Leo-III---1.8.0.THM-Ref.s

%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : SCT171_3 : TPTP v9.3.1. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39

% Computer : n017.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun Sep 27 08:27:29 AM UTC 2026

% Result   : Theorem 27.36s 8.39s
% Output   : Refutation 30.33s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  578
% Syntax   : Number of formulae    : 1158 ( 312 unt;   0 typ;   0 def)
%            Number of atoms       : 3294 ( 851 equ;   0 cnn)
%            Maximal formula atoms :   22 (   2 avg)
%            Number of connectives : 21403 ( 392   ~;  90   |; 295   &;18875   @)
%                                         ( 138 <=>;1613  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   25 (  10 avg)
%            Number of types       :  295 ( 294 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  232 ( 230 usr;  87 con; 0-3 aty)
%            Number of variables   : 2869 (   0   ^;2835   !;  34   ?;2869   :)

% Comments : 
%------------------------------------------------------------------------------
thf(arrow_1893660431le_alt_type,type,
    arrow_1893660431le_alt: $tType ).

thf(arrow_856714788e_indi_type,type,
    arrow_856714788e_indi: $tType ).

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

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

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

thf(fun_Ar17477381t_bool_type,type,
    fun_Ar17477381t_bool: $tType ).

thf(fun_Ar331856045t_bool_type,type,
    fun_Ar331856045t_bool: $tType ).

thf(fun_Ar1995913199l_bool_type,type,
    fun_Ar1995913199l_bool: $tType ).

thf(fun_Ar797671557t_bool_type,type,
    fun_Ar797671557t_bool: $tType ).

thf(fun_Ar2121501495le_alt_type,type,
    fun_Ar2121501495le_alt: $tType ).

thf(fun_Ar1753411852t_bool_type,type,
    fun_Ar1753411852t_bool: $tType ).

thf(fun_Ar1623257374t_bool_type,type,
    fun_Ar1623257374t_bool: $tType ).

thf(fun_Ar339057223l_bool_type,type,
    fun_Ar339057223l_bool: $tType ).

thf(fun_Ar636018671t_bool_type,type,
    fun_Ar636018671t_bool: $tType ).

thf(fun_Ar1573071255t_bool_type,type,
    fun_Ar1573071255t_bool: $tType ).

thf(fun_Ar245737999le_alt_type,type,
    fun_Ar245737999le_alt: $tType ).

thf(fun_Ar1809396326i_bool_type,type,
    fun_Ar1809396326i_bool: $tType ).

thf(fun_Ar671024215di_nat_type,type,
    fun_Ar671024215di_nat: $tType ).

thf(fun_Ar290235730t_bool_type,type,
    fun_Ar290235730t_bool: $tType ).

thf(fun_Ar64685412t_bool_type,type,
    fun_Ar64685412t_bool: $tType ).

thf(fun_Ar624010239t_bool_type,type,
    fun_Ar624010239t_bool: $tType ).

thf(fun_Ar603939593t_bool_type,type,
    fun_Ar603939593t_bool: $tType ).

thf(fun_Ar1047186533l_bool_type,type,
    fun_Ar1047186533l_bool: $tType ).

thf(fun_Ar1998664965l_bool_type,type,
    fun_Ar1998664965l_bool: $tType ).

thf(fun_Ar286530093t_bool_type,type,
    fun_Ar286530093t_bool: $tType ).

thf(fun_Ar1321653811l_bool_type,type,
    fun_Ar1321653811l_bool: $tType ).

thf(fun_Ar1474557608l_bool_type,type,
    fun_Ar1474557608l_bool: $tType ).

thf(fun_Ar535288606t_bool_type,type,
    fun_Ar535288606t_bool: $tType ).

thf(fun_Ar516759882t_bool_type,type,
    fun_Ar516759882t_bool: $tType ).

thf(fun_Ar274636406t_bool_type,type,
    fun_Ar274636406t_bool: $tType ).

thf(fun_Ar338949104le_alt_type,type,
    fun_Ar338949104le_alt: $tType ).

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

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

thf(fun_bo1933551930i_bool_type,type,
    fun_bo1933551930i_bool: $tType ).

thf(fun_bo1476023096t_bool_type,type,
    fun_bo1476023096t_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_bo2107365004l_bool_type,type,
    fun_bo2107365004l_bool: $tType ).

thf(fun_bo559790694t_bool_type,type,
    fun_bo559790694t_bool: $tType ).

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

thf(fun_bo1445676730l_bool_type,type,
    fun_bo1445676730l_bool: $tType ).

thf(fun_bo377688929l_bool_type,type,
    fun_bo377688929l_bool: $tType ).

thf(fun_bo1945492389t_bool_type,type,
    fun_bo1945492389t_bool: $tType ).

thf(fun_bo1431306493t_bool_type,type,
    fun_bo1431306493t_bool: $tType ).

thf(fun_bo1682907689le_alt_type,type,
    fun_bo1682907689le_alt: $tType ).

thf(fun_na699243463e_indi_type,type,
    fun_na699243463e_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_na300967376t_bool_type,type,
    fun_na300967376t_bool: $tType ).

thf(fun_na2037635353i_bool_type,type,
    fun_na2037635353i_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_na6909291l_bool_type,type,
    fun_na6909291l_bool: $tType ).

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

thf(fun_na138495129l_bool_type,type,
    fun_na138495129l_bool: $tType ).

thf(fun_na144630978l_bool_type,type,
    fun_na144630978l_bool: $tType ).

thf(fun_na998785244t_bool_type,type,
    fun_na998785244t_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_Pr1531194158t_bool_type,type,
    fun_Pr1531194158t_bool: $tType ).

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

thf(fun_Pr537467670l_bool_type,type,
    fun_Pr537467670l_bool: $tType ).

thf(fun_Pr2016729180t_bool_type,type,
    fun_Pr2016729180t_bool: $tType ).

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

thf(fun_Pr151242052l_bool_type,type,
    fun_Pr151242052l_bool: $tType ).

thf(fun_Pr1791323223l_bool_type,type,
    fun_Pr1791323223l_bool: $tType ).

thf(fun_Pr1887398791t_bool_type,type,
    fun_Pr1887398791t_bool: $tType ).

thf(fun_Pr2090226719le_alt_type,type,
    fun_Pr2090226719le_alt: $tType ).

thf(fun_fu1618786247l_bool_type,type,
    fun_fu1618786247l_bool: $tType ).

thf(fun_fu1085384691l_bool_type,type,
    fun_fu1085384691l_bool: $tType ).

thf(fun_fu573468015l_bool_type,type,
    fun_fu573468015l_bool: $tType ).

thf(fun_fu1677555470ol_nat_type,type,
    fun_fu1677555470ol_nat: $tType ).

thf(fun_fu1869722514t_bool_type,type,
    fun_fu1869722514t_bool: $tType ).

thf(fun_fu625013235l_bool_type,type,
    fun_fu625013235l_bool: $tType ).

thf(fun_fu596987971t_bool_type,type,
    fun_fu596987971t_bool: $tType ).

thf(fun_fu263774347l_bool_type,type,
    fun_fu263774347l_bool: $tType ).

