suc__eq) ).

thf(977,plain,
    ! [A: nat,B: nat] :
      ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) )
         => ( A = B ) )
        & ( ( A = B )
         => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(191,axiom,
    ( arrow_1190054106e_Prof
    = ( pi_Arr487970267t_bool @ top_to1678393681i_bool @ ( hAPP_f1793492343l_bool @ cOMBK_1595020336e_indi @ arrow_915577424le_Lin ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_375_Prof__def) ).

thf(1422,plain,
    ( arrow_1190054106e_Prof
    = ( pi_Arr487970267t_bool @ top_to1678393681i_bool @ ( hAPP_f1793492343l_bool @ cOMBK_1595020336e_indi @ arrow_915577424le_Lin ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(233,axiom,
    ! [A: nat,B: nat,C: fun_nat_nat] :
      ( ! [D: nat,E: nat] :
          ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ D ) @ E ) )
         => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ C @ D ) ) @ ( hAPP_nat_nat @ C @ E ) ) ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ C @ A ) ) @ ( hAPP_nat_nat @ C @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_569_less__mono__imp__le__mono) ).

thf(1569,plain,
    ! [A: nat,B: nat,C: fun_nat_nat] :
      ( ! [D: nat,E: nat] :
          ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ D ) @ E ) )
         => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ C @ D ) ) @ ( hAPP_nat_nat @ C @ E ) ) ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ C @ A ) ) @ ( hAPP_nat_nat @ C @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(333,axiom,
    ! [A: arrow_931160158le_alt,B: arrow_931160158le_alt] :
      ( ( A != B )
     => ? [C: fun_Pr1055212137t_bool] :
          ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ C ) @ arrow_915577424le_Lin ) )
          & ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ A ) @ B ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_complete__Lin) ).

thf(1939,plain,
    ! [A: arrow_931160158le_alt,B: arrow_931160158le_alt] :
      ( ( A != B )
     => ? [C: fun_Pr1055212137t_bool] :
          ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ C ) @ arrow_915577424le_Lin ) )
          & ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ A ) @ B ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(597,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_437_equalityI) ).

thf(3017,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).

thf(260,axiom,
    ! [A: bool,B: fun_bo1116297149t_bool,C: fun_bool_bool,D: fun_bo96602657l_bool] :
      ( ( hBOOL @ ( hAPP_f2041629639l_bool @ ( hAPP_f134102069l_bool @ member818572202t_bool @ B ) @ ( pi_boo98824211t_bool @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ ( hAPP_b1263785481t_bool @ B @ A ) ) @ ( hAPP_b1650070463l_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_PiE) ).

thf(1671,plain,
    ! [A: bool,B: fun_bo1116297149t_bool,C: fun_bool_bool,D: fun_bo96602657l_bool] :
      ( ( hBOOL @ ( hAPP_f2041629639l_bool @ ( hAPP_f134102069l_bool @ member818572202t_bool @ B ) @ ( pi_boo98824211t_bool @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ ( hAPP_b1263785481t_bool @ B @ A ) ) @ ( hAPP_b1650070463l_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(704,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_order__antisym) ).

thf(3439,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).

thf(258,axiom,
    ! [A: bool] :
      ( ~ ( ( hBOOL @ A )
        <=> ( hBOOL @ top_top_bool ) )
    <=> ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_bool @ A ) @ top_top_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_less__top) ).

thf(1655,plain,
    ! [A: bool] :
      ( ( ~ ( ( ( hBOOL @ A )
             => ( hBOOL @ top_top_bool ) )
            & ( ( hBOOL @ top_top_bool )
             => ( hBOOL @ A ) ) )
       => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_bool @ A ) @ top_top_bool ) ) )
      & ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_bool @ A ) @ top_top_bool ) )
       => ~ ( ( ( hBOOL @ A )
             => ( hBOOL @ top_top_bool ) )
            & ( ( hBOOL @ top_top_bool )
             => ( hBOOL @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(280,axiom,
    ! [A: fun_Pr1055212137t_bool,B: fun_bool_bool,C: fun_Pr1055212137t_bool] :
      ( ! [D: produc1840315303le_alt] :
          ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ D ) @ C ) )
         => ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ ( hAPP_P166437127t_bool @ A @ D ) ) @ B ) ) )
     => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ A ) @ ( pi_Pro226591613t_bool @ C @ ( hAPP_f1426772275l_bool @ cOMBK_1506144056le_alt @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_576_funcsetI) ).

thf(1756,plain,
    ! [A: fun_Pr1055212137t_bool,B: fun_bool_bool,C: fun_Pr1055212137t_bool] :
      ( ! [D: produc1840315303le_alt] :
          ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ D ) @ C ) )
         => ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ ( hAPP_P166437127t_bool @ A @ D ) ) @ B ) ) )
     => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ A ) @ ( pi_Pro226591613t_bool @ C @ ( hAPP_f1426772275l_bool @ cOMBK_1506144056le_alt @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(672,axiom,
    ! [A: fun_fu1595299477t_bool,B: fun_fu1138137687l_bool,C: fun_fu1138137687l_bool,D: fun_fu1460706235l_bool] :
      ( ( hBOOL @ ( hAPP_f2081160365l_bool @ ( hAPP_f481662541l_bool @ member213355690l_bool @ B ) @ ( pi_fun351900523l_bool @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ ( hAPP_f611501301l_bool @ B @ A ) ) @ ( hAPP_f352672903l_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_PiE) ).

thf(3332,plain,
    ! [A: fun_fu1595299477t_bool,B: fun_fu1138137687l_bool,C: fun_fu1138137687l_bool,D: fun_fu1460706235l_bool] :
      ( ( hBOOL @ ( hAPP_f2081160365l_bool @ ( hAPP_f481662541l_bool @ member213355690l_bool @ B ) @ ( pi_fun351900523l_bool @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ ( hAPP_f611501301l_bool @ B @ A ) ) @ ( hAPP_f352672903l_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).

thf(382,axiom,
    ! [A: fun_Pr1055212137t_bool,B: fun_fu1015689055l_bool,C: fun_fu1015689055l_bool] :
      ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f868566847l_bool @ ord_le1923264405l_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_484_in__mono) ).

thf(2184,plain,
    ! [A: fun_Pr1055212137t_bool,B: fun_fu1015689055l_bool,C: fun_fu1015689055l_bool] :
      ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f868566847l_bool @ ord_le1923264405l_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(15,axiom,
    ! [A: nat,B: nat] :
      ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
    <=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_linorder__not__le) ).

thf(797,plain,
    ! [A: nat,B: nat] :
      ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) )
      & ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) )
       => ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(154,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
    <=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
        | ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_556_le__eq__less__or__eq) ).

thf(1275,plain,
    ! [A: nat,B: nat] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
       => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
          | ( A = B ) ) )
      & ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
          | ( A = B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(435,axiom,
    ? [A: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( finite783399747e_indi @ top_to1678393681i_bool ) ) )
      & ! [B: nat] :
          ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
         => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ b ) @ a ) ) @ ( hAPP_f792184801t_bool @ f @ ( hAPP_f311418073t_bool @ ( hAPP_f1302245795t_bool @ cOMBC_1490589522t_bool @ ( hAPP_f1755759597t_bool @ ( hAPP_f1328803787t_bool @ cOMBC_1190055014t_bool @ ( hAPP_f509814255t_bool @ ( cOMBB_231886989e_indi @ if_fun1658569689t_bool ) @ ( hAPP_n924210722i_bool @ ( hAPP_f62620517i_bool @ cOMBC_922322901t_bool @ ( hAPP_f1381130897t_bool @ ( cOMBB_981137617e_indi @ ord_less_nat ) @ h ) ) @ B ) ) ) @ lab ) ) @ lba ) ) ) ) )
      & ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ a ) @ b ) ) @ ( hAPP_f792184801t_bool @ f @ ( hAPP_f311418073t_bool @ ( hAPP_f1302245795t_bool @ cOMBC_1490589522t_bool @ ( hAPP_f1755759597t_bool @ ( hAPP_f1328803787t_bool @ cOMBC_1190055014t_bool @ ( hAPP_f509814255t_bool @ ( cOMBB_231886989e_indi @ if_fun1658569689t_bool ) @ ( hAPP_n924210722i_bool @ ( hAPP_f62620517i_bool @ cOMBC_922322901t_bool @ ( hAPP_f1381130897t_bool @ ( cOMBB_981137617e_indi @ ord_less_nat ) @ h ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ one_one_nat ) ) ) ) @ lab ) ) @ lba ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I) ).

thf(2434,plain,
    ? [A: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( finite783399747e_indi @ top_to1678393681i_bool ) ) )
      & ! [B: nat] :
          ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
         => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ b ) @ a ) ) @ ( hAPP_f792184801t_bool @ f @ ( hAPP_f311418073t_bool @ ( hAPP_f1302245795t_bool @ cOMBC_1490589522t_bool @ ( hAPP_f1755759597t_bool @ ( hAPP_f1328803787t_bool @ cOMBC_1190055014t_bool @ ( hAPP_f509814255t_bool @ ( cOMBB_231886989e_indi @ if_fun1658569689t_bool ) @ ( hAPP_n924210722i_bool @ ( hAPP_f62620517i_bool @ cOMBC_922322901t_bool @ ( hAPP_f1381130897t_bool @ ( cOMBB_981137617e_indi @ ord_less_nat ) @ h ) ) @ B ) ) ) @ lab ) ) @ lba ) ) ) ) )
      & ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ a ) @ b ) ) @ ( hAPP_f792184801t_bool @ f @ ( hAPP_f311418073t_bool @ ( hAPP_f1302245795t_bool @ cOMBC_1490589522t_bool @ ( hAPP_f1755759597t_bool @ ( hAPP_f1328803787t_bool @ cOMBC_1190055014t_bool @ ( hAPP_f509814255t_bool @ ( cOMBB_231886989e_indi @ if_fun1658569689t_bool ) @ ( hAPP_n924210722i_bool @ ( hAPP_f62620517i_bool @ cOMBC_922322901t_bool @ ( hAPP_f1381130897t_bool @ ( cOMBB_981137617e_indi @ ord_less_nat ) @ h ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ one_one_nat ) ) ) ) @ lab ) ) @ lba ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).

thf(168,axiom,
    ! [A: bool,B: produc1840315303le_alt] :
      ( ( hAPP_P166437127t_bool @ ( hAPP_b1263785481t_bool @ cOMBK_1566242880le_alt @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__prod_Itc__Arrow____Order____Mirabe) ).

thf(1327,plain,
    ! [A: bool,B: produc1840315303le_alt] :
      ( ( hAPP_P166437127t_bool @ ( hAPP_b1263785481t_bool @ cOMBK_1566242880le_alt @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(492,axiom,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ A ) @ B ) )
    <=> ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ B ) )
        | ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_450_subset__iff__psubset__eq) ).

thf(2627,plain,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ A ) @ B ) )
       => ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ B ) )
          | ( A = B ) ) )
      & ( ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ B ) )
          | ( A = B ) )
       => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).

thf(60,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ D ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ D ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_424_add__mono) ).

thf(945,plain,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ D ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ D ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(549,axiom,
    ! [A: product_unit,B: fun_Pr1337256141t_bool,C: fun_Pr1643180309t_bool,D: fun_Pr1832937781l_bool] :
      ( ( hBOOL @ ( hAPP_f522449699l_bool @ ( hAPP_f1960079821l_bool @ member1948336672t_bool @ B ) @ ( pi_Pro1014195041t_bool @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ ( hAPP_P1339635435t_bool @ B @ A ) ) @ ( hAPP_P1470717569l_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_PiE) ).

thf(2844,plain,
    ! [A: product_unit,B: fun_Pr1337256141t_bool,C: fun_Pr1643180309t_bool,D: fun_Pr1832937781l_bool] :
      ( ( hBOOL @ ( hAPP_f522449699l_bool @ ( hAPP_f1960079821l_bool @ member1948336672t_bool @ B ) @ ( pi_Pro1014195041t_bool @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ ( hAPP_P1339635435t_bool @ B @ A ) ) @ ( hAPP_P1470717569l_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).

thf(739,axiom,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_300_order__less__imp__le) ).

thf(3577,plain,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).

thf(424,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_xt1_I10_J) ).

thf(2360,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).

thf(193,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
     => ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
      <=> ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_304_linorder__antisym__conv2) ).

thf(1426,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
     => ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
         => ( A = B ) )
        & ( ( A = B )
         => ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(725,axiom,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ B ) )
     => ( A != B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_order__less__imp__not__eq) ).

thf(3530,plain,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ B ) )
     => ( A != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).

thf(326,axiom,
    hBOOL @ fTrue,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fTrue_1_1_U) ).

thf(1919,plain,
    hBOOL @ fTrue,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(653,axiom,
    ! [A: fun_Ar1744566822di_nat,B: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( inj_on886403158di_nat @ A ) @ B ) )
    <=> ! [C: arrow_2115524757e_indi] :
          ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ C ) @ B ) )
         => ! [D: arrow_2115524757e_indi] :
              ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ D ) @ B ) )
             => ( ( ( hAPP_A1450069362di_nat @ A @ C )
                  = ( hAPP_A1450069362di_nat @ A @ D ) )
               => ( C = D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_365_inj__on__def) ).

thf(3253,plain,
    ! [A: fun_Ar1744566822di_nat,B: fun_Ar552120407i_bool] :
      ( ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( inj_on886403158di_nat @ A ) @ B ) )
       => ! [C: arrow_2115524757e_indi] :
            ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ C ) @ B ) )
           => ! [D: arrow_2115524757e_indi] :
                ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ D ) @ B ) )
               => ( ( ( hAPP_A1450069362di_nat @ A @ C )
                    = ( hAPP_A1450069362di_nat @ A @ D ) )
                 => ( C = D ) ) ) ) )
      & ( ! [C: arrow_2115524757e_indi] :
            ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ C ) @ B ) )
           => ! [D: arrow_2115524757e_indi] :
                ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ D ) @ B ) )
               => ( ( ( hAPP_A1450069362di_nat @ A @ C )
                    = ( hAPP_A1450069362di_nat @ A @ D ) )
                 => ( C = D ) ) ) )
       => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( inj_on886403158di_nat @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).

thf(338,axiom,
    ! [A: arrow_2115524757e_indi,B: arrow_2115524757e_indi,C: fun_Ar1744566822di_nat,D: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( inj_on886403158di_nat @ C ) @ D ) )
     => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ B ) @ D ) )
       => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ A ) @ D ) )
         => ( ( ( hAPP_A1450069362di_nat @ C @ B )
              = ( hAPP_A1450069362di_nat @ C @ A ) )
          <=> ( B = A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_369_inj__on__iff) ).

thf(1988,plain,
    ! [A: arrow_2115524757e_indi,B: arrow_2115524757e_indi,C: fun_Ar1744566822di_nat,D: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( inj_on886403158di_nat @ C ) @ D ) )
     => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ B ) @ D ) )
       => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ A ) @ D ) )
         => ( ( ( ( hAPP_A1450069362di_nat @ C @ B )
                = ( hAPP_A1450069362di_nat @ C @ A ) )
             => ( B = A ) )
            & ( ( B = A )
             => ( ( hAPP_A1450069362di_nat @ C @ B )
                = ( hAPP_A1450069362di_nat @ C @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(699,axiom,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ ( hAPP_f427533077t_bool @ ( hAPP_f1458726223t_bool @ cOMBC_2133163426l_bool @ member_Product_unit ) @ A ) ) @ ( hAPP_f427533077t_bool @ ( hAPP_f1458726223t_bool @ cOMBC_2133163426l_bool @ member_Product_unit ) @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_494_pred__subset__eq) ).

thf(3414,plain,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ ( hAPP_f427533077t_bool @ ( hAPP_f1458726223t_bool @ cOMBC_2133163426l_bool @ member_Product_unit ) @ A ) ) @ ( hAPP_f427533077t_bool @ ( hAPP_f1458726223t_bool @ cOMBC_2133163426l_bool @ member_Product_unit ) @ B ) ) )
       => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ A ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ ( hAPP_f427533077t_bool @ ( hAPP_f1458726223t_bool @ cOMBC_2133163426l_bool @ member_Product_unit ) @ A ) ) @ ( hAPP_f427533077t_bool @ ( hAPP_f1458726223t_bool @ cOMBC_2133163426l_bool @ member_Product_unit ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).

thf(51,axiom,
    ! [A: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
     => ? [B: nat] :
          ( A
          = ( hAPP_nat_nat @ suc @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_686_gr0__implies__Suc) ).

thf(913,plain,
    ! [A: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
     => ? [B: nat] :
          ( A
          = ( hAPP_nat_nat @ suc @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(735,axiom,
    ! [A: fun_Pr1055212137t_bool] :
      ( ( A != top_to126038883t_bool )
    <=> ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_f314169011l_bool @ ord_le466311871t_bool @ A ) @ top_to126038883t_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_less__top) ).

thf(3562,plain,
    ! [A: fun_Pr1055212137t_bool] :
      ( ( ( A != top_to126038883t_bool )
       => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_f314169011l_bool @ ord_le466311871t_bool @ A ) @ top_to126038883t_bool ) ) )
      & ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_f314169011l_bool @ ord_le466311871t_bool @ A ) @ top_to126038883t_bool ) )
       => ( A != top_to126038883t_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).

thf(253,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_455_psubset__subset__trans) ).

thf(1640,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(480,axiom,
    ! [A: fun_bool_bool,B: fun_bool_bool] :
      ( ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_f612708895l_bool @ ord_le742797417l_bool @ ( hAPP_f961197973l_bool @ ( hAPP_f1996228283l_bool @ cOMBC_1455277858l_bool @ member_bool ) @ A ) ) @ ( hAPP_f961197973l_bool @ ( hAPP_f1996228283l_bool @ cOMBC_1455277858l_bool @ member_bool ) @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_f612708895l_bool @ ord_le742797417l_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_493_pred__subset__eq) ).

thf(2580,plain,
    ! [A: fun_bool_bool,B: fun_bool_bool] :
      ( ( ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_f612708895l_bool @ ord_le742797417l_bool @ ( hAPP_f961197973l_bool @ ( hAPP_f1996228283l_bool @ cOMBC_1455277858l_bool @ member_bool ) @ A ) ) @ ( hAPP_f961197973l_bool @ ( hAPP_f1996228283l_bool @ cOMBC_1455277858l_bool @ member_bool ) @ B ) ) )
       => ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_f612708895l_bool @ ord_le742797417l_bool @ A ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_f612708895l_bool @ ord_le742797417l_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_f612708895l_bool @ ord_le742797417l_bool @ ( hAPP_f961197973l_bool @ ( hAPP_f1996228283l_bool @ cOMBC_1455277858l_bool @ member_bool ) @ A ) ) @ ( hAPP_f961197973l_bool @ ( hAPP_f1996228283l_bool @ cOMBC_1455277858l_bool @ member_bool ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).

thf(133,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
    <=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
        & ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_279_less__le__not__le) ).

thf(1196,plain,
    ! [A: nat,B: nat] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
       => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
          & ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
          & ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(396,axiom,
    ! [A: fun_nat_bool] :
      ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ top_top_fun_nat_bool ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_not__top__less) ).

thf(2216,plain,
    ! [A: fun_nat_bool] :
      ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ top_top_fun_nat_bool ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(511,axiom,
    ! [A: fun_fu1556412341l_bool,B: fun_fu1015689055l_bool,C: fun_Pr1055212137t_bool] :
      ( ( hAPP_f429946033l_bool @ ( hAPP_f1050277569l_bool @ ( hAPP_f639477379l_bool @ cOMBC_437066390l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ct) ).

thf(2723,plain,
    ! [A: fun_fu1556412341l_bool,B: fun_fu1015689055l_bool,C: fun_Pr1055212137t_bool] :
      ( ( hAPP_f429946033l_bool @ ( hAPP_f1050277569l_bool @ ( hAPP_f639477379l_bool @ cOMBC_437066390l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).

thf(589,axiom,
    ! [A: product_unit,B: fun_Pr1643180309t_bool,C: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_513_psubsetD) ).

thf(2972,plain,
    ! [A: product_unit,B: fun_Pr1643180309t_bool,C: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).

thf(472,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( B = C )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_ord__eq__less__trans) ).

thf(2548,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( B = C )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).

thf(28,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B )
        = ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ B ) )
     => ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_415_add__right__imp__eq) ).

thf(841,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B )
        = ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ B ) )
     => ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(342,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( B = C )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_xt1_I3_J) ).

thf(2010,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( B = C )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(463,axiom,
    ! [A: nat,B: fun_nat_nat] :
      ( ! [C: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ ( hAPP_nat_nat @ B @ C ) ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( hAPP_n1699378549t_bool @ ( hAPP_f229349961t_bool @ cOMBC_nat_nat_bool @ ( hAPP_f618557131t_bool @ ( cOMBB_800536526ol_nat @ ord_less_eq_nat ) @ B ) ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_609_finite__less__ub) ).

thf(2516,plain,
    ! [A: nat,B: fun_nat_nat] :
      ( ! [C: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ ( hAPP_nat_nat @ B @ C ) ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( hAPP_n1699378549t_bool @ ( hAPP_f229349961t_bool @ cOMBC_nat_nat_bool @ ( hAPP_f618557131t_bool @ ( cOMBB_800536526ol_nat @ ord_less_eq_nat ) @ B ) ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).

thf(368,axiom,
    ! [A: nat] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ top_top_fun_nat_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_UNIV__I) ).

thf(2136,plain,
    ! [A: nat] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ top_top_fun_nat_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(559,axiom,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool,C: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_322_order__less__le__trans) ).

thf(2869,plain,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool,C: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).

thf(434,axiom,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool,C: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_337_xt1_I8_J) ).

thf(2432,plain,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool,C: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).

thf(324,axiom,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool,C: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_order__less__trans) ).

thf(1914,plain,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool,C: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(10,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
    <=> ! [C: nat] : ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_nat_bool @ A @ C ) ) @ ( hAPP_nat_bool @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_266_le__fun__def) ).

thf(782,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
       => ! [C: nat] : ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_nat_bool @ A @ C ) ) @ ( hAPP_nat_bool @ B @ C ) ) ) )
      & ( ! [C: nat] : ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_nat_bool @ A @ C ) ) @ ( hAPP_nat_bool @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(196,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
    <=> ? [C: nat] :
          ( B
          = ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_664_less__iff__Suc__add) ).

thf(1441,plain,
    ! [A: nat,B: nat] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
       => ? [C: nat] :
            ( B
            = ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) ) )
      & ( ? [C: nat] :
            ( B
            = ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(541,axiom,
    ! [A: produc1840315303le_alt,B: fun_Pr1055212137t_bool,C: fun_Pr1055212137t_bool,D: fun_bool_bool] :
      ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ B ) @ ( pi_Pro226591613t_bool @ C @ ( hAPP_f1426772275l_bool @ cOMBK_1506144056le_alt @ D ) ) ) )
     => ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ ( hAPP_P166437127t_bool @ B @ A ) ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_377_funcset__mem) ).

thf(2825,plain,
    ! [A: produc1840315303le_alt,B: fun_Pr1055212137t_bool,C: fun_Pr1055212137t_bool,D: fun_bool_bool] :
      ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ B ) @ ( pi_Pro226591613t_bool @ C @ ( hAPP_f1426772275l_bool @ cOMBK_1506144056le_alt @ D ) ) ) )
     => ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ ( hAPP_P166437127t_bool @ B @ A ) ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).

thf(219,axiom,
    ! [A: nat,B: nat] :
      ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B )
      = ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_643_add__Suc) ).

thf(1529,plain,
    ! [A: nat,B: nat] :
      ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B )
      = ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(208,axiom,
    ! [A: fun_nat_bool,B: nat] :
      ( ( hAPP_n1699378549t_bool @ ( hAPP_f1570313510t_bool @ cOMBK_583454926ol_nat @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Nat__Ona) ).

thf(1482,plain,
    ! [A: fun_nat_bool,B: nat] :
      ( ( hAPP_n1699378549t_bool @ ( hAPP_f1570313510t_bool @ cOMBK_583454926ol_nat @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(748,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_order__less__imp__not__less) ).

thf(3597,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).

thf(149,axiom,
    ! [A: bool,B: fun_fu1595299477t_bool] :
      ( ( hAPP_f611501301l_bool @ ( hAPP_b816606711l_bool @ cOMBK_759924014t_bool @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Arrow____Order__) ).

thf(1254,plain,
    ! [A: bool,B: fun_fu1595299477t_bool] :
      ( ( hAPP_f611501301l_bool @ ( hAPP_b816606711l_bool @ cOMBK_759924014t_bool @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(705,axiom,
    ! [A: fun_Pr1055212137t_bool,B: fun_fu1015689055l_bool,C: fun_fu1015689055l_bool] :
      ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f868566847l_bool @ ord_le1923264405l_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_442_subsetD) ).

thf(3442,plain,
    ! [A: fun_Pr1055212137t_bool,B: fun_fu1015689055l_bool,C: fun_fu1015689055l_bool] :
      ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f868566847l_bool @ ord_le1923264405l_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).

thf(648,axiom,
    ! [A: fun_bo1479727337le_alt,B: fun_Pr1055212137t_bool,C: fun_Pr1055212137t_bool,D: fun_bool_bool] :
      ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ B ) @ ( pi_Pro226591613t_bool @ C @ ( hAPP_f1426772275l_bool @ cOMBK_1506144056le_alt @ D ) ) ) )
     => ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( inj_on899118883t_bool @ B ) @ C ) )
       => ( ( hBOOL @ ( hAPP_f1339624767l_bool @ ( hAPP_f1862158541l_bool @ member481633596le_alt @ A ) @ ( pi_boo1374671485le_alt @ D @ ( hAPP_f414777105t_bool @ cOMBK_382434616l_bool @ C ) ) ) )
         => ( ( hBOOL @ ( hAPP_f387058535l_bool @ ( inj_on2047198755le_alt @ A ) @ D ) )
           => ( ( hBOOL @ ( hAPP_f429946033l_bool @ finite788329492le_alt @ C ) )
             => ( ( hBOOL @ ( hAPP_f387058535l_bool @ finite_finite_bool @ D ) )
               => ( ( finite876838485le_alt @ C )
                  = ( finite_card_bool @ D ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_598_card__bij) ).

thf(3221,plain,
    ! [A: fun_bo1479727337le_alt,B: fun_Pr1055212137t_bool,C: fun_Pr1055212137t_bool,D: fun_bool_bool] :
      ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ B ) @ ( pi_Pro226591613t_bool @ C @ ( hAPP_f1426772275l_bool @ cOMBK_1506144056le_alt @ D ) ) ) )
     => ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( inj_on899118883t_bool @ B ) @ C ) )
       => ( ( hBOOL @ ( hAPP_f1339624767l_bool @ ( hAPP_f1862158541l_bool @ member481633596le_alt @ A ) @ ( pi_boo1374671485le_alt @ D @ ( hAPP_f414777105t_bool @ cOMBK_382434616l_bool @ C ) ) ) )
         => ( ( hBOOL @ ( hAPP_f387058535l_bool @ ( inj_on2047198755le_alt @ A ) @ D ) )
           => ( ( hBOOL @ ( hAPP_f429946033l_bool @ finite788329492le_alt @ C ) )
             => ( ( hBOOL @ ( hAPP_f387058535l_bool @ finite_finite_bool @ D ) )
               => ( ( finite876838485le_alt @ C )
                  = ( finite_card_bool @ D ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).

thf(575,axiom,
    ! [A: bool,B: bool] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ A ) )
      <=> ( ( hBOOL @ B )
        <=> ( hBOOL @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_order__antisym__conv) ).

thf(2916,plain,
    ! [A: bool,B: bool] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ B ) )
     => ( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ A ) )
         => ( ( ( hBOOL @ B )
             => ( hBOOL @ A ) )
            & ( ( hBOOL @ A )
             => ( hBOOL @ B ) ) ) )
        & ( ( ( ( hBOOL @ B )
             => ( hBOOL @ A ) )
            & ( ( hBOOL @ A )
             => ( hBOOL @ B ) ) )
         => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).

thf(657,axiom,
    ! [A: nat,B: nat] :
      ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( ( A != B )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_linorder__cases) ).

thf(3275,plain,
    ! [A: nat,B: nat] :
      ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( ( A != B )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).

thf(158,axiom,
    ! [A: nat,B: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_665_less__add__Suc2) ).

thf(1298,plain,
    ! [A: nat,B: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(675,axiom,
    ! [A: produc1840315303le_alt,B: fun_Pr1055212137t_bool,C: fun_Pr1055212137t_bool,D: fun_Pr359894313l_bool] :
      ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ B ) @ ( pi_Pro226591613t_bool @ C @ D ) ) )
     => ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ ( hAPP_P166437127t_bool @ B @ A ) ) @ ( hAPP_P1830623733l_bool @ D @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_372_Pi__mem) ).

thf(3342,plain,
    ! [A: produc1840315303le_alt,B: fun_Pr1055212137t_bool,C: fun_Pr1055212137t_bool,D: fun_Pr359894313l_bool] :
      ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ B ) @ ( pi_Pro226591613t_bool @ C @ D ) ) )
     => ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ ( hAPP_P166437127t_bool @ B @ A ) ) @ ( hAPP_P1830623733l_bool @ D @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).

thf(310,axiom,
    ! [A: bool,B: fun_bo266809543t_bool,C: fun_bool_bool,D: fun_bo645734555l_bool] :
      ( ( hBOOL @ ( hAPP_f976121117l_bool @ ( hAPP_f621492301l_bool @ member1283254298t_bool @ B ) @ ( pi_boo573599835t_bool @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ ( hAPP_b715352037t_bool @ B @ A ) ) @ ( hAPP_b1849744615l_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_PiE) ).

thf(1871,plain,
    ! [A: bool,B: fun_bo266809543t_bool,C: fun_bool_bool,D: fun_bo645734555l_bool] :
      ( ( hBOOL @ ( hAPP_f976121117l_bool @ ( hAPP_f621492301l_bool @ member1283254298t_bool @ B ) @ ( pi_boo573599835t_bool @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ ( hAPP_b715352037t_bool @ B @ A ) ) @ ( hAPP_b1849744615l_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(508,axiom,
    ! [A: fun_nat_fun_nat_bool,B: nat,C: nat] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ A @ C ) @ B ) ) )
     => ( ( ( B = C )
         => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ A @ C ) @ B ) ) )
       => ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ B ) )
           => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ A @ C ) @ B ) ) )
         => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ A @ C ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_533_nat__less__cases) ).

thf(2708,plain,
    ! [A: fun_nat_fun_nat_bool,B: nat,C: nat] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ A @ C ) @ B ) ) )
     => ( ( ( B = C )
         => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ A @ C ) @ B ) ) )
       => ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ B ) )
           => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ A @ C ) @ B ) ) )
         => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ A @ C ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).

thf(413,axiom,
    ! [A: arrow_2115524757e_indi] :
      ( ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_A1450069362di_nat @ h @ A ) ) @ n ) )
         => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ c ) @ e ) ) @ ( hAPP_A606737888t_bool @ ( hAPP_f786530292t_bool @ arrow_741591990_mktop @ ( hAPP_A1174518481t_bool @ p @ A ) ) @ e ) ) ) )
        & ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_A1450069362di_nat @ h @ A ) ) @ n ) )
         => ( ( ( ( hAPP_A1450069362di_nat @ h @ A )
                = n )
             => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ c ) @ e ) ) @ ( hAPP_A606737888t_bool @ ( hAPP_A501825983t_bool @ ( hAPP_f1909595219t_bool @ arrow_1475523868_above @ ( hAPP_A1174518481t_bool @ p @ A ) ) @ c ) @ e ) ) ) )
            & ( ( ( hAPP_A1450069362di_nat @ h @ A )
               != n )
             => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ c ) @ e ) ) @ ( hAPP_A606737888t_bool @ ( hAPP_f786530292t_bool @ arrow_592884904_mkbot @ ( hAPP_A1174518481t_bool @ p @ A ) ) @ e ) ) ) ) ) ) )
    <=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_A1450069362di_nat @ h @ A ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ n ) @ one_one_nat ) ) )
         => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ a ) @ b ) ) @ lab ) ) )
        & ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_A1450069362di_nat @ h @ A ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ n ) @ one_one_nat ) ) )
         => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ a ) @ b ) ) @ lba ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Am) ).

thf(2274,plain,
    ! [A: arrow_2115524757e_indi] :
      ( ( ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_A1450069362di_nat @ h @ A ) ) @ n ) )
           => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ c ) @ e ) ) @ ( hAPP_A606737888t_bool @ ( hAPP_f786530292t_bool @ arrow_741591990_mktop @ ( hAPP_A1174518481t_bool @ p @ A ) ) @ e ) ) ) )
          & ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_A1450069362di_nat @ h @ A ) ) @ n ) )
           => ( ( ( ( hAPP_A1450069362di_nat @ h @ A )
                  = n )
               => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ c ) @ e ) ) @ ( hAPP_A606737888t_bool @ ( hAPP_A501825983t_bool @ ( hAPP_f1909595219t_bool @ arrow_1475523868_above @ ( hAPP_A1174518481t_bool @ p @ A ) ) @ c ) @ e ) ) ) )
              & ( ( ( hAPP_A1450069362di_nat @ h @ A )
                 != n )
               => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ c ) @ e ) ) @ ( hAPP_A606737888t_bool @ ( hAPP_f786530292t_bool @ arrow_592884904_mkbot @ ( hAPP_A1174518481t_bool @ p @ A ) ) @ e ) ) ) ) ) ) )
       => ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_A1450069362di_nat @ h @ A ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ n ) @ one_one_nat ) ) )
           => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ a ) @ b ) ) @ lab ) ) )
          & ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_A1450069362di_nat @ h @ A ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ n ) @ one_one_nat ) ) )
           => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ a ) @ b ) ) @ lba ) ) ) ) )
      & ( ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_A1450069362di_nat @ h @ A ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ n ) @ one_one_nat ) ) )
           => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ a ) @ b ) ) @ lab ) ) )
          & ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_A1450069362di_nat @ h @ A ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ n ) @ one_one_nat ) ) )
           => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ a ) @ b ) ) @ lba ) ) ) )
       => ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_A1450069362di_nat @ h @ A ) ) @ n ) )
           => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ c ) @ e ) ) @ ( hAPP_A606737888t_bool @ ( hAPP_f786530292t_bool @ arrow_741591990_mktop @ ( hAPP_A1174518481t_bool @ p @ A ) ) @ e ) ) ) )
          & ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_A1450069362di_nat @ h @ A ) ) @ n ) )
           => ( ( ( ( hAPP_A1450069362di_nat @ h @ A )
                  = n )
               => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ c ) @ e ) ) @ ( hAPP_A606737888t_bool @ ( hAPP_A501825983t_bool @ ( hAPP_f1909595219t_bool @ arrow_1475523868_above @ ( hAPP_A1174518481t_bool @ p @ A ) ) @ c ) @ e ) ) ) )
              & ( ( ( hAPP_A1450069362di_nat @ h @ A )
                 != n )
               => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ c ) @ e ) ) @ ( hAPP_A606737888t_bool @ ( hAPP_f786530292t_bool @ arrow_592884904_mkbot @ ( hAPP_A1174518481t_bool @ p @ A ) ) @ e ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(16,axiom,
    ! [A: fun_nat_bool,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ A @ B ) )
     => ( ! [C: nat] :
            ( ( hBOOL @ ( hAPP_nat_bool @ A @ ( hAPP_nat_nat @ suc @ C ) ) )
           => ( hBOOL @ ( hAPP_nat_bool @ A @ C ) ) )
       => ( hBOOL @ ( hAPP_nat_bool @ A @ zero_zero_nat ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_694_zero__induct) ).

thf(802,plain,
    ! [A: fun_nat_bool,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ A @ B ) )
     => ( ! [C: nat] :
            ( ( hBOOL @ ( hAPP_nat_bool @ A @ ( hAPP_nat_nat @ suc @ C ) ) )
           => ( hBOOL @ ( hAPP_nat_bool @ A @ C ) ) )
       => ( hBOOL @ ( hAPP_nat_bool @ A @ zero_zero_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(501,axiom,
    ! [A: arrow_931160158le_alt,B: fun_Pr1055212137t_bool] :
      ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ B ) @ arrow_915577424le_Lin ) )
     => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ ( hAPP_A606737888t_bool @ ( hAPP_f786530292t_bool @ arrow_741591990_mktop @ B ) @ A ) ) @ arrow_915577424le_Lin ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_mktop__Lin) ).

thf(2682,plain,
    ! [A: arrow_931160158le_alt,B: fun_Pr1055212137t_bool] :
      ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ B ) @ arrow_915577424le_Lin ) )
     => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ ( hAPP_A606737888t_bool @ ( hAPP_f786530292t_bool @ arrow_741591990_mktop @ B ) @ A ) ) @ arrow_915577424le_Lin ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).

thf(659,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( A = B )
     => ~ ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
         => ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_461_equalityE) ).

thf(3280,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( A = B )
     => ~ ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
         => ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).

thf(452,axiom,
    ! [A: produc1840315303le_alt] : ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ A ) @ top_to126038883t_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_UNIV__I) ).

thf(2488,plain,
    ! [A: produc1840315303le_alt] : ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ A ) @ top_to126038883t_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).

thf(605,axiom,
    ! [A: nat] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ top_top_fun_nat_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_iso__tuple__UNIV__I) ).

thf(3043,plain,
    ! [A: nat] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ top_top_fun_nat_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).

thf(518,axiom,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool,C: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ B ) @ C ) )
     => ( ( C = A )
       => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_ord__less__eq__trans) ).

thf(2745,plain,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool,C: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ B ) @ C ) )
     => ( ( C = A )
       => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).

thf(507,axiom,
    ! [A: fun_Pr1055212137t_bool,B: arrow_931160158le_alt,C: arrow_931160158le_alt] :
      ( ( hBOOL @ ( in_rel267123714le_alt @ A @ B @ C ) )
    <=> ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ B ) @ C ) ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_575_in__rel__def) ).

thf(2703,plain,
    ! [A: fun_Pr1055212137t_bool,B: arrow_931160158le_alt,C: arrow_931160158le_alt] :
      ( ( ( hBOOL @ ( in_rel267123714le_alt @ A @ B @ C ) )
       => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ B ) @ C ) ) @ A ) ) )
      & ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ B ) @ C ) ) @ A ) )
       => ( hBOOL @ ( in_rel267123714le_alt @ A @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).

thf(169,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
     => ( ( A != B )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_558_le__neq__implies__less) ).

thf(1330,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
     => ( ( A != B )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(438,axiom,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( ( A != B )
     => ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_order__neq__le__trans) ).

thf(2444,plain,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( ( A != B )
     => ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).

thf(166,axiom,
    ! [A: nat,B: nat] :
      ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_leI) ).

thf(1323,plain,
    ! [A: nat,B: nat] :
      ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(27,axiom,
    ! [A: fun_fu709917073t_bool,B: fun_Ar1689125069l_bool,C: arrow_931160158le_alt] :
      ( ( hAPP_A1770325791t_bool @ ( hAPP_f1435501085t_bool @ ( cOMBB_1430402568le_alt @ A ) @ B ) @ C )
      = ( hAPP_f2087965871t_bool @ A @ ( hAPP_A1256181151l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm___329) ).

thf(838,plain,
    ! [A: fun_fu709917073t_bool,B: fun_Ar1689125069l_bool,C: arrow_931160158le_alt] :
      ( ( hAPP_A1770325791t_bool @ ( hAPP_f1435501085t_bool @ ( cOMBB_1430402568le_alt @ A ) @ B ) @ C )
      = ( hAPP_f2087965871t_bool @ A @ ( hAPP_A1256181151l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(121,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) )
    <=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_434_add__less__cancel__left) ).

thf(1147,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) ) )
      & ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(473,axiom,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ A ) @ B ) )
    <=> ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ B ) )
        | ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_order__le__less) ).

thf(2552,plain,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ A ) @ B ) )
       => ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ B ) )
          | ( A = B ) ) )
      & ( ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ B ) )
          | ( A = B ) )
       => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).

thf(234,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_573_termination__basic__simps_I1_J) ).

thf(1572,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(6,axiom,
    ! [A: fun_Ar552120407i_bool] :
      ( ( collec708328256e_indi @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_Collect__def) ).

thf(770,plain,
    ! [A: fun_Ar552120407i_bool] :
      ( ( collec708328256e_indi @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(42,axiom,
    ! [A: fun_Ar1492469401t_bool,B: fun_Ar500372357t_bool,C: arrow_2115524757e_indi] :
      ( ( hAPP_A1174518481t_bool @ ( cOMBS_1921392482t_bool @ A @ B ) @ C )
      = ( hAPP_f70231061t_bool @ ( hAPP_A892860133t_bool @ A @ C ) @ ( hAPP_A1174518481t_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_000) ).

thf(881,plain,
    ! [A: fun_Ar1492469401t_bool,B: fun_Ar500372357t_bool,C: arrow_2115524757e_indi] :
      ( ( hAPP_A1174518481t_bool @ ( cOMBS_1921392482t_bool @ A @ B ) @ C )
      = ( hAPP_f70231061t_bool @ ( hAPP_A892860133t_bool @ A @ C ) @ ( hAPP_A1174518481t_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(376,axiom,
    ! [A: fun_Pr359894313l_bool,B: fun_Pr1055212137t_bool,C: fun_Pr1055212137t_bool,D: fun_Pr1055212137t_bool] :
      ( ! [E: produc1840315303le_alt] :
          ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ E ) @ D ) )
         => ( ( hBOOL @ ( hAPP_P166437127t_bool @ C @ E ) )
          <=> ( hBOOL @ ( hAPP_P166437127t_bool @ B @ E ) ) ) )
     => ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ C ) @ ( pi_Pro226591613t_bool @ D @ A ) ) )
      <=> ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ B ) @ ( pi_Pro226591613t_bool @ D @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_580_Pi__cong) ).

thf(2158,plain,
    ! [A: fun_Pr359894313l_bool,B: fun_Pr1055212137t_bool,C: fun_Pr1055212137t_bool,D: fun_Pr1055212137t_bool] :
      ( ! [E: produc1840315303le_alt] :
          ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ E ) @ D ) )
         => ( ( ( hBOOL @ ( hAPP_P166437127t_bool @ C @ E ) )
             => ( hBOOL @ ( hAPP_P166437127t_bool @ B @ E ) ) )
            & ( ( hBOOL @ ( hAPP_P166437127t_bool @ B @ E ) )
             => ( hBOOL @ ( hAPP_P166437127t_bool @ C @ E ) ) ) ) )
     => ( ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ C ) @ ( pi_Pro226591613t_bool @ D @ A ) ) )
         => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ B ) @ ( pi_Pro226591613t_bool @ D @ A ) ) ) )
        & ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ B ) @ ( pi_Pro226591613t_bool @ D @ A ) ) )
         => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ C ) @ ( pi_Pro226591613t_bool @ D @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(294,axiom,
    ! [A: nat] :
      ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_527_less__not__refl) ).

thf(1815,plain,
    ! [A: nat] :
      ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(650,axiom,
    ! [A: fun_nat_nat,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ A ) @ B ) )
    <=> ! [C: nat] :
          ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ B ) )
         => ! [D: nat] :
              ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ D ) @ B ) )
             => ( ( ( hAPP_nat_nat @ A @ C )
                  = ( hAPP_nat_nat @ A @ D ) )
               => ( C = D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_364_inj__on__def) ).

thf(3231,plain,
    ! [A: fun_nat_nat,B: fun_nat_bool] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ A ) @ B ) )
       => ! [C: nat] :
            ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ B ) )
           => ! [D: nat] :
                ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ D ) @ B ) )
               => ( ( ( hAPP_nat_nat @ A @ C )
                    = ( hAPP_nat_nat @ A @ D ) )
                 => ( C = D ) ) ) ) )
      & ( ! [C: nat] :
            ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ B ) )
           => ! [D: nat] :
                ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ D ) @ B ) )
               => ( ( ( hAPP_nat_nat @ A @ C )
                    = ( hAPP_nat_nat @ A @ D ) )
                 => ( C = D ) ) ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).

thf(328,axiom,
    ! [A: fun_fu775006535l_bool,B: fun_fu775006535l_bool] :
      ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f95487087l_bool @ ord_le1871091345l_bool @ ( hAPP_f626396309l_bool @ ( hAPP_f228579435l_bool @ cOMBC_941833506l_bool @ member1159072754t_bool ) @ A ) ) @ ( hAPP_f626396309l_bool @ ( hAPP_f228579435l_bool @ cOMBC_941833506l_bool @ member1159072754t_bool ) @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f95487087l_bool @ ord_le1871091345l_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_499_pred__subset__eq) ).

thf(1922,plain,
    ! [A: fun_fu775006535l_bool,B: fun_fu775006535l_bool] :
      ( ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f95487087l_bool @ ord_le1871091345l_bool @ ( hAPP_f626396309l_bool @ ( hAPP_f228579435l_bool @ cOMBC_941833506l_bool @ member1159072754t_bool ) @ A ) ) @ ( hAPP_f626396309l_bool @ ( hAPP_f228579435l_bool @ cOMBC_941833506l_bool @ member1159072754t_bool ) @ B ) ) )
       => ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f95487087l_bool @ ord_le1871091345l_bool @ A ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f95487087l_bool @ ord_le1871091345l_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f95487087l_bool @ ord_le1871091345l_bool @ ( hAPP_f626396309l_bool @ ( hAPP_f228579435l_bool @ cOMBC_941833506l_bool @ member1159072754t_bool ) @ A ) ) @ ( hAPP_f626396309l_bool @ ( hAPP_f228579435l_bool @ cOMBC_941833506l_bool @ member1159072754t_bool ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(20,axiom,
    ! [A: nat,B: nat] :
      ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
    <=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ B ) ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_632_not__less__eq__eq) ).

thf(817,plain,
    ! [A: nat,B: nat] :
      ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ B ) ) @ A ) ) )
      & ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ B ) ) @ A ) )
       => ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(207,axiom,
    ! [A: nat] :
      ( ( hAPP_nat_nat @ cOMBI_nat @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBI_1_1_COMBI_000tc__Nat__Onat_U) ).

thf(1479,plain,
    ! [A: nat] :
      ( ( hAPP_nat_nat @ cOMBI_nat @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(245,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ B ) ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_423_add__le__imp__le__right) ).

thf(1609,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ B ) ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(596,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( A != B )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_order__neq__le__trans) ).

thf(3014,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( A != B )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).

thf(465,axiom,
    ! [A: fun_Ar500372357t_bool,B: fun_fu775006535l_bool,C: fun_fu775006535l_bool] :
      ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f95487087l_bool @ ord_le1871091345l_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_486_in__mono) ).

thf(2520,plain,
    ! [A: fun_Ar500372357t_bool,B: fun_fu775006535l_bool,C: fun_fu775006535l_bool] :
      ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f95487087l_bool @ ord_le1871091345l_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).

thf(514,axiom,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ B ) )
     => ( B != A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_order__less__imp__not__eq2) ).

thf(2730,plain,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ B ) )
     => ( B != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).

thf(751,axiom,
    ! [A: bool,B: bool,C: bool] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_order__trans) ).

thf(3602,plain,
    ! [A: bool,B: bool,C: bool] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).

thf(312,axiom,
    ! [A: fun_Ar1198543961l_bool,B: fun_Ar552120407i_bool,C: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f95487087l_bool @ ord_le1871091345l_bool @ ( pi_Arr487970267t_bool @ C @ A ) ) @ ( pi_Arr487970267t_bool @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_403_Pi__anti__mono) ).

thf(1875,plain,
    ! [A: fun_Ar1198543961l_bool,B: fun_Ar552120407i_bool,C: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f95487087l_bool @ ord_le1871091345l_bool @ ( pi_Arr487970267t_bool @ C @ A ) ) @ ( pi_Arr487970267t_bool @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(443,axiom,
    ! [A: bool,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ B ) )
       => ( hBOOL @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_order__less__imp__triv) ).

thf(2456,plain,
    ! [A: bool,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ B ) )
       => ( hBOOL @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).