thf(fun_fu696673523t_bool_type,type,
    fun_fu696673523t_bool: $tType ).

thf(fun_fu91004995t_bool_type,type,
    fun_fu91004995t_bool: $tType ).

thf(fun_fu1572237755l_bool_type,type,
    fun_fu1572237755l_bool: $tType ).

thf(fun_fu844176604l_bool_type,type,
    fun_fu844176604l_bool: $tType ).

thf(fun_fu1603738721ol_nat_type,type,
    fun_fu1603738721ol_nat: $tType ).

thf(fun_fu1712056765i_bool_type,type,
    fun_fu1712056765i_bool: $tType ).

thf(fun_fu1821795357t_bool_type,type,
    fun_fu1821795357t_bool: $tType ).

thf(fun_fu1254370943t_bool_type,type,
    fun_fu1254370943t_bool: $tType ).

thf(fun_fu591186160i_bool_type,type,
    fun_fu591186160i_bool: $tType ).

thf(fun_fu924966107l_bool_type,type,
    fun_fu924966107l_bool: $tType ).

thf(fun_fu2005129568i_bool_type,type,
    fun_fu2005129568i_bool: $tType ).

thf(fun_fu1858742706i_bool_type,type,
    fun_fu1858742706i_bool: $tType ).

thf(fun_fu2036492305i_bool_type,type,
    fun_fu2036492305i_bool: $tType ).

thf(fun_fu857388591i_bool_type,type,
    fun_fu857388591i_bool: $tType ).

thf(fun_fu2139962393t_bool_type,type,
    fun_fu2139962393t_bool: $tType ).

thf(fun_fu1372829539t_bool_type,type,
    fun_fu1372829539t_bool: $tType ).

thf(fun_fu1367082059l_bool_type,type,
    fun_fu1367082059l_bool: $tType ).

thf(fun_fu548876995t_bool_type,type,
    fun_fu548876995t_bool: $tType ).

thf(fun_fu2128130023t_bool_type,type,
    fun_fu2128130023t_bool: $tType ).

thf(fun_fu1771585781l_bool_type,type,
    fun_fu1771585781l_bool: $tType ).

thf(fun_fu846523317l_bool_type,type,
    fun_fu846523317l_bool: $tType ).

thf(fun_fu1610971917i_bool_type,type,
    fun_fu1610971917i_bool: $tType ).

thf(fun_fu2144981539l_bool_type,type,
    fun_fu2144981539l_bool: $tType ).

thf(fun_fu1072826421l_bool_type,type,
    fun_fu1072826421l_bool: $tType ).

thf(fun_fu2030607631t_bool_type,type,
    fun_fu2030607631t_bool: $tType ).

thf(fun_fu205223783t_bool_type,type,
    fun_fu205223783t_bool: $tType ).

thf(fun_fu1929591039e_indi_type,type,
    fun_fu1929591039e_indi: $tType ).

thf(fun_fu3835832l_bool_type,type,
    fun_fu3835832l_bool: $tType ).

thf(fun_fu1023022254t_unit_type,type,
    fun_fu1023022254t_unit: $tType ).

thf(fun_fu223278561i_bool_type,type,
    fun_fu223278561i_bool: $tType ).

thf(fun_fu1427663149t_bool_type,type,
    fun_fu1427663149t_bool: $tType ).

thf(fun_fu1896276031t_bool_type,type,
    fun_fu1896276031t_bool: $tType ).

thf(fun_fu419698981t_bool_type,type,
    fun_fu419698981t_bool: $tType ).

thf(fun_fu1037963345t_bool_type,type,
    fun_fu1037963345t_bool: $tType ).

thf(fun_fu916327706l_bool_type,type,
    fun_fu916327706l_bool: $tType ).

thf(fun_fu1734317328t_bool_type,type,
    fun_fu1734317328t_bool: $tType ).

thf(fun_fu361117961l_bool_type,type,
    fun_fu361117961l_bool: $tType ).

thf(fun_fu1863781882l_bool_type,type,
    fun_fu1863781882l_bool: $tType ).

thf(fun_fu2114379172t_bool_type,type,
    fun_fu2114379172t_bool: $tType ).

thf(fun_fu802339430t_bool_type,type,
    fun_fu802339430t_bool: $tType ).

thf(fun_fu2141985013l_bool_type,type,
    fun_fu2141985013l_bool: $tType ).

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

thf(fun_fu1932307120l_bool_type,type,
    fun_fu1932307120l_bool: $tType ).

thf(fun_fu2010474066l_bool_type,type,
    fun_fu2010474066l_bool: $tType ).

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

thf(fun_fu1185305252l_bool_type,type,
    fun_fu1185305252l_bool: $tType ).

thf(fun_fu1829593041l_bool_type,type,
    fun_fu1829593041l_bool: $tType ).

thf(fun_fu459284641l_bool_type,type,
    fun_fu459284641l_bool: $tType ).

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

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

thf(fun_fu625915566l_bool_type,type,
    fun_fu625915566l_bool: $tType ).

thf(fun_fu302299893l_bool_type,type,
    fun_fu302299893l_bool: $tType ).

thf(fun_fu962836700l_bool_type,type,
    fun_fu962836700l_bool: $tType ).

thf(fun_fu1407717749l_bool_type,type,
    fun_fu1407717749l_bool: $tType ).

thf(fun_fu1618772927l_bool_type,type,
    fun_fu1618772927l_bool: $tType ).

thf(fun_fu827796887l_bool_type,type,
    fun_fu827796887l_bool: $tType ).

thf(fun_fu1168191263t_bool_type,type,
    fun_fu1168191263t_bool: $tType ).

thf(fun_fu662095797l_bool_type,type,
    fun_fu662095797l_bool: $tType ).

thf(fun_fu902912905i_bool_type,type,
    fun_fu902912905i_bool: $tType ).

thf(fun_fu1544203051l_bool_type,type,
    fun_fu1544203051l_bool: $tType ).

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

thf(fun_fun_nat_bool_nat_type,type,
    fun_fun_nat_bool_nat: $tType ).

thf(fun_fu221658642t_bool_type,type,
    fun_fu221658642t_bool: $tType ).

thf(fun_fu1415967063i_bool_type,type,
    fun_fu1415967063i_bool: $tType ).

thf(fun_fu191830394t_bool_type,type,
    fun_fu191830394t_bool: $tType ).

thf(fun_fu1094602547t_bool_type,type,
    fun_fu1094602547t_bool: $tType ).

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

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

thf(fun_fu1096920966t_bool_type,type,
    fun_fu1096920966t_bool: $tType ).

thf(fun_fu613111337t_bool_type,type,
    fun_fu613111337t_bool: $tType ).

thf(fun_fu138597289l_bool_type,type,
    fun_fu138597289l_bool: $tType ).

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

thf(fun_fu1927280855l_bool_type,type,
    fun_fu1927280855l_bool: $tType ).

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

thf(fun_fu1182412548l_bool_type,type,
    fun_fu1182412548l_bool: $tType ).

thf(fun_fu1778022682t_bool_type,type,
    fun_fu1778022682t_bool: $tType ).

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

thf(fun_fu1585362869l_bool_type,type,
    fun_fu1585362869l_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_fu572628082ol_nat_type,type,
    fun_fu572628082ol_nat: $tType ).

thf(fun_fu988033326t_bool_type,type,
    fun_fu988033326t_bool: $tType ).

thf(fun_fu26755632t_bool_type,type,
    fun_fu26755632t_bool: $tType ).

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

thf(fun_fu1463347262t_bool_type,type,
    fun_fu1463347262t_bool: $tType ).

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

thf(fun_fu1250976912t_bool_type,type,
    fun_fu1250976912t_bool: $tType ).

thf(fun_fu1093357393t_bool_type,type,
    fun_fu1093357393t_bool: $tType ).

thf(fun_fu32501645t_bool_type,type,
    fun_fu32501645t_bool: $tType ).

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

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

thf(fun_fu1638321572l_bool_type,type,
    fun_fu1638321572l_bool: $tType ).

thf(fun_fu1172193141l_bool_type,type,
    fun_fu1172193141l_bool: $tType ).

thf(fun_fu504370642l_bool_type,type,
    fun_fu504370642l_bool: $tType ).

thf(fun_fu1327602165l_bool_type,type,
    fun_fu1327602165l_bool: $tType ).

thf(fun_fu1110306633l_bool_type,type,
    fun_fu1110306633l_bool: $tType ).

thf(fun_fu1838150827l_bool_type,type,
    fun_fu1838150827l_bool: $tType ).

thf(fun_fu524263445t_bool_type,type,
    fun_fu524263445t_bool: $tType ).

thf(fun_fu323675445l_bool_type,type,
    fun_fu323675445l_bool: $tType ).

thf(fun_fu672155663l_bool_type,type,
    fun_fu672155663l_bool: $tType ).

thf(fun_fu1464218807l_bool_type,type,
    fun_fu1464218807l_bool: $tType ).

thf(fun_fu1108528357l_bool_type,type,
    fun_fu1108528357l_bool: $tType ).

thf(fun_fu1864062453i_bool_type,type,
    fun_fu1864062453i_bool: $tType ).

thf(fun_fu1607936949l_bool_type,type,
    fun_fu1607936949l_bool: $tType ).

thf(fun_fu1370139438l_bool_type,type,
    fun_fu1370139438l_bool: $tType ).

thf(fun_fu777705871ol_nat_type,type,
    fun_fu777705871ol_nat: $tType ).

thf(fun_fu1006882262l_bool_type,type,
    fun_fu1006882262l_bool: $tType ).

thf(fun_fu146711773l_bool_type,type,
    fun_fu146711773l_bool: $tType ).

thf(fun_fu1078872017t_bool_type,type,
    fun_fu1078872017t_bool: $tType ).

thf(fun_fu835523175l_bool_type,type,
    fun_fu835523175l_bool: $tType ).

thf(fun_fu973465149l_bool_type,type,
    fun_fu973465149l_bool: $tType ).

thf(fun_fu1785284735l_bool_type,type,
    fun_fu1785284735l_bool: $tType ).

thf(fun_fu2080348917l_bool_type,type,
    fun_fu2080348917l_bool: $tType ).

thf(fun_fu1318713124t_bool_type,type,
    fun_fu1318713124t_bool: $tType ).

thf(fun_fu1109942133l_bool_type,type,
    fun_fu1109942133l_bool: $tType ).

thf(fun_fu1741788849l_bool_type,type,
    fun_fu1741788849l_bool: $tType ).

thf(fun_fu748153389e_indi_type,type,
    fun_fu748153389e_indi: $tType ).

thf(fun_fu2098777574l_bool_type,type,
    fun_fu2098777574l_bool: $tType ).

thf(fun_fu1480298716t_unit_type,type,
    fun_fu1480298716t_unit: $tType ).

thf(fun_fu2109152051i_bool_type,type,
    fun_fu2109152051i_bool: $tType ).

thf(fun_fu1522163052l_bool_type,type,
    fun_fu1522163052l_bool: $tType ).

thf(fun_fu1143287650t_bool_type,type,
    fun_fu1143287650t_bool: $tType ).

thf(fun_fu1383920485l_bool_type,type,
    fun_fu1383920485l_bool: $tType ).

thf(fun_fu762833832l_bool_type,type,
    fun_fu762833832l_bool: $tType ).

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

thf(fun_fu500302576l_bool_type,type,
    fun_fu500302576l_bool: $tType ).

thf(fun_fu1489407006l_bool_type,type,
    fun_fu1489407006l_bool: $tType ).

thf(fun_fu422653621l_bool_type,type,
    fun_fu422653621l_bool: $tType ).

thf(fun_fu1304377569l_bool_type,type,
    fun_fu1304377569l_bool: $tType ).

thf(fun_fu1183182719l_bool_type,type,
    fun_fu1183182719l_bool: $tType ).

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

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

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

thf(fun_fu286455014l_bool_type,type,
    fun_fu286455014l_bool: $tType ).

thf(fun_fu1625211924l_bool_type,type,
    fun_fu1625211924l_bool: $tType ).

thf(fun_fu1164115775l_bool_type,type,
    fun_fu1164115775l_bool: $tType ).

thf(fun_fu152274135l_bool_type,type,
    fun_fu152274135l_bool: $tType ).

thf(fun_fu1304086967l_bool_type,type,
    fun_fu1304086967l_bool: $tType ).

thf(fun_fu761902960l_bool_type,type,
    fun_fu761902960l_bool: $tType ).

thf(fun_fu698572390l_bool_type,type,
    fun_fu698572390l_bool: $tType ).

thf(fun_fu523608611i_bool_type,type,
    fun_fu523608611i_bool: $tType ).

thf(fun_fu1843791925l_bool_type,type,
    fun_fu1843791925l_bool: $tType ).

thf(fun_fu1992232028l_bool_type,type,
    fun_fu1992232028l_bool: $tType ).

thf(fun_fu859131105ol_nat_type,type,
    fun_fu859131105ol_nat: $tType ).

thf(fun_fu546411570l_bool_type,type,
    fun_fu546411570l_bool: $tType ).

thf(fun_fu571526969l_bool_type,type,
    fun_fu571526969l_bool: $tType ).

thf(fun_fu309681663t_bool_type,type,
    fun_fu309681663t_bool: $tType ).

thf(fun_fu810527939l_bool_type,type,
    fun_fu810527939l_bool: $tType ).

thf(fun_fu1297042877l_bool_type,type,
    fun_fu1297042877l_bool: $tType ).

thf(fun_fu2060968923l_bool_type,type,
    fun_fu2060968923l_bool: $tType ).

thf(fun_fu2017702261l_bool_type,type,
    fun_fu2017702261l_bool: $tType ).

thf(fun_fu186682962t_bool_type,type,
    fun_fu186682962t_bool: $tType ).

thf(fun_fu224426485l_bool_type,type,
    fun_fu224426485l_bool: $tType ).

thf(fun_fu1818294997l_bool_type,type,
    fun_fu1818294997l_bool: $tType ).

thf(fun_fu424058085l_bool_type,type,
    fun_fu424058085l_bool: $tType ).