thf(402,axiom,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool,C: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_332_order__le__less__trans) ).

thf(2237,plain,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool,C: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(347,axiom,
    ! [A: fun_Pr1055212137t_bool] :
      ( ! [B: produc1840315303le_alt] : ( hBOOL @ ( hAPP_P166437127t_bool @ A @ B ) )
    <=> ! [B: arrow_931160158le_alt,C: arrow_931160158le_alt] : ( hBOOL @ ( hAPP_P166437127t_bool @ A @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_split__paired__All) ).

thf(2027,plain,
    ! [A: fun_Pr1055212137t_bool] :
      ( ( ! [B: produc1840315303le_alt] : ( hBOOL @ ( hAPP_P166437127t_bool @ A @ B ) )
       => ! [B: arrow_931160158le_alt,C: arrow_931160158le_alt] : ( hBOOL @ ( hAPP_P166437127t_bool @ A @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ B ) @ C ) ) ) )
      & ( ! [B: arrow_931160158le_alt,C: arrow_931160158le_alt] : ( hBOOL @ ( hAPP_P166437127t_bool @ A @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ B ) @ C ) ) )
       => ! [B: produc1840315303le_alt] : ( hBOOL @ ( hAPP_P166437127t_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(198,axiom,
    ! [A: fun_Pr1055212137t_bool,B: bool] :
      ( ( hAPP_b1263785481t_bool @ ( hAPP_f414777105t_bool @ cOMBK_382434616l_bool @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ct) ).

thf(1450,plain,
    ! [A: fun_Pr1055212137t_bool,B: bool] :
      ( ( hAPP_b1263785481t_bool @ ( hAPP_f414777105t_bool @ cOMBK_382434616l_bool @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(663,axiom,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ B ) )
     => ( A != B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_less__imp__neq) ).

thf(3295,plain,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ B ) )
     => ( A != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).

thf(106,axiom,
    ( top_to1257323279t_bool
    = ( collect_Product_unit @ ( hAPP_b1096750261t_bool @ cOMBK_790042732t_unit @ fTrue ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_UNIV__def) ).

thf(1109,plain,
    ( top_to1257323279t_bool
    = ( collect_Product_unit @ ( hAPP_b1096750261t_bool @ cOMBK_790042732t_unit @ fTrue ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(709,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
    <=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ B ) )
        | ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_449_subset__iff__psubset__eq) ).

thf(3453,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
       => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ B ) )
          | ( A = B ) ) )
      & ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ B ) )
          | ( A = B ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).

thf(711,axiom,
    hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ e ) @ d ) ) @ ( hAPP_f792184801t_bool @ f @ ( cOMBS_1921392482t_bool @ ( cOMBS_811328630t_bool @ ( hAPP_f509814255t_bool @ ( cOMBB_231886989e_indi @ if_fun1658569689t_bool ) @ ( hAPP_n924210722i_bool @ ( hAPP_f62620517i_bool @ cOMBC_922322901t_bool @ ( hAPP_f1381130897t_bool @ ( cOMBB_981137617e_indi @ ord_less_nat ) @ h ) ) @ n ) ) @ ( hAPP_A658738638t_bool @ ( hAPP_f293545699t_bool @ cOMBC_18834461t_bool @ ( hAPP_f842954860t_bool @ ( cOMBB_117136048e_indi @ arrow_741591990_mktop ) @ p ) ) @ e ) ) @ ( cOMBS_1921392482t_bool @ ( cOMBS_811328630t_bool @ ( hAPP_f509814255t_bool @ ( cOMBB_231886989e_indi @ if_fun1658569689t_bool ) @ ( hAPP_n924210722i_bool @ ( hAPP_f62620517i_bool @ cOMBC_922322901t_bool @ ( hAPP_f1381130897t_bool @ ( cOMBB_981137617e_indi @ fequal_nat ) @ h ) ) @ n ) ) @ ( hAPP_A658738638t_bool @ ( hAPP_f293545699t_bool @ cOMBC_18834461t_bool @ ( hAPP_A102926893t_bool @ ( hAPP_f141075873t_bool @ cOMBC_1505804284t_bool @ ( hAPP_f576849227t_bool @ ( cOMBB_656639247e_indi @ arrow_1475523868_above ) @ p ) ) @ c ) ) @ e ) ) @ ( hAPP_A658738638t_bool @ ( hAPP_f293545699t_bool @ cOMBC_18834461t_bool @ ( hAPP_f842954860t_bool @ ( cOMBB_117136048e_indi @ arrow_592884904_mkbot ) @ p ) ) @ e ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18__096e_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto) ).

thf(3473,plain,
    hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ e ) @ d ) ) @ ( hAPP_f792184801t_bool @ f @ ( cOMBS_1921392482t_bool @ ( cOMBS_811328630t_bool @ ( hAPP_f509814255t_bool @ ( cOMBB_231886989e_indi @ if_fun1658569689t_bool ) @ ( hAPP_n924210722i_bool @ ( hAPP_f62620517i_bool @ cOMBC_922322901t_bool @ ( hAPP_f1381130897t_bool @ ( cOMBB_981137617e_indi @ ord_less_nat ) @ h ) ) @ n ) ) @ ( hAPP_A658738638t_bool @ ( hAPP_f293545699t_bool @ cOMBC_18834461t_bool @ ( hAPP_f842954860t_bool @ ( cOMBB_117136048e_indi @ arrow_741591990_mktop ) @ p ) ) @ e ) ) @ ( cOMBS_1921392482t_bool @ ( cOMBS_811328630t_bool @ ( hAPP_f509814255t_bool @ ( cOMBB_231886989e_indi @ if_fun1658569689t_bool ) @ ( hAPP_n924210722i_bool @ ( hAPP_f62620517i_bool @ cOMBC_922322901t_bool @ ( hAPP_f1381130897t_bool @ ( cOMBB_981137617e_indi @ fequal_nat ) @ h ) ) @ n ) ) @ ( hAPP_A658738638t_bool @ ( hAPP_f293545699t_bool @ cOMBC_18834461t_bool @ ( hAPP_A102926893t_bool @ ( hAPP_f141075873t_bool @ cOMBC_1505804284t_bool @ ( hAPP_f576849227t_bool @ ( cOMBB_656639247e_indi @ arrow_1475523868_above ) @ p ) ) @ c ) ) @ e ) ) @ ( hAPP_A658738638t_bool @ ( hAPP_f293545699t_bool @ cOMBC_18834461t_bool @ ( hAPP_f842954860t_bool @ ( cOMBB_117136048e_indi @ arrow_592884904_mkbot ) @ p ) ) @ e ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).

thf(724,axiom,
    ! [A: fun_Ar500372357t_bool] :
      ( ( hBOOL @ ( hAPP_f1766661605l_bool @ top_to1324311617l_bool @ A ) )
    <=> ( hBOOL @ top_top_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_top__apply) ).

thf(3525,plain,
    ! [A: fun_Ar500372357t_bool] :
      ( ( ( hBOOL @ ( hAPP_f1766661605l_bool @ top_to1324311617l_bool @ A ) )
       => ( hBOOL @ top_top_bool ) )
      & ( ( hBOOL @ top_top_bool )
       => ( hBOOL @ ( hAPP_f1766661605l_bool @ top_to1324311617l_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).

thf(57,axiom,
    ! [A: fun_nat_fun_nat_bool,B: fun_Ar1744566822di_nat,C: arrow_2115524757e_indi] :
      ( ( hAPP_A981395480t_bool @ ( hAPP_f1381130897t_bool @ ( cOMBB_981137617e_indi @ A ) @ B ) @ C )
      = ( hAPP_n1699378549t_bool @ A @ ( hAPP_A1450069362di_nat @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__318) ).

thf(937,plain,
    ! [A: fun_nat_fun_nat_bool,B: fun_Ar1744566822di_nat,C: arrow_2115524757e_indi] :
      ( ( hAPP_A981395480t_bool @ ( hAPP_f1381130897t_bool @ ( cOMBB_981137617e_indi @ A ) @ B ) @ C )
      = ( hAPP_n1699378549t_bool @ A @ ( hAPP_A1450069362di_nat @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(680,axiom,
    ! [A: arrow_2115524757e_indi,B: fun_Ar552120407i_bool,C: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_514_psubsetD) ).

thf(3357,plain,
    ! [A: arrow_2115524757e_indi,B: fun_Ar552120407i_bool,C: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).

thf(354,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_order__trans) ).

thf(2090,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(694,axiom,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool,C: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_456_psubset__subset__trans) ).

thf(3393,plain,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool,C: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).

thf(265,axiom,
    ! [A: fun_fu1595299477t_bool] : ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ A ) @ top_to2013953873l_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_UNIV__I) ).

thf(1682,plain,
    ! [A: fun_fu1595299477t_bool] : ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ A ) @ top_to2013953873l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(116,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_551_add__less__mono1) ).

thf(1136,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(736,axiom,
    ! [A: fun_fu1015689055l_bool,B: fun_fu1015689055l_bool] :
      ( ! [C: fun_Pr1055212137t_bool] :
          ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ C ) @ B ) )
         => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ C ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f868566847l_bool @ ord_le1923264405l_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_508_subsetI) ).

thf(3569,plain,
    ! [A: fun_fu1015689055l_bool,B: fun_fu1015689055l_bool] :
      ( ! [C: fun_Pr1055212137t_bool] :
          ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ C ) @ B ) )
         => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ C ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f868566847l_bool @ ord_le1923264405l_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).

thf(263,axiom,
    hBOOL @ ( hAPP_f611501301l_bool @ arrow_888693696le_IIA @ f ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_assms_I3_J) ).

thf(1677,plain,
    hBOOL @ ( hAPP_f611501301l_bool @ arrow_888693696le_IIA @ f ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(471,axiom,
    ! [A: fun_Ar1744566822di_nat,B: fun_Ar552120407i_bool] :
      ( ! [C: arrow_2115524757e_indi,D: arrow_2115524757e_indi] :
          ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ C ) @ B ) )
         => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ D ) @ B ) )
           => ( ( ( hAPP_A1450069362di_nat @ A @ C )
                = ( hAPP_A1450069362di_nat @ A @ D ) )
             => ( C = D ) ) ) )
     => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( inj_on886403158di_nat @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_592_inj__onI) ).

thf(2540,plain,
    ! [A: fun_Ar1744566822di_nat,B: fun_Ar552120407i_bool] :
      ( ! [C: arrow_2115524757e_indi,D: arrow_2115524757e_indi] :
          ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ C ) @ B ) )
         => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ D ) @ B ) )
           => ( ( ( hAPP_A1450069362di_nat @ A @ C )
                = ( hAPP_A1450069362di_nat @ A @ D ) )
             => ( C = D ) ) ) )
     => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( inj_on886403158di_nat @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).

thf(17,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B )
        = ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) )
    <=> ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_419_add__left__cancel) ).

thf(806,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B )
          = ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) )
       => ( B = C ) )
      & ( ( B = C )
       => ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B )
          = ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(613,axiom,
    ! [A: arrow_2115524757e_indi,B: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ A ) @ B ) )
    <=> ( hBOOL @ ( hAPP_A1888055029i_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_mem__def) ).

thf(3093,plain,
    ! [A: arrow_2115524757e_indi,B: fun_Ar552120407i_bool] :
      ( ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_A1888055029i_bool @ B @ A ) ) )
      & ( ( hBOOL @ ( hAPP_A1888055029i_bool @ B @ A ) )
       => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).

thf(460,axiom,
    ! [A: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ top_top_fun_nat_bool ) @ A ) )
     => ( A = top_top_fun_nat_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_361_top__le) ).

thf(2508,plain,
    ! [A: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ top_top_fun_nat_bool ) @ A ) )
     => ( A = top_top_fun_nat_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).

thf(350,axiom,
    ! [A: arrow_2115524757e_indi,B: fun_fu1595299477t_bool] :
      ( ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ B ) @ ( pi_fun530160875t_bool @ arrow_1190054106e_Prof @ ( hAPP_f422714471l_bool @ cOMBK_1446432t_bool @ arrow_915577424le_Lin ) ) ) )
     => ( ! [C: fun_Ar500372357t_bool] :
            ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ C ) @ arrow_1190054106e_Prof ) )
           => ! [D: arrow_931160158le_alt,E: arrow_931160158le_alt] :
                ( ( D != E )
               => ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ D ) @ E ) ) @ ( hAPP_A1174518481t_bool @ C @ A ) ) )
                 => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ D ) @ E ) ) @ ( hAPP_f792184801t_bool @ B @ C ) ) ) ) ) )
       => ( hBOOL @ ( hAPP_A1888055029i_bool @ ( hAPP_f740807359i_bool @ arrow_1472924909ctator @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_dictatorI) ).

thf(2058,plain,
    ! [A: arrow_2115524757e_indi,B: fun_fu1595299477t_bool] :
      ( ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ B ) @ ( pi_fun530160875t_bool @ arrow_1190054106e_Prof @ ( hAPP_f422714471l_bool @ cOMBK_1446432t_bool @ arrow_915577424le_Lin ) ) ) )
     => ( ! [C: fun_Ar500372357t_bool] :
            ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ C ) @ arrow_1190054106e_Prof ) )
           => ! [D: arrow_931160158le_alt,E: arrow_931160158le_alt] :
                ( ( D != E )
               => ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ D ) @ E ) ) @ ( hAPP_A1174518481t_bool @ C @ A ) ) )
                 => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ D ) @ E ) ) @ ( hAPP_f792184801t_bool @ B @ C ) ) ) ) ) )
       => ( hBOOL @ ( hAPP_A1888055029i_bool @ ( hAPP_f740807359i_bool @ arrow_1472924909ctator @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(179,axiom,
    ! [A: fun_nat_bool,B: arrow_2115524757e_indi] :
      ( ( hAPP_A981395480t_bool @ ( hAPP_f426535095t_bool @ cOMBK_2091851729e_indi @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Arrow___) ).

thf(1377,plain,
    ! [A: fun_nat_bool,B: arrow_2115524757e_indi] :
      ( ( hAPP_A981395480t_bool @ ( hAPP_f426535095t_bool @ cOMBK_2091851729e_indi @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(317,axiom,
    ! [A: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ top_to1257323279t_bool ) @ A ) )
    <=> ( A = top_to1257323279t_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_354_top__unique) ).

thf(1886,plain,
    ! [A: fun_Pr1643180309t_bool] :
      ( ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ top_to1257323279t_bool ) @ A ) )
       => ( A = top_to1257323279t_bool ) )
      & ( ( A = top_to1257323279t_bool )
       => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ top_to1257323279t_bool ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(110,axiom,
    ! [A: nat,B: nat] :
      ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_not__leE) ).

thf(1119,plain,
    ! [A: nat,B: nat] :
      ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(218,axiom,
    ! [A: fun_Pr1055212137t_bool,B: fun_Pr1055212137t_bool] :
      ( ( hAPP_f70231061t_bool @ ( hAPP_f1409483817t_bool @ ( hAPP_b1061655857t_bool @ if_fun1658569689t_bool @ fTrue ) @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvq) ).

thf(1526,plain,
    ! [A: fun_Pr1055212137t_bool,B: fun_Pr1055212137t_bool] :
      ( ( hAPP_f70231061t_bool @ ( hAPP_f1409483817t_bool @ ( hAPP_b1061655857t_bool @ if_fun1658569689t_bool @ fTrue ) @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(172,axiom,
    ! [A: fun_nat_fun_nat_bool,B: nat,C: nat] :
      ( ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ( hAPP_f229349961t_bool @ cOMBC_nat_nat_bool @ A ) @ B ) @ C )
      = ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__HOL__Obool_U) ).

thf(1345,plain,
    ! [A: fun_nat_fun_nat_bool,B: nat,C: nat] :
      ( ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ( hAPP_f229349961t_bool @ cOMBC_nat_nat_bool @ A ) @ B ) @ C )
      = ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(358,axiom,
    ! [A: fun_fu1138137687l_bool] :
      ( ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f173704847l_bool @ ord_le161055137l_bool @ top_to2013953873l_bool ) @ A ) )
    <=> ( A = top_to2013953873l_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_350_top__unique) ).

thf(2103,plain,
    ! [A: fun_fu1138137687l_bool] :
      ( ( ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f173704847l_bool @ ord_le161055137l_bool @ top_to2013953873l_bool ) @ A ) )
       => ( A = top_to2013953873l_bool ) )
      & ( ( A = top_to2013953873l_bool )
       => ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f173704847l_bool @ ord_le161055137l_bool @ top_to2013953873l_bool ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(587,axiom,
    ! [A: nat] : ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ ( hAPP_f311418073t_bool @ ( hAPP_f1302245795t_bool @ cOMBC_1490589522t_bool @ ( hAPP_f1755759597t_bool @ ( hAPP_f1328803787t_bool @ cOMBC_1190055014t_bool @ ( hAPP_f509814255t_bool @ ( cOMBB_231886989e_indi @ if_fun1658569689t_bool ) @ ( hAPP_n924210722i_bool @ ( hAPP_f62620517i_bool @ cOMBC_922322901t_bool @ ( hAPP_f1381130897t_bool @ ( cOMBB_981137617e_indi @ ord_less_nat ) @ h ) ) @ A ) ) ) @ lab ) ) @ lba ) ) @ arrow_1190054106e_Prof ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_PiProf) ).

thf(2965,plain,
    ! [A: nat] : ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ ( hAPP_f311418073t_bool @ ( hAPP_f1302245795t_bool @ cOMBC_1490589522t_bool @ ( hAPP_f1755759597t_bool @ ( hAPP_f1328803787t_bool @ cOMBC_1190055014t_bool @ ( hAPP_f509814255t_bool @ ( cOMBB_231886989e_indi @ if_fun1658569689t_bool ) @ ( hAPP_n924210722i_bool @ ( hAPP_f62620517i_bool @ cOMBC_922322901t_bool @ ( hAPP_f1381130897t_bool @ ( cOMBB_981137617e_indi @ ord_less_nat ) @ h ) ) @ A ) ) ) @ lab ) ) @ lba ) ) @ arrow_1190054106e_Prof ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).

thf(733,axiom,
    ! [A: fun_fu1595299477t_bool,B: fun_fu775006535l_bool,C: fun_fu1015689055l_bool] :
      ( ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ A ) @ ( pi_fun530160875t_bool @ B @ ( hAPP_f422714471l_bool @ cOMBK_1446432t_bool @ C ) ) ) )
     => ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( inj_on937360581t_bool @ A ) @ B ) )
       => ( ( hBOOL @ ( hAPP_f1021703871l_bool @ finite775027132t_bool @ C ) )
         => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( finite1418900531t_bool @ B ) ) @ ( finite1445836347t_bool @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_590_card__inj) ).

thf(3559,plain,
    ! [A: fun_fu1595299477t_bool,B: fun_fu775006535l_bool,C: fun_fu1015689055l_bool] :
      ( ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ A ) @ ( pi_fun530160875t_bool @ B @ ( hAPP_f422714471l_bool @ cOMBK_1446432t_bool @ C ) ) ) )
     => ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( inj_on937360581t_bool @ A ) @ B ) )
       => ( ( hBOOL @ ( hAPP_f1021703871l_bool @ finite775027132t_bool @ C ) )
         => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( finite1418900531t_bool @ B ) ) @ ( finite1445836347t_bool @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).

thf(292,axiom,
    ! [A: arrow_931160158le_alt,B: arrow_931160158le_alt,C: fun_Pr1055212137t_bool] :
      ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ C ) @ arrow_915577424le_Lin ) )
     => ( ( A != B )
       => ( ~ ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ A ) @ B ) ) @ C ) )
        <=> ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ B ) @ A ) ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_notin__Lin__iff) ).

thf(1796,plain,
    ! [A: arrow_931160158le_alt,B: arrow_931160158le_alt,C: fun_Pr1055212137t_bool] :
      ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ C ) @ arrow_915577424le_Lin ) )
     => ( ( A != B )
       => ( ( ~ ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ A ) @ B ) ) @ C ) )
           => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ B ) @ A ) ) @ C ) ) )
          & ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ B ) @ A ) ) @ C ) )
           => ~ ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ A ) @ B ) ) @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(98,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) )
    <=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_662_less__Suc__eq__le) ).

thf(1072,plain,
    ! [A: nat,B: nat] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(603,axiom,
    ! [A: bool,B: bool,C: bool] :
      ( ( ( hBOOL @ C )
      <=> ( hBOOL @ B ) )
     => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_xt1_I3_J) ).

thf(3036,plain,
    ! [A: bool,B: bool,C: bool] :
      ( ( ( ( hBOOL @ C )
         => ( hBOOL @ B ) )
        & ( ( hBOOL @ B )
         => ( hBOOL @ C ) ) )
     => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).

thf(682,axiom,
    hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ c ) @ d ) ) @ ( hAPP_A1174518481t_bool @ p @ ( hAPP_n1048492170e_indi @ ( hilber506087739di_nat @ top_to1678393681i_bool @ h ) @ n ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12__096c_A_060_092_060_094bsub_062P_A_Iinv_Ah_An_J_092_060_094esub_062_Ad_0) ).

thf(3361,plain,
    hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ c ) @ d ) ) @ ( hAPP_A1174518481t_bool @ p @ ( hAPP_n1048492170e_indi @ ( hilber506087739di_nat @ top_to1678393681i_bool @ h ) @ n ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).

thf(539,axiom,
    ! [A: bool,B: bool,C: bool] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_334_order__le__less__trans) ).

thf(2809,plain,
    ! [A: bool,B: bool,C: bool] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).

thf(753,axiom,
    ! [A: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ top_top_fun_nat_bool @ A ) )
    <=> ( hBOOL @ top_top_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_top__apply) ).

thf(3606,plain,
    ! [A: nat] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ top_top_fun_nat_bool @ A ) )
       => ( hBOOL @ top_top_bool ) )
      & ( ( hBOOL @ top_top_bool )
       => ( hBOOL @ ( hAPP_nat_bool @ top_top_fun_nat_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).

thf(374,axiom,
    ! [A: fun_fu1595299477t_bool,B: fun_fu1138137687l_bool,C: fun_fu1138137687l_bool] :
      ( ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f173704847l_bool @ ord_le161055137l_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_443_subsetD) ).

thf(2154,plain,
    ! [A: fun_fu1595299477t_bool,B: fun_fu1138137687l_bool,C: fun_fu1138137687l_bool] :
      ( ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f173704847l_bool @ ord_le161055137l_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(509,axiom,
    ! [A: bool,B: bool,C: bool] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_324_order__less__le__trans) ).

thf(2718,plain,
    ! [A: bool,B: bool,C: bool] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).

thf(392,axiom,
    ! [A: fun_fu1595299477t_bool,B: fun_fu1138137687l_bool,C: fun_fu1138137687l_bool] :
      ( ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f173704847l_bool @ ord_le161055137l_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_468_set__mp) ).

thf(2205,plain,
    ! [A: fun_fu1595299477t_bool,B: fun_fu1138137687l_bool,C: fun_fu1138137687l_bool] :
      ( ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f173704847l_bool @ ord_le161055137l_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(582,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_335_xt1_I8_J) ).

thf(2954,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).

thf(244,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) )
    <=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_427_add__le__cancel__left) ).

thf(1604,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) )
      & ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(708,axiom,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ B ) )
        | ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_306_order__le__imp__less__or__eq) ).

thf(3450,plain,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ B ) )
        | ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).

thf(448,axiom,
    ! [A: fun_fu787660105l_bool,B: fun_fu1595299477t_bool,C: fun_fu1595299477t_bool,D: fun_fu775006535l_bool] :
      ( ! [E: fun_Ar500372357t_bool] :
          ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ E ) @ D ) )
         => ( ( hAPP_f792184801t_bool @ B @ E )
            = ( hAPP_f792184801t_bool @ C @ E ) ) )
     => ( ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ B ) @ ( pi_fun530160875t_bool @ D @ A ) ) )
      <=> ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ C ) @ ( pi_fun530160875t_bool @ D @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_582_Pi__cong) ).

thf(2473,plain,
    ! [A: fun_fu787660105l_bool,B: fun_fu1595299477t_bool,C: fun_fu1595299477t_bool,D: fun_fu775006535l_bool] :
      ( ! [E: fun_Ar500372357t_bool] :
          ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ E ) @ D ) )
         => ( ( hAPP_f792184801t_bool @ B @ E )
            = ( hAPP_f792184801t_bool @ C @ E ) ) )
     => ( ( ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ B ) @ ( pi_fun530160875t_bool @ D @ A ) ) )
         => ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ C ) @ ( pi_fun530160875t_bool @ D @ A ) ) ) )
        & ( ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ C ) @ ( pi_fun530160875t_bool @ D @ A ) ) )
         => ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ B ) @ ( pi_fun530160875t_bool @ D @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).

thf(204,axiom,
    ! [A: bool,B: nat] :
      ( ( hAPP_nat_bool @ ( hAPP_b1013836512t_bool @ cOMBK_bool_nat @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Nat__Onat_U) ).

thf(1470,plain,
    ! [A: bool,B: nat] :
      ( ( hAPP_nat_bool @ ( hAPP_b1013836512t_bool @ cOMBK_bool_nat @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(415,axiom,
    ! [A: arrow_2115524757e_indi] :
      ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ c ) @ d ) ) @ ( hAPP_A1174518481t_bool @ p @ A ) ) )
    <=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_A1450069362di_nat @ h @ A ) ) @ n ) )
         => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ c ) @ d ) ) @ ( hAPP_A606737888t_bool @ ( hAPP_f786530292t_bool @ arrow_741591990_mktop @ ( hAPP_A1174518481t_bool @ p @ A ) ) @ e ) ) ) )
        & ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_A1450069362di_nat @ h @ A ) ) @ n ) )
         => ( ( ( ( hAPP_A1450069362di_nat @ h @ A )
                = n )
             => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ c ) @ d ) ) @ ( hAPP_A606737888t_bool @ ( hAPP_A501825983t_bool @ ( hAPP_f1909595219t_bool @ arrow_1475523868_above @ ( hAPP_A1174518481t_bool @ p @ A ) ) @ c ) @ e ) ) ) )
            & ( ( ( hAPP_A1450069362di_nat @ h @ A )
               != n )
             => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ c ) @ d ) ) @ ( hAPP_A606737888t_bool @ ( hAPP_f786530292t_bool @ arrow_592884904_mkbot @ ( hAPP_A1174518481t_bool @ p @ A ) ) @ e ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ad_J) ).

thf(2307,plain,
    ! [A: arrow_2115524757e_indi] :
      ( ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ c ) @ d ) ) @ ( hAPP_A1174518481t_bool @ p @ A ) ) )
       => ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_A1450069362di_nat @ h @ A ) ) @ n ) )
           => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ c ) @ d ) ) @ ( hAPP_A606737888t_bool @ ( hAPP_f786530292t_bool @ arrow_741591990_mktop @ ( hAPP_A1174518481t_bool @ p @ A ) ) @ e ) ) ) )
          & ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_A1450069362di_nat @ h @ A ) ) @ n ) )
           => ( ( ( ( hAPP_A1450069362di_nat @ h @ A )
                  = n )
               => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ c ) @ d ) ) @ ( hAPP_A606737888t_bool @ ( hAPP_A501825983t_bool @ ( hAPP_f1909595219t_bool @ arrow_1475523868_above @ ( hAPP_A1174518481t_bool @ p @ A ) ) @ c ) @ e ) ) ) )
              & ( ( ( hAPP_A1450069362di_nat @ h @ A )
                 != n )
               => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ c ) @ d ) ) @ ( hAPP_A606737888t_bool @ ( hAPP_f786530292t_bool @ arrow_592884904_mkbot @ ( hAPP_A1174518481t_bool @ p @ A ) ) @ e ) ) ) ) ) ) ) )
      & ( ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_A1450069362di_nat @ h @ A ) ) @ n ) )
           => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ c ) @ d ) ) @ ( hAPP_A606737888t_bool @ ( hAPP_f786530292t_bool @ arrow_741591990_mktop @ ( hAPP_A1174518481t_bool @ p @ A ) ) @ e ) ) ) )
          & ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_A1450069362di_nat @ h @ A ) ) @ n ) )
           => ( ( ( ( hAPP_A1450069362di_nat @ h @ A )
                  = n )
               => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ c ) @ d ) ) @ ( hAPP_A606737888t_bool @ ( hAPP_A501825983t_bool @ ( hAPP_f1909595219t_bool @ arrow_1475523868_above @ ( hAPP_A1174518481t_bool @ p @ A ) ) @ c ) @ e ) ) ) )
              & ( ( ( hAPP_A1450069362di_nat @ h @ A )
                 != n )
               => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ c ) @ d ) ) @ ( hAPP_A606737888t_bool @ ( hAPP_f786530292t_bool @ arrow_592884904_mkbot @ ( hAPP_A1174518481t_bool @ p @ A ) ) @ e ) ) ) ) ) ) )
       => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ c ) @ d ) ) @ ( hAPP_A1174518481t_bool @ p @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

thf(456,axiom,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar1744566822di_nat,C: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( inj_on886403158di_nat @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( inj_on886403158di_nat @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_414_subset__inj__on) ).

thf(2496,plain,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar1744566822di_nat,C: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( inj_on886403158di_nat @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( inj_on886403158di_nat @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).

thf(284,axiom,
    ! [A: produc1840315303le_alt] : ( hBOOL @ ( hAPP_P166437127t_bool @ top_to126038883t_bool @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_top1I) ).

thf(1768,plain,
    ! [A: produc1840315303le_alt] : ( hBOOL @ ( hAPP_P166437127t_bool @ top_to126038883t_bool @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(528,axiom,
    ! [A: fun_fu243393031t_bool,B: fun_fu1595299477t_bool,C: fun_fu775006535l_bool,D: fun_fu1015689055l_bool] :
      ( ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ B ) @ ( pi_fun530160875t_bool @ C @ ( hAPP_f422714471l_bool @ cOMBK_1446432t_bool @ D ) ) ) )
     => ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( inj_on937360581t_bool @ B ) @ C ) )
       => ( ( hBOOL @ ( hAPP_f2106732305l_bool @ ( hAPP_f2071392713l_bool @ member449535860t_bool @ A ) @ ( pi_fun49394147t_bool @ D @ ( hAPP_f1197023401l_bool @ cOMBK_2140692976t_bool @ C ) ) ) )
         => ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( inj_on456593853t_bool @ A ) @ D ) )
           => ( ( hBOOL @ ( hAPP_f1465510031l_bool @ finite1217814770t_bool @ C ) )
             => ( ( hBOOL @ ( hAPP_f1021703871l_bool @ finite775027132t_bool @ D ) )
               => ( ( finite1418900531t_bool @ C )
                  = ( finite1445836347t_bool @ D ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_600_card__bij) ).

thf(2773,plain,
    ! [A: fun_fu243393031t_bool,B: fun_fu1595299477t_bool,C: fun_fu775006535l_bool,D: fun_fu1015689055l_bool] :
      ( ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ B ) @ ( pi_fun530160875t_bool @ C @ ( hAPP_f422714471l_bool @ cOMBK_1446432t_bool @ D ) ) ) )
     => ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( inj_on937360581t_bool @ B ) @ C ) )
       => ( ( hBOOL @ ( hAPP_f2106732305l_bool @ ( hAPP_f2071392713l_bool @ member449535860t_bool @ A ) @ ( pi_fun49394147t_bool @ D @ ( hAPP_f1197023401l_bool @ cOMBK_2140692976t_bool @ C ) ) ) )
         => ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( inj_on456593853t_bool @ A ) @ D ) )
           => ( ( hBOOL @ ( hAPP_f1465510031l_bool @ finite1217814770t_bool @ C ) )
             => ( ( hBOOL @ ( hAPP_f1021703871l_bool @ finite775027132t_bool @ D ) )
               => ( ( finite1418900531t_bool @ C )
                  = ( finite1445836347t_bool @ D ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).

thf(91,axiom,
    ! [A: fun_bool_bool,B: produc1840315303le_alt] :
      ( ( hAPP_P1830623733l_bool @ ( hAPP_f1426772275l_bool @ cOMBK_1506144056le_alt @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__prod_It) ).

thf(1047,plain,
    ! [A: fun_bool_bool,B: produc1840315303le_alt] :
      ( ( hAPP_P1830623733l_bool @ ( hAPP_f1426772275l_bool @ cOMBK_1506144056le_alt @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(59,axiom,
    ! [A: fun_nat_bool] :
      ( ( collect_nat @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_Collect__def) ).

thf(942,plain,
    ! [A: fun_nat_bool] :
      ( ( collect_nat @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(745,axiom,
    ! [A: fun_fu1595299477t_bool,B: fun_fu1138137687l_bool,C: fun_fu1138137687l_bool] :
      ( ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f173704847l_bool @ ord_le1306091181l_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_517_psubsetD) ).

thf(3591,plain,
    ! [A: fun_fu1595299477t_bool,B: fun_fu1138137687l_bool,C: fun_fu1138137687l_bool] :
      ( ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f173704847l_bool @ ord_le1306091181l_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).

thf(665,axiom,
    ! [A: nat,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ B ) )
    <=> ( hBOOL @ ( hAPP_nat_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_mem__def) ).

thf(3301,plain,
    ! [A: nat,B: fun_nat_bool] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ B @ A ) ) )
      & ( ( hBOOL @ ( hAPP_nat_bool @ B @ A ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).

thf(391,axiom,
    hBOOL @ ( hAPP_f611501301l_bool @ arrow_22284131nimity @ f ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_u) ).

thf(2204,plain,
    hBOOL @ ( hAPP_f611501301l_bool @ arrow_22284131nimity @ f ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(478,axiom,
    ! [A: fun_Pr1055212137t_bool,B: arrow_931160158le_alt,C: arrow_931160158le_alt] :
      ( ( B != C )
     => ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ A ) @ arrow_915577424le_Lin ) )
       => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ ( hAPP_A606737888t_bool @ ( hAPP_A501825983t_bool @ ( hAPP_f1909595219t_bool @ arrow_1475523868_above @ A ) @ B ) @ C ) ) @ arrow_915577424le_Lin ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_above__Lin) ).

thf(2574,plain,
    ! [A: fun_Pr1055212137t_bool,B: arrow_931160158le_alt,C: arrow_931160158le_alt] :
      ( ( B != C )
     => ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ A ) @ arrow_915577424le_Lin ) )
       => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ ( hAPP_A606737888t_bool @ ( hAPP_A501825983t_bool @ ( hAPP_f1909595219t_bool @ arrow_1475523868_above @ A ) @ B ) @ C ) ) @ arrow_915577424le_Lin ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).

thf(195,axiom,
    ! [A: nat,B: nat] :
      ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) )
       => ( B = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_649_less__antisym) ).

thf(1438,plain,
    ! [A: nat,B: nat] :
      ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(3,axiom,
    ! [A: fun_Pr1055212137t_bool,B: fun_Pr1055212137t_bool] :
      ( ( hAPP_f70231061t_bool @ ( hAPP_f1409483817t_bool @ ( hAPP_b1061655857t_bool @ if_fun1658569689t_bool @ fFalse ) @ A ) @ B )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvq) ).

thf(761,plain,
    ! [A: fun_Pr1055212137t_bool,B: fun_Pr1055212137t_bool] :
      ( ( hAPP_f70231061t_bool @ ( hAPP_f1409483817t_bool @ ( hAPP_b1061655857t_bool @ if_fun1658569689t_bool @ fFalse ) @ A ) @ B )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(639,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ B ) )
     => ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_order__less__imp__not__less) ).

thf(3186,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ B ) )
     => ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).

thf(500,axiom,
    ! [A: fun_fu1595299477t_bool] :
      ( ( hBOOL @ ( hAPP_f611501301l_bool @ arrow_22284131nimity @ A ) )
    <=> ! [B: fun_Ar500372357t_bool] :
          ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ B ) @ arrow_1190054106e_Prof ) )
         => ! [C: arrow_931160158le_alt,D: arrow_931160158le_alt] :
              ( ! [E: arrow_2115524757e_indi] : ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ C ) @ D ) ) @ ( hAPP_A1174518481t_bool @ B @ E ) ) )
             => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ C ) @ D ) ) @ ( hAPP_f792184801t_bool @ A @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_unanimity__def) ).

thf(2673,plain,
    ! [A: fun_fu1595299477t_bool] :
      ( ( ( hBOOL @ ( hAPP_f611501301l_bool @ arrow_22284131nimity @ A ) )
       => ! [B: fun_Ar500372357t_bool] :
            ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ B ) @ arrow_1190054106e_Prof ) )
           => ! [C: arrow_931160158le_alt,D: arrow_931160158le_alt] :
                ( ! [E: arrow_2115524757e_indi] : ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ C ) @ D ) ) @ ( hAPP_A1174518481t_bool @ B @ E ) ) )
               => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ C ) @ D ) ) @ ( hAPP_f792184801t_bool @ A @ B ) ) ) ) ) )
      & ( ! [B: fun_Ar500372357t_bool] :
            ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ B ) @ arrow_1190054106e_Prof ) )
           => ! [C: arrow_931160158le_alt,D: arrow_931160158le_alt] :
                ( ! [E: arrow_2115524757e_indi] : ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ C ) @ D ) ) @ ( hAPP_A1174518481t_bool @ B @ E ) ) )
               => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ C ) @ D ) ) @ ( hAPP_f792184801t_bool @ A @ B ) ) ) ) )
       => ( hBOOL @ ( hAPP_f611501301l_bool @ arrow_22284131nimity @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).

thf(46,axiom,
    ! [A: fun_fu1628463836t_bool,B: fun_Ar500372357t_bool,C: arrow_2115524757e_indi] :
      ( ( hAPP_A1020253872t_bool @ ( hAPP_f842954860t_bool @ ( cOMBB_117136048e_indi @ A ) @ B ) @ C )
      = ( hAPP_f786530292t_bool @ A @ ( hAPP_A1174518481t_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ct) ).

thf(894,plain,
    ! [A: fun_fu1628463836t_bool,B: fun_Ar500372357t_bool,C: arrow_2115524757e_indi] :
      ( ( hAPP_A1020253872t_bool @ ( hAPP_f842954860t_bool @ ( cOMBB_117136048e_indi @ A ) @ B ) @ C )
      = ( hAPP_f786530292t_bool @ A @ ( hAPP_A1174518481t_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(89,axiom,
    ! [A: nat] :
      ( ( finite_card_nat @ ( collect_nat @ ( hAPP_n1699378549t_bool @ ( hAPP_f229349961t_bool @ cOMBC_nat_nat_bool @ ord_less_eq_nat ) @ A ) ) )
      = ( hAPP_nat_nat @ suc @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_680_card__Collect__le__nat) ).

thf(1042,plain,
    ! [A: nat] :
      ( ( finite_card_nat @ ( collect_nat @ ( hAPP_n1699378549t_bool @ ( hAPP_f229349961t_bool @ cOMBC_nat_nat_bool @ ord_less_eq_nat ) @ A ) ) )
      = ( hAPP_nat_nat @ suc @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(485,axiom,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ B ) )
     => ~ ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_order__less__imp__not__less) ).

thf(2596,plain,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ B ) )
     => ~ ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).

thf(237,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B )
        = ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) )
     => ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_417_add__left__imp__eq) ).

thf(1580,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B )
        = ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) )
     => ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(125,axiom,
    ! [A: nat,B: fun_nat_bool] :
      ( ~ ( hBOOL @ ( hAPP_nat_bool @ B @ zero_zero_nat ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ B @ A ) )
       => ? [C: nat] :
            ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ A ) )
            & ! [D: nat] :
                ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ D ) @ C ) )
               => ~ ( hBOOL @ ( hAPP_nat_bool @ B @ D ) ) )
            & ( hBOOL @ ( hAPP_nat_bool @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_626_ex__least__nat__le) ).

thf(1174,plain,
    ! [A: nat,B: fun_nat_bool] :
      ( ~ ( hBOOL @ ( hAPP_nat_bool @ B @ zero_zero_nat ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ B @ A ) )
       => ? [C: nat] :
            ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ A ) )
            & ! [D: nat] :
                ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ D ) @ C ) )
               => ~ ( hBOOL @ ( hAPP_nat_bool @ B @ D ) ) )
            & ( hBOOL @ ( hAPP_nat_bool @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(138,axiom,
    ! [A: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) )
    <=> ? [B: nat] :
        ! [C: nat] :
          ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ A ) )
         => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_607_finite__nat__set__iff__bounded__le) ).

thf(1217,plain,
    ! [A: fun_nat_bool] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) )
       => ? [B: nat] :
          ! [C: nat] :
            ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ A ) )
           => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ B ) ) ) )
      & ( ? [B: nat] :
          ! [C: nat] :
            ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ A ) )
           => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ B ) ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(278,axiom,
    ! [A: bool,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ C ) @ B ) )
       => ( hBOOL @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_order__less__imp__triv) ).

thf(1751,plain,
    ! [A: bool,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ C ) @ B ) )
       => ( hBOOL @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(645,axiom,
    ! [A: fun_nat_bool] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_492_subset__refl) ).

thf(3207,plain,
    ! [A: fun_nat_bool] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).

thf(411,axiom,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ B ) )
     => ( A != B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_order__less__imp__not__eq) ).

thf(2264,plain,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ B ) )
     => ( A != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(432,axiom,
    ! [A: fun_fu1015689055l_bool] :
      ( ( A != top_to1690334693l_bool )
    <=> ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f868566847l_bool @ ord_le2104736649l_bool @ A ) @ top_to1690334693l_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_less__top) ).

thf(2409,plain,
    ! [A: fun_fu1015689055l_bool] :
      ( ( ( A != top_to1690334693l_bool )
       => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f868566847l_bool @ ord_le2104736649l_bool @ A ) @ top_to1690334693l_bool ) ) )
      & ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f868566847l_bool @ ord_le2104736649l_bool @ A ) @ top_to1690334693l_bool ) )
       => ( A != top_to1690334693l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

thf(321,axiom,
    hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ c ) @ d ) ) @ ( hAPP_f792184801t_bool @ f @ ( cOMBS_1921392482t_bool @ ( cOMBS_811328630t_bool @ ( hAPP_f509814255t_bool @ ( cOMBB_231886989e_indi @ if_fun1658569689t_bool ) @ ( hAPP_n924210722i_bool @ ( hAPP_f62620517i_bool @ cOMBC_922322901t_bool @ ( hAPP_f1381130897t_bool @ ( cOMBB_981137617e_indi @ ord_less_nat ) @ h ) ) @ n ) ) @ ( hAPP_A658738638t_bool @ ( hAPP_f293545699t_bool @ cOMBC_18834461t_bool @ ( hAPP_f842954860t_bool @ ( cOMBB_117136048e_indi @ arrow_741591990_mktop ) @ p ) ) @ e ) ) @ ( cOMBS_1921392482t_bool @ ( cOMBS_811328630t_bool @ ( hAPP_f509814255t_bool @ ( cOMBB_231886989e_indi @ if_fun1658569689t_bool ) @ ( hAPP_n924210722i_bool @ ( hAPP_f62620517i_bool @ cOMBC_922322901t_bool @ ( hAPP_f1381130897t_bool @ ( cOMBB_981137617e_indi @ fequal_nat ) @ h ) ) @ n ) ) @ ( hAPP_A658738638t_bool @ ( hAPP_f293545699t_bool @ cOMBC_18834461t_bool @ ( hAPP_A102926893t_bool @ ( hAPP_f141075873t_bool @ cOMBC_1505804284t_bool @ ( hAPP_f576849227t_bool @ ( cOMBB_656639247e_indi @ arrow_1475523868_above ) @ p ) ) @ c ) ) @ e ) ) @ ( hAPP_A658738638t_bool @ ( hAPP_f293545699t_bool @ cOMBC_18834461t_bool @ ( hAPP_f842954860t_bool @ ( cOMBB_117136048e_indi @ arrow_592884904_mkbot ) @ p ) ) @ e ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto) ).

thf(1900,plain,
    hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ c ) @ d ) ) @ ( hAPP_f792184801t_bool @ f @ ( cOMBS_1921392482t_bool @ ( cOMBS_811328630t_bool @ ( hAPP_f509814255t_bool @ ( cOMBB_231886989e_indi @ if_fun1658569689t_bool ) @ ( hAPP_n924210722i_bool @ ( hAPP_f62620517i_bool @ cOMBC_922322901t_bool @ ( hAPP_f1381130897t_bool @ ( cOMBB_981137617e_indi @ ord_less_nat ) @ h ) ) @ n ) ) @ ( hAPP_A658738638t_bool @ ( hAPP_f293545699t_bool @ cOMBC_18834461t_bool @ ( hAPP_f842954860t_bool @ ( cOMBB_117136048e_indi @ arrow_741591990_mktop ) @ p ) ) @ e ) ) @ ( cOMBS_1921392482t_bool @ ( cOMBS_811328630t_bool @ ( hAPP_f509814255t_bool @ ( cOMBB_231886989e_indi @ if_fun1658569689t_bool ) @ ( hAPP_n924210722i_bool @ ( hAPP_f62620517i_bool @ cOMBC_922322901t_bool @ ( hAPP_f1381130897t_bool @ ( cOMBB_981137617e_indi @ fequal_nat ) @ h ) ) @ n ) ) @ ( hAPP_A658738638t_bool @ ( hAPP_f293545699t_bool @ cOMBC_18834461t_bool @ ( hAPP_A102926893t_bool @ ( hAPP_f141075873t_bool @ cOMBC_1505804284t_bool @ ( hAPP_f576849227t_bool @ ( cOMBB_656639247e_indi @ arrow_1475523868_above ) @ p ) ) @ c ) ) @ e ) ) @ ( hAPP_A658738638t_bool @ ( hAPP_f293545699t_bool @ cOMBC_18834461t_bool @ ( hAPP_f842954860t_bool @ ( cOMBB_117136048e_indi @ arrow_592884904_mkbot ) @ p ) ) @ e ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(50,axiom,
    ! [A: fun_Ar500372357t_bool,B: fun_fu1015689055l_bool,C: fun_Ar552120407i_bool] :
      ( ! [D: arrow_2115524757e_indi] :
          ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ D ) @ C ) )
         => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ ( hAPP_A1174518481t_bool @ A @ D ) ) @ B ) ) )
     => ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ A ) @ ( pi_Arr487970267t_bool @ C @ ( hAPP_f1793492343l_bool @ cOMBK_1595020336e_indi @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_577_funcsetI) ).

thf(910,plain,
    ! [A: fun_Ar500372357t_bool,B: fun_fu1015689055l_bool,C: fun_Ar552120407i_bool] :
      ( ! [D: arrow_2115524757e_indi] :
          ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ D ) @ C ) )
         => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ ( hAPP_A1174518481t_bool @ A @ D ) ) @ B ) ) )
     => ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ A ) @ ( pi_Arr487970267t_bool @ C @ ( hAPP_f1793492343l_bool @ cOMBK_1595020336e_indi @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(22,axiom,
    ! [A: nat] :
      ( ( finite_card_nat @ ( collect_nat @ ( hAPP_n1699378549t_bool @ ( hAPP_f229349961t_bool @ cOMBC_nat_nat_bool @ ord_less_nat ) @ A ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_604_card__Collect__less__nat) ).

thf(825,plain,
    ! [A: nat] :
      ( ( finite_card_nat @ ( collect_nat @ ( hAPP_n1699378549t_bool @ ( hAPP_f229349961t_bool @ cOMBC_nat_nat_bool @ ord_less_nat ) @ A ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(538,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( B = C )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_ord__eq__le__trans) ).

thf(2805,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( B = C )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).

thf(406,axiom,
    ! [A: fun_Ar500372357t_bool,B: fun_fu908353023e_indi,C: fun_fu775006535l_bool,D: fun_fu1765260675i_bool] :
      ( ( hBOOL @ ( hAPP_f1298495829l_bool @ ( hAPP_f1690559309l_bool @ member1408848082e_indi @ B ) @ ( pi_fun64467091e_indi @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ ( hAPP_f146696477e_indi @ B @ A ) ) @ ( hAPP_f109229519i_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_PiE) ).

thf(2249,plain,
    ! [A: fun_Ar500372357t_bool,B: fun_fu908353023e_indi,C: fun_fu775006535l_bool,D: fun_fu1765260675i_bool] :
      ( ( hBOOL @ ( hAPP_f1298495829l_bool @ ( hAPP_f1690559309l_bool @ member1408848082e_indi @ B ) @ ( pi_fun64467091e_indi @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ ( hAPP_f146696477e_indi @ B @ A ) ) @ ( hAPP_f109229519i_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).

thf(82,axiom,
    ! [A: nat] :
      ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ zero_zero_nat ) @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_618_plus__nat_Oadd__0) ).

thf(1021,plain,
    ! [A: nat] :
      ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ zero_zero_nat ) @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(296,axiom,
    ! [A: fun_Pr1055212137t_bool,B: arrow_931160158le_alt,C: arrow_931160158le_alt] :
      ( ( B != C )
     => ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ A ) @ arrow_915577424le_Lin ) )
       => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ ( arrow_636638768_below @ A @ B @ C ) ) @ arrow_915577424le_Lin ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_544_below__Lin) ).

thf(1824,plain,
    ! [A: fun_Pr1055212137t_bool,B: arrow_931160158le_alt,C: arrow_931160158le_alt] :
      ( ( B != C )
     => ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ A ) @ arrow_915577424le_Lin ) )
       => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ ( arrow_636638768_below @ A @ B @ C ) ) @ arrow_915577424le_Lin ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(177,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_650_less__SucI) ).

thf(1370,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(348,axiom,
    ! [A: fun_fu1595299477t_bool] :
      ( ( hBOOL @ ( hAPP_f611501301l_bool @ arrow_888693696le_IIA @ A ) )
    <=> ! [B: fun_Ar500372357t_bool] :
          ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ B ) @ arrow_1190054106e_Prof ) )
         => ! [C: fun_Ar500372357t_bool] :
              ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ C ) @ arrow_1190054106e_Prof ) )
             => ! [D: arrow_931160158le_alt,E: arrow_931160158le_alt] :
                  ( ! [F: arrow_2115524757e_indi] :
                      ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ D ) @ E ) ) @ ( hAPP_A1174518481t_bool @ B @ F ) ) )
                    <=> ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ D ) @ E ) ) @ ( hAPP_A1174518481t_bool @ C @ F ) ) ) )
                 => ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ D ) @ E ) ) @ ( hAPP_f792184801t_bool @ A @ B ) ) )
                  <=> ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ D ) @ E ) ) @ ( hAPP_f792184801t_bool @ A @ C ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_IIA__def) ).

thf(2032,plain,
    ! [A: fun_fu1595299477t_bool] :
      ( ( ( hBOOL @ ( hAPP_f611501301l_bool @ arrow_888693696le_IIA @ A ) )
       => ! [B: fun_Ar500372357t_bool] :
            ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ B ) @ arrow_1190054106e_Prof ) )
           => ! [C: fun_Ar500372357t_bool] :
                ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ C ) @ arrow_1190054106e_Prof ) )
               => ! [D: arrow_931160158le_alt,E: arrow_931160158le_alt] :
                    ( ! [F: arrow_2115524757e_indi] :
                        ( ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ D ) @ E ) ) @ ( hAPP_A1174518481t_bool @ B @ F ) ) )
                         => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ D ) @ E ) ) @ ( hAPP_A1174518481t_bool @ C @ F ) ) ) )
                        & ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ D ) @ E ) ) @ ( hAPP_A1174518481t_bool @ C @ F ) ) )
                         => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ D ) @ E ) ) @ ( hAPP_A1174518481t_bool @ B @ F ) ) ) ) )
                   => ( ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ D ) @ E ) ) @ ( hAPP_f792184801t_bool @ A @ B ) ) )
                       => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ D ) @ E ) ) @ ( hAPP_f792184801t_bool @ A @ C ) ) ) )
                      & ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ D ) @ E ) ) @ ( hAPP_f792184801t_bool @ A @ C ) ) )
                       => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ D ) @ E ) ) @ ( hAPP_f792184801t_bool @ A @ B ) ) ) ) ) ) ) ) )
      & ( ! [B: fun_Ar500372357t_bool] :
            ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ B ) @ arrow_1190054106e_Prof ) )
           => ! [C: fun_Ar500372357t_bool] :
                ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ C ) @ arrow_1190054106e_Prof ) )
               => ! [D: arrow_931160158le_alt,E: arrow_931160158le_alt] :
                    ( ! [F: arrow_2115524757e_indi] :
                        ( ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ D ) @ E ) ) @ ( hAPP_A1174518481t_bool @ B @ F ) ) )
                         => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ D ) @ E ) ) @ ( hAPP_A1174518481t_bool @ C @ F ) ) ) )
                        & ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ D ) @ E ) ) @ ( hAPP_A1174518481t_bool @ C @ F ) ) )
                         => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ D ) @ E ) ) @ ( hAPP_A1174518481t_bool @ B @ F ) ) ) ) )
                   => ( ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ D ) @ E ) ) @ ( hAPP_f792184801t_bool @ A @ B ) ) )
                       => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ D ) @ E ) ) @ ( hAPP_f792184801t_bool @ A @ C ) ) ) )
                      & ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ D ) @ E ) ) @ ( hAPP_f792184801t_bool @ A @ C ) ) )
                       => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ D ) @ E ) ) @ ( hAPP_f792184801t_bool @ A @ B ) ) ) ) ) ) ) )
       => ( hBOOL @ ( hAPP_f611501301l_bool @ arrow_888693696le_IIA @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(19,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_303_order__less__imp__le) ).

thf(815,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(584,axiom,
    ~ ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ b ) @ a ) ) @ lab ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79__096_Ib_M_Aa_J_A_126_058_ALab_096) ).

thf(2958,plain,
    ~ ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ b ) @ a ) ) @ lab ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).

thf(327,axiom,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool,C: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_521_psubset__trans) ).

thf(1920,plain,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool,C: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(32,axiom,
    ! [A: nat] :
      ( ( A != zero_zero_nat )
    <=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_616_neq0__conv) ).

thf(852,plain,
    ! [A: nat] :
      ( ( ( A != zero_zero_nat )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) ) )
      & ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
       => ( A != zero_zero_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(126,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_574_termination__basic__simps_I5_J) ).

thf(1178,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(750,axiom,
    ! [A: fun_fu1595299477t_bool,B: fun_fu1596339983e_indi,C: fun_fu1138137687l_bool,D: fun_fu2127564915i_bool] :
      ( ( hBOOL @ ( hAPP_f1616443493l_bool @ ( hAPP_f1536115021l_bool @ member2095441122e_indi @ B ) @ ( pi_fun1073350051e_indi @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ ( hAPP_f1763702829e_indi @ B @ A ) ) @ ( hAPP_f740807359i_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_PiE) ).

thf(3600,plain,
    ! [A: fun_fu1595299477t_bool,B: fun_fu1596339983e_indi,C: fun_fu1138137687l_bool,D: fun_fu2127564915i_bool] :
      ( ( hBOOL @ ( hAPP_f1616443493l_bool @ ( hAPP_f1536115021l_bool @ member2095441122e_indi @ B ) @ ( pi_fun1073350051e_indi @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ ( hAPP_f1763702829e_indi @ B @ A ) ) @ ( hAPP_f740807359i_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).

thf(249,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( ( ( hAPP_nat_nat @ suc @ A )
         != B )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_651_Suc__lessI) ).

thf(1624,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( ( ( hAPP_nat_nat @ suc @ A )
         != B )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(487,axiom,
    ! [A: nat,B: nat] :
      ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) )
      <=> ( B = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_linorder__antisym__conv3) ).

thf(2609,plain,
    ! [A: nat,B: nat] :
      ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) )
         => ( B = A ) )
        & ( ( B = A )
         => ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).

thf(380,axiom,
    ! [A: product_unit,B: fun_Pr1887046367le_alt,C: fun_Pr1643180309t_bool,D: fun_Pr1572389447t_bool] :
      ( ( hBOOL @ ( hAPP_f403597109l_bool @ ( hAPP_f1413342797l_bool @ member666484274le_alt @ B ) @ ( pi_Pro1041002611le_alt @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_P1763651581le_alt @ B @ A ) ) @ ( hAPP_P902017683t_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_PiE) ).

thf(2179,plain,
    ! [A: product_unit,B: fun_Pr1887046367le_alt,C: fun_Pr1643180309t_bool,D: fun_Pr1572389447t_bool] :
      ( ( hBOOL @ ( hAPP_f403597109l_bool @ ( hAPP_f1413342797l_bool @ member666484274le_alt @ B ) @ ( pi_Pro1041002611le_alt @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_P1763651581le_alt @ B @ A ) ) @ ( hAPP_P902017683t_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

thf(728,axiom,
    ! [A: arrow_2115524757e_indi,B: arrow_2115524757e_indi,C: fun_Ar1744566822di_nat,D: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( inj_on886403158di_nat @ C ) @ D ) )
     => ( ( ( hAPP_A1450069362di_nat @ C @ A )
          = ( hAPP_A1450069362di_nat @ C @ B ) )
       => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ A ) @ D ) )
         => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ B ) @ D ) )
           => ( A = B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_371_inj__onD) ).

thf(3546,plain,
    ! [A: arrow_2115524757e_indi,B: arrow_2115524757e_indi,C: fun_Ar1744566822di_nat,D: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( inj_on886403158di_nat @ C ) @ D ) )
     => ( ( ( hAPP_A1450069362di_nat @ C @ A )
          = ( hAPP_A1450069362di_nat @ C @ B ) )
       => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ A ) @ D ) )
         => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ B ) @ D ) )
           => ( A = B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).

thf(84,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_433_add__strict__right__mono) ).

thf(1027,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(251,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( B != zero_zero_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_614_gr__implies__not0) ).

thf(1634,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( B != zero_zero_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(360,axiom,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool,C: fun_Ar552120407i_bool] :
      ( ( B = C )
     => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_ord__eq__less__trans) ).

thf(2112,plain,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool,C: fun_Ar552120407i_bool] :
      ( ( B = C )
     => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(275,axiom,
    ! [A: fun_nat_nat,B: fun_nat_nat,C: fun_nat_bool] :
      ( ! [D: nat] :
          ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ D ) @ C ) )
         => ( ( hAPP_nat_nat @ A @ D )
            = ( hAPP_nat_nat @ B @ D ) ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ A ) @ C ) )
      <=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_593_inj__on__cong) ).

thf(1740,plain,
    ! [A: fun_nat_nat,B: fun_nat_nat,C: fun_nat_bool] :
      ( ! [D: nat] :
          ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ D ) @ C ) )
         => ( ( hAPP_nat_nat @ A @ D )
            = ( hAPP_nat_nat @ B @ D ) ) )
     => ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ A ) @ C ) )
         => ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ B ) @ C ) ) )
        & ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ B ) @ C ) )
         => ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ A ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(747,axiom,
    ! [A: fun_Pr1055212137t_bool] : ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ A ) @ top_to1690334693l_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_UNIV__I) ).

thf(3595,plain,
    ! [A: fun_Pr1055212137t_bool] : ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ A ) @ top_to1690334693l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).

thf(52,axiom,
    ! [A: nat,B: nat] :
      ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
    <=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_linorder__not__less) ).

thf(916,plain,
    ! [A: nat,B: nat] :
      ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) )
      & ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
       => ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(635,axiom,
    ! [A: nat,B: nat] :
      ( ( A != B )
    <=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
        | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_528_nat__neq__iff) ).

thf(3166,plain,
    ! [A: nat,B: nat] :
      ( ( ( A != B )
       => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) )
       => ( A != B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).

thf(641,axiom,
    ! [A: fun_Ar1744566822di_nat,B: fun_Ar1744566822di_nat,C: fun_Ar552120407i_bool] :
      ( ! [D: arrow_2115524757e_indi] :
          ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ D ) @ C ) )
         => ( ( hAPP_A1450069362di_nat @ A @ D )
            = ( hAPP_A1450069362di_nat @ B @ D ) ) )
     => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( inj_on886403158di_nat @ A ) @ C ) )
      <=> ( hBOOL @ ( hAPP_f1397511071l_bool @ ( inj_on886403158di_nat @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_594_inj__on__cong) ).

thf(3191,plain,
    ! [A: fun_Ar1744566822di_nat,B: fun_Ar1744566822di_nat,C: fun_Ar552120407i_bool] :
      ( ! [D: arrow_2115524757e_indi] :
          ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ D ) @ C ) )
         => ( ( hAPP_A1450069362di_nat @ A @ D )
            = ( hAPP_A1450069362di_nat @ B @ D ) ) )
     => ( ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( inj_on886403158di_nat @ A ) @ C ) )
         => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( inj_on886403158di_nat @ B ) @ C ) ) )
        & ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( inj_on886403158di_nat @ B ) @ C ) )
         => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( inj_on886403158di_nat @ A ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).

thf(30,axiom,
    ! [A: nat,B: nat] :
      ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B )
      = ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_642_add__Suc__shift) ).

thf(847,plain,
    ! [A: nat,B: nat] :
      ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B )
      = ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(523,axiom,
    ! [A: arrow_2115524757e_indi,B: arrow_2115524757e_indi,C: fun_Ar1744566822di_nat] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( inj_on886403158di_nat @ C ) @ top_to1678393681i_bool ) )
     => ( ( ( hAPP_A1450069362di_nat @ C @ A )
          = ( hAPP_A1450069362di_nat @ C @ B ) )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_384_injD) ).

thf(2758,plain,
    ! [A: arrow_2115524757e_indi,B: arrow_2115524757e_indi,C: fun_Ar1744566822di_nat] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( inj_on886403158di_nat @ C ) @ top_to1678393681i_bool ) )
     => ( ( ( hAPP_A1450069362di_nat @ C @ A )
          = ( hAPP_A1450069362di_nat @ C @ B ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).

thf(655,axiom,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool,C: fun_Pr1643180309t_bool] :
      ( ( B = C )
     => ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_xt1_I1_J) ).

thf(3269,plain,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool,C: fun_Pr1643180309t_bool] :
      ( ( B = C )
     => ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).

thf(755,axiom,
    ! [A: fun_nat_nat,B: fun_nat_bool] :
      ( ! [C: nat,D: nat] :
          ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ B ) )
         => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ D ) @ B ) )
           => ( ( ( hAPP_nat_nat @ A @ C )
                = ( hAPP_nat_nat @ A @ D ) )
             => ( C = D ) ) ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_591_inj__onI) ).

thf(3618,plain,
    ! [A: fun_nat_nat,B: fun_nat_bool] :
      ( ! [C: nat,D: nat] :
          ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ B ) )
         => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ D ) @ B ) )
           => ( ( ( hAPP_nat_nat @ A @ C )
                = ( hAPP_nat_nat @ A @ D ) )
             => ( C = D ) ) ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).

thf(612,axiom,
    c != d,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__096c_A_126_061_Ad_096) ).

thf(3090,plain,
    c != d,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).

thf(642,axiom,
    ! [A: nat,B: nat] :
      ( ( A = B )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_order__eq__refl) ).

thf(3198,plain,
    ! [A: nat,B: nat] :
      ( ( A = B )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).

thf(41,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_659_Suc__leI) ).

thf(879,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(678,axiom,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool] :
      ( ( A != B )
     => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ B ) @ A ) )
       => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_xt1_I12_J) ).

thf(3349,plain,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool] :
      ( ( A != B )
     => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ B ) @ A ) )
       => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).

thf(732,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_543_le__antisym) ).

thf(3556,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).

thf(301,axiom,
    ! [A: arrow_2115524757e_indi] :
      ( ( hBOOL @ ( hAPP_A1888055029i_bool @ top_to1678393681i_bool @ A ) )
    <=> ( hBOOL @ top_top_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_top__apply) ).

thf(1836,plain,
    ! [A: arrow_2115524757e_indi] :
      ( ( ( hBOOL @ ( hAPP_A1888055029i_bool @ top_to1678393681i_bool @ A ) )
       => ( hBOOL @ top_top_bool ) )
      & ( ( hBOOL @ top_top_bool )
       => ( hBOOL @ ( hAPP_A1888055029i_bool @ top_to1678393681i_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(381,axiom,
    ! [A: fun_bool_bool,B: fun_bool_bool] :
      ( ! [C: bool] :
          ( ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ C ) @ B ) )
         => ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ C ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_f612708895l_bool @ ord_le742797417l_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_504_subsetI) ).

thf(2181,plain,
    ! [A: fun_bool_bool,B: fun_bool_bool] :
      ( ! [C: bool] :
          ( ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ C ) @ B ) )
         => ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ C ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_f612708895l_bool @ ord_le742797417l_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(601,axiom,
    ! [A: bool,B: bool] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_bool @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_301_order__less__imp__le) ).

thf(3028,plain,
    ! [A: bool,B: bool] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_bool @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).

thf(608,axiom,
    hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ c ) @ e ) ) @ ( hAPP_f792184801t_bool @ f @ ( cOMBS_1921392482t_bool @ ( cOMBS_811328630t_bool @ ( hAPP_f509814255t_bool @ ( cOMBB_231886989e_indi @ if_fun1658569689t_bool ) @ ( hAPP_n924210722i_bool @ ( hAPP_f62620517i_bool @ cOMBC_922322901t_bool @ ( hAPP_f1381130897t_bool @ ( cOMBB_981137617e_indi @ ord_less_nat ) @ h ) ) @ n ) ) @ ( hAPP_A658738638t_bool @ ( hAPP_f293545699t_bool @ cOMBC_18834461t_bool @ ( hAPP_f842954860t_bool @ ( cOMBB_117136048e_indi @ arrow_741591990_mktop ) @ p ) ) @ e ) ) @ ( cOMBS_1921392482t_bool @ ( cOMBS_811328630t_bool @ ( hAPP_f509814255t_bool @ ( cOMBB_231886989e_indi @ if_fun1658569689t_bool ) @ ( hAPP_n924210722i_bool @ ( hAPP_f62620517i_bool @ cOMBC_922322901t_bool @ ( hAPP_f1381130897t_bool @ ( cOMBB_981137617e_indi @ fequal_nat ) @ h ) ) @ n ) ) @ ( hAPP_A658738638t_bool @ ( hAPP_f293545699t_bool @ cOMBC_18834461t_bool @ ( hAPP_A102926893t_bool @ ( hAPP_f141075873t_bool @ cOMBC_1505804284t_bool @ ( hAPP_f576849227t_bool @ ( cOMBB_656639247e_indi @ arrow_1475523868_above ) @ p ) ) @ c ) ) @ e ) ) @ ( hAPP_A658738638t_bool @ ( hAPP_f293545699t_bool @ cOMBC_18834461t_bool @ ( hAPP_f842954860t_bool @ ( cOMBB_117136048e_indi @ arrow_592884904_mkbot ) @ p ) ) @ e ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto) ).

thf(3050,plain,
    hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ c ) @ e ) ) @ ( hAPP_f792184801t_bool @ f @ ( cOMBS_1921392482t_bool @ ( cOMBS_811328630t_bool @ ( hAPP_f509814255t_bool @ ( cOMBB_231886989e_indi @ if_fun1658569689t_bool ) @ ( hAPP_n924210722i_bool @ ( hAPP_f62620517i_bool @ cOMBC_922322901t_bool @ ( hAPP_f1381130897t_bool @ ( cOMBB_981137617e_indi @ ord_less_nat ) @ h ) ) @ n ) ) @ ( hAPP_A658738638t_bool @ ( hAPP_f293545699t_bool @ cOMBC_18834461t_bool @ ( hAPP_f842954860t_bool @ ( cOMBB_117136048e_indi @ arrow_741591990_mktop ) @ p ) ) @ e ) ) @ ( cOMBS_1921392482t_bool @ ( cOMBS_811328630t_bool @ ( hAPP_f509814255t_bool @ ( cOMBB_231886989e_indi @ if_fun1658569689t_bool ) @ ( hAPP_n924210722i_bool @ ( hAPP_f62620517i_bool @ cOMBC_922322901t_bool @ ( hAPP_f1381130897t_bool @ ( cOMBB_981137617e_indi @ fequal_nat ) @ h ) ) @ n ) ) @ ( hAPP_A658738638t_bool @ ( hAPP_f293545699t_bool @ cOMBC_18834461t_bool @ ( hAPP_A102926893t_bool @ ( hAPP_f141075873t_bool @ cOMBC_1505804284t_bool @ ( hAPP_f576849227t_bool @ ( cOMBB_656639247e_indi @ arrow_1475523868_above ) @ p ) ) @ c ) ) @ e ) ) @ ( hAPP_A658738638t_bool @ ( hAPP_f293545699t_bool @ cOMBC_18834461t_bool @ ( hAPP_f842954860t_bool @ ( cOMBB_117136048e_indi @ arrow_592884904_mkbot ) @ p ) ) @ e ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).

thf(113,axiom,
    ! [A: fun_Ar1492469401t_bool,B: fun_Pr1055212137t_bool,C: arrow_2115524757e_indi] :
      ( ( hAPP_A1174518481t_bool @ ( hAPP_f311418073t_bool @ ( hAPP_f1302245795t_bool @ cOMBC_1490589522t_bool @ A ) @ B ) @ C )
      = ( hAPP_f70231061t_bool @ ( hAPP_A892860133t_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_000_324) ).

thf(1128,plain,
    ! [A: fun_Ar1492469401t_bool,B: fun_Pr1055212137t_bool,C: arrow_2115524757e_indi] :
      ( ( hAPP_A1174518481t_bool @ ( hAPP_f311418073t_bool @ ( hAPP_f1302245795t_bool @ cOMBC_1490589522t_bool @ A ) @ B ) @ C )
      = ( hAPP_f70231061t_bool @ ( hAPP_A892860133t_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(454,axiom,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ B ) )
     => ~ ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_order__less__asym) ).

thf(2492,plain,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ B ) )
     => ~ ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).

thf(185,axiom,
    ! [A: nat,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_nat_bool @ B @ A ) ) @ ( hAPP_nat_bool @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_le__funE) ).

thf(1402,plain,
    ! [A: nat,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_nat_bool @ B @ A ) ) @ ( hAPP_nat_bool @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(336,axiom,
    ! [A: bool,B: bool] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ A ) )
       => ( ( hBOOL @ A )
        <=> ( hBOOL @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_order__antisym) ).

thf(1983,plain,
    ! [A: bool,B: bool] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ A ) )
       => ( ( ( hBOOL @ A )
           => ( hBOOL @ B ) )
          & ( ( hBOOL @ B )
           => ( hBOOL @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(547,axiom,
    ! [A: bool,B: bool,C: bool] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_xt1_I6_J) ).

thf(2840,plain,
    ! [A: bool,B: bool,C: bool] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).

thf(151,axiom,
    ! [A: nat] :
      ( ( hAPP_nat_nat @ suc @ A )
     != A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_640_Suc__n__not__n) ).

thf(1259,plain,
    ! [A: nat] :
      ( ( hAPP_nat_nat @ suc @ A )
     != A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(111,axiom,
    ! [A: nat,B: nat] :
      ( ( A != B )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_292_order__neq__le__trans) ).

thf(1121,plain,
    ! [A: nat,B: nat] :
      ( ( A != B )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(647,axiom,
    ! [A: fun_fu1138137687l_bool] :
      ( ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f173704847l_bool @ ord_le161055137l_bool @ top_to2013953873l_bool ) @ A ) )
     => ( A = top_to2013953873l_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_358_top__le) ).

thf(3218,plain,
    ! [A: fun_fu1138137687l_bool] :
      ( ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f173704847l_bool @ ord_le161055137l_bool @ top_to2013953873l_bool ) @ A ) )
     => ( A = top_to2013953873l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).

thf(505,axiom,
    ! [A: fun_nat_nat,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f1426445843l_bool @ ( hAPP_f2040535501l_bool @ member_fun_nat_nat @ A ) @ ( pi_nat_nat @ B @ ( hAPP_f1570313510t_bool @ cOMBK_583454926ol_nat @ C ) ) ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ A ) @ B ) )
       => ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ C ) )
         => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( finite_card_nat @ B ) ) @ ( finite_card_nat @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_586_card__inj) ).

thf(2694,plain,
    ! [A: fun_nat_nat,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f1426445843l_bool @ ( hAPP_f2040535501l_bool @ member_fun_nat_nat @ A ) @ ( pi_nat_nat @ B @ ( hAPP_f1570313510t_bool @ cOMBK_583454926ol_nat @ C ) ) ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ A ) @ B ) )
       => ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ C ) )
         => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( finite_card_nat @ B ) ) @ ( finite_card_nat @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).

thf(101,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_660_le__imp__less__Suc) ).

thf(1096,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(38,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_657_Suc__le__lessD) ).

thf(869,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(494,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
    <=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ B ) )
        | ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_283_order__le__less) ).

thf(2638,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
       => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ B ) )
          | ( A = B ) ) )
      & ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ B ) )
          | ( A = B ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).

thf(636,axiom,
    ! [A: fun_Pr1055212137t_bool,B: fun_fu1015689055l_bool,C: fun_fu1015689055l_bool] :
      ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f868566847l_bool @ ord_le1923264405l_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_467_set__mp) ).

thf(3176,plain,
    ! [A: fun_Pr1055212137t_bool,B: fun_fu1015689055l_bool,C: fun_fu1015689055l_bool] :
      ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f868566847l_bool @ ord_le1923264405l_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).

thf(457,axiom,
    ~ ! [A: nat] :
        ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( finite783399747e_indi @ top_to1678393681i_bool ) ) )
       => ( ! [B: nat] :
              ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
             => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ b ) @ a ) ) @ ( hAPP_f792184801t_bool @ f @ ( hAPP_f311418073t_bool @ ( hAPP_f1302245795t_bool @ cOMBC_1490589522t_bool @ ( hAPP_f1755759597t_bool @ ( hAPP_f1328803787t_bool @ cOMBC_1190055014t_bool @ ( hAPP_f509814255t_bool @ ( cOMBB_231886989e_indi @ if_fun1658569689t_bool ) @ ( hAPP_n924210722i_bool @ ( hAPP_f62620517i_bool @ cOMBC_922322901t_bool @ ( hAPP_f1381130897t_bool @ ( cOMBB_981137617e_indi @ ord_less_nat ) @ h ) ) @ B ) ) ) @ lab ) ) @ lba ) ) ) ) )
         => ~ ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ a ) @ b ) ) @ ( hAPP_f792184801t_bool @ f @ ( hAPP_f311418073t_bool @ ( hAPP_f1302245795t_bool @ cOMBC_1490589522t_bool @ ( hAPP_f1755759597t_bool @ ( hAPP_f1328803787t_bool @ cOMBC_1190055014t_bool @ ( hAPP_f509814255t_bool @ ( cOMBB_231886989e_indi @ if_fun1658569689t_bool ) @ ( hAPP_n924210722i_bool @ ( hAPP_f62620517i_bool @ cOMBC_922322901t_bool @ ( hAPP_f1381130897t_bool @ ( cOMBB_981137617e_indi @ ord_less_nat ) @ h ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ one_one_nat ) ) ) ) @ lab ) ) @ lba ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228__096_B_Bthesis_O_A_I_B_Bn_O_A_091_124_An_A_060_AN_059_AALL_Am_060_061n_) ).

thf(2498,plain,
    ~ ! [A: nat] :
        ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( finite783399747e_indi @ top_to1678393681i_bool ) ) )
       => ( ! [B: nat] :
              ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
             => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ b ) @ a ) ) @ ( hAPP_f792184801t_bool @ f @ ( hAPP_f311418073t_bool @ ( hAPP_f1302245795t_bool @ cOMBC_1490589522t_bool @ ( hAPP_f1755759597t_bool @ ( hAPP_f1328803787t_bool @ cOMBC_1190055014t_bool @ ( hAPP_f509814255t_bool @ ( cOMBB_231886989e_indi @ if_fun1658569689t_bool ) @ ( hAPP_n924210722i_bool @ ( hAPP_f62620517i_bool @ cOMBC_922322901t_bool @ ( hAPP_f1381130897t_bool @ ( cOMBB_981137617e_indi @ ord_less_nat ) @ h ) ) @ B ) ) ) @ lab ) ) @ lba ) ) ) ) )
         => ~ ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ a ) @ b ) ) @ ( hAPP_f792184801t_bool @ f @ ( hAPP_f311418073t_bool @ ( hAPP_f1302245795t_bool @ cOMBC_1490589522t_bool @ ( hAPP_f1755759597t_bool @ ( hAPP_f1328803787t_bool @ cOMBC_1190055014t_bool @ ( hAPP_f509814255t_bool @ ( cOMBB_231886989e_indi @ if_fun1658569689t_bool ) @ ( hAPP_n924210722i_bool @ ( hAPP_f62620517i_bool @ cOMBC_922322901t_bool @ ( hAPP_f1381130897t_bool @ ( cOMBB_981137617e_indi @ ord_less_nat ) @ h ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ one_one_nat ) ) ) ) @ lab ) ) @ lba ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).

thf(143,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
    <=> ? [C: nat] :
          ( B
          = ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_562_le__iff__add) ).

thf(1234,plain,
    ! [A: nat,B: nat] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
       => ? [C: nat] :
            ( B
            = ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) )
      & ( ? [C: nat] :
            ( B
            = ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(223,axiom,
    ! [A: nat,B: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_666_less__add__Suc1) ).

thf(1541,plain,
    ! [A: nat,B: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(716,axiom,
    ! [A: fun_Pr1055212137t_bool] : ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ A ) @ top_to1690334693l_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_iso__tuple__UNIV__I) ).

thf(3482,plain,
    ! [A: fun_Pr1055212137t_bool] : ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ A ) @ top_to1690334693l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).

thf(282,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( B = C )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_xt1_I3_J) ).

thf(1762,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( B = C )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(221,axiom,
    ! [A: nat] :
      ( zero_zero_nat
     != ( hAPP_nat_nat @ suc @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_678_Zero__not__Suc) ).

thf(1534,plain,
    ! [A: nat] :
      ( zero_zero_nat
     != ( hAPP_nat_nat @ suc @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(291,axiom,
    ! [A: fun_Pr1055212137t_bool,B: fun_fu1015689055l_bool,C: fun_fu1015689055l_bool,D: fun_fu44268723l_bool] :
      ( ( hBOOL @ ( hAPP_f1656729961l_bool @ ( hAPP_f717334393l_bool @ member717964108l_bool @ B ) @ ( pi_fun1412468411l_bool @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ ( hAPP_f429946033l_bool @ B @ A ) ) @ ( hAPP_f269590987l_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_PiE) ).

thf(1794,plain,
    ! [A: fun_Pr1055212137t_bool,B: fun_fu1015689055l_bool,C: fun_fu1015689055l_bool,D: fun_fu44268723l_bool] :
      ( ( hBOOL @ ( hAPP_f1656729961l_bool @ ( hAPP_f717334393l_bool @ member717964108l_bool @ B ) @ ( pi_fun1412468411l_bool @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ ( hAPP_f429946033l_bool @ B @ A ) ) @ ( hAPP_f269590987l_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(479,axiom,
    ! [A: fun_Pr1055212137t_bool,B: fun_Pr359894313l_bool,C: fun_Pr1055212137t_bool] :
      ( ! [D: produc1840315303le_alt] :
          ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ D ) @ C ) )
         => ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ ( hAPP_P166437127t_bool @ A @ D ) ) @ ( hAPP_P1830623733l_bool @ B @ D ) ) ) )
     => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ A ) @ ( pi_Pro226591613t_bool @ C @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_583_Pi__I_H) ).

thf(2577,plain,
    ! [A: fun_Pr1055212137t_bool,B: fun_Pr359894313l_bool,C: fun_Pr1055212137t_bool] :
      ( ! [D: produc1840315303le_alt] :
          ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ D ) @ C ) )
         => ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ ( hAPP_P166437127t_bool @ A @ D ) ) @ ( hAPP_P1830623733l_bool @ B @ D ) ) ) )
     => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ A ) @ ( pi_Pro226591613t_bool @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).

thf(690,axiom,
    ! [A: fun_fu1595299477t_bool,B: fun_fu1138137687l_bool] :
      ( ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ A ) @ B ) )
    <=> ( hBOOL @ ( hAPP_f611501301l_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_mem__def) ).

thf(3381,plain,
    ! [A: fun_fu1595299477t_bool,B: fun_fu1138137687l_bool] :
      ( ( ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f611501301l_bool @ B @ A ) ) )
      & ( ( hBOOL @ ( hAPP_f611501301l_bool @ B @ A ) )
       => ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).

thf(107,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
        | ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_309_order__le__imp__less__or__eq) ).

thf(1111,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
        | ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(140,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_549_trans__less__add1) ).

thf(1227,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(691,axiom,
    ! [A: fun_nat_bool] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_order__refl) ).

thf(3386,plain,
    ! [A: fun_nat_bool] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).

thf(512,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_order__less__asym_H) ).

thf(2726,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).

thf(117,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ C ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_554_add__lessD1) ).

thf(1138,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ C ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(554,axiom,
    ! [A: produc1840315303le_alt,B: fun_Pr1055212137t_bool,C: fun_Pr1055212137t_bool,D: fun_Pr359894313l_bool] :
      ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ B ) @ ( pi_Pro226591613t_bool @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ ( hAPP_P166437127t_bool @ B @ A ) ) @ ( hAPP_P1830623733l_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_PiE) ).

thf(2858,plain,
    ! [A: produc1840315303le_alt,B: fun_Pr1055212137t_bool,C: fun_Pr1055212137t_bool,D: fun_Pr359894313l_bool] :
      ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ B ) @ ( pi_Pro226591613t_bool @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ ( hAPP_P166437127t_bool @ B @ A ) ) @ ( hAPP_P1830623733l_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).

thf(469,axiom,
    hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ lba ) @ arrow_915577424le_Lin ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74__096Lba_A_058_ALin_096) ).

thf(2537,plain,
    hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ lba ) @ arrow_915577424le_Lin ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).

thf(759,axiom,
    ! [A: bool,B: bool,C: bool] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ C ) )
     => ( ( ( hBOOL @ C )
        <=> ( hBOOL @ A ) )
       => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_ord__le__eq__trans) ).

thf(3632,plain,
    ! [A: bool,B: bool,C: bool] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ C ) )
     => ( ( ( ( hBOOL @ C )
           => ( hBOOL @ A ) )
          & ( ( hBOOL @ A )
           => ( hBOOL @ C ) ) )
       => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).

thf(622,axiom,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ ( hAPP_f1282576021i_bool @ ( hAPP_f833264203i_bool @ cOMBC_31215906l_bool @ member590466050e_indi ) @ A ) ) @ ( hAPP_f1282576021i_bool @ ( hAPP_f833264203i_bool @ cOMBC_31215906l_bool @ member590466050e_indi ) @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_495_pred__subset__eq) ).

thf(3119,plain,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool] :
      ( ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ ( hAPP_f1282576021i_bool @ ( hAPP_f833264203i_bool @ cOMBC_31215906l_bool @ member590466050e_indi ) @ A ) ) @ ( hAPP_f1282576021i_bool @ ( hAPP_f833264203i_bool @ cOMBC_31215906l_bool @ member590466050e_indi ) @ B ) ) )
       => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ A ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ ( hAPP_f1282576021i_bool @ ( hAPP_f833264203i_bool @ cOMBC_31215906l_bool @ member590466050e_indi ) @ A ) ) @ ( hAPP_f1282576021i_bool @ ( hAPP_f833264203i_bool @ cOMBC_31215906l_bool @ member590466050e_indi ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).

thf(412,axiom,
    ! [A: bool,B: bool] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_bool @ A ) @ B ) )
    <=> ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ B ) )
        & ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_less__le__not__le) ).

thf(2268,plain,
    ! [A: bool,B: bool] :
      ( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_bool @ A ) @ B ) )
       => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ B ) )
          & ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ A ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ B ) )
          & ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ A ) ) )
       => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(644,axiom,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool,C: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_336_xt1_I8_J) ).

thf(3205,plain,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool,C: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).

thf(232,axiom,
    ! [A: nat,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_nat_bool @ B @ A ) ) @ ( hAPP_nat_bool @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_le__funD) ).

thf(1567,plain,
    ! [A: nat,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_nat_bool @ B @ A ) ) @ ( hAPP_nat_bool @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(43,axiom,
    ! [A: nat] :
      ( zero_zero_nat
     != ( hAPP_nat_nat @ suc @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_674_Zero__neq__Suc) ).

thf(884,plain,
    ! [A: nat] :
      ( zero_zero_nat
     != ( hAPP_nat_nat @ suc @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(346,axiom,
    ! [A: arrow_2115524757e_indi,B: nat,C: fun_Ar1744566822di_nat] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( inj_on886403158di_nat @ C ) @ top_to1678393681i_bool ) )
     => ( ( ( hAPP_A1450069362di_nat @ C @ A )
          = B )
       => ( ( hAPP_n1048492170e_indi @ ( hilber506087739di_nat @ top_to1678393681i_bool @ C ) @ B )
          = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_inv__f__eq) ).

thf(2023,plain,
    ! [A: arrow_2115524757e_indi,B: nat,C: fun_Ar1744566822di_nat] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( inj_on886403158di_nat @ C ) @ top_to1678393681i_bool ) )
     => ( ( ( hAPP_A1450069362di_nat @ C @ A )
          = B )
       => ( ( hAPP_n1048492170e_indi @ ( hilber506087739di_nat @ top_to1678393681i_bool @ C ) @ B )
          = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(629,axiom,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_299_order__less__imp__le) ).

thf(3143,plain,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).

thf(474,axiom,
    ! [A: fun_fu775006535l_bool,B: fun_fu775006535l_bool] :
      ( ! [C: fun_Ar500372357t_bool] :
          ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ C ) @ B ) )
         => ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ C ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f95487087l_bool @ ord_le1871091345l_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_510_subsetI) ).

thf(2561,plain,
    ! [A: fun_fu775006535l_bool,B: fun_fu775006535l_bool] :
      ( ! [C: fun_Ar500372357t_bool] :
          ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ C ) @ B ) )
         => ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ C ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f95487087l_bool @ ord_le1871091345l_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).

thf(201,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) )
     => ? [C: nat] :
          ( B
          = ( hAPP_nat_nat @ suc @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_689_Suc__le__D) ).

thf(1461,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) )
     => ? [C: nat] :
          ( B
          = ( hAPP_nat_nat @ suc @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(192,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_571_termination__basic__simps_I4_J) ).

thf(1424,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(136,axiom,
    ! [A: nat,B: nat] :
      ( ( ( hAPP_nat_nat @ suc @ A )
        = ( hAPP_nat_nat @ suc @ B ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_639_nat_Oinject) ).

thf(1207,plain,
    ! [A: nat,B: nat] :
      ( ( ( ( hAPP_nat_nat @ suc @ A )
          = ( hAPP_nat_nat @ suc @ B ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( ( hAPP_nat_nat @ suc @ A )
          = ( hAPP_nat_nat @ suc @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(499,axiom,
    ! [A: fun_fu775006535l_bool] :
      ( ( A != top_to1324311617l_bool )
    <=> ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f95487087l_bool @ ord_le583255965l_bool @ A ) @ top_to1324311617l_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_less__top) ).

thf(2666,plain,
    ! [A: fun_fu775006535l_bool] :
      ( ( ( A != top_to1324311617l_bool )
       => ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f95487087l_bool @ ord_le583255965l_bool @ A ) @ top_to1324311617l_bool ) ) )
      & ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f95487087l_bool @ ord_le583255965l_bool @ A ) @ top_to1324311617l_bool ) )
       => ( A != top_to1324311617l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).

thf(255,axiom,
    ! [A: fun_Pr1055212137t_bool,B: fun_fu1015689055l_bool] :
      ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ A ) @ B ) )
    <=> ( hBOOL @ ( hAPP_f429946033l_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_mem__def) ).

thf(1644,plain,
    ! [A: fun_Pr1055212137t_bool,B: fun_fu1015689055l_bool] :
      ( ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f429946033l_bool @ B @ A ) ) )
      & ( ( hBOOL @ ( hAPP_f429946033l_bool @ B @ A ) )
       => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(190,axiom,
    ! [A: fun_Pr1055212137t_bool,B: arrow_2115524757e_indi] :
      ( ( hAPP_A1174518481t_bool @ ( hAPP_f311418073t_bool @ cOMBK_1522533360e_indi @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ct_320) ).

thf(1419,plain,
    ! [A: fun_Pr1055212137t_bool,B: arrow_2115524757e_indi] :
      ( ( hAPP_A1174518481t_bool @ ( hAPP_f311418073t_bool @ cOMBK_1522533360e_indi @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(445,axiom,
    ! [A: fun_Ar500372357t_bool,B: fun_fu775006535l_bool,C: fun_fu775006535l_bool] :
      ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f95487087l_bool @ ord_le583255965l_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_518_psubsetD) ).

thf(2460,plain,
    ! [A: fun_Ar500372357t_bool,B: fun_fu775006535l_bool,C: fun_fu775006535l_bool] :
      ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f95487087l_bool @ ord_le583255965l_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).

thf(535,axiom,
    ! [A: bool] : ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ A ) @ top_to1647826457l_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_UNIV__I) ).

thf(2798,plain,
    ! [A: bool] : ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ A ) @ top_to1647826457l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).

thf(628,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_xt1_I9_J) ).

thf(3141,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).

thf(561,axiom,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ B ) )
     => ( B != A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_order__less__imp__not__eq2) ).

thf(2877,plain,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ B ) )
     => ( B != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).

thf(188,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_550_trans__less__add2) ).

thf(1414,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(388,axiom,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ B ) )
     => ~ ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_order__less__asym_H) ).

thf(2196,plain,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ B ) )
     => ~ ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(268,axiom,
    ! [A: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ top_top_fun_nat_bool ) @ A ) )
    <=> ( A = top_top_fun_nat_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_353_top__unique) ).

thf(1700,plain,
    ! [A: fun_nat_bool] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ top_top_fun_nat_bool ) @ A ) )
       => ( A = top_top_fun_nat_bool ) )
      & ( ( A = top_top_fun_nat_bool )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ top_top_fun_nat_bool ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(332,axiom,
    ! [A: fun_Ar500372357t_bool] : ( hBOOL @ ( hAPP_f1766661605l_bool @ top_to1324311617l_bool @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_top1I) ).

thf(1937,plain,
    ! [A: fun_Ar500372357t_bool] : ( hBOOL @ ( hAPP_f1766661605l_bool @ top_to1324311617l_bool @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(137,axiom,
    ! [A: nat,B: nat] :
      ( ( ( hAPP_nat_nat @ suc @ A )
        = ( hAPP_nat_nat @ suc @ B ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_638_Suc__inject) ).

thf(1214,plain,
    ! [A: nat,B: nat] :
      ( ( ( hAPP_nat_nat @ suc @ A )
        = ( hAPP_nat_nat @ suc @ B ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(420,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_order__less__not__sym) ).

thf(2349,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).

thf(88,axiom,
    ! [A: fun_fu775006535l_bool,B: fun_Pr1055212137t_bool] :
      ( ( hAPP_f1410143987l_bool @ ( hAPP_f1197023401l_bool @ cOMBK_2140692976t_bool @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____ctu) ).

thf(1039,plain,
    ! [A: fun_fu775006535l_bool,B: fun_Pr1055212137t_bool] :
      ( ( hAPP_f1410143987l_bool @ ( hAPP_f1197023401l_bool @ cOMBK_2140692976t_bool @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(69,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_654_Suc__lessD) ).

thf(970,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(108,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ B ) @ C ) )
      = ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ B ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_535_nat__add__left__commute) ).

thf(1114,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ B ) @ C ) )
      = ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ B ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(624,axiom,
    ! [A: fun_fu1138137687l_bool,B: fun_fu1138137687l_bool] :
      ( ! [C: fun_fu1595299477t_bool] :
          ( ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ C ) @ B ) )
         => ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ C ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f173704847l_bool @ ord_le161055137l_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_509_subsetI) ).

thf(3126,plain,
    ! [A: fun_fu1138137687l_bool,B: fun_fu1138137687l_bool] :
      ( ! [C: fun_fu1595299477t_bool] :
          ( ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ C ) @ B ) )
         => ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ C ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f173704847l_bool @ ord_le161055137l_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).

thf(414,axiom,
    ! [A: nat,B: nat,C: fun_nat_nat] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ C ) @ top_top_fun_nat_bool ) )
     => ( ( ( hAPP_nat_nat @ C @ A )
          = ( hAPP_nat_nat @ C @ B ) )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_383_injD) ).

thf(2304,plain,
    ! [A: nat,B: nat,C: fun_nat_nat] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ C ) @ top_top_fun_nat_bool ) )
     => ( ( ( hAPP_nat_nat @ C @ A )
          = ( hAPP_nat_nat @ C @ B ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).

thf(486,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( A = B )
    <=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
        & ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_order__eq__iff) ).

thf(2598,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( ( A = B )
       => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
          & ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
          & ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).

thf(114,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_429_add__less__imp__less__left) ).

thf(1131,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(422,axiom,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ A ) @ B ) )
     => ( ( A != B )
       => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_310_order__le__neq__trans) ).

thf(2355,plain,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ A ) @ B ) )
     => ( ( A != B )
       => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).

thf(459,axiom,
    ! [A: arrow_2115524757e_indi,B: fun_Ar1744566822di_nat,C: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( inj_on886403158di_nat @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ A ) @ C ) )
       => ( ( hAPP_n1048492170e_indi @ ( hilber506087739di_nat @ C @ B ) @ ( hAPP_A1450069362di_nat @ B @ A ) )
          = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_386_inv__into__f__f) ).

thf(2505,plain,
    ! [A: arrow_2115524757e_indi,B: fun_Ar1744566822di_nat,C: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( inj_on886403158di_nat @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ A ) @ C ) )
       => ( ( hAPP_n1048492170e_indi @ ( hilber506087739di_nat @ C @ B ) @ ( hAPP_A1450069362di_nat @ B @ A ) )
          = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).

thf(476,axiom,
    ! [A: fun_fu1595299477t_bool,B: fun_fu1015689055l_bool,C: fun_fu775006535l_bool] :
      ( ! [D: fun_Ar500372357t_bool] :
          ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ D ) @ C ) )
         => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ ( hAPP_f792184801t_bool @ A @ D ) ) @ B ) ) )
     => ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ A ) @ ( pi_fun530160875t_bool @ C @ ( hAPP_f422714471l_bool @ cOMBK_1446432t_bool @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_578_funcsetI) ).

thf(2566,plain,
    ! [A: fun_fu1595299477t_bool,B: fun_fu1015689055l_bool,C: fun_fu775006535l_bool] :
      ( ! [D: fun_Ar500372357t_bool] :
          ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ D ) @ C ) )
         => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ ( hAPP_f792184801t_bool @ A @ D ) ) @ B ) ) )
     => ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ A ) @ ( pi_fun530160875t_bool @ C @ ( hAPP_f422714471l_bool @ cOMBK_1446432t_bool @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).

thf(652,axiom,
    ! [A: arrow_2115524757e_indi,B: arrow_2115524757e_indi,C: fun_Ar1744566822di_nat] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( inj_on886403158di_nat @ C ) @ top_to1678393681i_bool ) )
     => ( ( ( hAPP_A1450069362di_nat @ C @ A )
          = ( hAPP_A1450069362di_nat @ C @ B ) )
      <=> ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_382_inj__eq) ).

thf(3247,plain,
    ! [A: arrow_2115524757e_indi,B: arrow_2115524757e_indi,C: fun_Ar1744566822di_nat] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( inj_on886403158di_nat @ C ) @ top_to1678393681i_bool ) )
     => ( ( ( ( hAPP_A1450069362di_nat @ C @ A )
            = ( hAPP_A1450069362di_nat @ C @ B ) )
         => ( A = B ) )
        & ( ( A = B )
         => ( ( hAPP_A1450069362di_nat @ C @ A )
            = ( hAPP_A1450069362di_nat @ C @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).

thf(271,axiom,
    ! [A: fun_fu775006535l_bool] :
      ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f95487087l_bool @ ord_le1871091345l_bool @ top_to1324311617l_bool ) @ A ) )
    <=> ( A = top_to1324311617l_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_351_top__unique) ).