thf(fun_fu178397086l_bool_type,type,
    fun_fu178397086l_bool: $tType ).

thf(fun_fu1796799636l_bool_type,type,
    fun_fu1796799636l_bool: $tType ).

thf(fun_fu1975854110l_bool_type,type,
    fun_fu1975854110l_bool: $tType ).

thf(fun_fu1710953559l_bool_type,type,
    fun_fu1710953559l_bool: $tType ).

thf(fun_fu1215489613l_bool_type,type,
    fun_fu1215489613l_bool: $tType ).

thf(fun_fu1132933928l_bool_type,type,
    fun_fu1132933928l_bool: $tType ).

thf(fun_fu1406810280i_bool_type,type,
    fun_fu1406810280i_bool: $tType ).

thf(fun_fu687131369l_bool_type,type,
    fun_fu687131369l_bool: $tType ).

thf(fun_fu2013733473l_bool_type,type,
    fun_fu2013733473l_bool: $tType ).

thf(fun_fu955147676ol_nat_type,type,
    fun_fu955147676ol_nat: $tType ).

thf(fun_fu1868761018l_bool_type,type,
    fun_fu1868761018l_bool: $tType ).

thf(fun_fu151575155l_bool_type,type,
    fun_fu151575155l_bool: $tType ).

thf(fun_fu1632756612t_bool_type,type,
    fun_fu1632756612t_bool: $tType ).

thf(fun_fu109527913l_bool_type,type,
    fun_fu109527913l_bool: $tType ).

thf(fun_fu329401612l_bool_type,type,
    fun_fu329401612l_bool: $tType ).

thf(fun_fu1253304283l_bool_type,type,
    fun_fu1253304283l_bool: $tType ).

thf(fun_fu1265985907l_bool_type,type,
    fun_fu1265985907l_bool: $tType ).

thf(fun_fu1824295331l_bool_type,type,
    fun_fu1824295331l_bool: $tType ).

thf(fun_fu1703884119t_bool_type,type,
    fun_fu1703884119t_bool: $tType ).

thf(fun_fu2020020679l_bool_type,type,
    fun_fu2020020679l_bool: $tType ).

thf(fun_fu452089579l_bool_type,type,
    fun_fu452089579l_bool: $tType ).

thf(fun_fu627447383l_bool_type,type,
    fun_fu627447383l_bool: $tType ).

thf(fun_fu902545894i_bool_type,type,
    fun_fu902545894i_bool: $tType ).

thf(fun_fu916781301l_bool_type,type,
    fun_fu916781301l_bool: $tType ).

thf(fun_fu562005862e_indi_type,type,
    fun_fu562005862e_indi: $tType ).

thf(fun_fu638310559l_bool_type,type,
    fun_fu638310559l_bool: $tType ).

thf(fun_fu841105374ol_nat_type,type,
    fun_fu841105374ol_nat: $tType ).

thf(fun_fu665686165t_unit_type,type,
    fun_fu665686165t_unit: $tType ).

thf(fun_fu1534804551t_bool_type,type,
    fun_fu1534804551t_bool: $tType ).

thf(fun_fu1118734319t_bool_type,type,
    fun_fu1118734319t_bool: $tType ).

thf(fun_fu1287834969t_bool_type,type,
    fun_fu1287834969t_bool: $tType ).

thf(fun_fu1679793515t_bool_type,type,
    fun_fu1679793515t_bool: $tType ).

thf(fun_fu2142850746i_bool_type,type,
    fun_fu2142850746i_bool: $tType ).

thf(fun_fu230081932t_bool_type,type,
    fun_fu230081932t_bool: $tType ).

thf(fun_fu1847201208t_bool_type,type,
    fun_fu1847201208t_bool: $tType ).

thf(fun_fu237781875l_bool_type,type,
    fun_fu237781875l_bool: $tType ).

thf(fun_fu1414555455t_bool_type,type,
    fun_fu1414555455t_bool: $tType ).

thf(fun_fu477456066t_bool_type,type,
    fun_fu477456066t_bool: $tType ).

thf(fun_fu643686505t_bool_type,type,
    fun_fu643686505t_bool: $tType ).

thf(fun_fu1648543689t_bool_type,type,
    fun_fu1648543689t_bool: $tType ).

thf(fun_fu864675765l_bool_type,type,
    fun_fu864675765l_bool: $tType ).

thf(fun_fu643206625l_bool_type,type,
    fun_fu643206625l_bool: $tType ).

thf(fun_fu297564241t_bool_type,type,
    fun_fu297564241t_bool: $tType ).

thf(fun_fu1550952061t_bool_type,type,
    fun_fu1550952061t_bool: $tType ).

thf(fun_fu1428746645t_bool_type,type,
    fun_fu1428746645t_bool: $tType ).

thf(fun_fu318801205l_bool_type,type,
    fun_fu318801205l_bool: $tType ).

thf(fun_fu598681231t_bool_type,type,
    fun_fu598681231t_bool: $tType ).

thf(fun_Pr1509342064e_indi_type,type,
    fun_Pr1509342064e_indi: $tType ).

thf(fun_Pr2067565481t_bool_type,type,
    fun_Pr2067565481t_bool: $tType ).

thf(fun_Pr376858015t_unit_type,type,
    fun_Pr376858015t_unit: $tType ).

thf(fun_Pr895221296i_bool_type,type,
    fun_Pr895221296i_bool: $tType ).

thf(fun_Pr1780397033l_bool_type,type,
    fun_Pr1780397033l_bool: $tType ).

thf(fun_Pr1069395679t_bool_type,type,
    fun_Pr1069395679t_bool: $tType ).

thf(fun_Pr1085078251l_bool_type,type,
    fun_Pr1085078251l_bool: $tType ).

thf(produc472769767le_alt_type,type,
    produc472769767le_alt: $tType ).

thf(arrow_1335103695le_IIA_decl,type,
    arrow_1335103695le_IIA: fun_fu2098777574l_bool ).

thf(arrow_1361987423le_Lin_decl,type,
    arrow_1361987423le_Lin: fun_fu638310559l_bool ).

thf(arrow_5070731e_Prof_decl,type,
    arrow_5070731e_Prof: fun_fu3835832l_bool ).

thf(arrow_216713899_above_decl,type,
    arrow_216713899_above: fun_fu1287834969t_bool ).

thf(arrow_1525312447_below_decl,type,
    arrow_1525312447_below: fun_Pr2067565481t_bool > arrow_1893660431le_alt > arrow_1893660431le_alt > fun_Pr2067565481t_bool ).

thf(arrow_1765888670ctator_decl,type,
    arrow_1765888670ctator: fun_fu2109152051i_bool ).

thf(arrow_1481558583_mkbot_decl,type,
    arrow_1481558583_mkbot: fun_fu1679793515t_bool ).

thf(arrow_1630265669_mktop_decl,type,
    arrow_1630265669_mktop: fun_fu1679793515t_bool ).

thf(arrow_320876018nimity_decl,type,
    arrow_320876018nimity: fun_fu2098777574l_bool ).