thf(1715,plain,
    ! [A: fun_fu775006535l_bool] :
      ( ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f95487087l_bool @ ord_le1871091345l_bool @ top_to1324311617l_bool ) @ A ) )
       => ( A = top_to1324311617l_bool ) )
      & ( ( A = top_to1324311617l_bool )
       => ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f95487087l_bool @ ord_le1871091345l_bool @ top_to1324311617l_bool ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(152,axiom,
    ! [A: nat,B: nat] :
      ( ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B )
        = zero_zero_nat )
    <=> ( ( A = zero_zero_nat )
        & ( B = zero_zero_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_620_add__is__0) ).

thf(1263,plain,
    ! [A: nat,B: nat] :
      ( ( ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B )
          = zero_zero_nat )
       => ( ( A = zero_zero_nat )
          & ( B = zero_zero_nat ) ) )
      & ( ( ( A = zero_zero_nat )
          & ( B = zero_zero_nat ) )
       => ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B )
          = zero_zero_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(78,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_425_add__left__mono) ).

thf(997,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(754,axiom,
    ! [A: fun_Ar552120407i_bool] :
      ( ( A != top_to1678393681i_bool )
    <=> ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ top_to1678393681i_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_less__top) ).

thf(3611,plain,
    ! [A: fun_Ar552120407i_bool] :
      ( ( ( A != top_to1678393681i_bool )
       => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ top_to1678393681i_bool ) ) )
      & ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ top_to1678393681i_bool ) )
       => ( A != top_to1678393681i_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).

thf(440,axiom,
    ! [A: fun_Ar500372357t_bool,B: fun_Ar552120407i_bool,C: fun_fu1015689055l_bool] :
      ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ A ) @ ( pi_Arr487970267t_bool @ B @ ( hAPP_f1793492343l_bool @ cOMBK_1595020336e_indi @ C ) ) ) )
     => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( inj_on194063285t_bool @ A ) @ B ) )
       => ( ( hBOOL @ ( hAPP_f1021703871l_bool @ finite775027132t_bool @ C ) )
         => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( finite783399747e_indi @ B ) ) @ ( finite1445836347t_bool @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_589_card__inj) ).

thf(2450,plain,
    ! [A: fun_Ar500372357t_bool,B: fun_Ar552120407i_bool,C: fun_fu1015689055l_bool] :
      ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ A ) @ ( pi_Arr487970267t_bool @ B @ ( hAPP_f1793492343l_bool @ cOMBK_1595020336e_indi @ C ) ) ) )
     => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( inj_on194063285t_bool @ A ) @ B ) )
       => ( ( hBOOL @ ( hAPP_f1021703871l_bool @ finite775027132t_bool @ C ) )
         => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( finite783399747e_indi @ B ) ) @ ( finite1445836347t_bool @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).

thf(364,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_xt1_I10_J) ).

thf(2125,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(74,axiom,
    ! [A: nat,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_483_in__mono) ).

thf(985,plain,
    ! [A: nat,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(545,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_order__less__trans) ).

thf(2836,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).

thf(200,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ B ) ) )
    <=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_428_add__le__cancel__right) ).

thf(1456,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ B ) ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) ) )
      & ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(571,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) )
      <=> ( B = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_order__antisym__conv) ).

thf(2900,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
     => ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) )
         => ( B = A ) )
        & ( ( B = A )
         => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).

thf(299,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ B ) )
     => ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_order__less__asym_H) ).

thf(1831,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ B ) )
     => ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(142,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ D ) )
     => ( ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ D )
          = ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_553_less__add__eq__less) ).

thf(1231,plain,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ D ) )
     => ( ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ D )
          = ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(95,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_565_trans__le__add2) ).

thf(1060,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(92,axiom,
    ! [A: nat] :
      ( ( hAPP_nat_nat @ suc @ A )
      = ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ one_one_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_688_Suc__eq__plus1) ).

thf(1050,plain,
    ! [A: nat] :
      ( ( hAPP_nat_nat @ suc @ A )
      = ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ one_one_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(243,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
    <=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_663_less__eq__Suc__le) ).

thf(1599,plain,
    ! [A: nat,B: nat] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(146,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_338_xt1_I8_J) ).

thf(1246,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(618,axiom,
    ! [A: fun_Ar552120407i_bool] : ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ A ) @ top_to1678393681i_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_412_subset__UNIV) ).

thf(3109,plain,
    ! [A: fun_Ar552120407i_bool] : ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ A ) @ top_to1678393681i_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).

thf(9,axiom,
    ! [A: nat] :
      ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ zero_zero_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_617_not__less0) ).

thf(779,plain,
    ! [A: nat] :
      ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ zero_zero_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(370,axiom,
    ! [A: fun_Ar500372357t_bool,B: fun_fu775006535l_bool] :
      ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ A ) @ B ) )
    <=> ( hBOOL @ ( hAPP_f1766661605l_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_mem__def) ).

thf(2140,plain,
    ! [A: fun_Ar500372357t_bool,B: fun_fu775006535l_bool] :
      ( ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1766661605l_bool @ B @ A ) ) )
      & ( ( hBOOL @ ( hAPP_f1766661605l_bool @ B @ A ) )
       => ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(522,axiom,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ B ) )
     => ~ ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_xt1_I9_J) ).

thf(2756,plain,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ B ) )
     => ~ ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).

thf(634,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
     => ( ( B = A )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_xt1_I2_J) ).

thf(3162,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
     => ( ( B = A )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).

thf(281,axiom,
    ! [A: fun_Pr1055212137t_bool] :
      ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_f314169011l_bool @ ord_le565024179t_bool @ top_to126038883t_bool ) @ A ) )
     => ( A = top_to126038883t_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_360_top__le) ).

thf(1759,plain,
    ! [A: fun_Pr1055212137t_bool] :
      ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_f314169011l_bool @ ord_le565024179t_bool @ top_to126038883t_bool ) @ A ) )
     => ( A = top_to126038883t_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(182,axiom,
    ! [A: nat,B: nat] :
      ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B )
      = ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_534_nat__add__commute) ).

thf(1393,plain,
    ! [A: nat,B: nat] :
      ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B )
      = ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(250,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B )
        = ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ B ) )
    <=> ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_418_add__right__cancel) ).

thf(1627,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B )
          = ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ B ) )
       => ( A = C ) )
      & ( ( A = C )
       => ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B )
          = ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(427,axiom,
    ! [A: fun_nat_bool,B: fun_nat_nat,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_413_subset__inj__on) ).

thf(2370,plain,
    ! [A: fun_nat_bool,B: fun_nat_nat,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).

thf(288,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ B ) )
    <=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
        & ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_278_less__le__not__le) ).

thf(1779,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ B ) )
       => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
          & ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
          & ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(426,axiom,
    ! [A: nat,B: fun_nat_bool] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ ( hAPP_nat_fun_nat_nat @ ( hAPP_f416620757at_nat @ cOMBC_nat_nat_nat @ plus_plus_nat ) @ A ) ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_545_inj__on__add__nat) ).

thf(2368,plain,
    ! [A: nat,B: fun_nat_bool] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ ( hAPP_nat_fun_nat_nat @ ( hAPP_f416620757at_nat @ cOMBC_nat_nat_nat @ plus_plus_nat ) @ A ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).

thf(533,axiom,
    ! [A: fun_nat_bool] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ suc ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_672_inj__Suc) ).

thf(2793,plain,
    ! [A: fun_nat_bool] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ suc ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).

thf(319,axiom,
    ! [A: fun_Pr1643180309t_bool] :
      ~ ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_order__less__irrefl) ).

thf(1895,plain,
    ! [A: fun_Pr1643180309t_bool] :
      ~ ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(489,axiom,
    ! [A: bool,B: fun_Pr1055212137t_bool] :
      ( ( hAPP_f429946033l_bool @ ( hAPP_b1650070463l_bool @ cOMBK_1216274064t_bool @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__prod_Itc__Arrow____Order_) ).

thf(2617,plain,
    ! [A: bool,B: fun_Pr1055212137t_bool] :
      ( ( hAPP_f429946033l_bool @ ( hAPP_b1650070463l_bool @ cOMBK_1216274064t_bool @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).

thf(63,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_564_trans__le__add1) ).

thf(953,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(44,axiom,
    ! [A: nat,B: nat] :
      ( ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B )
        = A )
     => ( B = zero_zero_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_621_add__eq__self__zero) ).

thf(888,plain,
    ! [A: nat,B: nat] :
      ( ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B )
        = A )
     => ( B = zero_zero_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(713,axiom,
    hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ p ) @ arrow_1190054106e_Prof ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3__096P_A_058_AProf_096) ).

thf(3476,plain,
    hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ p ) @ arrow_1190054106e_Prof ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).

thf(170,axiom,
    ! [A: fun_Ar1583656131t_bool,B: arrow_931160158le_alt,C: arrow_2115524757e_indi] :
      ( ( hAPP_A1020253872t_bool @ ( hAPP_A102926893t_bool @ ( hAPP_f141075873t_bool @ cOMBC_1505804284t_bool @ A ) @ B ) @ C )
      = ( hAPP_A501825983t_bool @ ( hAPP_A131904271t_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_000_323) ).

thf(1333,plain,
    ! [A: fun_Ar1583656131t_bool,B: arrow_931160158le_alt,C: arrow_2115524757e_indi] :
      ( ( hAPP_A1020253872t_bool @ ( hAPP_A102926893t_bool @ ( hAPP_f141075873t_bool @ cOMBC_1505804284t_bool @ A ) @ B ) @ C )
      = ( hAPP_A501825983t_bool @ ( hAPP_A131904271t_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(519,axiom,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool] :
      ( ( A != B )
     => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_289_order__neq__le__trans) ).

thf(2749,plain,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool] :
      ( ( A != B )
     => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).

thf(305,axiom,
    ! [A: nat] : ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( hAPP_n1699378549t_bool @ ( hAPP_f229349961t_bool @ cOMBC_nat_nat_bool @ ord_less_nat ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_601_finite__Collect__less__nat) ).

thf(1857,plain,
    ! [A: nat] : ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( hAPP_n1699378549t_bool @ ( hAPP_f229349961t_bool @ cOMBC_nat_nat_bool @ ord_less_nat ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(134,axiom,
    ! [A: bool] :
      ( ( A = fTrue )
      | ( A = fFalse ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fTrue_1_1_T) ).

thf(1202,plain,
    ! [A: bool] :
      ( ( A = fTrue )
      | ( A = fFalse ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(13,axiom,
    ! [A: arrow_2115524757e_indi,B: fun_Ar500372357t_bool,C: fun_Ar552120407i_bool,D: fun_Ar1198543961l_bool] :
      ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ B ) @ ( pi_Arr487970267t_bool @ C @ D ) ) )
     => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ ( hAPP_A1174518481t_bool @ B @ A ) ) @ ( hAPP_A1279849719l_bool @ D @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_373_Pi__mem) ).

thf(792,plain,
    ! [A: arrow_2115524757e_indi,B: fun_Ar500372357t_bool,C: fun_Ar552120407i_bool,D: fun_Ar1198543961l_bool] :
      ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ B ) @ ( pi_Arr487970267t_bool @ C @ D ) ) )
     => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ ( hAPP_A1174518481t_bool @ B @ A ) ) @ ( hAPP_A1279849719l_bool @ D @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(144,axiom,
    ! [A: nat] :
      ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ zero_zero_nat )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_619_Nat_Oadd__0__right) ).

thf(1241,plain,
    ! [A: nat] :
      ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ zero_zero_nat )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(524,axiom,
    ! [A: nat,B: fun_nat_nat,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ C ) )
       => ( ( hAPP_nat_nat @ ( hilber195283148at_nat @ C @ B ) @ ( hAPP_nat_nat @ B @ A ) )
          = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_385_inv__into__f__f) ).

thf(2761,plain,
    ! [A: nat,B: fun_nat_nat,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ C ) )
       => ( ( hAPP_nat_nat @ ( hilber195283148at_nat @ C @ B ) @ ( hAPP_nat_nat @ B @ A ) )
          = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).

thf(563,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_302_order__less__imp__le) ).

thf(2883,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).

thf(53,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_635_le__SucI) ).

thf(921,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(303,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_xt1_I6_J) ).

thf(1846,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(270,axiom,
    ! [A: fun_Ar1026121174l_bool,B: fun_Pr1055212137t_bool,C: arrow_931160158le_alt] :
      ( ( hAPP_A674791462t_bool @ ( hAPP_f1099651112t_bool @ ( hAPP_f2087965871t_bool @ cOMBC_571858149l_bool @ A ) @ B ) @ C )
      = ( hAPP_f429946033l_bool @ ( hAPP_A1787768616l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_000t) ).

thf(1712,plain,
    ! [A: fun_Ar1026121174l_bool,B: fun_Pr1055212137t_bool,C: arrow_931160158le_alt] :
      ( ( hAPP_A674791462t_bool @ ( hAPP_f1099651112t_bool @ ( hAPP_f2087965871t_bool @ cOMBC_571858149l_bool @ A ) @ B ) @ C )
      = ( hAPP_f429946033l_bool @ ( hAPP_A1787768616l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(666,axiom,
    ! [A: nat,B: nat,C: fun_nat_nat,D: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ C ) @ D ) )
     => ( ( ( hAPP_nat_nat @ C @ A )
          = ( hAPP_nat_nat @ C @ B ) )
       => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ D ) )
         => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ D ) )
           => ( A = B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_370_inj__onD) ).

thf(3306,plain,
    ! [A: nat,B: nat,C: fun_nat_nat,D: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ C ) @ D ) )
     => ( ( ( hAPP_nat_nat @ C @ A )
          = ( hAPP_nat_nat @ C @ B ) )
       => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ D ) )
         => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ D ) )
           => ( A = B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).

thf(701,axiom,
    ! [A: nat,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_515_psubsetD) ).

thf(3422,plain,
    ! [A: nat,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).

thf(594,axiom,
    ! [A: fun_Ar500372357t_bool,B: fun_Ar500372357t_bool,C: arrow_931160158le_alt,D: arrow_931160158le_alt] :
      ( ( C != D )
     => ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ B ) @ arrow_1190054106e_Prof ) )
       => ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ A ) @ arrow_1190054106e_Prof ) )
         => ( ! [E: arrow_2115524757e_indi] :
                ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ C ) @ D ) ) @ ( hAPP_A1174518481t_bool @ B @ E ) ) )
              <=> ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ D ) @ C ) ) @ ( hAPP_A1174518481t_bool @ A @ E ) ) ) )
           => ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ C ) @ D ) ) @ ( hAPP_f792184801t_bool @ f @ B ) ) )
            <=> ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ D ) @ C ) ) @ ( hAPP_f792184801t_bool @ f @ A ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10__C3_C) ).

thf(2995,plain,
    ! [A: fun_Ar500372357t_bool,B: fun_Ar500372357t_bool,C: arrow_931160158le_alt,D: arrow_931160158le_alt] :
      ( ( C != D )
     => ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ B ) @ arrow_1190054106e_Prof ) )
       => ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ A ) @ arrow_1190054106e_Prof ) )
         => ( ! [E: arrow_2115524757e_indi] :
                ( ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ C ) @ D ) ) @ ( hAPP_A1174518481t_bool @ B @ E ) ) )
                 => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ D ) @ C ) ) @ ( hAPP_A1174518481t_bool @ A @ E ) ) ) )
                & ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ D ) @ C ) ) @ ( hAPP_A1174518481t_bool @ A @ E ) ) )
                 => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ C ) @ D ) ) @ ( hAPP_A1174518481t_bool @ B @ E ) ) ) ) )
           => ( ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ C ) @ D ) ) @ ( hAPP_f792184801t_bool @ f @ B ) ) )
               => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ D ) @ C ) ) @ ( hAPP_f792184801t_bool @ f @ A ) ) ) )
              & ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ D ) @ C ) ) @ ( hAPP_f792184801t_bool @ f @ A ) ) )
               => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ C ) @ D ) ) @ ( hAPP_f792184801t_bool @ f @ B ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).

thf(7,axiom,
    ! [A: fun_Pr1643180309t_bool] :
      ( ( collect_Product_unit @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_Collect__def) ).

thf(773,plain,
    ! [A: fun_Pr1643180309t_bool] :
      ( ( collect_Product_unit @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(14,axiom,
    ! [A: nat,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_nat_bool @ B @ zero_zero_nat ) )
     => ( ! [C: nat] :
            ( ( hBOOL @ ( hAPP_nat_bool @ B @ C ) )
           => ( hBOOL @ ( hAPP_nat_bool @ B @ ( hAPP_nat_nat @ suc @ C ) ) ) )
       => ( hBOOL @ ( hAPP_nat_bool @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_695_nat__induct) ).

thf(794,plain,
    ! [A: nat,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_nat_bool @ B @ zero_zero_nat ) )
     => ( ! [C: nat] :
            ( ( hBOOL @ ( hAPP_nat_bool @ B @ C ) )
           => ( hBOOL @ ( hAPP_nat_bool @ B @ ( hAPP_nat_nat @ suc @ C ) ) ) )
       => ( hBOOL @ ( hAPP_nat_bool @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(419,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( A = B )
    <=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
        & ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_491_set__eq__subset) ).

thf(2338,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( ( A = B )
       => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
          & ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
          & ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

thf(55,axiom,
    ! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ one_one_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_394_less__add__one) ).

thf(926,plain,
    ! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ one_one_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(573,axiom,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool] :
      ( ! [C: arrow_2115524757e_indi] :
          ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ C ) @ B ) )
         => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ C ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_506_subsetI) ).

thf(2909,plain,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool] :
      ( ! [C: arrow_2115524757e_indi] :
          ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ C ) @ B ) )
         => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ C ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).

thf(148,axiom,
    ! [A: nat,B: fun_nat_bool] :
      ( ! [C: nat] :
          ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ B ) )
         => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_610_bounded__nat__set__is__finite) ).

thf(1251,plain,
    ! [A: nat,B: fun_nat_bool] :
      ( ! [C: nat] :
          ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ B ) )
         => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(372,axiom,
    ! [A: fun_Pr1055212137t_bool,B: fun_Pr1055212137t_bool,C: fun_bool_bool] :
      ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ A ) @ ( pi_Pro226591613t_bool @ B @ ( hAPP_f1426772275l_bool @ cOMBK_1506144056le_alt @ C ) ) ) )
     => ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( inj_on899118883t_bool @ A ) @ B ) )
       => ( ( hBOOL @ ( hAPP_f387058535l_bool @ finite_finite_bool @ C ) )
         => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( finite876838485le_alt @ B ) ) @ ( finite_card_bool @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_588_card__inj) ).

thf(2149,plain,
    ! [A: fun_Pr1055212137t_bool,B: fun_Pr1055212137t_bool,C: fun_bool_bool] :
      ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ A ) @ ( pi_Pro226591613t_bool @ B @ ( hAPP_f1426772275l_bool @ cOMBK_1506144056le_alt @ C ) ) ) )
     => ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( inj_on899118883t_bool @ A ) @ B ) )
       => ( ( hBOOL @ ( hAPP_f387058535l_bool @ finite_finite_bool @ C ) )
         => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( finite876838485le_alt @ B ) ) @ ( finite_card_bool @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(481,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( ( hBOOL @ B )
        <=> ( hBOOL @ A ) )
     => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ A ) )
       => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_order__neq__le__trans) ).

thf(2585,plain,
    ! [A: bool,B: bool] :
      ( ~ ( ( ( hBOOL @ B )
           => ( hBOOL @ A ) )
          & ( ( hBOOL @ A )
           => ( hBOOL @ B ) ) )
     => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ A ) )
       => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).

thf(276,axiom,
    ! [A: bool,B: bool,C: bool] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_329_xt1_I7_J) ).

thf(1747,plain,
    ! [A: bool,B: bool,C: bool] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(329,axiom,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool,C: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_331_order__le__less__trans) ).

thf(1927,plain,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool,C: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(619,axiom,
    ! [A: fun_Pr1643180309t_bool,B: product_unit,C: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_472_set__rev__mp) ).

thf(3111,plain,
    ! [A: fun_Pr1643180309t_bool,B: product_unit,C: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).

thf(568,axiom,
    ! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_order__refl) ).

thf(2894,plain,
    ! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).

thf(632,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
      | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_linorder__linear) ).

thf(3158,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
      | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).

thf(67,axiom,
    ( top_to1690334693l_bool
    = ( collec1113178622t_bool @ ( hAPP_b1650070463l_bool @ cOMBK_1216274064t_bool @ fTrue ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_UNIV__def) ).

thf(965,plain,
    ( top_to1690334693l_bool
    = ( collec1113178622t_bool @ ( hAPP_b1650070463l_bool @ cOMBK_1216274064t_bool @ fTrue ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(214,axiom,
    ! [A: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) )
    <=> ? [B: nat] :
        ! [C: nat] :
          ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ A ) )
         => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_608_finite__nat__set__iff__bounded) ).

thf(1510,plain,
    ! [A: fun_nat_bool] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) )
       => ? [B: nat] :
          ! [C: nat] :
            ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ A ) )
           => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ B ) ) ) )
      & ( ? [B: nat] :
          ! [C: nat] :
            ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ A ) )
           => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ B ) ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(267,axiom,
    ! [A: fun_Pr1055212137t_bool,B: fun_fu2016509975e_indi,C: fun_fu1015689055l_bool,D: fun_fu1766473067i_bool] :
      ( ( hBOOL @ ( hAPP_f372503329l_bool @ ( hAPP_f43388905l_bool @ member527726724e_indi @ B ) @ ( pi_fun1342736627e_indi @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ ( hAPP_f2029284841e_indi @ B @ A ) ) @ ( hAPP_f1957024259i_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_PiE) ).

thf(1698,plain,
    ! [A: fun_Pr1055212137t_bool,B: fun_fu2016509975e_indi,C: fun_fu1015689055l_bool,D: fun_fu1766473067i_bool] :
      ( ( hBOOL @ ( hAPP_f372503329l_bool @ ( hAPP_f43388905l_bool @ member527726724e_indi @ B ) @ ( pi_fun1342736627e_indi @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ ( hAPP_f2029284841e_indi @ B @ A ) ) @ ( hAPP_f1957024259i_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(104,axiom,
    ( one_one_nat
    = ( hAPP_nat_nat @ suc @ zero_zero_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_656_One__nat__def) ).

thf(1103,plain,
    ( one_one_nat
    = ( hAPP_nat_nat @ suc @ zero_zero_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(687,axiom,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool,C: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_order__less__trans) ).

thf(3375,plain,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool,C: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).

thf(723,axiom,
    ! [A: produc1840315303le_alt,B: fun_Pr215145567t_unit,C: fun_Pr1055212137t_bool,D: fun_Pr1907279903t_bool] :
      ( ( hBOOL @ ( hAPP_f1685685l_bool @ ( hAPP_f106186317l_bool @ member1142067122t_unit @ B ) @ ( pi_Pro185129843t_unit @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ ( hAPP_P907778813t_unit @ B @ A ) ) @ ( hAPP_P728132331t_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_PiE) ).

thf(3523,plain,
    ! [A: produc1840315303le_alt,B: fun_Pr215145567t_unit,C: fun_Pr1055212137t_bool,D: fun_Pr1907279903t_bool] :
      ( ( hBOOL @ ( hAPP_f1685685l_bool @ ( hAPP_f106186317l_bool @ member1142067122t_unit @ B ) @ ( pi_Pro185129843t_unit @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ ( hAPP_P907778813t_unit @ B @ A ) ) @ ( hAPP_P728132331t_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).

thf(515,axiom,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ B ) )
     => ~ ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_order__less__not__sym) ).

thf(2734,plain,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ B ) )
     => ~ ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).

thf(686,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ B ) )
        | ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_308_order__le__imp__less__or__eq) ).

thf(3372,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ B ) )
        | ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).

thf(300,axiom,
    ! [A: bool,B: bool] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ B ) )
     => ( ~ ( ( hBOOL @ B )
          <=> ( hBOOL @ A ) )
       => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_bool @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_319_xt1_I11_J) ).

thf(1833,plain,
    ! [A: bool,B: bool] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ B ) )
     => ( ~ ( ( ( hBOOL @ B )
             => ( hBOOL @ A ) )
            & ( ( hBOOL @ A )
             => ( hBOOL @ B ) ) )
       => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(325,axiom,
    ! [A: bool,B: bool] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ A ) )
       => ( ( hBOOL @ B )
        <=> ( hBOOL @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_xt1_I5_J) ).

thf(1916,plain,
    ! [A: bool,B: bool] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ A ) )
       => ( ( ( hBOOL @ B )
           => ( hBOOL @ A ) )
          & ( ( hBOOL @ A )
           => ( hBOOL @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(316,axiom,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool,C: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_457_psubset__subset__trans) ).

thf(1884,plain,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool,C: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(532,axiom,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ B ) )
     => ~ ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_xt1_I9_J) ).

thf(2791,plain,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ B ) )
     => ~ ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).

thf(531,axiom,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_454_psubset__imp__subset) ).

thf(2789,plain,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).

thf(467,axiom,
    ! [A: fun_Ar500372357t_bool,B: fun_Ar500372357t_bool,C: arrow_931160158le_alt,D: arrow_931160158le_alt,E: arrow_931160158le_alt,F: arrow_931160158le_alt] :
      ( ( E != F )
     => ( ( C != D )
       => ( ( E != D )
         => ( ( F != C )
           => ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ B ) @ arrow_1190054106e_Prof ) )
             => ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ A ) @ arrow_1190054106e_Prof ) )
               => ( ! [G: arrow_2115524757e_indi] :
                      ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ E ) @ F ) ) @ ( hAPP_A1174518481t_bool @ B @ G ) ) )
                    <=> ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ C ) @ D ) ) @ ( hAPP_A1174518481t_bool @ A @ G ) ) ) )
                 => ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ E ) @ F ) ) @ ( hAPP_f792184801t_bool @ f @ B ) ) )
                  <=> ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ C ) @ D ) ) @ ( hAPP_f792184801t_bool @ f @ A ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6__C2_C) ).

thf(2525,plain,
    ! [A: fun_Ar500372357t_bool,B: fun_Ar500372357t_bool,C: arrow_931160158le_alt,D: arrow_931160158le_alt,E: arrow_931160158le_alt,F: arrow_931160158le_alt] :
      ( ( E != F )
     => ( ( C != D )
       => ( ( E != D )
         => ( ( F != C )
           => ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ B ) @ arrow_1190054106e_Prof ) )
             => ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ A ) @ arrow_1190054106e_Prof ) )
               => ( ! [G: arrow_2115524757e_indi] :
                      ( ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ E ) @ F ) ) @ ( hAPP_A1174518481t_bool @ B @ G ) ) )
                       => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ C ) @ D ) ) @ ( hAPP_A1174518481t_bool @ A @ G ) ) ) )
                      & ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ C ) @ D ) ) @ ( hAPP_A1174518481t_bool @ A @ G ) ) )
                       => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ E ) @ F ) ) @ ( hAPP_A1174518481t_bool @ B @ G ) ) ) ) )
                 => ( ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ E ) @ F ) ) @ ( hAPP_f792184801t_bool @ f @ B ) ) )
                     => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ C ) @ D ) ) @ ( hAPP_f792184801t_bool @ f @ A ) ) ) )
                    & ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ C ) @ D ) ) @ ( hAPP_f792184801t_bool @ f @ A ) ) )
                     => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ E ) @ F ) ) @ ( hAPP_f792184801t_bool @ f @ B ) ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).

thf(385,axiom,
    ! [A: fun_fu1476972377l_bool,B: fun_Ar2049444117le_alt,C: arrow_931160158le_alt] :
      ( ( hAPP_A1256181151l_bool @ ( hAPP_f1176598245l_bool @ ( cOMBB_1605735744le_alt @ A ) @ B ) @ C )
      = ( hAPP_f1395387255l_bool @ A @ ( hAPP_A1485971815le_alt @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__) ).

thf(2188,plain,
    ! [A: fun_fu1476972377l_bool,B: fun_Ar2049444117le_alt,C: arrow_931160158le_alt] :
      ( ( hAPP_A1256181151l_bool @ ( hAPP_f1176598245l_bool @ ( cOMBB_1605735744le_alt @ A ) @ B ) @ C )
      = ( hAPP_f1395387255l_bool @ A @ ( hAPP_A1485971815le_alt @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(462,axiom,
    ! [A: fun_fu775006535l_bool] : ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f95487087l_bool @ ord_le1871091345l_bool @ A ) @ top_to1324311617l_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_408_subset__UNIV) ).

thf(2514,plain,
    ! [A: fun_fu775006535l_bool] : ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f95487087l_bool @ ord_le1871091345l_bool @ A ) @ top_to1324311617l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).

thf(752,axiom,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool,C: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_326_xt1_I7_J) ).

thf(3604,plain,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool,C: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).

thf(216,axiom,
    ! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_628_lessI) ).

thf(1520,plain,
    ! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(112,axiom,
    ! [A: nat] :
      ( ( hAPP_nat_nat @ suc @ A )
     != zero_zero_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_676_Suc__not__Zero) ).

thf(1124,plain,
    ! [A: nat] :
      ( ( hAPP_nat_nat @ suc @ A )
     != zero_zero_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(48,axiom,
    ! [A: nat] :
      ( ( A != zero_zero_nat )
     => ? [B: nat] :
          ( A
          = ( hAPP_nat_nat @ suc @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_692_not0__implies__Suc) ).

thf(904,plain,
    ! [A: nat] :
      ( ( A != zero_zero_nat )
     => ? [B: nat] :
          ( A
          = ( hAPP_nat_nat @ suc @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(71,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ D ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ D ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_567_add__le__mono) ).

thf(975,plain,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ D ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ D ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(257,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
      | ( A = B )
      | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_linorder__less__linear) ).

thf(1652,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
      | ( A = B )
      | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(330,axiom,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool,C: fun_Ar552120407i_bool] :
      ( ( B = C )
     => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_xt1_I1_J) ).

thf(1929,plain,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool,C: fun_Ar552120407i_bool] :
      ( ( B = C )
     => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(542,axiom,
    ! [A: nat,B: nat] :
      ( ( A != B )
      | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Nat__Onat_T) ).

thf(2827,plain,
    ! [A: nat,B: nat] :
      ( ( A != B )
      | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).

thf(367,axiom,
    ! [A: bool] : ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_order__refl) ).

thf(2134,plain,
    ! [A: bool] : ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(749,axiom,
    hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ n ) @ ( finite783399747e_indi @ top_to1678393681i_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_n_I1_J) ).

thf(3599,plain,
    hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ n ) @ ( finite783399747e_indi @ top_to1678393681i_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).

thf(567,axiom,
    ! [A: nat] :
      ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_order__less__irrefl) ).

thf(2891,plain,
    ! [A: nat] :
      ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).

thf(162,axiom,
    ! [A: fun_bo462718181t_bool,B: fun_Ar552120407i_bool,C: arrow_2115524757e_indi] :
      ( ( hAPP_A594708985t_bool @ ( hAPP_f509814255t_bool @ ( cOMBB_231886989e_indi @ A ) @ B ) @ C )
      = ( hAPP_b1061655857t_bool @ A @ ( hAPP_A1888055029i_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow_) ).

thf(1312,plain,
    ! [A: fun_bo462718181t_bool,B: fun_Ar552120407i_bool,C: arrow_2115524757e_indi] :
      ( ( hAPP_A594708985t_bool @ ( hAPP_f509814255t_bool @ ( cOMBB_231886989e_indi @ A ) @ B ) @ C )
      = ( hAPP_b1061655857t_bool @ A @ ( hAPP_A1888055029i_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(11,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) )
     => ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
       => ( A
          = ( hAPP_nat_nat @ suc @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_636_le__SucE) ).

thf(787,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) )
     => ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
       => ( A
          = ( hAPP_nat_nat @ suc @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(94,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_432_add__strict__left__mono) ).

thf(1058,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(423,axiom,
    ! [A: bool,B: fun_bool_bool,C: fun_bool_bool] :
      ( ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_f612708895l_bool @ ord_le742797417l_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_438_subsetD) ).

thf(2358,plain,
    ! [A: bool,B: fun_bool_bool,C: fun_bool_bool] :
      ( ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_f612708895l_bool @ ord_le742797417l_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).

thf(262,axiom,
    ! [A: bool,B: fun_Ar552120407i_bool,C: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ C ) @ B ) )
       => ( hBOOL @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_order__less__imp__triv) ).

thf(1675,plain,
    ! [A: bool,B: fun_Ar552120407i_bool,C: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ C ) @ B ) )
       => ( hBOOL @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(387,axiom,
    ! [A: fun_Pr1228236907l_bool,B: fun_Pr1055212137t_bool,C: produc1840315303le_alt] :
      ( ( hAPP_P166437127t_bool @ ( hAPP_f70231061t_bool @ ( hAPP_f46399911t_bool @ cOMBC_697226658l_bool @ A ) @ B ) @ C )
      = ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm_) ).

thf(2193,plain,
    ! [A: fun_Pr1228236907l_bool,B: fun_Pr1055212137t_bool,C: produc1840315303le_alt] :
      ( ( hAPP_P166437127t_bool @ ( hAPP_f70231061t_bool @ ( hAPP_f46399911t_bool @ cOMBC_697226658l_bool @ A ) @ B ) @ C )
      = ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(599,axiom,
    ! [A: fun_nat_bool] :
      ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_order__less__irrefl) ).

thf(3023,plain,
    ! [A: fun_nat_bool] :
      ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).

thf(269,axiom,
    ! [A: bool,B: bool] :
      ( ( ( hBOOL @ B )
      <=> ( hBOOL @ A ) )
     => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_order__eq__refl) ).

thf(1707,plain,
    ! [A: bool,B: bool] :
      ( ( ( ( hBOOL @ B )
         => ( hBOOL @ A ) )
        & ( ( hBOOL @ A )
         => ( hBOOL @ B ) ) )
     => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(609,axiom,
    ! [A: fun_Ar500372357t_bool,B: fun_fu1595299477t_bool,C: fun_fu775006535l_bool,D: fun_fu787660105l_bool] :
      ( ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ B ) @ ( pi_fun530160875t_bool @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ ( hAPP_f792184801t_bool @ B @ A ) ) @ ( hAPP_f1498158055l_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_PiE) ).

thf(3051,plain,
    ! [A: fun_Ar500372357t_bool,B: fun_fu1595299477t_bool,C: fun_fu775006535l_bool,D: fun_fu787660105l_bool] :
      ( ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ B ) @ ( pi_fun530160875t_bool @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ ( hAPP_f792184801t_bool @ B @ A ) ) @ ( hAPP_f1498158055l_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).

thf(437,axiom,
    ! [A: produc1840315303le_alt,B: fun_Pr1055212137t_bool,C: fun_Pr1055212137t_bool] :
      ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_f314169011l_bool @ ord_le565024179t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_445_subsetD) ).

thf(2442,plain,
    ! [A: produc1840315303le_alt,B: fun_Pr1055212137t_bool,C: fun_Pr1055212137t_bool] :
      ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_f314169011l_bool @ ord_le565024179t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).

thf(703,axiom,
    ! [A: fun_Pr1643180309t_bool] :
      ~ ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ top_to1257323279t_bool ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_not__top__less) ).

thf(3436,plain,
    ! [A: fun_Pr1643180309t_bool] :
      ~ ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ top_to1257323279t_bool ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).

thf(377,axiom,
    ! [A: nat,B: nat] :
      ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
    <=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) )
        | ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_not__less__iff__gr__or__eq) ).

thf(2166,plain,
    ! [A: nat,B: nat] :
      ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
       => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) )
          | ( A = B ) ) )
      & ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) )
          | ( A = B ) )
       => ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(740,axiom,
    ! [A: nat,B: fun_nat_Product_unit,C: fun_nat_bool,D: fun_na1041622088t_bool] :
      ( ( hBOOL @ ( hAPP_f537623936l_bool @ ( hAPP_f1598887207l_bool @ member1024687843t_unit @ B ) @ ( pi_nat_Product_unit @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ ( hAPP_n633340360t_unit @ B @ A ) ) @ ( hAPP_n454528608t_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_PiE) ).

thf(3579,plain,
    ! [A: nat,B: fun_nat_Product_unit,C: fun_nat_bool,D: fun_na1041622088t_bool] :
      ( ( hBOOL @ ( hAPP_f537623936l_bool @ ( hAPP_f1598887207l_bool @ member1024687843t_unit @ B ) @ ( pi_nat_Product_unit @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ ( hAPP_n633340360t_unit @ B @ A ) ) @ ( hAPP_n454528608t_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).

thf(202,axiom,
    ! [A: nat,B: nat] :
      ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_546_not__add__less1) ).

thf(1464,plain,
    ! [A: nat,B: nat] :
      ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(61,axiom,
    ! [A: fun_Ar1364097613t_bool,B: fun_Pr1055212137t_bool,C: arrow_931160158le_alt] :
      ( ( hAPP_A1858212765t_bool @ ( hAPP_f1810968607t_bool @ ( hAPP_f15758621t_bool @ cOMBC_1947566172t_bool @ A ) @ B ) @ C )
      = ( hAPP_f1099651112t_bool @ ( hAPP_A1770325791t_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_000t_322) ).

thf(947,plain,
    ! [A: fun_Ar1364097613t_bool,B: fun_Pr1055212137t_bool,C: arrow_931160158le_alt] :
      ( ( hAPP_A1858212765t_bool @ ( hAPP_f1810968607t_bool @ ( hAPP_f15758621t_bool @ cOMBC_1947566172t_bool @ A ) @ B ) @ C )
      = ( hAPP_f1099651112t_bool @ ( hAPP_A1770325791t_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(252,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_426_add__right__mono) ).

thf(1638,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(139,axiom,
    ! [A: fun_fu446267975l_bool,B: fun_fu1138137687l_bool,C: fun_fu1595299477t_bool] :
      ( ( hAPP_f611501301l_bool @ ( hAPP_f1077478037l_bool @ ( hAPP_f230252107l_bool @ cOMBC_1452216610l_bool @ A ) @ B ) @ C )
      = ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____ctu) ).

thf(1224,plain,
    ! [A: fun_fu446267975l_bool,B: fun_fu1138137687l_bool,C: fun_fu1595299477t_bool] :
      ( ( hAPP_f611501301l_bool @ ( hAPP_f1077478037l_bool @ ( hAPP_f230252107l_bool @ cOMBC_1452216610l_bool @ A ) @ B ) @ C )
      = ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(4,axiom,
    ! [A: bool,B: arrow_2115524757e_indi] :
      ( ( hAPP_A1888055029i_bool @ ( hAPP_b1439777783i_bool @ cOMBK_1820189998e_indi @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Arrow____Order____Mirabelle____ctu) ).

thf(764,plain,
    ! [A: bool,B: arrow_2115524757e_indi] :
      ( ( hAPP_A1888055029i_bool @ ( hAPP_b1439777783i_bool @ cOMBK_1820189998e_indi @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(679,axiom,
    ! [A: bool,B: bool,C: bool] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ C ) )
     => ( ( ( hBOOL @ B )
        <=> ( hBOOL @ A ) )
       => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_xt1_I4_J) ).

thf(3352,plain,
    ! [A: bool,B: bool,C: bool] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ C ) )
     => ( ( ( ( hBOOL @ B )
           => ( hBOOL @ A ) )
          & ( ( hBOOL @ A )
           => ( hBOOL @ B ) ) )
       => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).

thf(24,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ C ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_526_add__leD2) ).

thf(831,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ C ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(470,axiom,
    ! [A: arrow_2115524757e_indi,B: fun_Ar1939863823t_bool,C: fun_Ar552120407i_bool,D: fun_Ar1270429299l_bool] :
      ( ( hBOOL @ ( hAPP_f2076228197l_bool @ ( hAPP_f467714381l_bool @ member291481314t_bool @ B ) @ ( pi_Arr353983907t_bool @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ ( hAPP_A1044336685t_bool @ B @ A ) ) @ ( hAPP_A1538515647l_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_PiE) ).

thf(2538,plain,
    ! [A: arrow_2115524757e_indi,B: fun_Ar1939863823t_bool,C: fun_Ar552120407i_bool,D: fun_Ar1270429299l_bool] :
      ( ( hBOOL @ ( hAPP_f2076228197l_bool @ ( hAPP_f467714381l_bool @ member291481314t_bool @ B ) @ ( pi_Arr353983907t_bool @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ ( hAPP_A1044336685t_bool @ B @ A ) ) @ ( hAPP_A1538515647l_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).

thf(395,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_order__trans) ).

thf(2214,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).

thf(109,axiom,
    ! [A: nat,B: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_560_le__add2) ).

thf(1117,plain,
    ! [A: nat,B: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(660,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ B ) @ C ) )
     => ( ( B = A )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_xt1_I2_J) ).

thf(3287,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ B ) @ C ) )
     => ( ( B = A )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).

thf(357,axiom,
    ! [A: nat,B: nat,C: fun_nat_nat,D: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ C ) @ D ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ D ) )
       => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ D ) )
         => ( ( ( hAPP_nat_nat @ C @ B )
              = ( hAPP_nat_nat @ C @ A ) )
          <=> ( B = A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_368_inj__on__iff) ).

thf(2097,plain,
    ! [A: nat,B: nat,C: fun_nat_nat,D: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ C ) @ D ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ D ) )
       => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ D ) )
         => ( ( ( ( hAPP_nat_nat @ C @ B )
                = ( hAPP_nat_nat @ C @ A ) )
             => ( B = A ) )
            & ( ( B = A )
             => ( ( hAPP_nat_nat @ C @ B )
                = ( hAPP_nat_nat @ C @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(617,axiom,
    ! [A: fun_fu775006535l_bool] :
      ~ ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f95487087l_bool @ ord_le583255965l_bool @ top_to1324311617l_bool ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_not__top__less) ).

thf(3106,plain,
    ! [A: fun_fu775006535l_bool] :
      ~ ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f95487087l_bool @ ord_le583255965l_bool @ top_to1324311617l_bool ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).

thf(272,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( A != B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_532_less__not__refl3) ).

thf(1722,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( A != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(361,axiom,
    ! [A: nat,B: nat] :
      ( ( A = B )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_541_eq__imp__le) ).

thf(2116,plain,
    ! [A: nat,B: nat] :
      ( ( A = B )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(293,axiom,
    ! [A: fun_Ar500372357t_bool,B: fun_Ar500372357t_bool,C: arrow_931160158le_alt,D: arrow_931160158le_alt,E: arrow_931160158le_alt] :
      ( ( D != E )
     => ( ( E != C )
       => ( ( D != C )
         => ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ B ) @ arrow_1190054106e_Prof ) )
           => ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ A ) @ arrow_1190054106e_Prof ) )
             => ( ! [F: arrow_2115524757e_indi] :
                    ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ D ) @ E ) ) @ ( hAPP_A1174518481t_bool @ B @ F ) ) )
                  <=> ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ E ) @ C ) ) @ ( hAPP_A1174518481t_bool @ A @ F ) ) ) )
               => ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ D ) @ E ) ) @ ( hAPP_f792184801t_bool @ f @ B ) ) )
                <=> ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ E ) @ C ) ) @ ( hAPP_f792184801t_bool @ f @ A ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8__C4_C) ).

thf(1801,plain,
    ! [A: fun_Ar500372357t_bool,B: fun_Ar500372357t_bool,C: arrow_931160158le_alt,D: arrow_931160158le_alt,E: arrow_931160158le_alt] :
      ( ( D != E )
     => ( ( E != C )
       => ( ( D != C )
         => ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ B ) @ arrow_1190054106e_Prof ) )
           => ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ A ) @ arrow_1190054106e_Prof ) )
             => ( ! [F: arrow_2115524757e_indi] :
                    ( ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ D ) @ E ) ) @ ( hAPP_A1174518481t_bool @ B @ F ) ) )
                     => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ E ) @ C ) ) @ ( hAPP_A1174518481t_bool @ A @ F ) ) ) )
                    & ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ E ) @ C ) ) @ ( hAPP_A1174518481t_bool @ A @ F ) ) )
                     => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ D ) @ E ) ) @ ( hAPP_A1174518481t_bool @ B @ F ) ) ) ) )
               => ( ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ D ) @ E ) ) @ ( hAPP_f792184801t_bool @ f @ B ) ) )
                   => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ E ) @ C ) ) @ ( hAPP_f792184801t_bool @ f @ A ) ) ) )
                  & ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ E ) @ C ) ) @ ( hAPP_f792184801t_bool @ f @ A ) ) )
                   => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ D ) @ E ) ) @ ( hAPP_f792184801t_bool @ f @ B ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(569,axiom,
    ! [A: fun_Ar552120407i_bool,B: arrow_2115524757e_indi,C: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_473_set__rev__mp) ).

thf(2896,plain,
    ! [A: fun_Ar552120407i_bool,B: arrow_2115524757e_indi,C: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).

thf(560,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
      <=> ( B = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_order__antisym__conv) ).

thf(2871,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
     => ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
         => ( B = A ) )
        & ( ( B = A )
         => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).

thf(35,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_323_order__less__le__trans) ).

thf(863,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(373,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
     => ( ( A != B )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_313_order__le__neq__trans) ).

thf(2151,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
     => ( ( A != B )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(631,axiom,
    ! [A: fun_Pr1055212137t_bool,B: fun_Pr1055212137t_bool] :
      ( ! [C: produc1840315303le_alt] :
          ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ C ) @ B ) )
         => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ C ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_f314169011l_bool @ ord_le565024179t_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_511_subsetI) ).

thf(3155,plain,
    ! [A: fun_Pr1055212137t_bool,B: fun_Pr1055212137t_bool] :
      ( ! [C: produc1840315303le_alt] :
          ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ C ) @ B ) )
         => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ C ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_f314169011l_bool @ ord_le565024179t_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).

thf(399,axiom,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ B ) )
     => ~ ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_order__less__asym) ).

thf(2229,plain,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ B ) )
     => ~ ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(235,axiom,
    ! [A: fun_nat_bool,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ A @ C ) )
       => ( ! [D: nat] :
              ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ D ) @ C ) )
             => ( ( hBOOL @ ( hAPP_nat_bool @ A @ ( hAPP_nat_nat @ suc @ D ) ) )
               => ( hBOOL @ ( hAPP_nat_bool @ A @ D ) ) ) )
         => ( hBOOL @ ( hAPP_nat_bool @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_684_inc__induct) ).

thf(1574,plain,
    ! [A: fun_nat_bool,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ A @ C ) )
       => ( ! [D: nat] :
              ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ D ) @ C ) )
             => ( ( hBOOL @ ( hAPP_nat_bool @ A @ ( hAPP_nat_nat @ suc @ D ) ) )
               => ( hBOOL @ ( hAPP_nat_bool @ A @ D ) ) ) )
         => ( hBOOL @ ( hAPP_nat_bool @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(80,axiom,
    ! [A: fun_Ar1519997101t_bool,B: fun_Pr1055212137t_bool,C: arrow_2115524757e_indi] :
      ( ( hAPP_A892860133t_bool @ ( hAPP_f1755759597t_bool @ ( hAPP_f1328803787t_bool @ cOMBC_1190055014t_bool @ A ) @ B ) @ C )
      = ( hAPP_f1409483817t_bool @ ( hAPP_A594708985t_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_000_327) ).

thf(1011,plain,
    ! [A: fun_Ar1519997101t_bool,B: fun_Pr1055212137t_bool,C: arrow_2115524757e_indi] :
      ( ( hAPP_A892860133t_bool @ ( hAPP_f1755759597t_bool @ ( hAPP_f1328803787t_bool @ cOMBC_1190055014t_bool @ A ) @ B ) @ C )
      = ( hAPP_f1409483817t_bool @ ( hAPP_A594708985t_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(572,axiom,
    ! [A: bool,B: bool] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ B ) )
     => ( ~ ( ( hBOOL @ A )
          <=> ( hBOOL @ B ) )
       => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_bool @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_312_order__le__neq__trans) ).

thf(2906,plain,
    ! [A: bool,B: bool] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ B ) )
     => ( ~ ( ( ( hBOOL @ A )
             => ( hBOOL @ B ) )
            & ( ( hBOOL @ B )
             => ( hBOOL @ A ) ) )
       => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).

thf(700,axiom,
    ! [A: fun_fu1138137687l_bool] :
      ~ ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f173704847l_bool @ ord_le1306091181l_bool @ top_to2013953873l_bool ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_not__top__less) ).

thf(3419,plain,
    ! [A: fun_fu1138137687l_bool] :
      ~ ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f173704847l_bool @ ord_le1306091181l_bool @ top_to2013953873l_bool ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).

thf(331,axiom,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ B ) )
     => ( A != B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_less__imp__neq) ).

thf(1933,plain,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ B ) )
     => ( A != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(409,axiom,
    ! [A: fun_Ar1744566822di_nat] :
      ( ! [B: arrow_2115524757e_indi,C: arrow_2115524757e_indi] :
          ( ( ( hAPP_A1450069362di_nat @ A @ B )
            = ( hAPP_A1450069362di_nat @ A @ C ) )
         => ( B = C ) )
     => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( inj_on886403158di_nat @ A ) @ top_to1678393681i_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_398_injI) ).

thf(2257,plain,
    ! [A: fun_Ar1744566822di_nat] :
      ( ! [B: arrow_2115524757e_indi,C: arrow_2115524757e_indi] :
          ( ( ( hAPP_A1450069362di_nat @ A @ B )
            = ( hAPP_A1450069362di_nat @ A @ C ) )
         => ( B = C ) )
     => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( inj_on886403158di_nat @ A ) @ top_to1678393681i_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(240,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) )
    <=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_661_Suc__le__eq) ).

thf(1589,plain,
    ! [A: nat,B: nat] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(579,axiom,
    ! [A: product_unit,B: fun_Pr321980605t_bool,C: fun_Pr1643180309t_bool,D: fun_Pr1223320869l_bool] :
      ( ( hBOOL @ ( hAPP_f1221487891l_bool @ ( hAPP_f1119259085l_bool @ member1302538000t_bool @ B ) @ ( pi_Pro1008448593t_bool @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ ( hAPP_P1139363291t_bool @ B @ A ) ) @ ( hAPP_P1055953777l_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_PiE) ).

thf(2943,plain,
    ! [A: product_unit,B: fun_Pr321980605t_bool,C: fun_Pr1643180309t_bool,D: fun_Pr1223320869l_bool] :
      ( ( hBOOL @ ( hAPP_f1221487891l_bool @ ( hAPP_f1119259085l_bool @ member1302538000t_bool @ B ) @ ( pi_Pro1008448593t_bool @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ ( hAPP_P1139363291t_bool @ B @ A ) ) @ ( hAPP_P1055953777l_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).

thf(580,axiom,
    ! [A: fun_fu1015689055l_bool] :
      ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f868566847l_bool @ ord_le1923264405l_bool @ top_to1690334693l_bool ) @ A ) )
    <=> ( A = top_to1690334693l_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_349_top__unique) ).

thf(2945,plain,
    ! [A: fun_fu1015689055l_bool] :
      ( ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f868566847l_bool @ ord_le1923264405l_bool @ top_to1690334693l_bool ) @ A ) )
       => ( A = top_to1690334693l_bool ) )
      & ( ( A = top_to1690334693l_bool )
       => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f868566847l_bool @ ord_le1923264405l_bool @ top_to1690334693l_bool ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).

thf(553,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_542_le__trans) ).

thf(2856,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).

thf(627,axiom,
    ! [A: fun_fu775006535l_bool] :
      ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f95487087l_bool @ ord_le1871091345l_bool @ top_to1324311617l_bool ) @ A ) )
     => ( A = top_to1324311617l_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_359_top__le) ).

thf(3138,plain,
    ! [A: fun_fu775006535l_bool] :
      ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f95487087l_bool @ ord_le1871091345l_bool @ top_to1324311617l_bool ) @ A ) )
     => ( A = top_to1324311617l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).

thf(633,axiom,
    ! [A: arrow_2115524757e_indi] : ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ A ) @ top_to1678393681i_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_iso__tuple__UNIV__I) ).

thf(3160,plain,
    ! [A: arrow_2115524757e_indi] : ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ A ) @ top_to1678393681i_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).

thf(160,axiom,
    ! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ suc @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_630_zero__less__Suc) ).

thf(1307,plain,
    ! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ suc @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(259,axiom,
    ~ ! [A: fun_Pr1055212137t_bool] :
        ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ a ) @ b ) ) @ A ) )
       => ~ ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ A ) @ arrow_915577424le_Lin ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_) ).

thf(1667,plain,
    ~ ! [A: fun_Pr1055212137t_bool] :
        ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ a ) @ b ) ) @ A ) )
       => ~ ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ A ) @ arrow_915577424le_Lin ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(313,axiom,
    ! [A: fun_Ar552120407i_bool] :
      ~ ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_order__less__irrefl) ).

thf(1877,plain,
    ! [A: fun_Ar552120407i_bool] :
      ~ ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(100,axiom,
    ! [A: nat,B: nat] :
      ( ( ( hAPP_nat_nat @ suc @ zero_zero_nat )
        = ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) )
    <=> ( ( ( A
            = ( hAPP_nat_nat @ suc @ zero_zero_nat ) )
          & ( B = zero_zero_nat ) )
        | ( ( A = zero_zero_nat )
          & ( B
            = ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_667_one__is__add) ).

thf(1080,plain,
    ! [A: nat,B: nat] :
      ( ( ( ( hAPP_nat_nat @ suc @ zero_zero_nat )
          = ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) )
       => ( ( ( A
              = ( hAPP_nat_nat @ suc @ zero_zero_nat ) )
            & ( B = zero_zero_nat ) )
          | ( ( A = zero_zero_nat )
            & ( B
              = ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) ) ) )
      & ( ( ( ( A
              = ( hAPP_nat_nat @ suc @ zero_zero_nat ) )
            & ( B = zero_zero_nat ) )
          | ( ( A = zero_zero_nat )
            & ( B
              = ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) ) )
       => ( ( hAPP_nat_nat @ suc @ zero_zero_nat )
          = ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(611,axiom,
    ! [A: arrow_931160158le_alt,B: arrow_931160158le_alt,C: fun_Pr1055212137t_bool,D: arrow_931160158le_alt,E: arrow_931160158le_alt] :
      ( ( D != E )
     => ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ C ) @ arrow_915577424le_Lin ) )
       => ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ A ) @ B ) ) @ ( hAPP_A606737888t_bool @ ( hAPP_A501825983t_bool @ ( hAPP_f1909595219t_bool @ arrow_1475523868_above @ C ) @ D ) @ E ) ) )
        <=> ( ( A != B )
            & ( ( A = E )
             => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ D ) @ B ) ) @ C ) ) )
            & ( ( A != E )
             => ( ( ( B = E )
                 => ( ( A = D )
                    | ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ A ) @ D ) ) @ C ) ) ) )
                & ( ( B != E )
                 => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ A ) @ B ) ) @ C ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_in__above) ).

thf(3055,plain,
    ! [A: arrow_931160158le_alt,B: arrow_931160158le_alt,C: fun_Pr1055212137t_bool,D: arrow_931160158le_alt,E: arrow_931160158le_alt] :
      ( ( D != E )
     => ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ C ) @ arrow_915577424le_Lin ) )
       => ( ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ A ) @ B ) ) @ ( hAPP_A606737888t_bool @ ( hAPP_A501825983t_bool @ ( hAPP_f1909595219t_bool @ arrow_1475523868_above @ C ) @ D ) @ E ) ) )
           => ( ( A != B )
              & ( ( A = E )
               => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ D ) @ B ) ) @ C ) ) )
              & ( ( A != E )
               => ( ( ( B = E )
                   => ( ( A = D )
                      | ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ A ) @ D ) ) @ C ) ) ) )
                  & ( ( B != E )
                   => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ A ) @ B ) ) @ C ) ) ) ) ) ) )
          & ( ( ( A != B )
              & ( ( A = E )
               => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ D ) @ B ) ) @ C ) ) )
              & ( ( A != E )
               => ( ( ( B = E )
                   => ( ( A = D )
                      | ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ A ) @ D ) ) @ C ) ) ) )
                  & ( ( B != E )
                   => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ A ) @ B ) ) @ C ) ) ) ) ) )
           => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ A ) @ B ) ) @ ( hAPP_A606737888t_bool @ ( hAPP_A501825983t_bool @ ( hAPP_f1909595219t_bool @ arrow_1475523868_above @ C ) @ D ) @ E ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).

thf(737,axiom,
    ! [A: fun_nat_nat,B: fun_nat_nat] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ B ) @ top_top_fun_nat_bool ) )
     => ( ! [C: nat] :
            ( ( hAPP_nat_nat @ B @ ( hAPP_nat_nat @ A @ C ) )
            = C )
       => ( ( hilber195283148at_nat @ top_top_fun_nat_bool @ B )
          = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_392_inj__imp__inv__eq) ).

thf(3572,plain,
    ! [A: fun_nat_nat,B: fun_nat_nat] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ B ) @ top_top_fun_nat_bool ) )
     => ( ! [C: nat] :
            ( ( hAPP_nat_nat @ B @ ( hAPP_nat_nat @ A @ C ) )
            = C )
       => ( ( hilber195283148at_nat @ top_top_fun_nat_bool @ B )
          = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).

thf(742,axiom,
    ! [A: product_unit,B: fun_Pr1643180309t_bool,C: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_439_subsetD) ).

thf(3583,plain,
    ! [A: product_unit,B: fun_Pr1643180309t_bool,C: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).

thf(495,axiom,
    ! [A: bool,B: bool,C: bool] :
      ( ( ( hBOOL @ C )
      <=> ( hBOOL @ B ) )
     => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ A ) )
       => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_ord__eq__le__trans) ).

thf(2647,plain,
    ! [A: bool,B: bool,C: bool] :
      ( ( ( ( hBOOL @ C )
         => ( hBOOL @ B ) )
        & ( ( hBOOL @ B )
         => ( hBOOL @ C ) ) )
     => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ A ) )
       => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).

thf(498,axiom,
    ! [A: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ n ) )
     => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ b ) @ a ) ) @ ( hAPP_f792184801t_bool @ f @ ( hAPP_f311418073t_bool @ ( hAPP_f1302245795t_bool @ cOMBC_1490589522t_bool @ ( hAPP_f1755759597t_bool @ ( hAPP_f1328803787t_bool @ cOMBC_1190055014t_bool @ ( hAPP_f509814255t_bool @ ( cOMBB_231886989e_indi @ if_fun1658569689t_bool ) @ ( hAPP_n924210722i_bool @ ( hAPP_f62620517i_bool @ cOMBC_922322901t_bool @ ( hAPP_f1381130897t_bool @ ( cOMBB_981137617e_indi @ ord_less_nat ) @ h ) ) @ A ) ) ) @ lab ) ) @ lba ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_n_I2_J) ).

thf(2664,plain,
    ! [A: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ n ) )
     => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ b ) @ a ) ) @ ( hAPP_f792184801t_bool @ f @ ( hAPP_f311418073t_bool @ ( hAPP_f1302245795t_bool @ cOMBC_1490589522t_bool @ ( hAPP_f1755759597t_bool @ ( hAPP_f1328803787t_bool @ cOMBC_1190055014t_bool @ ( hAPP_f509814255t_bool @ ( cOMBB_231886989e_indi @ if_fun1658569689t_bool ) @ ( hAPP_n924210722i_bool @ ( hAPP_f62620517i_bool @ cOMBC_922322901t_bool @ ( hAPP_f1381130897t_bool @ ( cOMBB_981137617e_indi @ ord_less_nat ) @ h ) ) @ A ) ) ) @ lab ) ) @ lba ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).

thf(156,axiom,
    ( ( image_391852738di_nat @ h @ top_to1678393681i_bool )
    = ( hAPP_n1699378549t_bool @ ( ord_at4362885an_nat @ zero_zero_nat ) @ ( finite783399747e_indi @ top_to1678393681i_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_696_surjh) ).

thf(1293,plain,
    ( ( image_391852738di_nat @ h @ top_to1678393681i_bool )
    = ( hAPP_n1699378549t_bool @ ( ord_at4362885an_nat @ zero_zero_nat ) @ ( finite783399747e_indi @ top_to1678393681i_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(590,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ B ) )
    <=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
        & ( A != B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_446_psubset__eq) ).

thf(2974,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ B ) )
       => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
          & ( A != B ) ) )
      & ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
          & ( A != B ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).

thf(548,axiom,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ B ) )
     => ~ ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_order__less__imp__not__less) ).

thf(2842,plain,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ B ) )
     => ~ ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).

thf(576,axiom,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool,C: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ B ) @ C ) )
     => ( ( C = A )
       => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_ord__less__eq__trans) ).

thf(2923,plain,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool,C: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ B ) @ C ) )
     => ( ( C = A )
       => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).

thf(167,axiom,
    ! [A: arrow_2115524757e_indi,B: fun_Ar500372357t_bool,C: fun_Ar552120407i_bool,D: fun_Ar1198543961l_bool] :
      ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ B ) @ ( pi_Arr487970267t_bool @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ ( hAPP_A1174518481t_bool @ B @ A ) ) @ ( hAPP_A1279849719l_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_PiE) ).

thf(1325,plain,
    ! [A: arrow_2115524757e_indi,B: fun_Ar500372357t_bool,C: fun_Ar552120407i_bool,D: fun_Ar1198543961l_bool] :
      ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ B ) @ ( pi_Arr487970267t_bool @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ ( hAPP_A1174518481t_bool @ B @ A ) ) @ ( hAPP_A1279849719l_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(484,axiom,
    ! [A: bool] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ top_top_bool ) @ A ) )
     => ( ( hBOOL @ A )
      <=> ( hBOOL @ top_top_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_356_top__le) ).

thf(2593,plain,
    ! [A: bool] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ top_top_bool ) @ A ) )
     => ( ( ( hBOOL @ A )
         => ( hBOOL @ top_top_bool ) )
        & ( ( hBOOL @ top_top_bool )
         => ( hBOOL @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).

thf(85,axiom,
    ! [A: nat,B: nat] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
        | ( A = B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_559_less__or__eq__imp__le) ).

thf(1029,plain,
    ! [A: nat,B: nat] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
        | ( A = B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(586,axiom,
    ! [A: nat,B: nat,C: fun_nat_nat,D: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ C ) @ D ) )
     => ( ( A != B )
       => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ D ) )
         => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ D ) )
           => ( ( hAPP_nat_nat @ C @ A )
             != ( hAPP_nat_nat @ C @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_366_inj__on__contraD) ).

thf(2962,plain,
    ! [A: nat,B: nat,C: fun_nat_nat,D: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ C ) @ D ) )
     => ( ( A != B )
       => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ D ) )
         => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ D ) )
           => ( ( hAPP_nat_nat @ C @ A )
             != ( hAPP_nat_nat @ C @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).

thf(241,axiom,
    ! [A: nat] :
      ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ zero_zero_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_615_less__nat__zero__code) ).

thf(1594,plain,
    ! [A: nat] :
      ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ zero_zero_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(757,axiom,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( ! [C: product_unit] :
          ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ C ) @ B ) )
         => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ C ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_505_subsetI) ).

thf(3627,plain,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( ! [C: product_unit] :
          ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ C ) @ B ) )
         => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ C ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).

thf(490,axiom,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ A ) @ B ) )
     => ( ( B != A )
       => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_316_xt1_I11_J) ).

thf(2620,plain,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ A ) @ B ) )
     => ( ( B != A )
       => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).

thf(352,axiom,
    ! [A: arrow_931160158le_alt,B: arrow_931160158le_alt,C: fun_Pr1055212137t_bool] :
      ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ C ) @ arrow_915577424le_Lin ) )
     => ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ A ) @ B ) ) @ C ) )
       => ~ ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ B ) @ A ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_Lin__irrefl) ).

thf(2086,plain,
    ! [A: arrow_931160158le_alt,B: arrow_931160158le_alt,C: fun_Pr1055212137t_bool] :
      ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ C ) @ arrow_915577424le_Lin ) )
     => ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ A ) @ B ) ) @ C ) )
       => ~ ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ B ) @ A ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(351,axiom,
    ! [A: arrow_931160158le_alt,B: arrow_931160158le_alt,C: fun_Pr1055212137t_bool,D: arrow_931160158le_alt] :
      ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ A ) @ B ) ) @ ( hAPP_A606737888t_bool @ ( hAPP_f786530292t_bool @ arrow_592884904_mkbot @ C ) @ D ) ) )
    <=> ( ( B != D )
        & ( ( A = D )
         => ( A != B ) )
        & ( ( A != D )
         => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ A ) @ B ) ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_in__mkbot) ).

thf(2064,plain,
    ! [A: arrow_931160158le_alt,B: arrow_931160158le_alt,C: fun_Pr1055212137t_bool,D: arrow_931160158le_alt] :
      ( ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ A ) @ B ) ) @ ( hAPP_A606737888t_bool @ ( hAPP_f786530292t_bool @ arrow_592884904_mkbot @ C ) @ D ) ) )
       => ( ( B != D )
          & ( ( A = D )
           => ( A != B ) )
          & ( ( A != D )
           => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ A ) @ B ) ) @ C ) ) ) ) )
      & ( ( ( B != D )
          & ( ( A = D )
           => ( A != B ) )
          & ( ( A != D )
           => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ A ) @ B ) ) @ C ) ) ) )
       => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ A ) @ B ) ) @ ( hAPP_A606737888t_bool @ ( hAPP_f786530292t_bool @ arrow_592884904_mkbot @ C ) @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(578,axiom,
    ! [A: bool] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ top_top_bool ) @ A ) )
    <=> ( ( hBOOL @ A )
      <=> ( hBOOL @ top_top_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_348_top__unique) ).

thf(2931,plain,
    ! [A: bool] :
      ( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ top_top_bool ) @ A ) )
       => ( ( ( hBOOL @ A )
           => ( hBOOL @ top_top_bool ) )
          & ( ( hBOOL @ top_top_bool )
           => ( hBOOL @ A ) ) ) )
      & ( ( ( ( hBOOL @ A )
           => ( hBOOL @ top_top_bool ) )
          & ( ( hBOOL @ top_top_bool )
           => ( hBOOL @ A ) ) )
       => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ top_top_bool ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).

thf(468,axiom,
    ! [A: fun_Ar552120407i_bool] : ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ A ) @ top_to1678393681i_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_347_top__greatest) ).

thf(2535,plain,
    ! [A: fun_Ar552120407i_bool] : ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ A ) @ top_to1678393681i_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).

thf(211,axiom,
    ! [A: fun_bo492988759l_bool,B: fun_bool_bool,C: bool] :
      ( ( hAPP_bool_bool @ ( hAPP_f961197973l_bool @ ( hAPP_f1996228283l_bool @ cOMBC_1455277858l_bool @ A ) @ B ) @ C )
      = ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo) ).

thf(1496,plain,
    ! [A: fun_bo492988759l_bool,B: fun_bool_bool,C: bool] :
      ( ( hAPP_bool_bool @ ( hAPP_f961197973l_bool @ ( hAPP_f1996228283l_bool @ cOMBC_1455277858l_bool @ A ) @ B ) @ C )
      = ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(637,axiom,
    ! [A: fun_fu1138137687l_bool] :
      ( ( A != top_to2013953873l_bool )
    <=> ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f173704847l_bool @ ord_le1306091181l_bool @ A ) @ top_to2013953873l_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_less__top) ).

thf(3178,plain,
    ! [A: fun_fu1138137687l_bool] :
      ( ( ( A != top_to2013953873l_bool )
       => ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f173704847l_bool @ ord_le1306091181l_bool @ A ) @ top_to2013953873l_bool ) ) )
      & ( ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f173704847l_bool @ ord_le1306091181l_bool @ A ) @ top_to2013953873l_bool ) )
       => ( A != top_to2013953873l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).

thf(375,axiom,
    ! [A: produc1840315303le_alt,B: fun_Pr1055212137t_bool,C: fun_Pr1055212137t_bool] :
      ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_f314169011l_bool @ ord_le466311871t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_519_psubsetD) ).

thf(2156,plain,
    ! [A: produc1840315303le_alt,B: fun_Pr1055212137t_bool,C: fun_Pr1055212137t_bool] :
      ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_f314169011l_bool @ ord_le466311871t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(393,axiom,
    ! [A: bool,B: fun_bool_bool,C: fun_bool_bool] :
      ( ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_f612708895l_bool @ ord_le742797417l_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_463_set__mp) ).

thf(2207,plain,
    ! [A: bool,B: fun_bool_bool,C: fun_bool_bool] :
      ( ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_f612708895l_bool @ ord_le742797417l_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(558,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ B ) )
     => ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_order__less__asym) ).

thf(2867,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ B ) )
     => ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).

thf(527,axiom,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ A ) @ B ) )
     => ( ( B != A )
       => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_317_xt1_I11_J) ).

thf(2770,plain,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ A ) @ B ) )
     => ( ( B != A )
       => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).

thf(73,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ D ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ D ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_431_add__strict__mono) ).

thf(983,plain,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ D ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ D ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(302,axiom,
    ! [A: fun_Pr1055212137t_bool,B: fun_Pr1055212137t_bool] :
      ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_f314169011l_bool @ ord_le565024179t_bool @ ( hAPP_f70231061t_bool @ ( hAPP_f46399911t_bool @ cOMBC_697226658l_bool @ member553230100le_alt ) @ A ) ) @ ( hAPP_f70231061t_bool @ ( hAPP_f46399911t_bool @ cOMBC_697226658l_bool @ member553230100le_alt ) @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_f314169011l_bool @ ord_le565024179t_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_500_pred__subset__eq) ).

thf(1841,plain,
    ! [A: fun_Pr1055212137t_bool,B: fun_Pr1055212137t_bool] :
      ( ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_f314169011l_bool @ ord_le565024179t_bool @ ( hAPP_f70231061t_bool @ ( hAPP_f46399911t_bool @ cOMBC_697226658l_bool @ member553230100le_alt ) @ A ) ) @ ( hAPP_f70231061t_bool @ ( hAPP_f46399911t_bool @ cOMBC_697226658l_bool @ member553230100le_alt ) @ B ) ) )
       => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_f314169011l_bool @ ord_le565024179t_bool @ A ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_f314169011l_bool @ ord_le565024179t_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_f314169011l_bool @ ord_le565024179t_bool @ ( hAPP_f70231061t_bool @ ( hAPP_f46399911t_bool @ cOMBC_697226658l_bool @ member553230100le_alt ) @ A ) ) @ ( hAPP_f70231061t_bool @ ( hAPP_f46399911t_bool @ cOMBC_697226658l_bool @ member553230100le_alt ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(183,axiom,
    ! [A: fun_Ar1198543961l_bool,B: fun_Ar1198543961l_bool,C: fun_Ar552120407i_bool] :
      ( ! [D: arrow_2115524757e_indi] :
          ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ D ) @ C ) )
         => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f868566847l_bool @ ord_le1923264405l_bool @ ( hAPP_A1279849719l_bool @ A @ D ) ) @ ( hAPP_A1279849719l_bool @ B @ D ) ) ) )
     => ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f95487087l_bool @ ord_le1871091345l_bool @ ( pi_Arr487970267t_bool @ C @ A ) ) @ ( pi_Arr487970267t_bool @ C @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_502_Pi__mono) ).

thf(1396,plain,
    ! [A: fun_Ar1198543961l_bool,B: fun_Ar1198543961l_bool,C: fun_Ar552120407i_bool] :
      ( ! [D: arrow_2115524757e_indi] :
          ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ D ) @ C ) )
         => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f868566847l_bool @ ord_le1923264405l_bool @ ( hAPP_A1279849719l_bool @ A @ D ) ) @ ( hAPP_A1279849719l_bool @ B @ D ) ) ) )
     => ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f95487087l_bool @ ord_le1871091345l_bool @ ( pi_Arr487970267t_bool @ C @ A ) ) @ ( pi_Arr487970267t_bool @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(286,axiom,
    ! [A: fun_fu1015689055l_bool] : ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f868566847l_bool @ ord_le1923264405l_bool @ A ) @ top_to1690334693l_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_406_subset__UNIV) ).

thf(1775,plain,
    ! [A: fun_fu1015689055l_bool] : ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f868566847l_bool @ ord_le1923264405l_bool @ A ) @ top_to1690334693l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(405,axiom,
    ! [A: fun_Pr1055212137t_bool] :
      ( ( hBOOL @ ( hAPP_f429946033l_bool @ top_to1690334693l_bool @ A ) )
    <=> ( hBOOL @ top_top_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_top__apply) ).

thf(2244,plain,
    ! [A: fun_Pr1055212137t_bool] :
      ( ( ( hBOOL @ ( hAPP_f429946033l_bool @ top_to1690334693l_bool @ A ) )
       => ( hBOOL @ top_top_bool ) )
      & ( ( hBOOL @ top_top_bool )
       => ( hBOOL @ ( hAPP_f429946033l_bool @ top_to1690334693l_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(520,axiom,
    ! [A: product_unit,B: fun_Pr1572389447t_bool,C: fun_Pr1643180309t_bool,D: fun_Pr1510236951l_bool] :
      ( ( hBOOL @ ( hAPP_f922750545l_bool @ ( hAPP_f2046606153l_bool @ member488877876t_bool @ B ) @ ( pi_Pro278326941t_bool @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ ( hAPP_P902017683t_bool @ B @ A ) ) @ ( hAPP_P1132296885l_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_PiE) ).

thf(2752,plain,
    ! [A: product_unit,B: fun_Pr1572389447t_bool,C: fun_Pr1643180309t_bool,D: fun_Pr1510236951l_bool] :
      ( ( hBOOL @ ( hAPP_f922750545l_bool @ ( hAPP_f2046606153l_bool @ member488877876t_bool @ B ) @ ( pi_Pro278326941t_bool @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ ( hAPP_P902017683t_bool @ B @ A ) ) @ ( hAPP_P1132296885l_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).

thf(273,axiom,
    ! [A: bool,B: bool] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_bool @ A ) @ B ) )
    <=> ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ B ) )
        & ~ ( ( hBOOL @ A )
          <=> ( hBOOL @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_272_order__less__le) ).

thf(1726,plain,
    ! [A: bool,B: bool] :
      ( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_bool @ A ) @ B ) )
       => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ B ) )
          & ~ ( ( ( hBOOL @ A )
               => ( hBOOL @ B ) )
              & ( ( hBOOL @ B )
               => ( hBOOL @ A ) ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ B ) )
          & ~ ( ( ( hBOOL @ A )
               => ( hBOOL @ B ) )
              & ( ( hBOOL @ B )
               => ( hBOOL @ A ) ) ) )
       => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(175,axiom,
    ! [A: fun_Ar500372357t_bool,B: fun_Ar1198543961l_bool,C: fun_Ar552120407i_bool] :
      ( ! [D: arrow_2115524757e_indi] :
          ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ D ) @ C ) )
         => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ ( hAPP_A1174518481t_bool @ A @ D ) ) @ ( hAPP_A1279849719l_bool @ B @ D ) ) ) )
     => ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ A ) @ ( pi_Arr487970267t_bool @ C @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_390_Pi__I) ).

thf(1364,plain,
    ! [A: fun_Ar500372357t_bool,B: fun_Ar1198543961l_bool,C: fun_Ar552120407i_bool] :
      ( ! [D: arrow_2115524757e_indi] :
          ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ D ) @ C ) )
         => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ ( hAPP_A1174518481t_bool @ A @ D ) ) @ ( hAPP_A1279849719l_bool @ B @ D ) ) ) )
     => ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ A ) @ ( pi_Arr487970267t_bool @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(588,axiom,
    ~ ! [A: fun_Ar1744566822di_nat] :
        ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( inj_on886403158di_nat @ A ) @ top_to1678393681i_bool ) )
       => ( ( image_391852738di_nat @ A @ top_to1678393681i_bool )
         != ( hAPP_n1699378549t_bool @ ( ord_at4362885an_nat @ zero_zero_nat ) @ ( finite783399747e_indi @ top_to1678393681i_bool ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_698__096_B_Bthesis_O_A_I_B_Bh_O_A_091_124_Ainj_Ah_059_Arange_Ah_A_061_A_123) ).

thf(2967,plain,
    ~ ! [A: fun_Ar1744566822di_nat] :
        ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( inj_on886403158di_nat @ A ) @ top_to1678393681i_bool ) )
       => ( ( image_391852738di_nat @ A @ top_to1678393681i_bool )
         != ( hAPP_n1699378549t_bool @ ( ord_at4362885an_nat @ zero_zero_nat ) @ ( finite783399747e_indi @ top_to1678393681i_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).

thf(719,axiom,
    ! [A: fun_fu1595299477t_bool,B: fun_fu787660105l_bool,C: fun_fu775006535l_bool] :
      ( ! [D: fun_Ar500372357t_bool] :
          ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ D ) @ C ) )
         => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ ( hAPP_f792184801t_bool @ A @ D ) ) @ ( hAPP_f1498158055l_bool @ B @ D ) ) ) )
     => ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ A ) @ ( pi_fun530160875t_bool @ C @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_585_Pi__I_H) ).

thf(3490,plain,
    ! [A: fun_fu1595299477t_bool,B: fun_fu787660105l_bool,C: fun_fu775006535l_bool] :
      ( ! [D: fun_Ar500372357t_bool] :
          ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ D ) @ C ) )
         => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ ( hAPP_f792184801t_bool @ A @ D ) ) @ ( hAPP_f1498158055l_bool @ B @ D ) ) ) )
     => ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ A ) @ ( pi_fun530160875t_bool @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).

thf(230,axiom,
    ! [A: nat] :
      ( ( hAPP_nat_nat @ suc @ A )
      = ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ one_one_nat ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_687_Suc__eq__plus1__left) ).

thf(1562,plain,
    ! [A: nat] :
      ( ( hAPP_nat_nat @ suc @ A )
      = ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ one_one_nat ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(595,axiom,
    ! [A: fun_fu1015689055l_bool,B: fun_fu1015689055l_bool] :
      ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f868566847l_bool @ ord_le1923264405l_bool @ ( hAPP_f1050277569l_bool @ ( hAPP_f639477379l_bool @ cOMBC_437066390l_bool @ member57118396t_bool ) @ A ) ) @ ( hAPP_f1050277569l_bool @ ( hAPP_f639477379l_bool @ cOMBC_437066390l_bool @ member57118396t_bool ) @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f868566847l_bool @ ord_le1923264405l_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_497_pred__subset__eq) ).

thf(3009,plain,
    ! [A: fun_fu1015689055l_bool,B: fun_fu1015689055l_bool] :
      ( ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f868566847l_bool @ ord_le1923264405l_bool @ ( hAPP_f1050277569l_bool @ ( hAPP_f639477379l_bool @ cOMBC_437066390l_bool @ member57118396t_bool ) @ A ) ) @ ( hAPP_f1050277569l_bool @ ( hAPP_f639477379l_bool @ cOMBC_437066390l_bool @ member57118396t_bool ) @ B ) ) )
       => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f868566847l_bool @ ord_le1923264405l_bool @ A ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f868566847l_bool @ ord_le1923264405l_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f868566847l_bool @ ord_le1923264405l_bool @ ( hAPP_f1050277569l_bool @ ( hAPP_f639477379l_bool @ cOMBC_437066390l_bool @ member57118396t_bool ) @ A ) ) @ ( hAPP_f1050277569l_bool @ ( hAPP_f639477379l_bool @ cOMBC_437066390l_bool @ member57118396t_bool ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).

thf(335,axiom,
    ! [A: arrow_931160158le_alt,B: arrow_931160158le_alt,C: fun_Pr1055212137t_bool,D: arrow_931160158le_alt,E: arrow_931160158le_alt] :
      ( ( D != E )
     => ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ C ) @ arrow_915577424le_Lin ) )
       => ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ A ) @ B ) ) @ ( arrow_636638768_below @ C @ D @ E ) ) )
        <=> ( ( A != B )
            & ( ( B = D )
             => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ A ) @ E ) ) @ C ) ) )
            & ( ( B != D )
             => ( ( ( A = D )
                 => ( ( B = E )
                    | ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ E ) @ B ) ) @ C ) ) ) )
                & ( ( A != D )
                 => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ A ) @ B ) ) @ C ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_523_in__below) ).

thf(1948,plain,
    ! [A: arrow_931160158le_alt,B: arrow_931160158le_alt,C: fun_Pr1055212137t_bool,D: arrow_931160158le_alt,E: arrow_931160158le_alt] :
      ( ( D != E )
     => ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ C ) @ arrow_915577424le_Lin ) )
       => ( ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ A ) @ B ) ) @ ( arrow_636638768_below @ C @ D @ E ) ) )
           => ( ( A != B )
              & ( ( B = D )
               => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ A ) @ E ) ) @ C ) ) )
              & ( ( B != D )
               => ( ( ( A = D )
                   => ( ( B = E )
                      | ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ E ) @ B ) ) @ C ) ) ) )
                  & ( ( A != D )
                   => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ A ) @ B ) ) @ C ) ) ) ) ) ) )
          & ( ( ( A != B )
              & ( ( B = D )
               => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ A ) @ E ) ) @ C ) ) )
              & ( ( B != D )
               => ( ( ( A = D )
                   => ( ( B = E )
                      | ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ E ) @ B ) ) @ C ) ) ) )
                  & ( ( A != D )
                   => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ A ) @ B ) ) @ C ) ) ) ) ) )
           => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ A ) @ B ) ) @ ( arrow_636638768_below @ C @ D @ E ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(238,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) )
     => ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_653_less__SucE) ).

thf(1583,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) )
     => ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(581,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_order__less__asym) ).

thf(2952,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).

thf(311,axiom,
    ! [A: arrow_2115524757e_indi,B: fun_Ar1744566822di_nat,C: fun_Ar552120407i_bool,D: fun_Ar2045874810t_bool] :
      ( ( hBOOL @ ( hAPP_f1290810160l_bool @ ( hAPP_f516936199l_bool @ member428554515di_nat @ B ) @ ( pi_Arr159321468di_nat @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ ( hAPP_A1450069362di_nat @ B @ A ) ) @ ( hAPP_A981395480t_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_PiE) ).

thf(1873,plain,
    ! [A: arrow_2115524757e_indi,B: fun_Ar1744566822di_nat,C: fun_Ar552120407i_bool,D: fun_Ar2045874810t_bool] :
      ( ( hBOOL @ ( hAPP_f1290810160l_bool @ ( hAPP_f516936199l_bool @ member428554515di_nat @ B ) @ ( pi_Arr159321468di_nat @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ ( hAPP_A1450069362di_nat @ B @ A ) ) @ ( hAPP_A981395480t_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(203,axiom,
    ! [A: fun_Pr1863373635l_bool,B: fun_Pr1643180309t_bool,C: product_unit] :
      ( ( hAPP_P1676879539t_bool @ ( hAPP_f427533077t_bool @ ( hAPP_f1458726223t_bool @ cOMBC_2133163426l_bool @ A ) @ B ) @ C )
      = ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Product____Type__Ounit_000tc__fun_Itc__Product____Ty) ).

thf(1467,plain,
    ! [A: fun_Pr1863373635l_bool,B: fun_Pr1643180309t_bool,C: product_unit] :
      ( ( hAPP_P1676879539t_bool @ ( hAPP_f427533077t_bool @ ( hAPP_f1458726223t_bool @ cOMBC_2133163426l_bool @ A ) @ B ) @ C )
      = ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(695,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_325_xt1_I7_J) ).

thf(3395,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).

thf(323,axiom,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ A ) @ B ) )
    <=> ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ B ) )
        | ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_451_subset__iff__psubset__eq) ).

thf(1905,plain,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool] :
      ( ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ A ) @ B ) )
       => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ B ) )
          | ( A = B ) ) )
      & ( ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ B ) )
          | ( A = B ) )
       => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(401,axiom,
    ! [A: nat,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ zero_zero_nat ) @ B ) )
     => ( ( finite_card_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( hAPP_f1146629647l_bool @ ( cOMBB_1015721476ol_nat @ fconj ) @ ( hAPP_f800510211t_bool @ ( hAPP_f1722879237t_bool @ cOMBC_226598744l_bool @ member_nat ) @ B ) ) @ ( hAPP_n1699378549t_bool @ ( hAPP_f229349961t_bool @ cOMBC_nat_nat_bool @ ord_less_nat ) @ ( hAPP_nat_nat @ suc @ A ) ) ) ) )
       != zero_zero_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_682_card__less) ).

thf(2234,plain,
    ! [A: nat,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ zero_zero_nat ) @ B ) )
     => ( ( finite_card_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( hAPP_f1146629647l_bool @ ( cOMBB_1015721476ol_nat @ fconj ) @ ( hAPP_f800510211t_bool @ ( hAPP_f1722879237t_bool @ cOMBC_226598744l_bool @ member_nat ) @ B ) ) @ ( hAPP_n1699378549t_bool @ ( hAPP_f229349961t_bool @ cOMBC_nat_nat_bool @ ord_less_nat ) @ ( hAPP_nat_nat @ suc @ A ) ) ) ) )
       != zero_zero_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

thf(577,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ B ) )
     => ( B != A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_order__less__imp__not__eq2) ).

thf(2927,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ B ) )
     => ( B != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).

thf(502,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( A != B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_order__less__imp__not__eq) ).

thf(2684,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( A != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).

thf(658,axiom,
    ! [A: fun_fu1015689055l_bool,B: fun_Pr1055212137t_bool,C: fun_fu1015689055l_bool] :
      ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f868566847l_bool @ ord_le1923264405l_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_475_set__rev__mp) ).

thf(3278,plain,
    ! [A: fun_fu1015689055l_bool,B: fun_Pr1055212137t_bool,C: fun_fu1015689055l_bool] :
      ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f868566847l_bool @ ord_le1923264405l_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).

thf(227,axiom,
    ! [A: arrow_2115524757e_indi,B: fun_Ar500372357t_bool,C: fun_Ar552120407i_bool,D: fun_fu1015689055l_bool] :
      ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ B ) @ ( pi_Arr487970267t_bool @ C @ ( hAPP_f1793492343l_bool @ cOMBK_1595020336e_indi @ D ) ) ) )
     => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ ( hAPP_A1174518481t_bool @ B @ A ) ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_378_funcset__mem) ).

thf(1551,plain,
    ! [A: arrow_2115524757e_indi,B: fun_Ar500372357t_bool,C: fun_Ar552120407i_bool,D: fun_fu1015689055l_bool] :
      ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ B ) @ ( pi_Arr487970267t_bool @ C @ ( hAPP_f1793492343l_bool @ cOMBK_1595020336e_indi @ D ) ) ) )
     => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ ( hAPP_A1174518481t_bool @ B @ A ) ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(706,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ B ) @ C ) )
     => ( ( C = A )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_ord__less__eq__trans) ).

thf(3444,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ B ) @ C ) )
     => ( ( C = A )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).

thf(86,axiom,
    ! [A: nat] :
      ( ( hAPP_n1699378549t_bool @ ord_less_nat @ A )
      = ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_679_less__eq__Suc__le__raw) ).

thf(1034,plain,
    ! [A: nat] :
      ( ( hAPP_n1699378549t_bool @ ord_less_nat @ A )
      = ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(403,axiom,
    ! [A: nat,B: fun_nat_bool,C: fun_nat_bool,D: fun_na1469252690l_bool] :
      ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ B ) @ ( pi_nat_bool @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ ( hAPP_nat_bool @ B @ A ) ) @ ( hAPP_n1006566506l_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_PiE) ).

thf(2239,plain,
    ! [A: nat,B: fun_nat_bool,C: fun_nat_bool,D: fun_na1469252690l_bool] :
      ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ B ) @ ( pi_nat_bool @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ ( hAPP_nat_bool @ B @ A ) ) @ ( hAPP_n1006566506l_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(447,axiom,
    ! [A: fun_Ar500372357t_bool,B: fun_fu1595299477t_bool,C: fun_fu775006535l_bool,D: fun_fu787660105l_bool] :
      ( ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ B ) @ ( pi_fun530160875t_bool @ C @ D ) ) )
     => ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ ( hAPP_f792184801t_bool @ B @ A ) ) @ ( hAPP_f1498158055l_bool @ D @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_374_Pi__mem) ).

thf(2471,plain,
    ! [A: fun_Ar500372357t_bool,B: fun_fu1595299477t_bool,C: fun_fu775006535l_bool,D: fun_fu787660105l_bool] :
      ( ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ B ) @ ( pi_fun530160875t_bool @ C @ D ) ) )
     => ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ ( hAPP_f792184801t_bool @ B @ A ) ) @ ( hAPP_f1498158055l_bool @ D @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).

thf(496,axiom,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ B ) )
    <=> ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ A ) @ B ) )
        & ( A != B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_447_psubset__eq) ).

thf(2652,plain,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ B ) )
       => ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ A ) @ B ) )
          & ( A != B ) ) )
      & ( ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ A ) @ B ) )
          & ( A != B ) )
       => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).

thf(662,axiom,
    ! [A: bool,B: fun_bool_bool,C: fun_bool_bool] :
      ( ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_f612708895l_bool @ ord_le197158773l_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_512_psubsetD) ).

thf(3293,plain,
    ! [A: bool,B: fun_bool_bool,C: fun_bool_bool] :
      ( ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_f612708895l_bool @ ord_le197158773l_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).

thf(458,axiom,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool,C: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_321_order__less__le__trans) ).

thf(2503,plain,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool,C: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).

thf(266,axiom,
    ! [A: fun_Ar500372357t_bool,B: fun_Ar500372357t_bool,C: arrow_931160158le_alt,D: arrow_931160158le_alt,E: arrow_931160158le_alt,F: arrow_931160158le_alt] :
      ( ( E != F )
     => ( ( C != D )
       => ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ B ) @ arrow_1190054106e_Prof ) )
         => ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ A ) @ arrow_1190054106e_Prof ) )
           => ( ! [G: arrow_2115524757e_indi] :
                  ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ E ) @ F ) ) @ ( hAPP_A1174518481t_bool @ B @ G ) ) )
                <=> ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ C ) @ D ) ) @ ( hAPP_A1174518481t_bool @ A @ G ) ) ) )
             => ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ E ) @ F ) ) @ ( hAPP_f792184801t_bool @ f @ B ) ) )
              <=> ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ C ) @ D ) ) @ ( hAPP_f792184801t_bool @ f @ A ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_pairwise__neutrality) ).

thf(1684,plain,
    ! [A: fun_Ar500372357t_bool,B: fun_Ar500372357t_bool,C: arrow_931160158le_alt,D: arrow_931160158le_alt,E: arrow_931160158le_alt,F: arrow_931160158le_alt] :
      ( ( E != F )
     => ( ( C != D )
       => ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ B ) @ arrow_1190054106e_Prof ) )
         => ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ A ) @ arrow_1190054106e_Prof ) )
           => ( ! [G: arrow_2115524757e_indi] :
                  ( ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ E ) @ F ) ) @ ( hAPP_A1174518481t_bool @ B @ G ) ) )
                   => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ C ) @ D ) ) @ ( hAPP_A1174518481t_bool @ A @ G ) ) ) )
                  & ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ C ) @ D ) ) @ ( hAPP_A1174518481t_bool @ A @ G ) ) )
                   => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ E ) @ F ) ) @ ( hAPP_A1174518481t_bool @ B @ G ) ) ) ) )
             => ( ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ E ) @ F ) ) @ ( hAPP_f792184801t_bool @ f @ B ) ) )
                 => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ C ) @ D ) ) @ ( hAPP_f792184801t_bool @ f @ A ) ) ) )
                & ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ C ) @ D ) ) @ ( hAPP_f792184801t_bool @ f @ A ) ) )
                 => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ E ) @ F ) ) @ ( hAPP_f792184801t_bool @ f @ B ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(120,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_557_less__imp__le__nat) ).

thf(1145,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(550,axiom,
    ! [A: fun_Pr1643180309t_bool] :
      ( ( A != top_to1257323279t_bool )
    <=> ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ top_to1257323279t_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_less__top) ).

thf(2846,plain,
    ! [A: fun_Pr1643180309t_bool] :
      ( ( ( A != top_to1257323279t_bool )
       => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ top_to1257323279t_bool ) ) )
      & ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ top_to1257323279t_bool ) )
       => ( A != top_to1257323279t_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).

thf(475,axiom,
    ! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_539_le__refl) ).

thf(2564,plain,
    ! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).

thf(8,axiom,
    ! [A: nat,B: nat] :
      ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_547_not__add__less2) ).

thf(776,plain,
    ! [A: nat,B: nat] :
      ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(693,axiom,
    ! [A: fun_Ar500372357t_bool,B: fun_fu775006535l_bool,C: fun_fu775006535l_bool] :
      ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f95487087l_bool @ ord_le1871091345l_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_469_set__mp) ).

thf(3391,plain,
    ! [A: fun_Ar500372357t_bool,B: fun_fu775006535l_bool,C: fun_fu775006535l_bool] :
      ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f95487087l_bool @ ord_le1871091345l_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).

thf(285,axiom,
    ! [A: fun_fu1138137687l_bool,B: fun_fu1138137687l_bool] :
      ( ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f173704847l_bool @ ord_le161055137l_bool @ ( hAPP_f1077478037l_bool @ ( hAPP_f230252107l_bool @ cOMBC_1452216610l_bool @ member1801442306t_bool ) @ A ) ) @ ( hAPP_f1077478037l_bool @ ( hAPP_f230252107l_bool @ cOMBC_1452216610l_bool @ member1801442306t_bool ) @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f173704847l_bool @ ord_le161055137l_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_498_pred__subset__eq) ).

thf(1770,plain,
    ! [A: fun_fu1138137687l_bool,B: fun_fu1138137687l_bool] :
      ( ( ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f173704847l_bool @ ord_le161055137l_bool @ ( hAPP_f1077478037l_bool @ ( hAPP_f230252107l_bool @ cOMBC_1452216610l_bool @ member1801442306t_bool ) @ A ) ) @ ( hAPP_f1077478037l_bool @ ( hAPP_f230252107l_bool @ cOMBC_1452216610l_bool @ member1801442306t_bool ) @ B ) ) )
       => ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f173704847l_bool @ ord_le161055137l_bool @ A ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f173704847l_bool @ ord_le161055137l_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f173704847l_bool @ ord_le161055137l_bool @ ( hAPP_f1077478037l_bool @ ( hAPP_f230252107l_bool @ cOMBC_1452216610l_bool @ member1801442306t_bool ) @ A ) ) @ ( hAPP_f1077478037l_bool @ ( hAPP_f230252107l_bool @ cOMBC_1452216610l_bool @ member1801442306t_bool ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(668,axiom,
    ! [A: product_unit] : ( hBOOL @ ( hAPP_P1676879539t_bool @ top_to1257323279t_bool @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_top1I) ).

thf(3315,plain,
    ! [A: product_unit] : ( hBOOL @ ( hAPP_P1676879539t_bool @ top_to1257323279t_bool @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).

thf(497,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ A ) @ B ) )
      | ( hBOOL @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_2_1_U) ).

thf(2661,plain,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ A ) @ B ) )
      | ( hBOOL @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).

thf(482,axiom,
    ! [A: bool,B: bool,C: bool] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_339_xt1_I8_J) ).

thf(2588,plain,
    ! [A: bool,B: bool,C: bool] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).

thf(710,axiom,
    ! [A: nat,B: nat] :
      ( ( A = B )
    <=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
        & ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_order__eq__iff) ).

thf(3462,plain,
    ! [A: nat,B: nat] :
      ( ( ( A = B )
       => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
          & ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
          & ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).

thf(625,axiom,
    ! [A: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ top_to1678393681i_bool ) @ A ) )
    <=> ( A = top_to1678393681i_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_355_top__unique) ).

thf(3129,plain,
    ! [A: fun_Ar552120407i_bool] :
      ( ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ top_to1678393681i_bool ) @ A ) )
       => ( A = top_to1678393681i_bool ) )
      & ( ( A = top_to1678393681i_bool )
       => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ top_to1678393681i_bool ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).

thf(464,axiom,
    ! [A: fun_nat_bool] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ top_top_fun_nat_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_410_subset__UNIV) ).