thf(cOMBB_1061985500e_indi_decl,type,
    cOMBB_1061985500e_indi: fun_bo1945492389t_bool > fun_fu1821795357t_bool ).

thf(cOMBB_1869811296e_indi_decl,type,
    cOMBB_1869811296e_indi: fun_nat_fun_nat_bool > fun_fu1372829539t_bool ).

thf(cOMBB_652885079le_alt_decl,type,
    cOMBB_652885079le_alt: fun_fu696673523t_bool > fun_fu596987971t_bool ).

thf(cOMBB_1575576719le_alt_decl,type,
    cOMBB_1575576719le_alt: fun_fu1572237755l_bool > fun_fu263774347l_bool ).

thf(cOMBB_1876517692e_indi_decl,type,
    cOMBB_1876517692e_indi: fun_fu1287834969t_bool > fun_fu1427663149t_bool ).

thf(cOMBB_80760910e_indi_decl,type,
    cOMBB_80760910e_indi: fun_fu1679793515t_bool > fun_fu1896276031t_bool ).

thf(cOMBB_1660064607le_alt_decl,type,
    cOMBB_1660064607le_alt: fun_Pr1085078251l_bool > fun_fu1572237755l_bool ).

thf(cOMBC_395465908l_bool_decl,type,
    cOMBC_395465908l_bool: fun_fu696673523t_bool ).

thf(cOMBC_557453916t_bool_decl,type,
    cOMBC_557453916t_bool: fun_fu91004995t_bool ).

thf(cOMBC_1486904681t_bool_decl,type,
    cOMBC_1486904681t_bool: fun_fu548876995t_bool ).

thf(cOMBC_1417338747t_bool_decl,type,
    cOMBC_1417338747t_bool: fun_fu2128130023t_bool ).

thf(cOMBC_722552198t_bool_decl,type,
    cOMBC_722552198t_bool: fun_fu1610971917i_bool ).

thf(cOMBC_156709173t_bool_decl,type,
    cOMBC_156709173t_bool: fun_fu2030607631t_bool ).

thf(cOMBC_750853729t_bool_decl,type,
    cOMBC_750853729t_bool: fun_fu205223783t_bool ).

thf(cOMBC_2133093654l_bool_decl,type,
    cOMBC_2133093654l_bool: fun_fu452089579l_bool ).

thf(cOMBC_593569186l_bool_decl,type,
    cOMBC_593569186l_bool: fun_fu598681231t_bool ).

thf(cOMBI_nat_decl,type,
    cOMBI_nat: fun_nat_nat ).

thf(cOMBK_81143760t_bool_decl,type,
    cOMBK_81143760t_bool: fun_bo377688929l_bool ).

thf(cOMBK_198697344le_alt_decl,type,
    cOMBK_198697344le_alt: fun_bo1431306493t_bool ).

thf(cOMBK_1987648063le_alt_decl,type,
    cOMBK_1987648063le_alt: fun_fu857388591i_bool ).

thf(cOMBK_138598520le_alt_decl,type,
    cOMBK_138598520le_alt: fun_fu459284641l_bool ).

thf(cOMBK_751896174le_alt_decl,type,
    cOMBK_751896174le_alt: fun_fu32501645t_bool ).

thf(cOMBK_1520063231e_indi_decl,type,
    cOMBK_1520063231e_indi: fun_fu1868761018l_bool ).

thf(cOMBK_650639032l_bool_decl,type,
    cOMBK_650639032l_bool: fun_fu151575155l_bool ).

thf(cOMBK_1701906001t_bool_decl,type,
    cOMBK_1701906001t_bool: fun_fu329401612l_bool ).

thf(cOMBK_1650320063e_indi_decl,type,
    cOMBK_1650320063e_indi: fun_fu1847201208t_bool ).

thf(cOMBK_5056120l_bool_decl,type,
    cOMBK_5056120l_bool: fun_fu1414555455t_bool ).

thf(cOMBK_681766254t_unit_decl,type,
    cOMBK_681766254t_unit: fun_fu1648543689t_bool ).

thf(cOMBS_1925466437t_bool_decl,type,
    cOMBS_1925466437t_bool: fun_Ar535288606t_bool > fun_fu419698981t_bool ).

thf(cOMBS_1181656689t_bool_decl,type,
    cOMBS_1181656689t_bool: fun_Ar516759882t_bool > fun_fu1037963345t_bool ).

thf(finite1672073426e_indi_decl,type,
    finite1672073426e_indi: fun_fu1603738721ol_nat ).

thf(finite92092049e_indi_decl,type,
    finite92092049e_indi: fun_fu844176604l_bool ).

thf(inj_on1960344199di_nat_decl,type,
    inj_on1960344199di_nat: fun_Ar671024215di_nat > fun_fu844176604l_bool ).

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

thf(pi_Arr959578316t_bool_decl,type,
    pi_Arr959578316t_bool: fun_Ar1809396326i_bool > fun_Ar1474557608l_bool > fun_fu3835832l_bool ).

thf(pi_Arr1460528004le_alt_decl,type,
    pi_Arr1460528004le_alt: fun_Ar1809396326i_bool > fun_Ar274636406t_bool > fun_fu802339430t_bool ).

thf(pi_boo1111177555t_bool_decl,type,
    pi_boo1111177555t_bool: fun_bool_bool > fun_bo377688929l_bool > fun_fu1618772927l_bool ).

thf(pi_boo7125949le_alt_decl,type,
    pi_boo7125949le_alt: fun_bool_bool > fun_bo1431306493t_bool > fun_fu1168191263t_bool ).

thf(pi_Pro1820940723le_alt_decl,type,
    pi_Pro1820940723le_alt: fun_Pr1643180309t_bool > fun_Pr1887398791t_bool > fun_fu524263445t_bool ).

thf(pi_fun1746584570t_bool_decl,type,
    pi_fun1746584570t_bool: fun_fu3835832l_bool > fun_fu1863781882l_bool > fun_fu2098777574l_bool ).

thf(pi_Pro837265796e_indi_decl,type,
    pi_Pro837265796e_indi: fun_Pr2067565481t_bool > fun_Pr895221296i_bool > fun_fu902545894i_bool ).

thf(pi_Pro1238944957t_bool_decl,type,
    pi_Pro1238944957t_bool: fun_Pr2067565481t_bool > fun_Pr1780397033l_bool > fun_fu638310559l_bool ).

thf(pi_Pro346842291t_unit_decl,type,
    pi_Pro346842291t_unit: fun_Pr2067565481t_bool > fun_Pr1069395679t_bool > fun_fu1428746645t_bool ).

thf(one_one_nat_decl,type,
    one_one_nat: nat ).

thf(plus_plus_nat_decl,type,
    plus_plus_nat: fun_nat_fun_nat_nat ).

thf(times_times_nat_decl,type,
    times_times_nat: nat > fun_nat_nat ).

thf(zero_zero_nat_decl,type,
    zero_zero_nat: nat ).

thf(hilber1580028780di_nat_decl,type,
    hilber1580028780di_nat: fun_Ar1809396326i_bool > fun_Ar671024215di_nat > fun_na699243463e_indi ).

thf(hilber195283148at_nat_decl,type,
    hilber195283148at_nat: fun_nat_bool > fun_nat_nat > fun_nat_nat ).