thf(2518,plain,
    ! [A: fun_nat_bool] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ top_top_fun_nat_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).

thf(378,axiom,
    ! [A: bool,B: fun_Pr1643180309t_bool,C: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ C ) @ B ) )
       => ( hBOOL @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_order__less__imp__triv) ).

thf(2175,plain,
    ! [A: bool,B: fun_Pr1643180309t_bool,C: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ C ) @ B ) )
       => ( hBOOL @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

thf(646,axiom,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ B ) )
    <=> ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ A ) @ B ) )
        & ( A != B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_order__less__le) ).

thf(3209,plain,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ B ) )
       => ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ A ) @ B ) )
          & ( A != B ) ) )
      & ( ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ A ) @ B ) )
          & ( A != B ) )
       => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).

thf(510,axiom,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ B ) )
        | ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_305_order__le__imp__less__or__eq) ).

thf(2720,plain,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ B ) )
        | ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).

thf(102,axiom,
    ! [A: nat] :
      ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_631_Suc__n__not__le__n) ).

thf(1098,plain,
    ! [A: nat] :
      ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(543,axiom,
    ! [A: arrow_2115524757e_indi,B: arrow_2115524757e_indi,C: fun_Ar1744566822di_nat,D: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( inj_on886403158di_nat @ C ) @ D ) )
     => ( ( A != B )
       => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ A ) @ D ) )
         => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ B ) @ D ) )
           => ( ( hAPP_A1450069362di_nat @ C @ A )
             != ( hAPP_A1450069362di_nat @ C @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_367_inj__on__contraD) ).

thf(2831,plain,
    ! [A: arrow_2115524757e_indi,B: arrow_2115524757e_indi,C: fun_Ar1744566822di_nat,D: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( inj_on886403158di_nat @ C ) @ D ) )
     => ( ( A != B )
       => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ A ) @ D ) )
         => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ B ) @ D ) )
           => ( ( hAPP_A1450069362di_nat @ C @ A )
             != ( hAPP_A1450069362di_nat @ C @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).

thf(246,axiom,
    ! [A: bool,B: fun_Ar500372357t_bool] :
      ( ( hAPP_f1766661605l_bool @ ( hAPP_b1849744615l_bool @ cOMBK_670822686t_bool @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabel) ).

thf(1611,plain,
    ! [A: bool,B: fun_Ar500372357t_bool] :
      ( ( hAPP_f1766661605l_bool @ ( hAPP_b1849744615l_bool @ cOMBK_670822686t_bool @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(123,axiom,
    ! [A: nat,B: nat] :
      ( ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B )
        = ( hAPP_nat_nat @ suc @ zero_zero_nat ) )
    <=> ( ( ( A
            = ( hAPP_nat_nat @ suc @ zero_zero_nat ) )
          & ( B = zero_zero_nat ) )
        | ( ( A = zero_zero_nat )
          & ( B
            = ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_668_add__is__1) ).

thf(1156,plain,
    ! [A: nat,B: nat] :
      ( ( ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B )
          = ( hAPP_nat_nat @ suc @ zero_zero_nat ) )
       => ( ( ( A
              = ( hAPP_nat_nat @ suc @ zero_zero_nat ) )
            & ( B = zero_zero_nat ) )
          | ( ( A = zero_zero_nat )
            & ( B
              = ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) ) ) )
      & ( ( ( ( A
              = ( hAPP_nat_nat @ suc @ zero_zero_nat ) )
            & ( B = zero_zero_nat ) )
          | ( ( A = zero_zero_nat )
            & ( B
              = ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) ) )
       => ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B )
          = ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(279,axiom,
    ! [A: nat,B: fun_nat_nat] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ B ) @ top_top_fun_nat_bool ) )
     => ( ( hAPP_nat_nat @ ( hilber195283148at_nat @ top_top_fun_nat_bool @ B ) @ ( hAPP_nat_nat @ B @ A ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_inv__f__f) ).

thf(1753,plain,
    ! [A: nat,B: fun_nat_nat] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ B ) @ top_top_fun_nat_bool ) )
     => ( ( hAPP_nat_nat @ ( hilber195283148at_nat @ top_top_fun_nat_bool @ B ) @ ( hAPP_nat_nat @ B @ A ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(431,axiom,
    ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ top_top_fun_nat_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_605_infinite__UNIV__nat) ).

thf(2407,plain,
    ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ top_top_fun_nat_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).

thf(477,axiom,
    ! [A: product_unit] :
      ( ( hBOOL @ ( hAPP_P1676879539t_bool @ top_to1257323279t_bool @ A ) )
    <=> ( hBOOL @ top_top_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_top__apply) ).

thf(2569,plain,
    ! [A: product_unit] :
      ( ( ( hBOOL @ ( hAPP_P1676879539t_bool @ top_to1257323279t_bool @ A ) )
       => ( hBOOL @ top_top_bool ) )
      & ( ( hBOOL @ top_top_bool )
       => ( hBOOL @ ( hAPP_P1676879539t_bool @ top_to1257323279t_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).

thf(707,axiom,
    ! [A: bool,B: fun_bo1479727337le_alt,C: fun_bool_bool,D: fun_bo1116297149t_bool] :
      ( ( hBOOL @ ( hAPP_f1339624767l_bool @ ( hAPP_f1862158541l_bool @ member481633596le_alt @ B ) @ ( pi_boo1374671485le_alt @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_b1314516999le_alt @ B @ A ) ) @ ( hAPP_b1263785481t_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_PiE) ).

thf(3448,plain,
    ! [A: bool,B: fun_bo1479727337le_alt,C: fun_bool_bool,D: fun_bo1116297149t_bool] :
      ( ( hBOOL @ ( hAPP_f1339624767l_bool @ ( hAPP_f1862158541l_bool @ member481633596le_alt @ B ) @ ( pi_boo1374671485le_alt @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_b1314516999le_alt @ B @ A ) ) @ ( hAPP_b1263785481t_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).

thf(355,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_462_subset__trans) ).

thf(2092,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(194,axiom,
    ! [A: nat,B: nat] :
      ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
      <=> ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_287_linorder__antisym__conv1) ).

thf(1432,plain,
    ! [A: nat,B: nat] :
      ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
         => ( A = B ) )
        & ( ( A = B )
         => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(731,axiom,
    ! [A: fun_Ar500372357t_bool,B: fun_fu1595299477t_bool,C: fun_fu775006535l_bool,D: fun_fu1015689055l_bool] :
      ( ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ B ) @ ( pi_fun530160875t_bool @ C @ ( hAPP_f422714471l_bool @ cOMBK_1446432t_bool @ D ) ) ) )
     => ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ ( hAPP_f792184801t_bool @ B @ A ) ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_379_funcset__mem) ).

thf(3554,plain,
    ! [A: fun_Ar500372357t_bool,B: fun_fu1595299477t_bool,C: fun_fu775006535l_bool,D: fun_fu1015689055l_bool] :
      ( ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ B ) @ ( pi_fun530160875t_bool @ C @ ( hAPP_f422714471l_bool @ cOMBK_1446432t_bool @ D ) ) ) )
     => ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ ( hAPP_f792184801t_bool @ B @ A ) ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).

thf(676,axiom,
    ! [A: fun_Ar500372357t_bool,B: fun_fu2016509975e_indi,C: fun_fu1015689055l_bool,D: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f372503329l_bool @ ( hAPP_f43388905l_bool @ member527726724e_indi @ B ) @ ( pi_fun1342736627e_indi @ C @ ( hAPP_f676424105i_bool @ cOMBK_854051296t_bool @ D ) ) ) )
     => ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( inj_on1048829645e_indi @ B ) @ C ) )
       => ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ A ) @ ( pi_Arr487970267t_bool @ D @ ( hAPP_f1793492343l_bool @ cOMBK_1595020336e_indi @ C ) ) ) )
         => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( inj_on194063285t_bool @ A ) @ D ) )
           => ( ( hBOOL @ ( hAPP_f1021703871l_bool @ finite775027132t_bool @ C ) )
             => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ finite1350902018e_indi @ D ) )
               => ( ( finite1445836347t_bool @ C )
                  = ( finite783399747e_indi @ D ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_596_card__bij) ).

thf(3344,plain,
    ! [A: fun_Ar500372357t_bool,B: fun_fu2016509975e_indi,C: fun_fu1015689055l_bool,D: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f372503329l_bool @ ( hAPP_f43388905l_bool @ member527726724e_indi @ B ) @ ( pi_fun1342736627e_indi @ C @ ( hAPP_f676424105i_bool @ cOMBK_854051296t_bool @ D ) ) ) )
     => ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( inj_on1048829645e_indi @ B ) @ C ) )
       => ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ A ) @ ( pi_Arr487970267t_bool @ D @ ( hAPP_f1793492343l_bool @ cOMBK_1595020336e_indi @ C ) ) ) )
         => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( inj_on194063285t_bool @ A ) @ D ) )
           => ( ( hBOOL @ ( hAPP_f1021703871l_bool @ finite775027132t_bool @ C ) )
             => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ finite1350902018e_indi @ D ) )
               => ( ( finite1445836347t_bool @ C )
                  = ( finite783399747e_indi @ D ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).

thf(289,axiom,
    ! [A: fun_Pr1055212137t_bool,B: fun_Pr1055212137t_bool] :
      ( ( hBOOL @ ( hAPP_f1733046827l_bool @ ( hAPP_f2062231615l_bool @ ord_le1254553345t_bool @ ( hAPP_f1810968607t_bool @ ( hAPP_f15758621t_bool @ cOMBC_1947566172t_bool @ ( hAPP_f1435501085t_bool @ ( cOMBB_1430402568le_alt @ cOMBC_571858149l_bool ) @ ( hAPP_f1176598245l_bool @ ( cOMBB_1605735744le_alt @ ( cOMBB_480104238le_alt @ member553230100le_alt ) ) @ produc362059031le_alt ) ) ) @ A ) ) @ ( hAPP_f1810968607t_bool @ ( hAPP_f15758621t_bool @ cOMBC_1947566172t_bool @ ( hAPP_f1435501085t_bool @ ( cOMBB_1430402568le_alt @ cOMBC_571858149l_bool ) @ ( hAPP_f1176598245l_bool @ ( cOMBB_1605735744le_alt @ ( cOMBB_480104238le_alt @ member553230100le_alt ) ) @ produc362059031le_alt ) ) ) @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_f314169011l_bool @ ord_le565024179t_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_405_pred__subset__eq2) ).

thf(1785,plain,
    ! [A: fun_Pr1055212137t_bool,B: fun_Pr1055212137t_bool] :
      ( ( ( hBOOL @ ( hAPP_f1733046827l_bool @ ( hAPP_f2062231615l_bool @ ord_le1254553345t_bool @ ( hAPP_f1810968607t_bool @ ( hAPP_f15758621t_bool @ cOMBC_1947566172t_bool @ ( hAPP_f1435501085t_bool @ ( cOMBB_1430402568le_alt @ cOMBC_571858149l_bool ) @ ( hAPP_f1176598245l_bool @ ( cOMBB_1605735744le_alt @ ( cOMBB_480104238le_alt @ member553230100le_alt ) ) @ produc362059031le_alt ) ) ) @ A ) ) @ ( hAPP_f1810968607t_bool @ ( hAPP_f15758621t_bool @ cOMBC_1947566172t_bool @ ( hAPP_f1435501085t_bool @ ( cOMBB_1430402568le_alt @ cOMBC_571858149l_bool ) @ ( hAPP_f1176598245l_bool @ ( cOMBB_1605735744le_alt @ ( cOMBB_480104238le_alt @ member553230100le_alt ) ) @ produc362059031le_alt ) ) ) @ B ) ) )
       => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_f314169011l_bool @ ord_le565024179t_bool @ A ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_f314169011l_bool @ ord_le565024179t_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1733046827l_bool @ ( hAPP_f2062231615l_bool @ ord_le1254553345t_bool @ ( hAPP_f1810968607t_bool @ ( hAPP_f15758621t_bool @ cOMBC_1947566172t_bool @ ( hAPP_f1435501085t_bool @ ( cOMBB_1430402568le_alt @ cOMBC_571858149l_bool ) @ ( hAPP_f1176598245l_bool @ ( cOMBB_1605735744le_alt @ ( cOMBB_480104238le_alt @ member553230100le_alt ) ) @ produc362059031le_alt ) ) ) @ A ) ) @ ( hAPP_f1810968607t_bool @ ( hAPP_f15758621t_bool @ cOMBC_1947566172t_bool @ ( hAPP_f1435501085t_bool @ ( cOMBB_1430402568le_alt @ cOMBC_571858149l_bool ) @ ( hAPP_f1176598245l_bool @ ( cOMBB_1605735744le_alt @ ( cOMBB_480104238le_alt @ member553230100le_alt ) ) @ produc362059031le_alt ) ) ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(600,axiom,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool,C: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_459_subset__psubset__trans) ).

thf(3026,plain,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool,C: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).

thf(397,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
     => ( ( C = A )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_ord__le__eq__trans) ).

thf(2219,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
     => ( ( C = A )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(164,axiom,
    ! [A: nat] :
      ( zero_zero_nat
     != ( hAPP_nat_nat @ suc @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_677_nat_Osimps_I2_J) ).

thf(1317,plain,
    ! [A: nat] :
      ( zero_zero_nat
     != ( hAPP_nat_nat @ suc @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(322,axiom,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool,C: fun_Pr1643180309t_bool] :
      ( ( B = C )
     => ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_ord__eq__less__trans) ).

thf(1901,plain,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool,C: fun_Pr1643180309t_bool] :
      ( ( B = C )
     => ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(604,axiom,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool,C: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_327_xt1_I7_J) ).

thf(3041,plain,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool,C: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).

thf(171,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) )
    <=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
        | ( A
          = ( hAPP_nat_nat @ suc @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_633_le__Suc__eq) ).

thf(1336,plain,
    ! [A: nat,B: nat] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) )
       => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
          | ( A
            = ( hAPP_nat_nat @ suc @ B ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
          | ( A
            = ( hAPP_nat_nat @ suc @ B ) ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(49,axiom,
    a != b,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75__096a_A_126_061_Ab_096) ).

thf(907,plain,
    a != b,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(93,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ ( hAPP_nat_nat @ suc @ B ) ) )
    <=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_647_Suc__less__eq) ).

thf(1053,plain,
    ! [A: nat,B: nat] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ ( hAPP_nat_nat @ suc @ B ) ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ ( hAPP_nat_nat @ suc @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(212,axiom,
    ! [A: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
    <=> ? [B: nat] :
          ( A
          = ( hAPP_nat_nat @ suc @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_669_gr0__conv__Suc) ).

thf(1499,plain,
    ! [A: nat] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
       => ? [B: nat] :
            ( A
            = ( hAPP_nat_nat @ suc @ B ) ) )
      & ( ? [B: nat] :
            ( A
            = ( hAPP_nat_nat @ suc @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(290,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( B = C )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_ord__eq__le__trans) ).

thf(1790,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( B = C )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(442,axiom,
    ! [A: fun_Pr1055212137t_bool] : ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_f314169011l_bool @ ord_le565024179t_bool @ A ) @ top_to126038883t_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_409_subset__UNIV) ).

thf(2454,plain,
    ! [A: fun_Pr1055212137t_bool] : ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_f314169011l_bool @ ord_le565024179t_bool @ A ) @ top_to126038883t_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).

thf(159,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) )
    <=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
        | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_624_add__gr__0) ).

thf(1300,plain,
    ! [A: nat,B: nat] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) )
       => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(503,axiom,
    ! [A: nat,B: nat] :
      ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_linorder__le__cases) ).

thf(2688,plain,
    ! [A: nat,B: nat] :
      ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).

thf(656,axiom,
    ! [A: fun_Ar500372357t_bool] : ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ A ) @ top_to1324311617l_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_iso__tuple__UNIV__I) ).

thf(3273,plain,
    ! [A: fun_Ar500372357t_bool] : ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ A ) @ top_to1324311617l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).

thf(673,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_order__antisym) ).

thf(3334,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).

thf(130,axiom,
    ( top_to126038883t_bool
    = ( collec1209019986le_alt @ ( hAPP_b1263785481t_bool @ cOMBK_1566242880le_alt @ fTrue ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_UNIV__def) ).

thf(1188,plain,
    ( top_to126038883t_bool
    = ( collec1209019986le_alt @ ( hAPP_b1263785481t_bool @ cOMBK_1566242880le_alt @ fTrue ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(129,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ C ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_525_add__leD1) ).

thf(1186,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ C ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(643,axiom,
    ! [A: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ top_to1257323279t_bool ) @ A ) )
     => ( A = top_to1257323279t_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_362_top__le) ).

thf(3202,plain,
    ! [A: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ top_to1257323279t_bool ) @ A ) )
     => ( A = top_to1257323279t_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).

thf(309,axiom,
    ! [A: fun_Pr1055212137t_bool] : ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_f314169011l_bool @ ord_le565024179t_bool @ A ) @ top_to126038883t_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_344_top__greatest) ).

thf(1869,plain,
    ! [A: fun_Pr1055212137t_bool] : ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_f314169011l_bool @ ord_le565024179t_bool @ A ) @ top_to126038883t_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(222,axiom,
    ! [A: fun_Ar552120407i_bool,B: fun_Pr1055212137t_bool] :
      ( ( hAPP_f1957024259i_bool @ ( hAPP_f676424105i_bool @ cOMBK_854051296t_bool @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__) ).

thf(1538,plain,
    ! [A: fun_Ar552120407i_bool,B: fun_Pr1055212137t_bool] :
      ( ( hAPP_f1957024259i_bool @ ( hAPP_f676424105i_bool @ cOMBK_854051296t_bool @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(451,axiom,
    ~ ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ a ) @ b ) ) @ lba ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78__096_Ia_M_Ab_J_A_126_058_ALba_096) ).

thf(2486,plain,
    ~ ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ a ) @ b ) ) @ lba ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).

thf(681,axiom,
    ! [A: nat] : ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( hAPP_n1699378549t_bool @ ( hAPP_f229349961t_bool @ cOMBC_nat_nat_bool @ ord_less_eq_nat ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_602_finite__Collect__le__nat) ).

thf(3359,plain,
    ! [A: nat] : ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( hAPP_n1699378549t_bool @ ( hAPP_f229349961t_bool @ cOMBC_nat_nat_bool @ ord_less_eq_nat ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).

thf(671,axiom,
    ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ e ) @ d ) ) @ ( hAPP_f792184801t_bool @ f @ ( cOMBS_1921392482t_bool @ ( cOMBS_811328630t_bool @ ( hAPP_f509814255t_bool @ ( cOMBB_231886989e_indi @ if_fun1658569689t_bool ) @ ( hAPP_n924210722i_bool @ ( hAPP_f62620517i_bool @ cOMBC_922322901t_bool @ ( hAPP_f1381130897t_bool @ ( cOMBB_981137617e_indi @ ord_less_nat ) @ h ) ) @ n ) ) @ ( hAPP_A658738638t_bool @ ( hAPP_f293545699t_bool @ cOMBC_18834461t_bool @ ( hAPP_f842954860t_bool @ ( cOMBB_117136048e_indi @ arrow_741591990_mktop ) @ p ) ) @ e ) ) @ ( cOMBS_1921392482t_bool @ ( cOMBS_811328630t_bool @ ( hAPP_f509814255t_bool @ ( cOMBB_231886989e_indi @ if_fun1658569689t_bool ) @ ( hAPP_n924210722i_bool @ ( hAPP_f62620517i_bool @ cOMBC_922322901t_bool @ ( hAPP_f1381130897t_bool @ ( cOMBB_981137617e_indi @ fequal_nat ) @ h ) ) @ n ) ) @ ( hAPP_A658738638t_bool @ ( hAPP_f293545699t_bool @ cOMBC_18834461t_bool @ ( hAPP_A102926893t_bool @ ( hAPP_f141075873t_bool @ cOMBC_1505804284t_bool @ ( hAPP_f576849227t_bool @ ( cOMBB_656639247e_indi @ arrow_1475523868_above ) @ p ) ) @ c ) ) @ e ) ) @ ( hAPP_A658738638t_bool @ ( hAPP_f293545699t_bool @ cOMBC_18834461t_bool @ ( hAPP_f842954860t_bool @ ( cOMBB_117136048e_indi @ arrow_592884904_mkbot ) @ p ) ) @ e ) ) ) ) ) )
  <=> ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ b ) @ a ) ) @ ( hAPP_f792184801t_bool @ f @ ( hAPP_f311418073t_bool @ ( hAPP_f1302245795t_bool @ cOMBC_1490589522t_bool @ ( hAPP_f1755759597t_bool @ ( hAPP_f1328803787t_bool @ cOMBC_1190055014t_bool @ ( hAPP_f509814255t_bool @ ( cOMBB_231886989e_indi @ if_fun1658569689t_bool ) @ ( hAPP_n924210722i_bool @ ( hAPP_f62620517i_bool @ cOMBC_922322901t_bool @ ( hAPP_f1381130897t_bool @ ( cOMBB_981137617e_indi @ ord_less_nat ) @ h ) ) @ n ) ) ) @ lab ) ) @ lba ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72__096_Ie_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amk) ).

thf(3329,plain,
    ( ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ e ) @ d ) ) @ ( hAPP_f792184801t_bool @ f @ ( cOMBS_1921392482t_bool @ ( cOMBS_811328630t_bool @ ( hAPP_f509814255t_bool @ ( cOMBB_231886989e_indi @ if_fun1658569689t_bool ) @ ( hAPP_n924210722i_bool @ ( hAPP_f62620517i_bool @ cOMBC_922322901t_bool @ ( hAPP_f1381130897t_bool @ ( cOMBB_981137617e_indi @ ord_less_nat ) @ h ) ) @ n ) ) @ ( hAPP_A658738638t_bool @ ( hAPP_f293545699t_bool @ cOMBC_18834461t_bool @ ( hAPP_f842954860t_bool @ ( cOMBB_117136048e_indi @ arrow_741591990_mktop ) @ p ) ) @ e ) ) @ ( cOMBS_1921392482t_bool @ ( cOMBS_811328630t_bool @ ( hAPP_f509814255t_bool @ ( cOMBB_231886989e_indi @ if_fun1658569689t_bool ) @ ( hAPP_n924210722i_bool @ ( hAPP_f62620517i_bool @ cOMBC_922322901t_bool @ ( hAPP_f1381130897t_bool @ ( cOMBB_981137617e_indi @ fequal_nat ) @ h ) ) @ n ) ) @ ( hAPP_A658738638t_bool @ ( hAPP_f293545699t_bool @ cOMBC_18834461t_bool @ ( hAPP_A102926893t_bool @ ( hAPP_f141075873t_bool @ cOMBC_1505804284t_bool @ ( hAPP_f576849227t_bool @ ( cOMBB_656639247e_indi @ arrow_1475523868_above ) @ p ) ) @ c ) ) @ e ) ) @ ( hAPP_A658738638t_bool @ ( hAPP_f293545699t_bool @ cOMBC_18834461t_bool @ ( hAPP_f842954860t_bool @ ( cOMBB_117136048e_indi @ arrow_592884904_mkbot ) @ p ) ) @ e ) ) ) ) ) )
     => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ b ) @ a ) ) @ ( hAPP_f792184801t_bool @ f @ ( hAPP_f311418073t_bool @ ( hAPP_f1302245795t_bool @ cOMBC_1490589522t_bool @ ( hAPP_f1755759597t_bool @ ( hAPP_f1328803787t_bool @ cOMBC_1190055014t_bool @ ( hAPP_f509814255t_bool @ ( cOMBB_231886989e_indi @ if_fun1658569689t_bool ) @ ( hAPP_n924210722i_bool @ ( hAPP_f62620517i_bool @ cOMBC_922322901t_bool @ ( hAPP_f1381130897t_bool @ ( cOMBB_981137617e_indi @ ord_less_nat ) @ h ) ) @ n ) ) ) @ lab ) ) @ lba ) ) ) ) )
    & ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ b ) @ a ) ) @ ( hAPP_f792184801t_bool @ f @ ( hAPP_f311418073t_bool @ ( hAPP_f1302245795t_bool @ cOMBC_1490589522t_bool @ ( hAPP_f1755759597t_bool @ ( hAPP_f1328803787t_bool @ cOMBC_1190055014t_bool @ ( hAPP_f509814255t_bool @ ( cOMBB_231886989e_indi @ if_fun1658569689t_bool ) @ ( hAPP_n924210722i_bool @ ( hAPP_f62620517i_bool @ cOMBC_922322901t_bool @ ( hAPP_f1381130897t_bool @ ( cOMBB_981137617e_indi @ ord_less_nat ) @ h ) ) @ n ) ) ) @ lab ) ) @ lba ) ) ) )
     => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ e ) @ d ) ) @ ( hAPP_f792184801t_bool @ f @ ( cOMBS_1921392482t_bool @ ( cOMBS_811328630t_bool @ ( hAPP_f509814255t_bool @ ( cOMBB_231886989e_indi @ if_fun1658569689t_bool ) @ ( hAPP_n924210722i_bool @ ( hAPP_f62620517i_bool @ cOMBC_922322901t_bool @ ( hAPP_f1381130897t_bool @ ( cOMBB_981137617e_indi @ ord_less_nat ) @ h ) ) @ n ) ) @ ( hAPP_A658738638t_bool @ ( hAPP_f293545699t_bool @ cOMBC_18834461t_bool @ ( hAPP_f842954860t_bool @ ( cOMBB_117136048e_indi @ arrow_741591990_mktop ) @ p ) ) @ e ) ) @ ( cOMBS_1921392482t_bool @ ( cOMBS_811328630t_bool @ ( hAPP_f509814255t_bool @ ( cOMBB_231886989e_indi @ if_fun1658569689t_bool ) @ ( hAPP_n924210722i_bool @ ( hAPP_f62620517i_bool @ cOMBC_922322901t_bool @ ( hAPP_f1381130897t_bool @ ( cOMBB_981137617e_indi @ fequal_nat ) @ h ) ) @ n ) ) @ ( hAPP_A658738638t_bool @ ( hAPP_f293545699t_bool @ cOMBC_18834461t_bool @ ( hAPP_A102926893t_bool @ ( hAPP_f141075873t_bool @ cOMBC_1505804284t_bool @ ( hAPP_f576849227t_bool @ ( cOMBB_656639247e_indi @ arrow_1475523868_above ) @ p ) ) @ c ) ) @ e ) ) @ ( hAPP_A658738638t_bool @ ( hAPP_f293545699t_bool @ cOMBC_18834461t_bool @ ( hAPP_f842954860t_bool @ ( cOMBB_117136048e_indi @ arrow_592884904_mkbot ) @ p ) ) @ e ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).

thf(718,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ B )
      | ~ ( hBOOL @ A )
      | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_1_1_U) ).

thf(3488,plain,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ B )
      | ~ ( hBOOL @ A )
      | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).

thf(546,axiom,
    ! [A: product_unit] : ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ A ) @ top_to1257323279t_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_iso__tuple__UNIV__I) ).

thf(2838,plain,
    ! [A: product_unit] : ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ A ) @ top_to1257323279t_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).

thf(720,axiom,
    ! [A: bool,B: fun_bool_bool] :
      ( ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ A ) @ B ) )
    <=> ( hBOOL @ ( hAPP_bool_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_mem__def) ).

thf(3493,plain,
    ! [A: bool,B: fun_bool_bool] :
      ( ( ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_bool_bool @ B @ A ) ) )
      & ( ( hBOOL @ ( hAPP_bool_bool @ B @ A ) )
       => ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).

thf(155,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) )
    <=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
        | ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_646_less__Suc__eq) ).

thf(1284,plain,
    ! [A: nat,B: nat] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) )
       => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
          | ( A = B ) ) )
      & ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
          | ( A = B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(371,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ B ) )
     => ( A != B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_less__imp__neq) ).

thf(2145,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ B ) )
     => ( A != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(692,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
     => ( ( B != A )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_315_xt1_I11_J) ).

thf(3388,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
     => ( ( B != A )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).

thf(513,axiom,
    ! [A: nat,B: fun_na1392860600e_indi,C: fun_nat_bool,D: fun_na457272970i_bool] :
      ( ( hBOOL @ ( hAPP_f728118466l_bool @ ( hAPP_f138236715l_bool @ member76848293e_indi @ B ) @ ( pi_nat1905227924e_indi @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ ( hAPP_n1048492170e_indi @ B @ A ) ) @ ( hAPP_n924210722i_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_PiE) ).

thf(2728,plain,
    ! [A: nat,B: fun_na1392860600e_indi,C: fun_nat_bool,D: fun_na457272970i_bool] :
      ( ( hBOOL @ ( hAPP_f728118466l_bool @ ( hAPP_f138236715l_bool @ member76848293e_indi @ B ) @ ( pi_nat1905227924e_indi @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ ( hAPP_n1048492170e_indi @ B @ A ) ) @ ( hAPP_n924210722i_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).

thf(178,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) )
    <=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_548_nat__add__left__cancel__less) ).

thf(1372,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) ) )
      & ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(153,axiom,
    ! [A: fun_fu1015689055l_bool,B: fun_Ar500372357t_bool] :
      ( ( hAPP_f1498158055l_bool @ ( hAPP_f422714471l_bool @ cOMBK_1446432t_bool @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_325) ).

thf(1272,plain,
    ! [A: fun_fu1015689055l_bool,B: fun_Ar500372357t_bool] :
      ( ( hAPP_f1498158055l_bool @ ( hAPP_f422714471l_bool @ cOMBK_1446432t_bool @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(40,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ C ) )
     => ~ ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) )
         => ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_524_add__leE) ).

thf(876,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ C ) )
     => ~ ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) )
         => ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(33,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ ( hAPP_nat_nat @ suc @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_629_Suc__mono) ).

thf(859,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ ( hAPP_nat_nat @ suc @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(248,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B )
        = ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ B ) )
    <=> ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_538_nat__add__right__cancel) ).

thf(1617,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B )
          = ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ B ) )
       => ( A = C ) )
      & ( ( A = C )
       => ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B )
          = ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(349,axiom,
    ! [A: produc1840315303le_alt,B: fun_Pr1055212137t_bool,C: fun_Pr1055212137t_bool] :
      ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_f314169011l_bool @ ord_le565024179t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_487_in__mono) ).

thf(2056,plain,
    ! [A: produc1840315303le_alt,B: fun_Pr1055212137t_bool,C: fun_Pr1055212137t_bool] :
      ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_f314169011l_bool @ ord_le565024179t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(186,axiom,
    ! [A: nat] :
      ( ( one_one_nat = A )
    <=> ( A = one_one_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_421_one__reorient) ).

thf(1404,plain,
    ! [A: nat] :
      ( ( ( one_one_nat = A )
       => ( A = one_one_nat ) )
      & ( ( A = one_one_nat )
       => ( one_one_nat = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(224,axiom,
    ! [A: fun_fu1291054887l_bool,B: fun_fu775006535l_bool,C: fun_Ar500372357t_bool] :
      ( ( hAPP_f1766661605l_bool @ ( hAPP_f626396309l_bool @ ( hAPP_f228579435l_bool @ cOMBC_941833506l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__) ).

thf(1543,plain,
    ! [A: fun_fu1291054887l_bool,B: fun_fu775006535l_bool,C: fun_Ar500372357t_bool] :
      ( ( hAPP_f1766661605l_bool @ ( hAPP_f626396309l_bool @ ( hAPP_f228579435l_bool @ cOMBC_941833506l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(283,axiom,
    ! [A: fun_fu775006535l_bool,B: fun_Ar500372357t_bool,C: fun_fu775006535l_bool] :
      ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f95487087l_bool @ ord_le1871091345l_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_477_set__rev__mp) ).

thf(1766,plain,
    ! [A: fun_fu775006535l_bool,B: fun_Ar500372357t_bool,C: fun_fu775006535l_bool] :
      ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f95487087l_bool @ ord_le1871091345l_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(320,axiom,
    ! [A: fun_fu775006535l_bool] : ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f95487087l_bool @ ord_le1871091345l_bool @ A ) @ top_to1324311617l_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_343_top__greatest) ).

thf(1898,plain,
    ! [A: fun_fu775006535l_bool] : ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f95487087l_bool @ ord_le1871091345l_bool @ A ) @ top_to1324311617l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(150,axiom,
    ! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_612_le0) ).

thf(1257,plain,
    ! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(623,axiom,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool,C: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_522_psubset__trans) ).

thf(3124,plain,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool,C: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).

thf(593,axiom,
    ! [A: fun_Pr1055212137t_bool,B: fun_Pr359894313l_bool,C: fun_Pr1055212137t_bool] :
      ( ! [D: produc1840315303le_alt] :
          ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ D ) @ C ) )
         => ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ ( hAPP_P166437127t_bool @ A @ D ) ) @ ( hAPP_P1830623733l_bool @ B @ D ) ) ) )
     => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ A ) @ ( pi_Pro226591613t_bool @ C @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_389_Pi__I) ).

thf(2992,plain,
    ! [A: fun_Pr1055212137t_bool,B: fun_Pr359894313l_bool,C: fun_Pr1055212137t_bool] :
      ( ! [D: produc1840315303le_alt] :
          ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ D ) @ C ) )
         => ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ ( hAPP_P166437127t_bool @ A @ D ) ) @ ( hAPP_P1830623733l_bool @ B @ D ) ) ) )
     => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ A ) @ ( pi_Pro226591613t_bool @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).

thf(209,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ suc @ A ) ) )
      <=> ( B = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_658_le__less__Suc__eq) ).

thf(1485,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
     => ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ suc @ A ) ) )
         => ( B = A ) )
        & ( ( B = A )
         => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ suc @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(213,axiom,
    ! [A: nat] :
      ( A
     != ( hAPP_nat_nat @ suc @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_641_n__not__Suc__n) ).

thf(1506,plain,
    ! [A: nat] :
      ( A
     != ( hAPP_nat_nat @ suc @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(277,axiom,
    ! [A: arrow_2115524757e_indi,B: fun_Ar369661729le_alt,C: fun_Ar552120407i_bool,D: fun_Ar500372357t_bool] :
      ( ( hBOOL @ ( hAPP_f1625336439l_bool @ ( hAPP_f1269190349l_bool @ member418553588le_alt @ B ) @ ( pi_Arr914482869le_alt @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A353813823le_alt @ B @ A ) ) @ ( hAPP_A1174518481t_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_PiE) ).

thf(1749,plain,
    ! [A: arrow_2115524757e_indi,B: fun_Ar369661729le_alt,C: fun_Ar552120407i_bool,D: fun_Ar500372357t_bool] :
      ( ( hBOOL @ ( hAPP_f1625336439l_bool @ ( hAPP_f1269190349l_bool @ member418553588le_alt @ B ) @ ( pi_Arr914482869le_alt @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A353813823le_alt @ B @ A ) ) @ ( hAPP_A1174518481t_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(649,axiom,
    ! [A: fun_nat_bool] :
      ( ( A != top_top_fun_nat_bool )
    <=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ top_top_fun_nat_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_less__top) ).

thf(3224,plain,
    ! [A: fun_nat_bool] :
      ( ( ( A != top_top_fun_nat_bool )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ top_top_fun_nat_bool ) ) )
      & ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ top_top_fun_nat_bool ) )
       => ( A != top_top_fun_nat_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).

thf(118,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_572_termination__basic__simps_I2_J) ).

thf(1140,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(461,axiom,
    ! [A: nat,B: fun_nat_bool] :
      ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ zero_zero_nat ) @ B ) )
     => ( ( finite_card_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( hAPP_f1146629647l_bool @ ( cOMBB_1015721476ol_nat @ fconj ) @ ( hAPP_f800510211t_bool @ ( hAPP_f1722879237t_bool @ cOMBC_226598744l_bool @ ( hAPP_f66927821l_bool @ ( cOMBB_1146692694ol_nat @ member_nat ) @ suc ) ) @ B ) ) @ ( hAPP_n1699378549t_bool @ ( hAPP_f229349961t_bool @ cOMBC_nat_nat_bool @ ord_less_nat ) @ A ) ) ) )
        = ( finite_card_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( hAPP_f1146629647l_bool @ ( cOMBB_1015721476ol_nat @ fconj ) @ ( hAPP_f800510211t_bool @ ( hAPP_f1722879237t_bool @ cOMBC_226598744l_bool @ member_nat ) @ B ) ) @ ( hAPP_n1699378549t_bool @ ( hAPP_f229349961t_bool @ cOMBC_nat_nat_bool @ ord_less_nat ) @ ( hAPP_nat_nat @ suc @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_683_card__less__Suc2) ).

thf(2511,plain,
    ! [A: nat,B: fun_nat_bool] :
      ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ zero_zero_nat ) @ B ) )
     => ( ( finite_card_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( hAPP_f1146629647l_bool @ ( cOMBB_1015721476ol_nat @ fconj ) @ ( hAPP_f800510211t_bool @ ( hAPP_f1722879237t_bool @ cOMBC_226598744l_bool @ ( hAPP_f66927821l_bool @ ( cOMBB_1146692694ol_nat @ member_nat ) @ suc ) ) @ B ) ) @ ( hAPP_n1699378549t_bool @ ( hAPP_f229349961t_bool @ cOMBC_nat_nat_bool @ ord_less_nat ) @ A ) ) ) )
        = ( finite_card_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( hAPP_f1146629647l_bool @ ( cOMBB_1015721476ol_nat @ fconj ) @ ( hAPP_f800510211t_bool @ ( hAPP_f1722879237t_bool @ cOMBC_226598744l_bool @ member_nat ) @ B ) ) @ ( hAPP_n1699378549t_bool @ ( hAPP_f229349961t_bool @ cOMBC_nat_nat_bool @ ord_less_nat ) @ ( hAPP_nat_nat @ suc @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).

thf(621,axiom,
    ! [A: fun_Ar500372357t_bool] : ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ A ) @ top_to1324311617l_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_UNIV__I) ).

thf(3117,plain,
    ! [A: fun_Ar500372357t_bool] : ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ A ) @ top_to1324311617l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).

thf(555,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
     => ( ( C = A )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_ord__less__eq__trans) ).

thf(2860,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
     => ( ( C = A )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).

thf(722,axiom,
    ! [A: fun_Pr1055212137t_bool] :
      ~ ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_f314169011l_bool @ ord_le466311871t_bool @ top_to126038883t_bool ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_not__top__less) ).

thf(3520,plain,
    ! [A: fun_Pr1055212137t_bool] :
      ~ ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_f314169011l_bool @ ord_le466311871t_bool @ top_to126038883t_bool ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).

thf(684,axiom,
    ! [A: fun_Pr1055212137t_bool,B: fun_fu603957077t_unit,C: fun_fu1015689055l_bool,D: fun_fu105994665t_bool] :
      ( ( hBOOL @ ( hAPP_f1919464799l_bool @ ( hAPP_f803471205l_bool @ member1667929154t_unit @ B ) @ ( pi_fun116255921t_unit @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ ( hAPP_f739946663t_unit @ B @ A ) ) @ ( hAPP_f862859457t_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_PiE) ).

thf(3366,plain,
    ! [A: fun_Pr1055212137t_bool,B: fun_fu603957077t_unit,C: fun_fu1015689055l_bool,D: fun_fu105994665t_bool] :
      ( ( hBOOL @ ( hAPP_f1919464799l_bool @ ( hAPP_f803471205l_bool @ member1667929154t_unit @ B ) @ ( pi_fun116255921t_unit @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ ( hAPP_f739946663t_unit @ B @ A ) ) @ ( hAPP_f862859457t_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).

thf(557,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ B ) )
     => ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_order__less__not__sym) ).

thf(2865,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ B ) )
     => ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).

thf(697,axiom,
    ! [A: produc1840315303le_alt,B: fun_Pr1055212137t_bool] :
      ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ A ) @ B ) )
    <=> ( hBOOL @ ( hAPP_P166437127t_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_mem__def) ).

thf(3400,plain,
    ! [A: produc1840315303le_alt,B: fun_Pr1055212137t_bool] :
      ( ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_P166437127t_bool @ B @ A ) ) )
      & ( ( hBOOL @ ( hAPP_P166437127t_bool @ B @ A ) )
       => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).

thf(444,axiom,
    ! [A: nat,B: nat] : ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( hAPP_n1699378549t_bool @ ( ord_at4362885an_nat @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_697_finite__atLeastLessThan) ).

thf(2458,plain,
    ! [A: nat,B: nat] : ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( hAPP_n1699378549t_bool @ ( ord_at4362885an_nat @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).

thf(256,axiom,
    ! [A: fun_fu2016509975e_indi,B: fun_Ar500372357t_bool,C: fun_Ar552120407i_bool,D: fun_fu1015689055l_bool] :
      ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ B ) @ ( pi_Arr487970267t_bool @ C @ ( hAPP_f1793492343l_bool @ cOMBK_1595020336e_indi @ D ) ) ) )
     => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( inj_on194063285t_bool @ B ) @ C ) )
       => ( ( hBOOL @ ( hAPP_f372503329l_bool @ ( hAPP_f43388905l_bool @ member527726724e_indi @ A ) @ ( pi_fun1342736627e_indi @ D @ ( hAPP_f676424105i_bool @ cOMBK_854051296t_bool @ C ) ) ) )
         => ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( inj_on1048829645e_indi @ A ) @ D ) )
           => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ finite1350902018e_indi @ C ) )
             => ( ( hBOOL @ ( hAPP_f1021703871l_bool @ finite775027132t_bool @ D ) )
               => ( ( finite783399747e_indi @ C )
                  = ( finite1445836347t_bool @ D ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_599_card__bij) ).

thf(1649,plain,
    ! [A: fun_fu2016509975e_indi,B: fun_Ar500372357t_bool,C: fun_Ar552120407i_bool,D: fun_fu1015689055l_bool] :
      ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ B ) @ ( pi_Arr487970267t_bool @ C @ ( hAPP_f1793492343l_bool @ cOMBK_1595020336e_indi @ D ) ) ) )
     => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( inj_on194063285t_bool @ B ) @ C ) )
       => ( ( hBOOL @ ( hAPP_f372503329l_bool @ ( hAPP_f43388905l_bool @ member527726724e_indi @ A ) @ ( pi_fun1342736627e_indi @ D @ ( hAPP_f676424105i_bool @ cOMBK_854051296t_bool @ C ) ) ) )
         => ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( inj_on1048829645e_indi @ A ) @ D ) )
           => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ finite1350902018e_indi @ C ) )
             => ( ( hBOOL @ ( hAPP_f1021703871l_bool @ finite775027132t_bool @ D ) )
               => ( ( finite783399747e_indi @ C )
                  = ( finite1445836347t_bool @ D ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(353,axiom,
    ! [A: product_unit,B: fun_Product_unit_nat,C: fun_Pr1643180309t_bool,D: fun_Pr1029464120t_bool] :
      ( ( hBOOL @ ( hAPP_f339859954l_bool @ ( hAPP_f1950626059l_bool @ member87760213it_nat @ B ) @ ( pi_Product_unit_nat @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ ( hAPP_P426034740it_nat @ B @ A ) ) @ ( hAPP_P32877782t_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_PiE) ).

thf(2088,plain,
    ! [A: product_unit,B: fun_Product_unit_nat,C: fun_Pr1643180309t_bool,D: fun_Pr1029464120t_bool] :
      ( ( hBOOL @ ( hAPP_f339859954l_bool @ ( hAPP_f1950626059l_bool @ member87760213it_nat @ B ) @ ( pi_Product_unit_nat @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ ( hAPP_P426034740it_nat @ B @ A ) ) @ ( hAPP_P32877782t_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(744,axiom,
    ! [A: produc1840315303le_alt,B: fun_Pr1055212137t_bool,C: fun_Pr1055212137t_bool] :
      ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_f314169011l_bool @ ord_le565024179t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_470_set__mp) ).

thf(3589,plain,
    ! [A: produc1840315303le_alt,B: fun_Pr1055212137t_bool,C: fun_Pr1055212137t_bool] :
      ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_f314169011l_bool @ ord_le565024179t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).

thf(127,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) )
     => ~ ! [C: nat] :
            ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) )
           => ( B
             != ( hAPP_nat_nat @ suc @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_691_Suc__lessE) ).

thf(1180,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) )
     => ~ ! [C: nat] :
            ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) )
           => ( B
             != ( hAPP_nat_nat @ suc @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(564,axiom,
    ! [A: fun_nat_bool,B: nat] : ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( hAPP_f1146629647l_bool @ ( cOMBB_1015721476ol_nat @ fconj ) @ A ) @ ( hAPP_n1699378549t_bool @ ( hAPP_f229349961t_bool @ cOMBC_nat_nat_bool @ ord_less_nat ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_606_finite__M__bounded__by__nat) ).

thf(2885,plain,
    ! [A: fun_nat_bool,B: nat] : ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( hAPP_f1146629647l_bool @ ( cOMBB_1015721476ol_nat @ fconj ) @ A ) @ ( hAPP_n1699378549t_bool @ ( hAPP_f229349961t_bool @ cOMBC_nat_nat_bool @ ord_less_nat ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).

thf(585,axiom,
    ! [A: product_unit,B: fun_Pr1643180309t_bool,C: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_464_set__mp) ).

thf(2960,plain,
    ! [A: product_unit,B: fun_Pr1643180309t_bool,C: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).

thf(165,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_566_add__le__mono1) ).

thf(1321,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(640,axiom,
    ! [A: arrow_2115524757e_indi,B: fun_Ar1744566822di_nat] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( inj_on886403158di_nat @ B ) @ top_to1678393681i_bool ) )
     => ( ( hAPP_n1048492170e_indi @ ( hilber506087739di_nat @ top_to1678393681i_bool @ B ) @ ( hAPP_A1450069362di_nat @ B @ A ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_inv__f__f) ).

thf(3188,plain,
    ! [A: arrow_2115524757e_indi,B: fun_Ar1744566822di_nat] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( inj_on886403158di_nat @ B ) @ top_to1678393681i_bool ) )
     => ( ( hAPP_n1048492170e_indi @ ( hilber506087739di_nat @ top_to1678393681i_bool @ B ) @ ( hAPP_A1450069362di_nat @ B @ A ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).

thf(187,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_422_add__le__imp__le__left) ).

thf(1412,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(215,axiom,
    ! [A: fun_Ar2045874810t_bool,B: nat,C: arrow_2115524757e_indi] :
      ( ( hAPP_A1888055029i_bool @ ( hAPP_n924210722i_bool @ ( hAPP_f62620517i_bool @ cOMBC_922322901t_bool @ A ) @ B ) @ C )
      = ( hAPP_nat_bool @ ( hAPP_A981395480t_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_000) ).

thf(1517,plain,
    ! [A: fun_Ar2045874810t_bool,B: nat,C: arrow_2115524757e_indi] :
      ( ( hAPP_A1888055029i_bool @ ( hAPP_n924210722i_bool @ ( hAPP_f62620517i_bool @ cOMBC_922322901t_bool @ A ) @ B ) @ C )
      = ( hAPP_nat_bool @ ( hAPP_A981395480t_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(308,axiom,
    ! [A: fun_na1392860600e_indi,B: fun_Ar1744566822di_nat] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( inj_on886403158di_nat @ B ) @ top_to1678393681i_bool ) )
     => ( ! [C: nat] :
            ( ( hAPP_A1450069362di_nat @ B @ ( hAPP_n1048492170e_indi @ A @ C ) )
            = C )
       => ( ( hilber506087739di_nat @ top_to1678393681i_bool @ B )
          = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_393_inj__imp__inv__eq) ).

thf(1866,plain,
    ! [A: fun_na1392860600e_indi,B: fun_Ar1744566822di_nat] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( inj_on886403158di_nat @ B ) @ top_to1678393681i_bool ) )
     => ( ! [C: nat] :
            ( ( hAPP_A1450069362di_nat @ B @ ( hAPP_n1048492170e_indi @ A @ C ) )
            = C )
       => ( ( hilber506087739di_nat @ top_to1678393681i_bool @ B )
          = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(746,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_330_order__le__less__trans) ).

thf(3593,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).