thf(if_fun523439385t_bool_decl,type,
    if_fun523439385t_bool: fun_bo1945492389t_bool ).

thf(suc_decl,type,
    suc: fun_nat_nat ).

thf(nat_size_decl,type,
    nat_size: fun_nat_nat ).

thf(size_size_nat_decl,type,
    size_size_nat: fun_nat_nat ).

thf(ord_less_nat_decl,type,
    ord_less_nat: fun_nat_fun_nat_bool ).

thf(ord_le19409623t_bool_decl,type,
    ord_le19409623t_bool: fun_fu625013235l_bool ).

thf(ord_le1478665215t_bool_decl,type,
    ord_le1478665215t_bool: fun_fu643206625l_bool ).

thf(ord_less_eq_nat_decl,type,
    ord_less_eq_nat: fun_nat_fun_nat_bool ).

thf(ord_le172225251t_bool_decl,type,
    ord_le172225251t_bool: fun_fu625013235l_bool ).

thf(ord_le742797417l_bool_decl,type,
    ord_le742797417l_bool: fun_fu1393819981l_bool ).

thf(ord_le1545885909l_bool_decl,type,
    ord_le1545885909l_bool: fun_fu1265985907l_bool ).

thf(ord_le1577377523t_bool_decl,type,
    ord_le1577377523t_bool: fun_fu643206625l_bool ).

thf(top_top_bool_decl,type,
    top_top_bool: bool ).

thf(top_to951839027t_bool_decl,type,
    top_to951839027t_bool: fun_Ar331856045t_bool ).

thf(top_to788185952i_bool_decl,type,
    top_to788185952i_bool: fun_Ar1809396326i_bool ).

thf(top_to1647826457l_bool_decl,type,
    top_to1647826457l_bool: fun_bool_bool ).

thf(top_top_fun_nat_bool_decl,type,
    top_top_fun_nat_bool: fun_nat_bool ).

thf(top_to1257323279t_bool_decl,type,
    top_to1257323279t_bool: fun_Pr1643180309t_bool ).

thf(top_to553140914l_bool_decl,type,
    top_to553140914l_bool: fun_fu3835832l_bool ).

thf(top_to827110112l_bool_decl,type,
    top_to827110112l_bool: fun_fu2098777574l_bool ).

thf(top_to1312956197l_bool_decl,type,
    top_to1312956197l_bool: fun_fu638310559l_bool ).

thf(top_to1138392227t_bool_decl,type,
    top_to1138392227t_bool: fun_Pr2067565481t_bool ).

thf(produc1590937303le_alt_decl,type,
    produc1590937303le_alt: fun_Ar2121501495le_alt ).

thf(collec2125531966t_bool_decl,type,
    collec2125531966t_bool: fun_fu1824295331l_bool ).

thf(collec1988958098le_alt_decl,type,
    collec1988958098le_alt: fun_fu1550952061t_bool ).

thf(fFalse_decl,type,
    fFalse: bool ).

thf(fTrue_decl,type,
    fTrue: bool ).

thf(fequal_nat_decl,type,
    fequal_nat: fun_nat_fun_nat_bool ).

thf(hAPP_A1748732503t_bool_decl,type,
    hAPP_A1748732503t_bool: fun_Ar17477381t_bool > arrow_1893660431le_alt > bool ).

thf(hAPP_A2063800319t_bool_decl,type,
    hAPP_A2063800319t_bool: fun_Ar331856045t_bool > arrow_1893660431le_alt > fun_Ar17477381t_bool ).

thf(hAPP_A1608658241l_bool_decl,type,
    hAPP_A1608658241l_bool: fun_Ar1995913199l_bool > arrow_1893660431le_alt > fun_Ar339057223l_bool ).

thf(hAPP_A1058422557t_bool_decl,type,
    hAPP_A1058422557t_bool: fun_Ar797671557t_bool > arrow_1893660431le_alt > fun_Ar1573071255t_bool ).

thf(hAPP_A1146194953le_alt_decl,type,
    hAPP_A1146194953le_alt: fun_Ar2121501495le_alt > arrow_1893660431le_alt > fun_Ar245737999le_alt ).

thf(hAPP_A1889513822t_bool_decl,type,
    hAPP_A1889513822t_bool: fun_Ar1753411852t_bool > arrow_1893660431le_alt > fun_Ar64685412t_bool ).

thf(hAPP_A425126512t_bool_decl,type,
    hAPP_A425126512t_bool: fun_Ar1623257374t_bool > arrow_1893660431le_alt > fun_Ar274636406t_bool ).

thf(hAPP_A442239897l_bool_decl,type,
    hAPP_A442239897l_bool: fun_Ar339057223l_bool > arrow_1893660431le_alt > fun_fu638310559l_bool ).

thf(hAPP_A656921921t_bool_decl,type,
    hAPP_A656921921t_bool: fun_Ar636018671t_bool > arrow_1893660431le_alt > fun_fu1534804551t_bool ).

thf(hAPP_A1601437999t_bool_decl,type,
    hAPP_A1601437999t_bool: fun_Ar1573071255t_bool > arrow_1893660431le_alt > fun_Pr2067565481t_bool ).

thf(hAPP_A1299015393le_alt_decl,type,
    hAPP_A1299015393le_alt: fun_Ar245737999le_alt > arrow_1893660431le_alt > produc472769767le_alt ).

thf(hAPP_A997847300i_bool_decl,type,
    hAPP_A997847300i_bool: fun_Ar1809396326i_bool > arrow_856714788e_indi > bool ).

thf(hAPP_A376526755di_nat_decl,type,
    hAPP_A376526755di_nat: fun_Ar671024215di_nat > arrow_856714788e_indi > nat ).

thf(hAPP_A38124190t_bool_decl,type,
    hAPP_A38124190t_bool: fun_Ar290235730t_bool > arrow_856714788e_indi > fun_Ar797671557t_bool ).

thf(hAPP_A1309733808t_bool_decl,type,
    hAPP_A1309733808t_bool: fun_Ar64685412t_bool > arrow_856714788e_indi > fun_Ar1573071255t_bool ).

thf(hAPP_A1686943911t_bool_decl,type,
    hAPP_A1686943911t_bool: fun_Ar603939593t_bool > arrow_856714788e_indi > fun_nat_bool ).

thf(hAPP_A1597696899l_bool_decl,type,
    hAPP_A1597696899l_bool: fun_Ar1047186533l_bool > arrow_856714788e_indi > fun_fu844176604l_bool ).

thf(hAPP_A897398598l_bool_decl,type,
    hAPP_A897398598l_bool: fun_Ar1474557608l_bool > arrow_856714788e_indi > fun_fu638310559l_bool ).

thf(hAPP_A1395684458t_bool_decl,type,
    hAPP_A1395684458t_bool: fun_Ar535288606t_bool > arrow_856714788e_indi > fun_fu297564241t_bool ).

thf(hAPP_A834130326t_bool_decl,type,
    hAPP_A834130326t_bool: fun_Ar516759882t_bool > arrow_856714788e_indi > fun_fu1550952061t_bool ).

thf(hAPP_A1646126530t_bool_decl,type,
    hAPP_A1646126530t_bool: fun_Ar274636406t_bool > arrow_856714788e_indi > fun_Pr2067565481t_bool ).

thf(hAPP_A899858958le_alt_decl,type,
    hAPP_A899858958le_alt: fun_Ar338949104le_alt > arrow_856714788e_indi > produc472769767le_alt ).

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

thf(hAPP_b1787118453l_bool_decl,type,
    hAPP_b1787118453l_bool: fun_bo492988759l_bool > bool > fun_fu1255657237l_bool ).

thf(hAPP_b1272691967l_bool_decl,type,
    hAPP_b1272691967l_bool: fun_bo377688929l_bool > bool > fun_fu638310559l_bool ).

thf(hAPP_b35146737t_bool_decl,type,
    hAPP_b35146737t_bool: fun_bo1945492389t_bool > bool > fun_fu297564241t_bool ).

thf(hAPP_b128655177t_bool_decl,type,
    hAPP_b128655177t_bool: fun_bo1431306493t_bool > bool > fun_Pr2067565481t_bool ).

thf(hAPP_b2094455111le_alt_decl,type,
    hAPP_b2094455111le_alt: fun_bo1682907689le_alt > bool > produc472769767le_alt ).

thf(hAPP_n1937165849e_indi_decl,type,
    hAPP_n1937165849e_indi: fun_na699243463e_indi > nat > arrow_856714788e_indi ).

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

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

thf(hAPP_n1312530466t_bool_decl,type,
    hAPP_n1312530466t_bool: fun_na300967376t_bool > nat > fun_Ar331856045t_bool ).

thf(hAPP_n34002993i_bool_decl,type,
    hAPP_n34002993i_bool: fun_na2037635353i_bool > nat > fun_Ar1809396326i_bool ).

thf(hAPP_n1699378549t_bool_decl,type,
    hAPP_n1699378549t_bool: fun_nat_fun_nat_bool > nat > fun_nat_bool ).

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

thf(hAPP_n1161265524t_bool_decl,type,
    hAPP_n1161265524t_bool: fun_na998785244t_bool > nat > fun_Pr2067565481t_bool ).

thf(hAPP_P1676879539t_bool_decl,type,
    hAPP_P1676879539t_bool: fun_Pr1643180309t_bool > product_unit > bool ).

thf(hAPP_P607165281l_bool_decl,type,
    hAPP_P607165281l_bool: fun_Pr1863373635l_bool > product_unit > fun_fu309829899l_bool ).

thf(hAPP_P1914371027t_bool_decl,type,
    hAPP_P1914371027t_bool: fun_Pr1887398791t_bool > product_unit > fun_Pr2067565481t_bool ).

thf(hAPP_P396106045le_alt_decl,type,
    hAPP_P396106045le_alt: fun_Pr2090226719le_alt > product_unit > produc472769767le_alt ).

thf(hAPP_f1452856589l_bool_decl,type,
    hAPP_f1452856589l_bool: fun_fu573468015l_bool > fun_Ar331856045t_bool > bool ).

thf(hAPP_f1403773274ol_nat_decl,type,
    hAPP_f1403773274ol_nat: fun_fu1677555470ol_nat > fun_Ar331856045t_bool > nat ).

thf(hAPP_f1055587775l_bool_decl,type,
    hAPP_f1055587775l_bool: fun_fu625013235l_bool > fun_Ar331856045t_bool > fun_fu573468015l_bool ).

thf(hAPP_f105674721t_bool_decl,type,
    hAPP_f105674721t_bool: fun_fu596987971t_bool > fun_Ar1995913199l_bool > fun_Ar636018671t_bool ).

thf(hAPP_f184584489l_bool_decl,type,
    hAPP_f184584489l_bool: fun_fu263774347l_bool > fun_Ar2121501495le_alt > fun_Ar1995913199l_bool ).

thf(hAPP_f1689397393t_bool_decl,type,
    hAPP_f1689397393t_bool: fun_fu696673523t_bool > fun_Ar339057223l_bool > fun_fu1534804551t_bool ).

thf(hAPP_f1081591777t_bool_decl,type,
    hAPP_f1081591777t_bool: fun_fu91004995t_bool > fun_Ar636018671t_bool > fun_fu1118734319t_bool ).

thf(hAPP_f1536341593l_bool_decl,type,
    hAPP_f1536341593l_bool: fun_fu1572237755l_bool > fun_Ar245737999le_alt > fun_Ar339057223l_bool ).

thf(hAPP_f584385070l_bool_decl,type,
    hAPP_f584385070l_bool: fun_fu844176604l_bool > fun_Ar1809396326i_bool > bool ).

thf(hAPP_f846027769ol_nat_decl,type,
    hAPP_f846027769ol_nat: fun_fu1603738721ol_nat > fun_Ar1809396326i_bool > nat ).

thf(hAPP_f668886383t_bool_decl,type,
    hAPP_f668886383t_bool: fun_fu1821795357t_bool > fun_Ar1809396326i_bool > fun_Ar535288606t_bool ).

thf(hAPP_f359069313i_bool_decl,type,
    hAPP_f359069313i_bool: fun_fu857388591i_bool > fun_Ar1809396326i_bool > fun_Pr895221296i_bool ).

thf(hAPP_f966656047t_bool_decl,type,
    hAPP_f966656047t_bool: fun_fu1372829539t_bool > fun_Ar671024215di_nat > fun_Ar603939593t_bool ).

thf(hAPP_f2102110817t_bool_decl,type,
    hAPP_f2102110817t_bool: fun_fu548876995t_bool > fun_Ar290235730t_bool > fun_Ar1753411852t_bool ).

thf(hAPP_f1631649925t_bool_decl,type,
    hAPP_f1631649925t_bool: fun_fu2128130023t_bool > fun_Ar64685412t_bool > fun_Ar1623257374t_bool ).

thf(hAPP_f721434149i_bool_decl,type,
    hAPP_f721434149i_bool: fun_fu1610971917i_bool > fun_Ar603939593t_bool > fun_na2037635353i_bool ).

thf(hAPP_f1908974253t_bool_decl,type,
    hAPP_f1908974253t_bool: fun_fu2030607631t_bool > fun_Ar535288606t_bool > fun_fu230081932t_bool ).

thf(hAPP_f601594885t_bool_decl,type,
    hAPP_f601594885t_bool: fun_fu205223783t_bool > fun_Ar516759882t_bool > fun_fu1847201208t_bool ).

thf(hAPP_f995490902l_bool_decl,type,
    hAPP_f995490902l_bool: fun_fu3835832l_bool > fun_Ar274636406t_bool > bool ).

thf(hAPP_f1751344075t_bool_decl,type,
    hAPP_f1751344075t_bool: fun_fu1427663149t_bool > fun_Ar274636406t_bool > fun_Ar290235730t_bool ).

thf(hAPP_f831214557t_bool_decl,type,
    hAPP_f831214557t_bool: fun_fu1896276031t_bool > fun_Ar274636406t_bool > fun_Ar64685412t_bool ).