thf(506,axiom,
    ! [A: fun_Pr1055212137t_bool] :
      ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_f314169011l_bool @ ord_le565024179t_bool @ top_to126038883t_bool ) @ A ) )
    <=> ( A = top_to126038883t_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_352_top__unique) ).

thf(2696,plain,
    ! [A: fun_Pr1055212137t_bool] :
      ( ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_f314169011l_bool @ ord_le565024179t_bool @ top_to126038883t_bool ) @ A ) )
       => ( A = top_to126038883t_bool ) )
      & ( ( A = top_to126038883t_bool )
       => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_f314169011l_bool @ ord_le565024179t_bool @ top_to126038883t_bool ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).

thf(228,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( ( B
         != ( hAPP_nat_nat @ suc @ A ) )
       => ~ ! [C: nat] :
              ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) )
             => ( B
               != ( hAPP_nat_nat @ suc @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_690_lessE) ).

thf(1553,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( ( B
         != ( hAPP_nat_nat @ suc @ A ) )
       => ~ ! [C: nat] :
              ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) )
             => ( B
               != ( hAPP_nat_nat @ suc @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(45,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
     => ( ( B != A )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_318_xt1_I11_J) ).

thf(891,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
     => ( ( B != A )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(394,axiom,
    ! [A: fun_nat_nat] :
      ( ! [B: nat,C: nat] :
          ( ( ( hAPP_nat_nat @ A @ B )
            = ( hAPP_nat_nat @ A @ C ) )
         => ( B = C ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ A ) @ top_top_fun_nat_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_397_injI) ).

thf(2209,plain,
    ! [A: fun_nat_nat] :
      ( ! [B: nat,C: nat] :
          ( ( ( hAPP_nat_nat @ A @ B )
            = ( hAPP_nat_nat @ A @ C ) )
         => ( B = C ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ A ) @ top_top_fun_nat_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).

thf(197,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ D ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ D ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_552_add__less__mono) ).

thf(1448,plain,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ D ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ D ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(453,axiom,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_453_psubset__imp__subset) ).

thf(2490,plain,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).

thf(384,axiom,
    hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ a ) @ b ) ) @ lab ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096) ).

thf(2187,plain,
    hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ a ) @ b ) ) @ lab ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(359,axiom,
    ! [A: fun_fu1595299477t_bool] : ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ A ) @ top_to2013953873l_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_iso__tuple__UNIV__I) ).

thf(2110,plain,
    ! [A: fun_fu1595299477t_bool] : ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ A ) @ top_to2013953873l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(670,axiom,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ B ) )
    <=> ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ A ) @ B ) )
        & ( A != B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_448_psubset__eq) ).

thf(3320,plain,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool] :
      ( ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ B ) )
       => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ A ) @ B ) )
          & ( A != B ) ) )
      & ( ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ A ) @ B ) )
          & ( A != B ) )
       => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).

thf(29,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ? [C: nat] :
          ( B
          = ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_685_less__imp__Suc__add) ).

thf(844,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ? [C: nat] :
          ( B
          = ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(199,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ! [C: nat] :
          ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ B ) )
         => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_507_subsetI) ).

thf(1453,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ! [C: nat] :
          ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ B ) )
         => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(206,axiom,
    ! [A: nat,B: nat,C: fun_nat_nat] :
      ( ! [D: nat,E: nat] :
          ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ D ) @ E ) )
         => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ C @ D ) ) @ ( hAPP_nat_nat @ C @ E ) ) ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ ( hAPP_nat_nat @ C @ A ) ) @ B ) ) @ ( hAPP_nat_nat @ C @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_568_mono__nat__linear__lb) ).

thf(1476,plain,
    ! [A: nat,B: nat,C: fun_nat_nat] :
      ( ! [D: nat,E: nat] :
          ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ D ) @ E ) )
         => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ C @ D ) ) @ ( hAPP_nat_nat @ C @ E ) ) ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ ( hAPP_nat_nat @ C @ A ) ) @ B ) ) @ ( hAPP_nat_nat @ C @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(717,axiom,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool,C: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ B ) @ C ) )
     => ( ( B = A )
       => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_xt1_I2_J) ).

thf(3484,plain,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool,C: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ B ) @ C ) )
     => ( ( B = A )
       => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).

thf(96,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
     => ( ( A != B )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_order__le__neq__trans) ).

thf(1062,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
     => ( ( A != B )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(103,axiom,
    ! [A: nat,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_441_subsetD) ).

thf(1101,plain,
    ! [A: nat,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(758,axiom,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool,C: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_xt1_I10_J) ).

thf(3630,plain,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool,C: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).

thf(734,axiom,
    hBOOL @ ( hAPP_f1397511071l_bool @ ( inj_on886403158di_nat @ h ) @ top_to1678393681i_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_injh) ).

thf(3561,plain,
    hBOOL @ ( hAPP_f1397511071l_bool @ ( inj_on886403158di_nat @ h ) @ top_to1678393681i_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).

thf(433,axiom,
    ! [A: fun_Pr1055212137t_bool,B: fun_Pr1055212137t_bool] :
      ( ! [C: arrow_931160158le_alt,D: arrow_931160158le_alt] :
          ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ C ) @ D ) ) @ B ) )
        <=> ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ C ) @ D ) ) @ A ) ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_pred__equals__eq2) ).

thf(2416,plain,
    ! [A: fun_Pr1055212137t_bool,B: fun_Pr1055212137t_bool] :
      ( ( ! [C: arrow_931160158le_alt,D: arrow_931160158le_alt] :
            ( ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ C ) @ D ) ) @ B ) ) ) )
       => ( B = A ) )
      & ( ( B = A )
       => ! [C: arrow_931160158le_alt,D: arrow_931160158le_alt] :
            ( ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ C ) @ D ) ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).

thf(18,axiom,
    ! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_623_less__eq__nat_Osimps_I1_J) ).

thf(813,plain,
    ! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(592,axiom,
    ! [A: nat,B: nat,C: fun_nat_nat] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ C ) @ top_top_fun_nat_bool ) )
     => ( ( ( hAPP_nat_nat @ C @ A )
          = B )
       => ( ( hAPP_nat_nat @ ( hilber195283148at_nat @ top_top_fun_nat_bool @ C ) @ B )
          = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_inv__f__eq) ).

thf(2988,plain,
    ! [A: nat,B: nat,C: fun_nat_nat] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ C ) @ top_top_fun_nat_bool ) )
     => ( ( ( hAPP_nat_nat @ C @ A )
          = B )
       => ( ( hAPP_nat_nat @ ( hilber195283148at_nat @ top_top_fun_nat_bool @ C ) @ B )
          = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).

thf(551,axiom,
    hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ ( cOMBS_1921392482t_bool @ ( cOMBS_811328630t_bool @ ( hAPP_f509814255t_bool @ ( cOMBB_231886989e_indi @ if_fun1658569689t_bool ) @ ( hAPP_n924210722i_bool @ ( hAPP_f62620517i_bool @ cOMBC_922322901t_bool @ ( hAPP_f1381130897t_bool @ ( cOMBB_981137617e_indi @ ord_less_nat ) @ h ) ) @ n ) ) @ ( hAPP_A658738638t_bool @ ( hAPP_f293545699t_bool @ cOMBC_18834461t_bool @ ( hAPP_f842954860t_bool @ ( cOMBB_117136048e_indi @ arrow_741591990_mktop ) @ p ) ) @ e ) ) @ ( cOMBS_1921392482t_bool @ ( cOMBS_811328630t_bool @ ( hAPP_f509814255t_bool @ ( cOMBB_231886989e_indi @ if_fun1658569689t_bool ) @ ( hAPP_n924210722i_bool @ ( hAPP_f62620517i_bool @ cOMBC_922322901t_bool @ ( hAPP_f1381130897t_bool @ ( cOMBB_981137617e_indi @ fequal_nat ) @ h ) ) @ n ) ) @ ( hAPP_A658738638t_bool @ ( hAPP_f293545699t_bool @ cOMBC_18834461t_bool @ ( hAPP_A102926893t_bool @ ( hAPP_f141075873t_bool @ cOMBC_1505804284t_bool @ ( hAPP_f576849227t_bool @ ( cOMBB_656639247e_indi @ arrow_1475523868_above ) @ p ) ) @ c ) ) @ e ) ) @ ( hAPP_A658738638t_bool @ ( hAPP_f293545699t_bool @ cOMBC_18834461t_bool @ ( hAPP_f842954860t_bool @ ( cOMBB_117136048e_indi @ arrow_592884904_mkbot ) @ p ) ) @ e ) ) ) ) @ arrow_1190054106e_Prof ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16__096_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai) ).

thf(2853,plain,
    hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ ( cOMBS_1921392482t_bool @ ( cOMBS_811328630t_bool @ ( hAPP_f509814255t_bool @ ( cOMBB_231886989e_indi @ if_fun1658569689t_bool ) @ ( hAPP_n924210722i_bool @ ( hAPP_f62620517i_bool @ cOMBC_922322901t_bool @ ( hAPP_f1381130897t_bool @ ( cOMBB_981137617e_indi @ ord_less_nat ) @ h ) ) @ n ) ) @ ( hAPP_A658738638t_bool @ ( hAPP_f293545699t_bool @ cOMBC_18834461t_bool @ ( hAPP_f842954860t_bool @ ( cOMBB_117136048e_indi @ arrow_741591990_mktop ) @ p ) ) @ e ) ) @ ( cOMBS_1921392482t_bool @ ( cOMBS_811328630t_bool @ ( hAPP_f509814255t_bool @ ( cOMBB_231886989e_indi @ if_fun1658569689t_bool ) @ ( hAPP_n924210722i_bool @ ( hAPP_f62620517i_bool @ cOMBC_922322901t_bool @ ( hAPP_f1381130897t_bool @ ( cOMBB_981137617e_indi @ fequal_nat ) @ h ) ) @ n ) ) @ ( hAPP_A658738638t_bool @ ( hAPP_f293545699t_bool @ cOMBC_18834461t_bool @ ( hAPP_A102926893t_bool @ ( hAPP_f141075873t_bool @ cOMBC_1505804284t_bool @ ( hAPP_f576849227t_bool @ ( cOMBB_656639247e_indi @ arrow_1475523868_above ) @ p ) ) @ c ) ) @ e ) ) @ ( hAPP_A658738638t_bool @ ( hAPP_f293545699t_bool @ cOMBC_18834461t_bool @ ( hAPP_f842954860t_bool @ ( cOMBB_117136048e_indi @ arrow_592884904_mkbot ) @ p ) ) @ e ) ) ) ) @ arrow_1190054106e_Prof ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).

thf(407,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( A != B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_less__imp__neq) ).

thf(2251,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( A != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

thf(540,axiom,
    ! [A: bool,B: bool] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ B ) )
    <=> ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_bool @ A ) @ B ) )
        | ( ( hBOOL @ A )
        <=> ( hBOOL @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_order__le__less) ).

thf(2811,plain,
    ! [A: bool,B: bool] :
      ( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ B ) )
       => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_bool @ A ) @ B ) )
          | ( ( ( hBOOL @ A )
             => ( hBOOL @ B ) )
            & ( ( hBOOL @ B )
             => ( hBOOL @ A ) ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_bool @ A ) @ B ) )
          | ( ( ( hBOOL @ A )
             => ( hBOOL @ B ) )
            & ( ( hBOOL @ B )
             => ( hBOOL @ A ) ) ) )
       => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).

thf(616,axiom,
    ! [A: arrow_931160158le_alt,B: fun_Pr1055212137t_bool] :
      ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ B ) @ arrow_915577424le_Lin ) )
     => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ ( hAPP_A606737888t_bool @ ( hAPP_f786530292t_bool @ arrow_592884904_mkbot @ B ) @ A ) ) @ arrow_915577424le_Lin ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_mkbot__Lin) ).

thf(3104,plain,
    ! [A: arrow_931160158le_alt,B: fun_Pr1055212137t_bool] :
      ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ B ) @ arrow_915577424le_Lin ) )
     => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ ( hAPP_A606737888t_bool @ ( hAPP_f786530292t_bool @ arrow_592884904_mkbot @ B ) @ A ) ) @ arrow_915577424le_Lin ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).

thf(145,axiom,
    ! [A: fun_nat_bool,B: nat,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_474_set__rev__mp) ).

thf(1244,plain,
    ! [A: fun_nat_bool,B: nat,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(525,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( B = C )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_xt1_I1_J) ).

thf(2764,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( B = C )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).

thf(626,axiom,
    ! [A: product_unit,B: fun_Pr1643180309t_bool,C: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_481_in__mono) ).

thf(3136,plain,
    ! [A: product_unit,B: fun_Pr1643180309t_bool,C: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).

thf(685,axiom,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool,C: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ B ) @ C ) )
     => ( ( B = A )
       => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_xt1_I2_J) ).

thf(3368,plain,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool,C: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ B ) @ C ) )
     => ( ( B = A )
       => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).

thf(77,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ D ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ D ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_395_add__less__le__mono) ).

thf(995,plain,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ D ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ D ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(229,axiom,
    ! [A: nat] :
      ( ( hAPP_nat_nat @ suc @ A )
     != zero_zero_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_675_nat_Osimps_I3_J) ).

thf(1558,plain,
    ! [A: nat] :
      ( ( hAPP_nat_nat @ suc @ A )
     != zero_zero_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(410,axiom,
    ! [A: fun_Ar500372357t_bool,B: fun_fu775006535l_bool,C: fun_fu775006535l_bool,D: fun_fu1471766731l_bool] :
      ( ( hBOOL @ ( hAPP_f1223452061l_bool @ ( hAPP_f120150093l_bool @ member1791451290l_bool @ B ) @ ( pi_fun1624909403l_bool @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ ( hAPP_f1766661605l_bool @ B @ A ) ) @ ( hAPP_f84039575l_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_PiE) ).

thf(2262,plain,
    ! [A: fun_Ar500372357t_bool,B: fun_fu775006535l_bool,C: fun_fu775006535l_bool,D: fun_fu1471766731l_bool] :
      ( ( hBOOL @ ( hAPP_f1223452061l_bool @ ( hAPP_f120150093l_bool @ member1791451290l_bool @ B ) @ ( pi_fun1624909403l_bool @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ ( hAPP_f1766661605l_bool @ B @ A ) ) @ ( hAPP_f84039575l_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

thf(439,axiom,
    ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ c ) @ e ) ) @ ( hAPP_f792184801t_bool @ f @ ( cOMBS_1921392482t_bool @ ( cOMBS_811328630t_bool @ ( hAPP_f509814255t_bool @ ( cOMBB_231886989e_indi @ if_fun1658569689t_bool ) @ ( hAPP_n924210722i_bool @ ( hAPP_f62620517i_bool @ cOMBC_922322901t_bool @ ( hAPP_f1381130897t_bool @ ( cOMBB_981137617e_indi @ ord_less_nat ) @ h ) ) @ n ) ) @ ( hAPP_A658738638t_bool @ ( hAPP_f293545699t_bool @ cOMBC_18834461t_bool @ ( hAPP_f842954860t_bool @ ( cOMBB_117136048e_indi @ arrow_741591990_mktop ) @ p ) ) @ e ) ) @ ( cOMBS_1921392482t_bool @ ( cOMBS_811328630t_bool @ ( hAPP_f509814255t_bool @ ( cOMBB_231886989e_indi @ if_fun1658569689t_bool ) @ ( hAPP_n924210722i_bool @ ( hAPP_f62620517i_bool @ cOMBC_922322901t_bool @ ( hAPP_f1381130897t_bool @ ( cOMBB_981137617e_indi @ fequal_nat ) @ h ) ) @ n ) ) @ ( hAPP_A658738638t_bool @ ( hAPP_f293545699t_bool @ cOMBC_18834461t_bool @ ( hAPP_A102926893t_bool @ ( hAPP_f141075873t_bool @ cOMBC_1505804284t_bool @ ( hAPP_f576849227t_bool @ ( cOMBB_656639247e_indi @ arrow_1475523868_above ) @ p ) ) @ c ) ) @ e ) ) @ ( hAPP_A658738638t_bool @ ( hAPP_f293545699t_bool @ cOMBC_18834461t_bool @ ( hAPP_f842954860t_bool @ ( cOMBB_117136048e_indi @ arrow_592884904_mkbot ) @ p ) ) @ e ) ) ) ) ) )
  <=> ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ a ) @ b ) ) @ ( hAPP_f792184801t_bool @ f @ ( hAPP_f311418073t_bool @ ( hAPP_f1302245795t_bool @ cOMBC_1490589522t_bool @ ( hAPP_f1755759597t_bool @ ( hAPP_f1328803787t_bool @ cOMBC_1190055014t_bool @ ( hAPP_f509814255t_bool @ ( cOMBB_231886989e_indi @ if_fun1658569689t_bool ) @ ( hAPP_n924210722i_bool @ ( hAPP_f62620517i_bool @ cOMBC_922322901t_bool @ ( hAPP_f1381130897t_bool @ ( cOMBB_981137617e_indi @ ord_less_nat ) @ h ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ n ) @ one_one_nat ) ) ) ) @ lab ) ) @ lba ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182__096_Ic_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Am) ).

thf(2447,plain,
    ( ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ c ) @ e ) ) @ ( hAPP_f792184801t_bool @ f @ ( cOMBS_1921392482t_bool @ ( cOMBS_811328630t_bool @ ( hAPP_f509814255t_bool @ ( cOMBB_231886989e_indi @ if_fun1658569689t_bool ) @ ( hAPP_n924210722i_bool @ ( hAPP_f62620517i_bool @ cOMBC_922322901t_bool @ ( hAPP_f1381130897t_bool @ ( cOMBB_981137617e_indi @ ord_less_nat ) @ h ) ) @ n ) ) @ ( hAPP_A658738638t_bool @ ( hAPP_f293545699t_bool @ cOMBC_18834461t_bool @ ( hAPP_f842954860t_bool @ ( cOMBB_117136048e_indi @ arrow_741591990_mktop ) @ p ) ) @ e ) ) @ ( cOMBS_1921392482t_bool @ ( cOMBS_811328630t_bool @ ( hAPP_f509814255t_bool @ ( cOMBB_231886989e_indi @ if_fun1658569689t_bool ) @ ( hAPP_n924210722i_bool @ ( hAPP_f62620517i_bool @ cOMBC_922322901t_bool @ ( hAPP_f1381130897t_bool @ ( cOMBB_981137617e_indi @ fequal_nat ) @ h ) ) @ n ) ) @ ( hAPP_A658738638t_bool @ ( hAPP_f293545699t_bool @ cOMBC_18834461t_bool @ ( hAPP_A102926893t_bool @ ( hAPP_f141075873t_bool @ cOMBC_1505804284t_bool @ ( hAPP_f576849227t_bool @ ( cOMBB_656639247e_indi @ arrow_1475523868_above ) @ p ) ) @ c ) ) @ e ) ) @ ( hAPP_A658738638t_bool @ ( hAPP_f293545699t_bool @ cOMBC_18834461t_bool @ ( hAPP_f842954860t_bool @ ( cOMBB_117136048e_indi @ arrow_592884904_mkbot ) @ p ) ) @ e ) ) ) ) ) )
     => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ a ) @ b ) ) @ ( hAPP_f792184801t_bool @ f @ ( hAPP_f311418073t_bool @ ( hAPP_f1302245795t_bool @ cOMBC_1490589522t_bool @ ( hAPP_f1755759597t_bool @ ( hAPP_f1328803787t_bool @ cOMBC_1190055014t_bool @ ( hAPP_f509814255t_bool @ ( cOMBB_231886989e_indi @ if_fun1658569689t_bool ) @ ( hAPP_n924210722i_bool @ ( hAPP_f62620517i_bool @ cOMBC_922322901t_bool @ ( hAPP_f1381130897t_bool @ ( cOMBB_981137617e_indi @ ord_less_nat ) @ h ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ n ) @ one_one_nat ) ) ) ) @ lab ) ) @ lba ) ) ) ) )
    & ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ a ) @ b ) ) @ ( hAPP_f792184801t_bool @ f @ ( hAPP_f311418073t_bool @ ( hAPP_f1302245795t_bool @ cOMBC_1490589522t_bool @ ( hAPP_f1755759597t_bool @ ( hAPP_f1328803787t_bool @ cOMBC_1190055014t_bool @ ( hAPP_f509814255t_bool @ ( cOMBB_231886989e_indi @ if_fun1658569689t_bool ) @ ( hAPP_n924210722i_bool @ ( hAPP_f62620517i_bool @ cOMBC_922322901t_bool @ ( hAPP_f1381130897t_bool @ ( cOMBB_981137617e_indi @ ord_less_nat ) @ h ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ n ) @ one_one_nat ) ) ) ) @ lab ) ) @ lba ) ) ) )
     => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ c ) @ e ) ) @ ( hAPP_f792184801t_bool @ f @ ( cOMBS_1921392482t_bool @ ( cOMBS_811328630t_bool @ ( hAPP_f509814255t_bool @ ( cOMBB_231886989e_indi @ if_fun1658569689t_bool ) @ ( hAPP_n924210722i_bool @ ( hAPP_f62620517i_bool @ cOMBC_922322901t_bool @ ( hAPP_f1381130897t_bool @ ( cOMBB_981137617e_indi @ ord_less_nat ) @ h ) ) @ n ) ) @ ( hAPP_A658738638t_bool @ ( hAPP_f293545699t_bool @ cOMBC_18834461t_bool @ ( hAPP_f842954860t_bool @ ( cOMBB_117136048e_indi @ arrow_741591990_mktop ) @ p ) ) @ e ) ) @ ( cOMBS_1921392482t_bool @ ( cOMBS_811328630t_bool @ ( hAPP_f509814255t_bool @ ( cOMBB_231886989e_indi @ if_fun1658569689t_bool ) @ ( hAPP_n924210722i_bool @ ( hAPP_f62620517i_bool @ cOMBC_922322901t_bool @ ( hAPP_f1381130897t_bool @ ( cOMBB_981137617e_indi @ fequal_nat ) @ h ) ) @ n ) ) @ ( hAPP_A658738638t_bool @ ( hAPP_f293545699t_bool @ cOMBC_18834461t_bool @ ( hAPP_A102926893t_bool @ ( hAPP_f141075873t_bool @ cOMBC_1505804284t_bool @ ( hAPP_f576849227t_bool @ ( cOMBB_656639247e_indi @ arrow_1475523868_above ) @ p ) ) @ c ) ) @ e ) ) @ ( hAPP_A658738638t_bool @ ( hAPP_f293545699t_bool @ cOMBC_18834461t_bool @ ( hAPP_f842954860t_bool @ ( cOMBB_117136048e_indi @ arrow_592884904_mkbot ) @ p ) ) @ e ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).

thf(307,axiom,
    ! [A: arrow_931160158le_alt,B: arrow_931160158le_alt,C: arrow_931160158le_alt,D: arrow_931160158le_alt] :
      ( ( ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ A ) @ B )
        = ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_Pair__inject) ).

thf(1861,plain,
    ! [A: arrow_931160158le_alt,B: arrow_931160158le_alt,C: arrow_931160158le_alt,D: arrow_931160158le_alt] :
      ( ( ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ A ) @ B )
        = ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(530,axiom,
    ! [A: bool] :
      ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_bool @ top_top_bool ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_not__top__less) ).

thf(2786,plain,
    ! [A: bool] :
      ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_bool @ top_top_bool ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).

thf(574,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
     => ( ( B = A )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_xt1_I4_J) ).

thf(2912,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
     => ( ( B = A )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).

thf(389,axiom,
    hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ lab ) @ arrow_915577424le_Lin ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73__096Lab_A_058_ALin_096) ).

thf(2198,plain,
    hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ lab ) @ arrow_915577424le_Lin ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(132,axiom,
    ! [A: nat] :
      ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ zero_zero_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_611_less__zeroE) ).

thf(1193,plain,
    ! [A: nat] :
      ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ zero_zero_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(362,axiom,
    ! [A: fun_Pr1228236907l_bool,B: fun_Ar836847646le_alt,C: arrow_931160158le_alt] :
      ( ( hAPP_A1787768616l_bool @ ( hAPP_f1395387255l_bool @ ( cOMBB_480104238le_alt @ A ) @ B ) @ C )
      = ( hAPP_P840149257l_bool @ A @ ( hAPP_A1313367280le_alt @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm_) ).

thf(2120,plain,
    ! [A: fun_Pr1228236907l_bool,B: fun_Ar836847646le_alt,C: arrow_931160158le_alt] :
      ( ( hAPP_A1787768616l_bool @ ( hAPP_f1395387255l_bool @ ( cOMBB_480104238le_alt @ A ) @ B ) @ C )
      = ( hAPP_P840149257l_bool @ A @ ( hAPP_A1313367280le_alt @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(491,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( B != A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_order__less__imp__not__eq2) ).

thf(2623,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( B != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).

thf(90,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ B @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) )
       => ( hBOOL @ ( hAPP_nat_bool @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_490_rev__predicate1D) ).

thf(1045,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ B @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) )
       => ( hBOOL @ ( hAPP_nat_bool @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(247,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B )
        = ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) )
     => ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_416_add__imp__eq) ).

thf(1614,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B )
        = ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) )
     => ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(583,axiom,
    ! [A: produc1840315303le_alt] : ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ A ) @ top_to126038883t_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_iso__tuple__UNIV__I) ).

thf(2956,plain,
    ! [A: produc1840315303le_alt] : ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ A ) @ top_to126038883t_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).

thf(210,axiom,
    ! [A: nat,B: nat] :
      ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
    <=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ suc @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_645_not__less__eq) ).

thf(1491,plain,
    ! [A: nat,B: nat] :
      ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ suc @ A ) ) ) )
      & ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ suc @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(743,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( A = B )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_order__eq__refl) ).

thf(3585,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( A = B )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).

thf(287,axiom,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ B ) )
     => ~ ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_order__less__asym_H) ).

thf(1777,plain,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ B ) )
     => ~ ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(654,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ B ) )
     => ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_xt1_I9_J) ).

thf(3267,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ B ) )
     => ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).

thf(446,axiom,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ A ) @ B ) )
    <=> ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ B ) )
        | ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281_order__le__less) ).

thf(2462,plain,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool] :
      ( ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ A ) @ B ) )
       => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ B ) )
          | ( A = B ) ) )
      & ( ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ B ) )
          | ( A = B ) )
       => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(99,axiom,
    ! [A: fun_Ar552120407i_bool] :
      ( ( pi_Arr487970267t_bool @ A @ ( hAPP_f1793492343l_bool @ cOMBK_1595020336e_indi @ top_to1690334693l_bool ) )
      = top_to1324311617l_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_Pi__UNIV) ).

thf(1077,plain,
    ! [A: fun_Ar552120407i_bool] :
      ( ( pi_Arr487970267t_bool @ A @ ( hAPP_f1793492343l_bool @ cOMBK_1595020336e_indi @ top_to1690334693l_bool ) )
      = top_to1324311617l_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(425,axiom,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ B ) )
    <=> ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ A ) @ B ) )
        & ~ ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_275_less__le__not__le) ).

thf(2362,plain,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ B ) )
       => ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ A ) @ B ) )
          & ~ ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ B ) @ A ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ A ) @ B ) )
          & ~ ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ B ) @ A ) ) )
       => ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).

thf(318,axiom,
    ! [A: arrow_2115524757e_indi,B: fun_Ar552120407i_bool,C: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_482_in__mono) ).

thf(1893,plain,
    ! [A: arrow_2115524757e_indi,B: fun_Ar552120407i_bool,C: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(161,axiom,
    ! [A: fun_nat_bool,B: nat] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ ( hAPP_n1699378549t_bool @ ( ord_at4362885an_nat @ B ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ B ) @ ( finite_card_nat @ A ) ) ) ) )
     => ( A
        = ( hAPP_n1699378549t_bool @ ( ord_at4362885an_nat @ B ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ B ) @ ( finite_card_nat @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_699_subset__card__intvl__is__intvl) ).

thf(1309,plain,
    ! [A: fun_nat_bool,B: nat] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ ( hAPP_n1699378549t_bool @ ( ord_at4362885an_nat @ B ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ B ) @ ( finite_card_nat @ A ) ) ) ) )
     => ( A
        = ( hAPP_n1699378549t_bool @ ( ord_at4362885an_nat @ B ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ B ) @ ( finite_card_nat @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(517,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ B ) )
    <=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
        & ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_399_less__fun__def) ).

thf(2739,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ B ) )
       => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
          & ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
          & ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).

thf(455,axiom,
    ? [A: fun_Pr1055212137t_bool] : ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ A ) @ arrow_915577424le_Lin ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_579_linear__alt) ).

thf(2494,plain,
    ? [A: fun_Pr1055212137t_bool] : ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ A ) @ arrow_915577424le_Lin ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).

thf(339,axiom,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ B ) )
    <=> ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ A ) @ B ) )
        & ( A != B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_271_order__less__le) ).

thf(1994,plain,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool] :
      ( ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ B ) )
       => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ A ) @ B ) )
          & ( A != B ) ) )
      & ( ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ A ) @ B ) )
          & ( A != B ) )
       => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(730,axiom,
    ! [A: fun_Pr1055212137t_bool] :
      ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ A ) @ arrow_915577424le_Lin ) )
     => ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ ( hAPP_f311418073t_bool @ cOMBK_1522533360e_indi @ A ) ) @ arrow_1190054106e_Prof ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_const__Lin__Prof) ).

thf(3552,plain,
    ! [A: fun_Pr1055212137t_bool] :
      ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ A ) @ arrow_915577424le_Lin ) )
     => ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ ( hAPP_f311418073t_bool @ cOMBK_1522533360e_indi @ A ) ) @ arrow_1190054106e_Prof ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).

thf(79,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) )
    <=> ( ( A = zero_zero_nat )
        | ? [C: nat] :
            ( ( A
              = ( hAPP_nat_nat @ suc @ C ) )
            & ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_671_less__Suc__eq__0__disj) ).

thf(999,plain,
    ! [A: nat,B: nat] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) )
       => ( ( A = zero_zero_nat )
          | ? [C: nat] :
              ( ( A
                = ( hAPP_nat_nat @ suc @ C ) )
              & ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ B ) ) ) ) )
      & ( ( ( A = zero_zero_nat )
          | ? [C: nat] :
              ( ( A
                = ( hAPP_nat_nat @ suc @ C ) )
              & ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ B ) ) ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(254,axiom,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool,C: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_460_subset__psubset__trans) ).

thf(1642,plain,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool,C: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(236,axiom,
    ( top_to2013953873l_bool
    = ( collec1699798848t_bool @ ( hAPP_b816606711l_bool @ cOMBK_759924014t_bool @ fTrue ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_UNIV__def) ).

thf(1578,plain,
    ( top_to2013953873l_bool
    = ( collec1699798848t_bool @ ( hAPP_b816606711l_bool @ cOMBK_759924014t_bool @ fTrue ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(264,axiom,
    ! [A: nat,B: nat,C: fun_nat_nat,D: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ C ) @ D ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ D ) )
       => ( ( ( hAPP_nat_nat @ C @ B )
            = A )
         => ( ( hAPP_nat_nat @ ( hilber195283148at_nat @ D @ C ) @ A )
            = B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_387_inv__into__f__eq) ).

thf(1678,plain,
    ! [A: nat,B: nat,C: fun_nat_nat,D: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ C ) @ D ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ D ) )
       => ( ( ( hAPP_nat_nat @ C @ B )
            = A )
         => ( ( hAPP_nat_nat @ ( hilber195283148at_nat @ D @ C ) @ A )
            = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(408,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_order__less__trans) ).

thf(2255,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(661,axiom,
    ! [A: fun_Ar1744566822di_nat,B: fun_Ar552120407i_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f1290810160l_bool @ ( hAPP_f516936199l_bool @ member428554515di_nat @ A ) @ ( pi_Arr159321468di_nat @ B @ ( hAPP_f426535095t_bool @ cOMBK_2091851729e_indi @ C ) ) ) )
     => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( inj_on886403158di_nat @ A ) @ B ) )
       => ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ C ) )
         => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( finite783399747e_indi @ B ) ) @ ( finite_card_nat @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_587_card__inj) ).

thf(3291,plain,
    ! [A: fun_Ar1744566822di_nat,B: fun_Ar552120407i_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f1290810160l_bool @ ( hAPP_f516936199l_bool @ member428554515di_nat @ A ) @ ( pi_Arr159321468di_nat @ B @ ( hAPP_f426535095t_bool @ cOMBK_2091851729e_indi @ C ) ) ) )
     => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( inj_on886403158di_nat @ A ) @ B ) )
       => ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ C ) )
         => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( finite783399747e_indi @ B ) ) @ ( finite_card_nat @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).

thf(141,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ B ) ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_430_add__less__imp__less__right) ).

thf(1229,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ B ) ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(225,axiom,
    ! [A: fun_Ar1380772935l_bool,B: fun_Ar552120407i_bool,C: arrow_2115524757e_indi] :
      ( ( hAPP_A1888055029i_bool @ ( hAPP_f1282576021i_bool @ ( hAPP_f833264203i_bool @ cOMBC_31215906l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_000_319) ).

thf(1546,plain,
    ! [A: fun_Ar1380772935l_bool,B: fun_Ar552120407i_bool,C: arrow_2115524757e_indi] :
      ( ( hAPP_A1888055029i_bool @ ( hAPP_f1282576021i_bool @ ( hAPP_f833264203i_bool @ cOMBC_31215906l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(180,axiom,
    ! [A: nat,B: fun_nat_bool] :
      ( ~ ( hBOOL @ ( hAPP_nat_bool @ B @ zero_zero_nat ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ B @ A ) )
       => ? [C: nat] :
            ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ A ) )
            & ! [D: nat] :
                ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ D ) @ C ) )
               => ~ ( hBOOL @ ( hAPP_nat_bool @ B @ D ) ) )
            & ( hBOOL @ ( hAPP_nat_bool @ B @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ one_one_nat ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_625_ex__least__nat__less) ).

thf(1380,plain,
    ! [A: nat,B: fun_nat_bool] :
      ( ~ ( hBOOL @ ( hAPP_nat_bool @ B @ zero_zero_nat ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ B @ A ) )
       => ? [C: nat] :
            ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ A ) )
            & ! [D: nat] :
                ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ D ) @ C ) )
               => ~ ( hBOOL @ ( hAPP_nat_bool @ B @ D ) ) )
            & ( hBOOL @ ( hAPP_nat_bool @ B @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ one_one_nat ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(37,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_637_Suc__leD) ).

thf(867,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(340,axiom,
    ! [A: produc1840315303le_alt] :
      ( ( hBOOL @ ( hAPP_P166437127t_bool @ top_to126038883t_bool @ A ) )
    <=> ( hBOOL @ top_top_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_top__apply) ).

thf(2003,plain,
    ! [A: produc1840315303le_alt] :
      ( ( ( hBOOL @ ( hAPP_P166437127t_bool @ top_to126038883t_bool @ A ) )
       => ( hBOOL @ top_top_bool ) )
      & ( ( hBOOL @ top_top_bool )
       => ( hBOOL @ ( hAPP_P166437127t_bool @ top_to126038883t_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(689,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ A ) @ B ) )
      | ( hBOOL @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_3_1_U) ).

thf(3379,plain,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ A ) @ B ) )
      | ( hBOOL @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).

thf(363,axiom,
    ! [A: fun_Pr1055212137t_bool,B: produc1840315303le_alt,C: fun_Pr1055212137t_bool] :
      ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_f314169011l_bool @ ord_le565024179t_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_478_set__rev__mp) ).

thf(2123,plain,
    ! [A: fun_Pr1055212137t_bool,B: produc1840315303le_alt,C: fun_Pr1055212137t_bool] :
      ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_f314169011l_bool @ ord_le565024179t_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(115,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ C )
      = ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_420_ab__semigroup__add__class_Oadd__ac_I1_J) ).

thf(1133,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ C )
      = ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(429,axiom,
    ! [A: arrow_2115524757e_indi] :
      ( ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_A1450069362di_nat @ h @ A ) ) @ n ) )
         => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ e ) @ d ) ) @ ( hAPP_A606737888t_bool @ ( hAPP_f786530292t_bool @ arrow_741591990_mktop @ ( hAPP_A1174518481t_bool @ p @ A ) ) @ e ) ) ) )
        & ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_A1450069362di_nat @ h @ A ) ) @ n ) )
         => ( ( ( ( hAPP_A1450069362di_nat @ h @ A )
                = n )
             => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ e ) @ d ) ) @ ( hAPP_A606737888t_bool @ ( hAPP_A501825983t_bool @ ( hAPP_f1909595219t_bool @ arrow_1475523868_above @ ( hAPP_A1174518481t_bool @ p @ A ) ) @ c ) @ e ) ) ) )
            & ( ( ( hAPP_A1450069362di_nat @ h @ A )
               != n )
             => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ e ) @ d ) ) @ ( hAPP_A606737888t_bool @ ( hAPP_f786530292t_bool @ arrow_592884904_mkbot @ ( hAPP_A1174518481t_bool @ p @ A ) ) @ e ) ) ) ) ) ) )
    <=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_A1450069362di_nat @ h @ A ) ) @ n ) )
         => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ b ) @ a ) ) @ lab ) ) )
        & ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_A1450069362di_nat @ h @ A ) ) @ n ) )
         => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ b ) @ a ) ) @ lba ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amk) ).

thf(2374,plain,
    ! [A: arrow_2115524757e_indi] :
      ( ( ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_A1450069362di_nat @ h @ A ) ) @ n ) )
           => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ e ) @ d ) ) @ ( hAPP_A606737888t_bool @ ( hAPP_f786530292t_bool @ arrow_741591990_mktop @ ( hAPP_A1174518481t_bool @ p @ A ) ) @ e ) ) ) )
          & ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_A1450069362di_nat @ h @ A ) ) @ n ) )
           => ( ( ( ( hAPP_A1450069362di_nat @ h @ A )
                  = n )
               => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ e ) @ d ) ) @ ( hAPP_A606737888t_bool @ ( hAPP_A501825983t_bool @ ( hAPP_f1909595219t_bool @ arrow_1475523868_above @ ( hAPP_A1174518481t_bool @ p @ A ) ) @ c ) @ e ) ) ) )
              & ( ( ( hAPP_A1450069362di_nat @ h @ A )
                 != n )
               => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ e ) @ d ) ) @ ( hAPP_A606737888t_bool @ ( hAPP_f786530292t_bool @ arrow_592884904_mkbot @ ( hAPP_A1174518481t_bool @ p @ A ) ) @ e ) ) ) ) ) ) )
       => ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_A1450069362di_nat @ h @ A ) ) @ n ) )
           => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ b ) @ a ) ) @ lab ) ) )
          & ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_A1450069362di_nat @ h @ A ) ) @ n ) )
           => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ b ) @ a ) ) @ lba ) ) ) ) )
      & ( ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_A1450069362di_nat @ h @ A ) ) @ n ) )
           => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ b ) @ a ) ) @ lab ) ) )
          & ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_A1450069362di_nat @ h @ A ) ) @ n ) )
           => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ b ) @ a ) ) @ lba ) ) ) )
       => ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_A1450069362di_nat @ h @ A ) ) @ n ) )
           => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ e ) @ d ) ) @ ( hAPP_A606737888t_bool @ ( hAPP_f786530292t_bool @ arrow_741591990_mktop @ ( hAPP_A1174518481t_bool @ p @ A ) ) @ e ) ) ) )
          & ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_A1450069362di_nat @ h @ A ) ) @ n ) )
           => ( ( ( ( hAPP_A1450069362di_nat @ h @ A )
                  = n )
               => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ e ) @ d ) ) @ ( hAPP_A606737888t_bool @ ( hAPP_A501825983t_bool @ ( hAPP_f1909595219t_bool @ arrow_1475523868_above @ ( hAPP_A1174518481t_bool @ p @ A ) ) @ c ) @ e ) ) ) )
              & ( ( ( hAPP_A1450069362di_nat @ h @ A )
                 != n )
               => ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ e ) @ d ) ) @ ( hAPP_A606737888t_bool @ ( hAPP_f786530292t_bool @ arrow_592884904_mkbot @ ( hAPP_A1174518481t_bool @ p @ A ) ) @ e ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).

thf(173,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
    <=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
        | ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_order__le__less) ).

thf(1348,plain,
    ! [A: nat,B: nat] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
       => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
          | ( A = B ) ) )
      & ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
          | ( A = B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(25,axiom,
    ( top_top_fun_nat_bool
    = ( collect_nat @ ( hAPP_b1013836512t_bool @ cOMBK_bool_nat @ fTrue ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_UNIV__def) ).

thf(833,plain,
    ( top_top_fun_nat_bool
    = ( collect_nat @ ( hAPP_b1013836512t_bool @ cOMBK_bool_nat @ fTrue ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(68,axiom,
    ! [A: nat] :
      ( ( A != zero_zero_nat )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_613_gr0I) ).

thf(967,plain,
    ! [A: nat] :
      ( ( A != zero_zero_nat )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(591,axiom,
    ! [A: fun_fu1595299477t_bool] :
      ( ( hBOOL @ ( hAPP_f611501301l_bool @ top_to2013953873l_bool @ A ) )
    <=> ( hBOOL @ top_top_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_top__apply) ).

thf(2983,plain,
    ! [A: fun_fu1595299477t_bool] :
      ( ( ( hBOOL @ ( hAPP_f611501301l_bool @ top_to2013953873l_bool @ A ) )
       => ( hBOOL @ top_top_bool ) )
      & ( ( hBOOL @ top_top_bool )
       => ( hBOOL @ ( hAPP_f611501301l_bool @ top_to2013953873l_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).

thf(62,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ C )
      = ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_536_nat__add__assoc) ).

thf(950,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ C )
      = ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(26,axiom,
    ! [A: fun_na1436237685l_bool,B: fun_nat_bool,C: nat] :
      ( ( hAPP_nat_bool @ ( hAPP_f800510211t_bool @ ( hAPP_f1722879237t_bool @ cOMBC_226598744l_bool @ A ) @ B ) @ C )
      = ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_) ).

thf(835,plain,
    ! [A: fun_na1436237685l_bool,B: fun_nat_bool,C: nat] :
      ( ( hAPP_nat_bool @ ( hAPP_f800510211t_bool @ ( hAPP_f1722879237t_bool @ cOMBC_226598744l_bool @ A ) @ B ) @ C )
      = ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(466,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( ( hBOOL @ B )
        <=> ( hBOOL @ A ) )
     => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_bool @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_xt1_I12_J) ).

thf(2522,plain,
    ! [A: bool,B: bool] :
      ( ~ ( ( ( hBOOL @ B )
           => ( hBOOL @ A ) )
          & ( ( hBOOL @ A )
           => ( hBOOL @ B ) ) )
     => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).

thf(615,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( ( B = A )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_xt1_I4_J) ).

thf(3100,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( ( B = A )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).

thf(516,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) )
       => ( B = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_xt1_I5_J) ).

thf(2736,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).

thf(341,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_xt1_I6_J) ).

thf(2008,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(337,axiom,
    ! [A: bool] : ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ A ) @ top_to1647826457l_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_iso__tuple__UNIV__I) ).

thf(1986,plain,
    ! [A: bool] : ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ A ) @ top_to1647826457l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(674,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( hAPP_f800510211t_bool @ ( hAPP_f1722879237t_bool @ cOMBC_226598744l_bool @ member_nat ) @ A ) ) @ ( hAPP_f800510211t_bool @ ( hAPP_f1722879237t_bool @ cOMBC_226598744l_bool @ member_nat ) @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_496_pred__subset__eq) ).

thf(3337,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( hAPP_f800510211t_bool @ ( hAPP_f1722879237t_bool @ cOMBC_226598744l_bool @ member_nat ) @ A ) ) @ ( hAPP_f800510211t_bool @ ( hAPP_f1722879237t_bool @ cOMBC_226598744l_bool @ member_nat ) @ B ) ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( hAPP_f800510211t_bool @ ( hAPP_f1722879237t_bool @ cOMBC_226598744l_bool @ member_nat ) @ A ) ) @ ( hAPP_f800510211t_bool @ ( hAPP_f1722879237t_bool @ cOMBC_226598744l_bool @ member_nat ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).

thf(261,axiom,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool,C: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_xt1_I10_J) ).

thf(1673,plain,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool,C: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(147,axiom,
    ! [A: nat,B: nat] :
      ( ( A != B )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_xt1_I12_J) ).

thf(1248,plain,
    ! [A: nat,B: nat] :
      ( ( A != B )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(12,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ B ) ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_652_less__trans__Suc) ).

thf(790,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ B ) ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(526,axiom,
    ! [A: arrow_2115524757e_indi,B: fun_Ar552120407i_bool,C: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_440_subsetD) ).

thf(2768,plain,
    ! [A: arrow_2115524757e_indi,B: fun_Ar552120407i_bool,C: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).

thf(36,axiom,
    ! [A: nat,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_466_set__mp) ).

thf(865,plain,
    ! [A: nat,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(306,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_320_order__less__le__trans) ).

thf(1859,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(536,axiom,
    ! [A: fun_fu1015689055l_bool] :
      ~ ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f868566847l_bool @ ord_le2104736649l_bool @ top_to1690334693l_bool ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_not__top__less) ).

thf(2800,plain,
    ! [A: fun_fu1015689055l_bool] :
      ~ ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f868566847l_bool @ ord_le2104736649l_bool @ top_to1690334693l_bool ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).

thf(417,axiom,
    ! [A: arrow_2115524757e_indi,B: fun_Ar552120407i_bool,C: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_465_set__mp) ).

thf(2334,plain,
    ! [A: arrow_2115524757e_indi,B: fun_Ar552120407i_bool,C: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

thf(430,axiom,
    ! [A: fun_Pr359894313l_bool,B: fun_Pr359894313l_bool,C: fun_Pr1055212137t_bool] :
      ( ! [D: produc1840315303le_alt] :
          ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ D ) @ C ) )
         => ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_f612708895l_bool @ ord_le742797417l_bool @ ( hAPP_P1830623733l_bool @ A @ D ) ) @ ( hAPP_P1830623733l_bool @ B @ D ) ) ) )
     => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f868566847l_bool @ ord_le1923264405l_bool @ ( pi_Pro226591613t_bool @ C @ A ) ) @ ( pi_Pro226591613t_bool @ C @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_501_Pi__mono) ).

thf(2404,plain,
    ! [A: fun_Pr359894313l_bool,B: fun_Pr359894313l_bool,C: fun_Pr1055212137t_bool] :
      ( ! [D: produc1840315303le_alt] :
          ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ D ) @ C ) )
         => ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_f612708895l_bool @ ord_le742797417l_bool @ ( hAPP_P1830623733l_bool @ A @ D ) ) @ ( hAPP_P1830623733l_bool @ B @ D ) ) ) )
     => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f868566847l_bool @ ord_le1923264405l_bool @ ( pi_Pro226591613t_bool @ C @ A ) ) @ ( pi_Pro226591613t_bool @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).

thf(345,axiom,
    ! [A: fun_Ar500372357t_bool,B: fun_fu834038077t_unit,C: fun_fu775006535l_bool,D: fun_fu587068865t_bool] :
      ( ( hBOOL @ ( hAPP_f345984403l_bool @ ( hAPP_f1505765837l_bool @ member1814595472t_unit @ B ) @ ( pi_fun1455727697t_unit @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ ( hAPP_f1586642395t_unit @ B @ A ) ) @ ( hAPP_f290914957t_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_PiE) ).

thf(2021,plain,
    ! [A: fun_Ar500372357t_bool,B: fun_fu834038077t_unit,C: fun_fu775006535l_bool,D: fun_fu587068865t_bool] :
      ( ( hBOOL @ ( hAPP_f345984403l_bool @ ( hAPP_f1505765837l_bool @ member1814595472t_unit @ B ) @ ( pi_fun1455727697t_unit @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ ( hAPP_f1586642395t_unit @ B @ A ) ) @ ( hAPP_f290914957t_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(56,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
    <=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
        & ( A != B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_order__less__le) ).

thf(928,plain,
    ! [A: nat,B: nat] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
       => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
          & ( A != B ) ) )
      & ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
          & ( A != B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(667,axiom,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ B ) )
    <=> ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ A ) @ B ) )
        & ~ ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_276_less__le__not__le) ).

thf(3309,plain,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool] :
      ( ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ B ) )
       => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ A ) @ B ) )
          & ~ ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ B ) @ A ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ A ) @ B ) )
          & ~ ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ B ) @ A ) ) )
       => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).

thf(630,axiom,
    ! [A: nat,B: nat] :
      ( ( A != B )
    <=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
        | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_linorder__neq__iff) ).

thf(3145,plain,
    ! [A: nat,B: nat] :
      ( ( ( A != B )
       => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) )
       => ( A != B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).

thf(493,axiom,
    ! [A: bool,B: fun_bo2027801303t_bool,C: fun_bool_bool,D: fun_bo979888811l_bool] :
      ( ( hBOOL @ ( hAPP_f1812901165l_bool @ ( hAPP_f674575949l_bool @ member1103019306t_bool @ B ) @ ( pi_boo250534251t_bool @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ ( hAPP_b510135029t_bool @ B @ A ) ) @ ( hAPP_b816606711l_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_PiE) ).

thf(2636,plain,
    ! [A: bool,B: fun_bo2027801303t_bool,C: fun_bool_bool,D: fun_bo979888811l_bool] :
      ( ( hBOOL @ ( hAPP_f1812901165l_bool @ ( hAPP_f674575949l_bool @ member1103019306t_bool @ B ) @ ( pi_boo250534251t_bool @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ ( hAPP_b510135029t_bool @ B @ A ) ) @ ( hAPP_b816606711l_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).

thf(383,axiom,
    hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ f ) @ ( pi_fun530160875t_bool @ arrow_1190054106e_Prof @ ( hAPP_f422714471l_bool @ cOMBK_1446432t_bool @ arrow_915577424le_Lin ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_assms_I1_J) ).

thf(2186,plain,
    hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ f ) @ ( pi_fun530160875t_bool @ arrow_1190054106e_Prof @ ( hAPP_f422714471l_bool @ cOMBK_1446432t_bool @ arrow_915577424le_Lin ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(677,axiom,
    ! [A: fun_nat_bool] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ cOMBI_nat ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_376_inj__on__id2) ).

thf(3347,plain,
    ! [A: fun_nat_bool] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ cOMBI_nat ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).

thf(124,axiom,
    ( ( finite1949902593t_unit @ top_to1257323279t_bool )
    = one_one_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_603_card__UNIV__unit) ).

thf(1172,plain,
    ( ( finite1949902593t_unit @ top_to1257323279t_bool )
    = one_one_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(47,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B )
        = ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) )
    <=> ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_537_nat__add__left__cancel) ).

thf(897,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B )
          = ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) )
       => ( B = C ) )
      & ( ( B = C )
       => ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B )
          = ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(715,axiom,
    ! [A: nat,B: nat] :
      ( ( A != B )
     => ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_linorder__neqE) ).

thf(3479,plain,
    ! [A: nat,B: nat] :
      ( ( A != B )
     => ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).

thf(5,axiom,
    ! [A: fun_Ar1519997101t_bool,B: fun_Ar500372357t_bool,C: arrow_2115524757e_indi] :
      ( ( hAPP_A892860133t_bool @ ( cOMBS_811328630t_bool @ A @ B ) @ C )
      = ( hAPP_f1409483817t_bool @ ( hAPP_A594708985t_bool @ A @ C ) @ ( hAPP_A1174518481t_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_000_328) ).

thf(767,plain,
    ! [A: fun_Ar1519997101t_bool,B: fun_Ar500372357t_bool,C: arrow_2115524757e_indi] :
      ( ( hAPP_A892860133t_bool @ ( cOMBS_811328630t_bool @ A @ B ) @ C )
      = ( hAPP_f1409483817t_bool @ ( hAPP_A594708985t_bool @ A @ C ) @ ( hAPP_A1174518481t_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(602,axiom,
    ! [A: nat,B: nat,C: fun_nat_nat] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ C ) @ top_top_fun_nat_bool ) )
     => ( ( ( hAPP_nat_nat @ C @ A )
          = ( hAPP_nat_nat @ C @ B ) )
      <=> ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_381_inj__eq) ).

thf(3030,plain,
    ! [A: nat,B: nat,C: fun_nat_nat] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ C ) @ top_top_fun_nat_bool ) )
     => ( ( ( ( hAPP_nat_nat @ C @ A )
            = ( hAPP_nat_nat @ C @ B ) )
         => ( A = B ) )
        & ( ( A = B )
         => ( ( hAPP_nat_nat @ C @ A )
            = ( hAPP_nat_nat @ C @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).

thf(23,axiom,
    ! [A: fun_fu699199419t_bool,B: fun_Ar500372357t_bool,C: arrow_2115524757e_indi] :
      ( ( hAPP_A131904271t_bool @ ( hAPP_f576849227t_bool @ ( cOMBB_656639247e_indi @ A ) @ B ) @ C )
      = ( hAPP_f1909595219t_bool @ A @ ( hAPP_A1174518481t_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ct_326) ).

thf(828,plain,
    ! [A: fun_fu699199419t_bool,B: fun_Ar500372357t_bool,C: arrow_2115524757e_indi] :
      ( ( hAPP_A131904271t_bool @ ( hAPP_f576849227t_bool @ ( cOMBB_656639247e_indi @ A ) @ B ) @ C )
      = ( hAPP_f1909595219t_bool @ A @ ( hAPP_A1174518481t_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(398,axiom,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ B ) )
    <=> ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ A ) @ B ) )
        & ~ ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_401_less__fun__def) ).

thf(2223,plain,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool] :
      ( ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ B ) )
       => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ A ) @ B ) )
          & ~ ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ B ) @ A ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ A ) @ B ) )
          & ~ ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le351904673i_bool @ B ) @ A ) ) )
       => ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

thf(65,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_333_order__le__less__trans) ).

thf(960,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(534,axiom,
    ! [A: nat,B: nat] :
      ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ A ) @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Nat__Onat_T) ).

thf(2795,plain,
    ! [A: nat,B: nat] :
      ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ A ) @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).

thf(205,axiom,
    ! [A: fun_na1469252690l_bool,B: fun_nat_bool,C: nat] :
      ( ( hAPP_nat_bool @ ( cOMBS_nat_bool_bool @ A @ B ) @ C )
      = ( hAPP_bool_bool @ ( hAPP_n1006566506l_bool @ A @ C ) @ ( hAPP_nat_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__HOL__Obool_000tc__HOL__Obool_U) ).

thf(1473,plain,
    ! [A: fun_na1469252690l_bool,B: fun_nat_bool,C: nat] :
      ( ( hAPP_nat_bool @ ( cOMBS_nat_bool_bool @ A @ B ) @ C )
      = ( hAPP_bool_bool @ ( hAPP_n1006566506l_bool @ A @ C ) @ ( hAPP_nat_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(702,axiom,
    ! [A: bool,B: bool] :
      ( ( ( hBOOL @ B )
      <=> ( hBOOL @ A ) )
    <=> ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ A ) )
        & ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_order__eq__iff) ).

thf(3424,plain,
    ! [A: bool,B: bool] :
      ( ( ( ( ( hBOOL @ B )
           => ( hBOOL @ A ) )
          & ( ( hBOOL @ A )
           => ( hBOOL @ B ) ) )
       => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ A ) )
          & ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ B ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ A ) )
          & ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ B ) ) )
       => ( ( ( hBOOL @ B )
           => ( hBOOL @ A ) )
          & ( ( hBOOL @ A )
           => ( hBOOL @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).

thf(97,axiom,
    ! [A: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) )
    <=> ( A = zero_zero_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_670_less__Suc0) ).

thf(1065,plain,
    ! [A: nat] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) )
       => ( A = zero_zero_nat ) )
      & ( ( A = zero_zero_nat )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(606,axiom,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ B ) )
     => ~ ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_order__less__not__sym) ).

thf(3045,plain,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ A ) @ B ) )
     => ~ ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1976645739t_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).

thf(64,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) )
    <=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_563_nat__add__left__cancel__le) ).

thf(955,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) )
      & ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(683,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( A = B )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_489_equalityD1) ).

thf(3362,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( A = B )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).

thf(298,axiom,
    ! [A: fun_fu1015689055l_bool] : ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f868566847l_bool @ ord_le1923264405l_bool @ A ) @ top_to1690334693l_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_341_top__greatest) ).

thf(1829,plain,
    ! [A: fun_fu1015689055l_bool] : ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f868566847l_bool @ ord_le1923264405l_bool @ A ) @ top_to1690334693l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(297,axiom,
    ! [A: fun_fu1595299477t_bool,B: fun_fu1138137687l_bool,C: fun_fu1138137687l_bool] :
      ( ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f173704847l_bool @ ord_le161055137l_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_485_in__mono) ).

thf(1827,plain,
    ! [A: fun_fu1595299477t_bool,B: fun_fu1138137687l_bool,C: fun_fu1138137687l_bool] :
      ( ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f173704847l_bool @ ord_le161055137l_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(727,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
       => ( B = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_xt1_I5_J) ).

thf(3543,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).

thf(122,axiom,
    ! [A: nat] :
      ( ( A != zero_zero_nat )
     => ~ ! [B: nat] :
            ( A
           != ( hAPP_nat_nat @ suc @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_693_nat_Oexhaust) ).

thf(1152,plain,
    ! [A: nat] :
      ( ( A != zero_zero_nat )
     => ~ ! [B: nat] :
            ( A
           != ( hAPP_nat_nat @ suc @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(174,axiom,
    ! [A: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ zero_zero_nat ) )
    <=> ( A = zero_zero_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_622_le__0__eq) ).

thf(1357,plain,
    ! [A: nat] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ zero_zero_nat ) )
       => ( A = zero_zero_nat ) )
      & ( ( A = zero_zero_nat )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ zero_zero_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(76,axiom,
    ! [A: fun_fu775006535l_bool] :
      ( ( pi_fun530160875t_bool @ A @ ( hAPP_f422714471l_bool @ cOMBK_1446432t_bool @ top_to1690334693l_bool ) )
      = top_to2013953873l_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_Pi__UNIV) ).

thf(992,plain,
    ! [A: fun_fu775006535l_bool] :
      ( ( pi_fun530160875t_bool @ A @ ( hAPP_f422714471l_bool @ cOMBK_1446432t_bool @ top_to1690334693l_bool ) )
      = top_to2013953873l_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(21,axiom,
    ! [A: bool] :
      ( ( A = fTrue )
      | ( A = fFalse ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvq) ).

thf(822,plain,
    ! [A: bool] :
      ( ( A = fTrue )
      | ( A = fFalse ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(31,axiom,
    ( top_to1678393681i_bool
    = ( collec708328256e_indi @ ( hAPP_b1439777783i_bool @ cOMBK_1820189998e_indi @ fTrue ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_UNIV__def) ).

thf(850,plain,
    ( top_to1678393681i_bool
    = ( collec708328256e_indi @ ( hAPP_b1439777783i_bool @ cOMBK_1820189998e_indi @ fTrue ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(620,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( ( C = A )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_ord__le__eq__trans) ).

thf(3113,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( ( C = A )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).

thf(450,axiom,
    ! [A: fun_fu1138137687l_bool] : ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f173704847l_bool @ ord_le161055137l_bool @ A ) @ top_to2013953873l_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_342_top__greatest) ).

thf(2484,plain,
    ! [A: fun_fu1138137687l_bool] : ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f173704847l_bool @ ord_le161055137l_bool @ A ) @ top_to2013953873l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).

thf(39,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ B ) ) )
    <=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_435_add__less__cancel__right) ).

thf(871,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ B ) ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) ) )
      & ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(184,axiom,
    ! [A: fun_na1436237685l_bool,B: fun_nat_nat,C: nat] :
      ( ( hAPP_n215258509l_bool @ ( hAPP_f66927821l_bool @ ( cOMBB_1146692694ol_nat @ A ) @ B ) @ C )
      = ( hAPP_n215258509l_bool @ A @ ( hAPP_nat_nat @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HO) ).

thf(1399,plain,
    ! [A: fun_na1436237685l_bool,B: fun_nat_nat,C: nat] :
      ( ( hAPP_n215258509l_bool @ ( hAPP_f66927821l_bool @ ( cOMBB_1146692694ol_nat @ A ) @ B ) @ C )
      = ( hAPP_n215258509l_bool @ A @ ( hAPP_nat_nat @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(428,axiom,
    ! [A: fun_fu1595299477t_bool,B: fun_fu1193945677t_unit,C: fun_fu1138137687l_bool,D: fun_fu327311537t_bool] :
      ( ( hBOOL @ ( hAPP_f1549513891l_bool @ ( hAPP_f1065603533l_bool @ member1805026208t_unit @ B ) @ ( pi_fun1254023521t_unit @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ ( hAPP_f1579463915t_unit @ B @ A ) ) @ ( hAPP_f1483290493t_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_PiE) ).

thf(2372,plain,
    ! [A: fun_fu1595299477t_bool,B: fun_fu1193945677t_unit,C: fun_fu1138137687l_bool,D: fun_fu327311537t_bool] :
      ( ( hBOOL @ ( hAPP_f1549513891l_bool @ ( hAPP_f1065603533l_bool @ member1805026208t_unit @ B ) @ ( pi_fun1254023521t_unit @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ ( hAPP_f1579463915t_unit @ B @ A ) ) @ ( hAPP_f1483290493t_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).

thf(369,axiom,
    ! [A: fun_Pr1055212137t_bool,B: fun_fu1015689055l_bool,C: fun_fu1015689055l_bool] :
      ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f868566847l_bool @ ord_le2104736649l_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_516_psubsetD) ).

thf(2138,plain,
    ! [A: fun_Pr1055212137t_bool,B: fun_fu1015689055l_bool,C: fun_fu1015689055l_bool] :
      ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f868566847l_bool @ ord_le2104736649l_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(404,axiom,
    ! [A: bool,B: bool] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_bool @ A ) @ B ) )
        | ( ( hBOOL @ A )
        <=> ( hBOOL @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_307_order__le__imp__less__or__eq) ).

thf(2241,plain,
    ! [A: bool,B: bool] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_bool @ A ) @ B ) )
        | ( ( ( hBOOL @ A )
           => ( hBOOL @ B ) )
          & ( ( hBOOL @ B )
           => ( hBOOL @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(75,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ ( hAPP_nat_nat @ suc @ B ) ) )
    <=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_634_Suc__le__mono) ).

thf(987,plain,
    ! [A: nat,B: nat] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ ( hAPP_nat_nat @ suc @ B ) ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ ( hAPP_nat_nat @ suc @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(365,axiom,
    ! [A: nat,B: arrow_2115524757e_indi,C: fun_Ar1744566822di_nat,D: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( inj_on886403158di_nat @ C ) @ D ) )
     => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ B ) @ D ) )
       => ( ( ( hAPP_A1450069362di_nat @ C @ B )
            = A )
         => ( ( hAPP_n1048492170e_indi @ ( hilber506087739di_nat @ D @ C ) @ A )
            = B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_388_inv__into__f__eq) ).

thf(2127,plain,
    ! [A: nat,B: arrow_2115524757e_indi,C: fun_Ar1744566822di_nat,D: fun_Ar552120407i_bool] :
      ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( inj_on886403158di_nat @ C ) @ D ) )
     => ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ B ) @ D ) )
       => ( ( ( hAPP_A1450069362di_nat @ C @ B )
            = A )
         => ( ( hAPP_n1048492170e_indi @ ( hilber506087739di_nat @ D @ C ) @ A )
            = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(537,axiom,
    ! [A: arrow_2115524757e_indi] : ( hBOOL @ ( hAPP_A1888055029i_bool @ top_to1678393681i_bool @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_top1I) ).

thf(2803,plain,
    ! [A: arrow_2115524757e_indi] : ( hBOOL @ ( hAPP_A1888055029i_bool @ top_to1678393681i_bool @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).

thf(220,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_xt1_I7_J) ).

thf(1532,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(570,axiom,
    ! [A: fun_fu1138137687l_bool,B: fun_fu1595299477t_bool,C: fun_fu1138137687l_bool] :
      ( ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f173704847l_bool @ ord_le161055137l_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_476_set__rev__mp) ).

thf(2898,plain,
    ! [A: fun_fu1138137687l_bool,B: fun_fu1595299477t_bool,C: fun_fu1138137687l_bool] :
      ( ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f173704847l_bool @ ord_le161055137l_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).

thf(181,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
    <=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
        & ( A != B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_555_nat__less__le) ).

thf(1384,plain,
    ! [A: nat,B: nat] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
       => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
          & ( A != B ) ) )
      & ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
          & ( A != B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(651,axiom,
    ! [A: fun_Ar500372357t_bool,B: fun_fu775006535l_bool,C: fun_fu775006535l_bool] :
      ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f95487087l_bool @ ord_le1871091345l_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_444_subsetD) ).

thf(3245,plain,
    ! [A: fun_Ar500372357t_bool,B: fun_fu775006535l_bool,C: fun_fu775006535l_bool] :
      ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f95487087l_bool @ ord_le1871091345l_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).

thf(598,axiom,
    ! [A: fun_Ar552120407i_bool] :
      ~ ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ top_to1678393681i_bool ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_not__top__less) ).

thf(3020,plain,
    ! [A: fun_Ar552120407i_bool] :
      ~ ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_f1938592399l_bool @ ord_le1115695277i_bool @ top_to1678393681i_bool ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).

thf(242,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_570_termination__basic__simps_I3_J) ).

thf(1597,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(556,axiom,
    hBOOL @ ( hAPP_f1397511071l_bool @ finite1350902018e_indi @ top_to1678393681i_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_595_finite__indi) ).

thf(2864,plain,
    hBOOL @ ( hAPP_f1397511071l_bool @ finite1350902018e_indi @ top_to1678393681i_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).

thf(314,axiom,
    ! [A: bool,B: fun_bool_nat,C: fun_bool_bool,D: fun_bo1570548802t_bool] :
      ( ( hBOOL @ ( hAPP_f67777128l_bool @ ( hAPP_f144393719l_bool @ member_fun_bool_nat @ B ) @ ( pi_bool_nat @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ ( hAPP_bool_nat @ B @ A ) ) @ ( hAPP_b1013836512t_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_PiE) ).

thf(1880,plain,
    ! [A: bool,B: fun_bool_nat,C: fun_bool_bool,D: fun_bo1570548802t_bool] :
      ( ( hBOOL @ ( hAPP_f67777128l_bool @ ( hAPP_f144393719l_bool @ member_fun_bool_nat @ B ) @ ( pi_bool_nat @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ ( hAPP_bool_nat @ B @ A ) ) @ ( hAPP_b1013836512t_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(712,axiom,
    ! [A: bool,B: fun_bool_bool,C: fun_bool_bool] :
      ( ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_f612708895l_bool @ ord_le742797417l_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_480_in__mono) ).

thf(3474,plain,
    ! [A: bool,B: fun_bool_bool,C: fun_bool_bool] :
      ( ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_f612708895l_bool @ ord_le742797417l_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).

thf(521,axiom,
    ! [A: fun_Pr1643180309t_bool] : ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ A ) @ top_to1257323279t_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_346_top__greatest) ).

thf(2754,plain,
    ! [A: fun_Pr1643180309t_bool] : ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_f272527115l_bool @ ord_le1874503007t_bool @ A ) @ top_to1257323279t_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).

thf(664,axiom,
    ! [A: product_unit] : ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ A ) @ top_to1257323279t_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_UNIV__I) ).

thf(3299,plain,
    ! [A: product_unit] : ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ A ) @ top_to1257323279t_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).

thf(344,axiom,
    ! [A: nat,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ zero_zero_nat ) @ B ) )
     => ( ( hAPP_nat_nat @ suc @ ( finite_card_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( hAPP_f1146629647l_bool @ ( cOMBB_1015721476ol_nat @ fconj ) @ ( hAPP_f800510211t_bool @ ( hAPP_f1722879237t_bool @ cOMBC_226598744l_bool @ ( hAPP_f66927821l_bool @ ( cOMBB_1146692694ol_nat @ member_nat ) @ suc ) ) @ B ) ) @ ( hAPP_n1699378549t_bool @ ( hAPP_f229349961t_bool @ cOMBC_nat_nat_bool @ ord_less_nat ) @ A ) ) ) ) )
        = ( finite_card_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( hAPP_f1146629647l_bool @ ( cOMBB_1015721476ol_nat @ fconj ) @ ( hAPP_f800510211t_bool @ ( hAPP_f1722879237t_bool @ cOMBC_226598744l_bool @ member_nat ) @ B ) ) @ ( hAPP_n1699378549t_bool @ ( hAPP_f229349961t_bool @ cOMBC_nat_nat_bool @ ord_less_nat ) @ ( hAPP_nat_nat @ suc @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_681_card__less__Suc) ).

thf(2018,plain,
    ! [A: nat,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ zero_zero_nat ) @ B ) )
     => ( ( hAPP_nat_nat @ suc @ ( finite_card_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( hAPP_f1146629647l_bool @ ( cOMBB_1015721476ol_nat @ fconj ) @ ( hAPP_f800510211t_bool @ ( hAPP_f1722879237t_bool @ cOMBC_226598744l_bool @ ( hAPP_f66927821l_bool @ ( cOMBB_1146692694ol_nat @ member_nat ) @ suc ) ) @ B ) ) @ ( hAPP_n1699378549t_bool @ ( hAPP_f229349961t_bool @ cOMBC_nat_nat_bool @ ord_less_nat ) @ A ) ) ) ) )
        = ( finite_card_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( hAPP_f1146629647l_bool @ ( cOMBB_1015721476ol_nat @ fconj ) @ ( hAPP_f800510211t_bool @ ( hAPP_f1722879237t_bool @ cOMBC_226598744l_bool @ member_nat ) @ B ) ) @ ( hAPP_n1699378549t_bool @ ( hAPP_f229349961t_bool @ cOMBC_nat_nat_bool @ ord_less_nat ) @ ( hAPP_nat_nat @ suc @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(304,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ B ) )
    <=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
        & ( A != B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_order__less__le) ).

thf(1848,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ B ) )
       => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
          & ( A != B ) ) )
      & ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
          & ( A != B ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(189,axiom,
    ! [A: fun_Ar500372357t_bool,B: fun_Ar1198543961l_bool,C: fun_Ar552120407i_bool] :
      ( ! [D: arrow_2115524757e_indi] :
          ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ D ) @ C ) )
         => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ ( hAPP_A1174518481t_bool @ A @ D ) ) @ ( hAPP_A1279849719l_bool @ B @ D ) ) ) )
     => ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ A ) @ ( pi_Arr487970267t_bool @ C @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_584_Pi__I_H) ).

thf(1416,plain,
    ! [A: fun_Ar500372357t_bool,B: fun_Ar1198543961l_bool,C: fun_Ar552120407i_bool] :
      ( ! [D: arrow_2115524757e_indi] :
          ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ D ) @ C ) )
         => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ ( hAPP_A1174518481t_bool @ A @ D ) ) @ ( hAPP_A1279849719l_bool @ B @ D ) ) ) )
     => ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ A ) @ ( pi_Arr487970267t_bool @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(488,axiom,
    ! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ top_top_fun_nat_bool @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_top1I) ).

thf(2615,plain,
    ! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ top_top_fun_nat_bool @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).

thf(386,axiom,
    ! [A: arrow_2115524757e_indi,B: fun_Ar687924991t_bool,C: fun_Ar552120407i_bool,D: fun_Ar684516451l_bool] :
      ( ( hBOOL @ ( hAPP_f1037107797l_bool @ ( hAPP_f162243405l_bool @ member1188420050t_bool @ B ) @ ( pi_Arr1376550035t_bool @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ ( hAPP_A1458779421t_bool @ B @ A ) ) @ ( hAPP_A182831535l_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_PiE) ).

thf(2191,plain,
    ! [A: arrow_2115524757e_indi,B: fun_Ar687924991t_bool,C: fun_Ar552120407i_bool,D: fun_Ar684516451l_bool] :
      ( ( hBOOL @ ( hAPP_f1037107797l_bool @ ( hAPP_f162243405l_bool @ member1188420050t_bool @ B ) @ ( pi_Arr1376550035t_bool @ C @ D ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ ( hAPP_A1458779421t_bool @ B @ A ) ) @ ( hAPP_A182831535l_bool @ D @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(607,axiom,
    ! [A: fun_fu1595299477t_bool,B: fun_fu787660105l_bool,C: fun_fu775006535l_bool] :
      ( ! [D: fun_Ar500372357t_bool] :
          ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ D ) @ C ) )
         => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ ( hAPP_f792184801t_bool @ A @ D ) ) @ ( hAPP_f1498158055l_bool @ B @ D ) ) ) )
     => ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ A ) @ ( pi_fun530160875t_bool @ C @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_391_Pi__I) ).

thf(3047,plain,
    ! [A: fun_fu1595299477t_bool,B: fun_fu787660105l_bool,C: fun_fu775006535l_bool] :
      ( ! [D: fun_Ar500372357t_bool] :
          ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ D ) @ C ) )
         => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ ( hAPP_f792184801t_bool @ A @ D ) ) @ ( hAPP_f1498158055l_bool @ B @ D ) ) ) )
     => ( hBOOL @ ( hAPP_f361555359l_bool @ ( hAPP_f1709225957l_bool @ member1801442306t_bool @ A ) @ ( pi_fun530160875t_bool @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).

thf(738,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_458_subset__psubset__trans) ).

thf(3575,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).

thf(379,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
      | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_540_nat__le__linear) ).

thf(2177,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
      | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(334,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( B = C )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_xt1_I1_J) ).

thf(1944,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( B = C )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(176,axiom,
    ! [A: fun_fu1015689055l_bool,B: arrow_2115524757e_indi] :
      ( ( hAPP_A1279849719l_bool @ ( hAPP_f1793492343l_bool @ cOMBK_1595020336e_indi @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe) ).

thf(1367,plain,
    ! [A: fun_fu1015689055l_bool,B: arrow_2115524757e_indi] :
      ( ( hAPP_A1279849719l_bool @ ( hAPP_f1793492343l_bool @ cOMBK_1595020336e_indi @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(58,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ ( hAPP_nat_nat @ suc @ B ) ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_655_Suc__less__SucD) ).

thf(940,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ ( hAPP_nat_nat @ suc @ B ) ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(562,axiom,
    ! [A: bool] : ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ top_top_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_340_top__greatest) ).

thf(2881,plain,
    ! [A: bool] : ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ top_top_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).

thf(756,axiom,
    hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ b ) @ a ) ) @ lba ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096) ).

thf(3626,plain,
    hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ b ) @ a ) ) @ lba ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).

thf(54,axiom,
    ! [A: fun_nat_fun_nat_nat,B: nat,C: nat] :
      ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ ( hAPP_f416620757at_nat @ cOMBC_nat_nat_nat @ A ) @ B ) @ C )
      = ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__Nat__Onat_U) ).

thf(923,plain,
    ! [A: fun_nat_fun_nat_nat,B: nat,C: nat] :
      ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ ( hAPP_f416620757at_nat @ cOMBC_nat_nat_nat @ A ) @ B ) @ C )
      = ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(274,axiom,
    ! [A: nat] :
      ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_530_less__irrefl__nat) ).

thf(1737,plain,
    ! [A: nat] :
      ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(565,axiom,
    ! [A: fun_Pr359894313l_bool,B: fun_Pr1055212137t_bool,C: fun_Pr1055212137t_bool] :
      ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_f314169011l_bool @ ord_le565024179t_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f868566847l_bool @ ord_le1923264405l_bool @ ( pi_Pro226591613t_bool @ C @ A ) ) @ ( pi_Pro226591613t_bool @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_402_Pi__anti__mono) ).

thf(2887,plain,
    ! [A: fun_Pr359894313l_bool,B: fun_Pr1055212137t_bool,C: fun_Pr1055212137t_bool] :
      ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_f314169011l_bool @ ord_le565024179t_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f868566847l_bool @ ord_le1923264405l_bool @ ( pi_Pro226591613t_bool @ C @ A ) ) @ ( pi_Pro226591613t_bool @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).

thf(128,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
     => ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_leD) ).

thf(1184,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
     => ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(698,axiom,
    ! [A: arrow_931160158le_alt,B: arrow_931160158le_alt,C: arrow_931160158le_alt,D: arrow_931160158le_alt] :
      ( ( ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ A ) @ B )
        = ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_Pair__eq) ).

thf(3405,plain,
    ! [A: arrow_931160158le_alt,B: arrow_931160158le_alt,C: arrow_931160158le_alt,D: arrow_931160158le_alt] :
      ( ( ( ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ A ) @ B )
          = ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ A ) @ B )
          = ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).

thf(504,axiom,
    ~ ! [A: fun_Pr1055212137t_bool] :
        ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ b ) @ a ) ) @ A ) )
       => ~ ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ A ) @ arrow_915577424le_Lin ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_) ).

thf(2690,plain,
    ~ ! [A: fun_Pr1055212137t_bool] :
        ( ( hBOOL @ ( hAPP_f429946033l_bool @ ( hAPP_P840149257l_bool @ member553230100le_alt @ ( hAPP_A1313367280le_alt @ ( hAPP_A1485971815le_alt @ produc362059031le_alt @ b ) @ a ) ) @ A ) )
       => ~ ( hBOOL @ ( hAPP_f1021703871l_bool @ ( hAPP_f1370368205l_bool @ member57118396t_bool @ A ) @ arrow_915577424le_Lin ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).

thf(231,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ! [C: nat] : ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_nat_bool @ A @ C ) ) @ ( hAPP_nat_bool @ B @ C ) ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_436_le__funI) ).

thf(1565,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ! [C: nat] : ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_nat_bool @ A @ C ) ) @ ( hAPP_nat_bool @ B @ C ) ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(436,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( B = C )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_ord__eq__less__trans) ).

thf(2438,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( B = C )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).

thf(87,axiom,
    ( top_to1324311617l_bool
    = ( collec1461897520t_bool @ ( hAPP_b1849744615l_bool @ cOMBK_670822686t_bool @ fTrue ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_UNIV__def) ).

thf(1037,plain,
    ( top_to1324311617l_bool
    = ( collec1461897520t_bool @ ( hAPP_b1849744615l_bool @ cOMBK_670822686t_bool @ fTrue ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(544,axiom,
    ! [A: fun_Pr1055212137t_bool] : ( hBOOL @ ( hAPP_f429946033l_bool @ top_to1690334693l_bool @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_top1I) ).

thf(2834,plain,
    ! [A: fun_Pr1055212137t_bool] : ( hBOOL @ ( hAPP_f429946033l_bool @ top_to1690334693l_bool @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).

thf(421,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ B ) )
     => ( A != B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_order__less__imp__not__eq) ).

thf(2351,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le382113706t_bool @ A ) @ B ) )
     => ( A != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).

thf(81,axiom,
    ! [A: fun_Ar1198543961l_bool,B: fun_Ar500372357t_bool,C: fun_Ar500372357t_bool,D: fun_Ar552120407i_bool] :
      ( ! [E: arrow_2115524757e_indi] :
          ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ E ) @ D ) )
         => ( ( hAPP_A1174518481t_bool @ B @ E )
            = ( hAPP_A1174518481t_bool @ C @ E ) ) )
     => ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ B ) @ ( pi_Arr487970267t_bool @ D @ A ) ) )
      <=> ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ C ) @ ( pi_Arr487970267t_bool @ D @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_581_Pi__cong) ).

thf(1014,plain,
    ! [A: fun_Ar1198543961l_bool,B: fun_Ar500372357t_bool,C: fun_Ar500372357t_bool,D: fun_Ar552120407i_bool] :
      ( ! [E: arrow_2115524757e_indi] :
          ( ( hBOOL @ ( hAPP_f1397511071l_bool @ ( hAPP_A605074405l_bool @ member590466050e_indi @ E ) @ D ) )
         => ( ( hAPP_A1174518481t_bool @ B @ E )
            = ( hAPP_A1174518481t_bool @ C @ E ) ) )
     => ( ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ B ) @ ( pi_Arr487970267t_bool @ D @ A ) ) )
         => ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ C ) @ ( pi_Arr487970267t_bool @ D @ A ) ) ) )
        & ( ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ C ) @ ( pi_Arr487970267t_bool @ D @ A ) ) )
         => ( hBOOL @ ( hAPP_f1465510031l_bool @ ( hAPP_f2029708741l_bool @ member1159072754t_bool @ B ) @ ( pi_Arr487970267t_bool @ D @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(70,axiom,
    ! [A: fun_Ar698916836t_bool,B: arrow_931160158le_alt,C: arrow_2115524757e_indi] :
      ( ( hAPP_A1174518481t_bool @ ( hAPP_A658738638t_bool @ ( hAPP_f293545699t_bool @ cOMBC_18834461t_bool @ A ) @ B ) @ C )
      = ( hAPP_A606737888t_bool @ ( hAPP_A1020253872t_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_000_321) ).

thf(972,plain,
    ! [A: fun_Ar698916836t_bool,B: arrow_931160158le_alt,C: arrow_2115524757e_indi] :
      ( ( hAPP_A1174518481t_bool @ ( hAPP_A658738638t_bool @ ( hAPP_f293545699t_bool @ cOMBC_18834461t_bool @ A ) @ B ) @ C )
      = ( hAPP_A606737888t_bool @ ( hAPP_A1020253872t_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(3637,plain,
    $false,
    inference(e,[status(thm)],[2199,2094,1024,1105,3477,3397,3581,1315,2331,1549,1586,2452,2889,1190,3053,760,2336,2131,2480,962,1818,1295,3534,3317,1882,2231,1522,3549,2776,3377,2590,3098,2014,1205,1142,3498,2854,861,3185,977,1422,1569,1939,3017,1671,3439,1655,1756,3332,2184,797,1275,2434,1327,2627,945,2844,3577,2360,1426,3530,1919,3253,1988,3414,913,3562,1640,2580,1196,2216,2723,2972,2548,841,2010,2516,2136,2869,2432,1914,782,1441,2825,1529,1482,3597,1254,3442,3221,2916,3275,1298,3342,1871,2708,2274,802,2682,3280,2488,3043,2745,2703,1330,2444,1323,838,1147,2552,1572,770,881,2158,1815,3231,1922,817,1479,1609,3014,2520,2730,3602,1875,2456,2237,2027,1450,3295,1109,3453,3473,3525,937,3357,2090,3393,1682,1136,3569,1677,2540,806,3093,2508,2058,1377,1886,1119,1526,1345,2103,2965,3559,1796,1072,3036,3361,2809,3606,2154,2718,2205,2954,1604,3450,2473,1470,2307,2496,1768,2773,1047,942,3591,3301,2204,2574,1438,761,3186,2673,894,1042,2596,1580,1174,1217,1751,3207,2264,2409,1900,910,825,2805,2249,1021,1824,1370,2032,815,2958,1920,852,1178,3600,1624,2609,2179,3546,1027,1634,2112,1740,3595,916,3166,3191,847,2758,3269,3618,3090,3198,879,3349,3556,1836,2181,3028,3050,1128,2492,1402,1983,2840,1259,1121,3218,2694,1096,869,2638,3176,2498,1234,1541,3482,1762,1534,1794,2577,3381,1111,1227,3386,2726,1138,2858,2537,3632,3119,2268,3205,1567,884,2023,3143,2561,1461,1424,1207,2666,1644,1419,2460,2798,3141,2877,1414,2196,1700,1937,1214,2349,1039,970,1114,3126,2304,2598,1131,2355,2505,2566,3247,1715,1263,997,3611,2450,2125,985,2836,1456,2900,1831,1231,1060,1050,1599,1246,3109,779,2140,2756,3162,1759,1393,1627,2370,1779,2368,2793,1895,2617,953,888,3476,1333,2749,1857,1202,792,1241,2761,2883,921,1846,1712,3306,3422,2995,773,794,2338,926,2909,1251,2149,2585,1747,1927,3111,2894,3158,965,1510,1698,1103,3375,3523,2734,3372,1833,1916,1884,2791,2789,2525,2188,2514,3604,1520,1124,904,975,1652,1929,2827,2134,3599,2891,1312,787,1058,2358,1675,2193,3023,1707,3051,2442,3436,2166,3579,1464,947,1638,1224,764,3352,831,2538,2214,1117,3287,2097,3106,1722,2116,1801,2896,2871,863,2151,3155,2229,1574,1011,2906,3419,1933,2257,1589,2943,2945,2856,3138,3160,1307,1667,1877,1080,3055,3572,3583,2647,2664,1293,2974,2842,2923,1325,2593,1029,2962,1594,3627,2620,2086,2064,2931,2535,1496,3178,2156,2207,2867,2770,983,1841,1396,1775,2244,2752,1726,1364,2967,3490,1562,3009,1948,1583,2952,1873,1467,3395,1905,2234,2927,2684,3278,1551,3444,1034,2239,2471,2652,3293,2503,1684,1145,2846,2564,776,3391,1770,3315,2661,2588,3462,3129,2518,2175,3209,2720,1098,2831,1611,1156,1753,2407,2569,3448,2092,1432,3554,3344,1785,3026,2219,1317,1901,3041,1336,907,1053,1499,1790,2454,1300,2688,3273,3334,1188,1186,3202,1869,1538,2486,3359,3329,3488,2838,3493,1284,2145,3388,2728,1372,1272,876,859,1617,2056,1404,1543,1766,1898,1257,3124,2992,1485,1506,1749,3224,1140,2511,3117,2860,3520,3366,2865,3400,2458,1649,2088,3589,1180,2885,2960,1321,3188,1412,1517,1866,3593,2696,1553,891,2209,1448,2490,2187,2110,3320,844,1453,1476,3484,1062,1101,3630,3561,2416,813,2988,2853,2251,2811,3104,1244,2764,3136,3368,995,1558,2262,2447,1861,2786,2912,2198,1193,2120,2623,1045,1614,2956,1491,3585,1777,3267,2462,1077,2362,1893,1309,2739,2494,1994,3552,999,1642,1578,1678,2255,3291,1229,1546,1380,867,2003,3379,2123,1133,2374,1348,833,967,2983,950,835,2522,3100,2736,2008,1986,3337,1673,1248,790,2768,865,1859,2800,2334,2404,2021,928,3309,3145,2636,2186,3347,1172,897,3479,767,3030,828,2223,960,2795,1473,3424,1065,3045,955,3362,1829,1827,3543,1152,1357,992,822,850,3113,2484,871,1399,2372,2138,2241,987,2127,2803,1532,2898,1384,3245,3020,1597,2864,1880,3474,2754,3299,2018,1848,1416,2615,2191,3047,3575,2177,1944,1367,940,2881,3626,923,1737,2887,1184,3405,2690,1565,2438,1037,2834,2351,1014,972]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : SCT171_2 : TPTP v8.1.2. Released v5.3.0.
% 0.15/0.16  % Command  : run_Leo-III %s %d
% 0.15/0.37  % Computer : n031.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 300
% 0.15/0.37  % DateTime : Thu May 18 15:50:56 EDT 2023
% 0.15/0.37  % CPUTime  : 
% 0.91/0.91  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 2.25/1.27  % [INFO] 	 Parsing done (362ms). 
% 2.25/1.28  % [INFO] 	 Running in sequential loop mode. 
% 2.82/1.50  % [INFO] 	 eprover registered as external prover. 
% 2.82/1.50  % [INFO] 	 cvc4 registered as external prover. 
% 2.82/1.51  % [INFO] 	 Scanning for conjecture ... 
% 3.70/1.79  % [INFO] 	 Found a conjecture and 757 axioms. Running axiom selection ... 
% 4.81/2.05  % [INFO] 	 Axiom selection finished. Selected 757 axioms (removed 0 axioms). 
% 5.89/2.38  % [INFO] 	 Problem is typed first-order (TPTP TFF). 
% 5.89/2.40  % [INFO] 	 Type checking passed. 
% 6.06/2.40  % [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 ... 
% 8.01/3.11  % [INFO] 	 [Domain constraints] Detected constraint on bool 
% 8.01/3.11  % [INFO] 	 [Domain constraints] dom(bool) ⊆ {fTrue,fFalse} 
% 9.46/3.41  % [INFO] 	 [Domain constraints] Detected constraint on bool 
% 9.46/3.41  % [INFO] 	 [Domain constraints] dom(bool) ⊆ {fTrue,fFalse} 
% 19.15/5.66  % External prover 'e' found a proof!
% 19.15/5.66  % [INFO] 	 Killing All external provers ... 
% 19.17/5.66  % Time passed: 5118ms (effective reasoning time: 4380ms)
% 19.17/5.66  % 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)>
% 19.17/5.67  % Axioms used in derivation (757): fact_266_le__fun__def, fact_25_top1I, fact_523_in__below, fact_337_xt1_I8_J, fact_82__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_, fact_222_Pi__UNIV, fact_132_order__less__imp__not__eq2, fact_509_subsetI, fact_566_add__le__mono1, fact_60_not__top__less, fact_673_Suc__neq__Zero, fact_679_less__eq__Suc__le__raw, fact_184_inv__f__eq, fact_130_order__less__imp__triv, fact_395_add__less__le__mono, fact_667_one__is__add, fact_556_le__eq__less__or__eq, fact_74__096Lba_A_058_ALin_096, fact_180_pred__equals__eq2, fact_493_pred__subset__eq, fact_572_termination__basic__simps_I2_J, fact_490_rev__predicate1D, fact_339_xt1_I8_J, help_COMBK_1_1_COMBK_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Arrow___, fact_158_order__less__irrefl, fact_336_xt1_I8_J, fact_67_less__top, fact_264_order__eq__iff, fact_602_finite__Collect__le__nat, help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ct, fact_400_less__fun__def, fact_448_psubset__eq, fact_144_order__less__not__sym, fact_98_xt1_I10_J, fact_684_inc__induct, fact_84_n_I2_J, fact_283_order__le__less, help_COMBS_1_1_COMBS_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_000_328, fact_175_mem__def, fact_494_pred__subset__eq, fact_275_less__le__not__le, fact_215_PiE, fact_218_PiE, fact_357_top__le, fact_663_less__eq__Suc__le, fact_199_PiE, help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__Nat__Onat_U, fact_616_neq0__conv, fact_133_order__less__imp__not__eq2, fact_166_UNIV__def, fact_111_ord__less__eq__trans, fact_346_top__greatest, fact_95_order__less__asym, fact_626_ex__least__nat__le, fact_397_injI, fact_689_Suc__le__D, fact_544_below__Lin, help_fconj_3_1_U, fact_52_top__apply, fact_64_less__top, fact_245_xt1_I4_J, fact_622_le__0__eq, fact_646_less__Suc__eq, fact_422_add__le__imp__le__left, fact_376_inj__on__id2, help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Nat__Onat_U, fact_385_inv__into__f__f, fact_471_set__rev__mp, fact_299_order__less__imp__le, help_fequal_2_1_fequal_000tc__Nat__Onat_T, help_COMBC_1_1_COMBC_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ct, fact_541_eq__imp__le, fact_358_top__le, fact_128_order__less__imp__triv, fact_323_order__less__le__trans, fact_76__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096, fact_440_subsetD, fact_126_order__less__asym_H, fact_488_equalityD2, fact_101_order__less__trans, fact_235_xt1_I5_J, fact_578_funcsetI, fact_643_add__Suc, fact_284_order__le__less, fact_540_nat__le__linear, fact_442_subsetD, fact_210_PiE, fact_224_order__refl, fact_160_order__less__irrefl, fact_474_set__rev__mp, fact_522_psubset__trans, fact_318_xt1_I11_J, fact_276_less__le__not__le, fact_156_linorder__neq__iff, fact_388_inv__into__f__eq, fact_499_pred__subset__eq, fact_404_Pi__anti__mono, fact_214_PiE, help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabel, fact_304_linorder__antisym__conv2, fact_255_order__antisym__conv, fact_30_top1I, fact_225_order__refl, fact_585_Pi__I_H, fact_6__C2_C, fact_405_pred__subset__eq2, fact_559_less__or__eq__imp__le, fact_461_equalityE, fact_444_subsetD, fact_306_order__le__imp__less__or__eq, fact_22_Pair__eq, fact_492_subset__refl, fact_648_not__less__less__Suc__eq, fact_624_add__gr__0, fact_94_order__less__asym, fact_421_one__reorient, fact_300_order__less__imp__le, fact_403_Pi__anti__mono, fact_464_set__mp, fact_319_xt1_I11_J, fact_61_not__top__less, fact_47_iso__tuple__UNIV__I, fact_528_nat__neq__iff, fact_50_top__apply, fact_0_assms_I3_J, fact_79__096_Ib_M_Aa_J_A_126_058_ALab_096, fact_354_top__unique, fact_209_PiE, fact_169_mem__def, fact_412_subset__UNIV, fact_413_subset__inj__on, fact_447_psubset__eq, fact_118_ord__eq__less__trans, fact_420_ab__semigroup__add__class_Oadd__ac_I1_J, fact_535_nat__add__left__commute, fact_653_less__SucE, fact_664_less__iff__Suc__add, fact_591_inj__onI, fact_120_xt1_I9_J, fact_551_add__less__mono1, fact_603_card__UNIV__unit, help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_000_321, fact_277_less__le__not__le, fact_428_add__le__cancel__right, help_fTrue_1_1_T, fact_293_xt1_I12_J, help_If_2_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvq, fact_644_add__Suc__right, fact_470_set__mp, fact_693_nat_Oexhaust, fact_201_PiE, fact_452_psubset__imp__subset, fact_41_iso__tuple__UNIV__I, fact_512_psubsetD, fact_239_order__trans, fact_137_order__less__imp__not__eq, fact_558_le__neq__implies__less, fact_309_order__le__imp__less__or__eq, fact_670_less__Suc0, fact_18__096e_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto, fact_3__096P_A_058_AProf_096, fact_650_less__SucI, fact_529_linorder__neqE__nat, fact_415_add__right__imp__eq, fact_476_set__rev__mp, fact_504_subsetI, fact_191_PiE, fact_345_top__greatest, help_COMBB_1_1_COMBB_000tc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm_, fact_243_xt1_I4_J, fact_666_less__add__Suc1, fact_676_Suc__not__Zero, fact_613_gr0I, fact_416_add__imp__eq, fact_135_order__less__imp__not__eq2, fact_100_order__less__trans, fact_517_psubsetD, fact_40_iso__tuple__UNIV__I, fact_399_less__fun__def, fact_145_order__less__not__sym, fact_355_top__unique, fact_545_inj__on__add__nat, fact_454_psubset__imp__subset, fact_29_top1I, fact_593_inj__on__cong, fact_263_order__eq__iff, fact_419_add__left__cancel, fact_288_order__neq__le__trans, fact_534_nat__add__commute, fact_287_linorder__antisym__conv1, fact_682_card__less, fact_189_PiE, fact_272_order__less__le, fact_659_Suc__leI, fact_637_Suc__leD, fact_258_le__funD, fact_451_subset__iff__psubset__eq, help_fTrue_1_1_U, fact_327_xt1_I7_J, fact_202_PiE, fact_524_add__leE, fact_55_not__top__less, fact_627_less__imp__add__positive, fact_553_less__add__eq__less, help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__HOL__Obool_U, fact_386_inv__into__f__f, fact_75__096a_A_126_061_Ab_096, fact_28_top1I, 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fact_36_UNIV__I, fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto, fact_409_subset__UNIV, fact_211_PiE, fact_460_subset__psubset__trans, fact_89_above__Lin, fact_49_top__apply, fact_12__096c_A_060_092_060_094bsub_062P_A_Iinv_Ah_An_J_092_060_094esub_062_Ad_0, fact_378_funcset__mem, fact_221_Pi__UNIV, fact_45_iso__tuple__UNIV__I, fact_658_le__less__Suc__eq, fact_153_linorder__antisym__conv3, fact_347_top__greatest, fact_131_order__less__imp__triv, fact_68_less__top, fact_290_order__neq__le__trans, fact_121_xt1_I9_J, fact_146_order__less__not__sym, fact_377_funcset__mem
% 19.17/5.67  % No. of inferences in proof: 1518
% 19.17/5.67  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 5118 ms resp. 4380 ms w/o parsing
% 20.42/5.97  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 20.42/5.98  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------