thf(hAPP_f1001205955t_bool_decl,type,
    hAPP_f1001205955t_bool: fun_fu419698981t_bool > fun_Ar274636406t_bool > fun_Ar516759882t_bool ).

thf(hAPP_f1302887663t_bool_decl,type,
    hAPP_f1302887663t_bool: fun_fu1037963345t_bool > fun_Ar274636406t_bool > fun_Ar274636406t_bool ).

thf(hAPP_f1225332775l_bool_decl,type,
    hAPP_f1225332775l_bool: fun_fu361117961l_bool > fun_Ar274636406t_bool > fun_fu1370139438l_bool ).

thf(hAPP_f1915815064l_bool_decl,type,
    hAPP_f1915815064l_bool: fun_fu1863781882l_bool > fun_Ar274636406t_bool > fun_fu638310559l_bool ).

thf(hAPP_f2008608496t_bool_decl,type,
    hAPP_f2008608496t_bool: fun_fu2114379172t_bool > fun_Ar274636406t_bool > fun_Pr2067565481t_bool ).

thf(hAPP_f766019597l_bool_decl,type,
    hAPP_f766019597l_bool: fun_fu2141985013l_bool > fun_Ar338949104le_alt > fun_fu762833832l_bool ).

thf(hAPP_f387058535l_bool_decl,type,
    hAPP_f387058535l_bool: fun_fu1255657237l_bool > fun_bool_bool > bool ).

thf(hAPP_f612708895l_bool_decl,type,
    hAPP_f612708895l_bool: fun_fu1393819981l_bool > fun_bool_bool > fun_fu1255657237l_bool ).

thf(hAPP_f699791347l_bool_decl,type,
    hAPP_f699791347l_bool: fun_fu459284641l_bool > fun_bool_bool > fun_Pr1780397033l_bool ).

thf(hAPP_f416878261l_bool_decl,type,
    hAPP_f416878261l_bool: fun_fu827796887l_bool > fun_bo1431306493t_bool > fun_fu422653621l_bool ).

thf(hAPP_f334747853l_bool_decl,type,
    hAPP_f334747853l_bool: fun_fu662095797l_bool > fun_bo1682907689le_alt > fun_fu1304377569l_bool ).

thf(hAPP_f54304608l_bool_decl,type,
    hAPP_f54304608l_bool: fun_fu425979586l_bool > fun_nat_bool > bool ).

thf(hAPP_f2028818269l_bool_decl,type,
    hAPP_f2028818269l_bool: fun_fu309829899l_bool > fun_Pr1643180309t_bool > bool ).

thf(hAPP_f723483871t_bool_decl,type,
    hAPP_f723483871t_bool: fun_fu32501645t_bool > fun_Pr1643180309t_bool > fun_Pr1069395679t_bool ).

thf(hAPP_f41367117l_bool_decl,type,
    hAPP_f41367117l_bool: fun_fu323675445l_bool > fun_Pr2090226719le_alt > fun_fu152274135l_bool ).

thf(hAPP_f73423488l_bool_decl,type,
    hAPP_f73423488l_bool: fun_fu1370139438l_bool > fun_fu3835832l_bool > bool ).

thf(hAPP_f1572141188l_bool_decl,type,
    hAPP_f1572141188l_bool: fun_fu2098777574l_bool > fun_fu2114379172t_bool > bool ).

thf(hAPP_f399308031i_bool_decl,type,
    hAPP_f399308031i_bool: fun_fu2109152051i_bool > fun_fu2114379172t_bool > fun_Ar1809396326i_bool ).

thf(hAPP_f1714503811l_bool_decl,type,
    hAPP_f1714503811l_bool: fun_fu1383920485l_bool > fun_fu2114379172t_bool > fun_fu1992232028l_bool ).

thf(hAPP_f1754488902l_bool_decl,type,
    hAPP_f1754488902l_bool: fun_fu762833832l_bool > fun_fu802339430t_bool > bool ).

thf(hAPP_f398210311l_bool_decl,type,
    hAPP_f398210311l_bool: fun_fu422653621l_bool > fun_fu1618772927l_bool > bool ).

thf(hAPP_f1620711039l_bool_decl,type,
    hAPP_f1620711039l_bool: fun_fu1304377569l_bool > fun_fu1168191263t_bool > bool ).

thf(hAPP_f684683381l_bool_decl,type,
    hAPP_f684683381l_bool: fun_fu152274135l_bool > fun_fu524263445t_bool > bool ).

thf(hAPP_f975209902l_bool_decl,type,
    hAPP_f975209902l_bool: fun_fu1992232028l_bool > fun_fu2098777574l_bool > bool ).

thf(hAPP_f2124588998l_bool_decl,type,
    hAPP_f2124588998l_bool: fun_fu1132933928l_bool > fun_fu902545894i_bool > bool ).

thf(hAPP_f182583295l_bool_decl,type,
    hAPP_f182583295l_bool: fun_fu2013733473l_bool > fun_fu638310559l_bool > bool ).

thf(hAPP_f1487854056ol_nat_decl,type,
    hAPP_f1487854056ol_nat: fun_fu955147676ol_nat > fun_fu638310559l_bool > nat ).

thf(hAPP_f1717907078l_bool_decl,type,
    hAPP_f1717907078l_bool: fun_fu1868761018l_bool > fun_fu638310559l_bool > fun_Ar1474557608l_bool ).

thf(hAPP_f86272063l_bool_decl,type,
    hAPP_f86272063l_bool: fun_fu151575155l_bool > fun_fu638310559l_bool > fun_bo377688929l_bool ).

thf(hAPP_f1104294872l_bool_decl,type,
    hAPP_f1104294872l_bool: fun_fu329401612l_bool > fun_fu638310559l_bool > fun_fu1863781882l_bool ).

thf(hAPP_f1722316607l_bool_decl,type,
    hAPP_f1722316607l_bool: fun_fu1265985907l_bool > fun_fu638310559l_bool > fun_fu2013733473l_bool ).

thf(hAPP_f1060563265l_bool_decl,type,
    hAPP_f1060563265l_bool: fun_fu1824295331l_bool > fun_fu638310559l_bool > fun_fu638310559l_bool ).

thf(hAPP_f1776355587l_bool_decl,type,
    hAPP_f1776355587l_bool: fun_fu452089579l_bool > fun_fu864675765l_bool > fun_fu1824295331l_bool ).

thf(hAPP_f1159856629l_bool_decl,type,
    hAPP_f1159856629l_bool: fun_fu627447383l_bool > fun_fu1428746645t_bool > bool ).

thf(hAPP_f1187850253l_bool_decl,type,
    hAPP_f1187850253l_bool: fun_fu916781301l_bool > fun_Pr1509342064e_indi > fun_fu1132933928l_bool ).

thf(hAPP_f52567537l_bool_decl,type,
    hAPP_f52567537l_bool: fun_fu638310559l_bool > fun_Pr2067565481t_bool > bool ).

thf(hAPP_f1842225014ol_nat_decl,type,
    hAPP_f1842225014ol_nat: fun_fu841105374ol_nat > fun_Pr2067565481t_bool > nat ).

thf(hAPP_f234621849t_bool_decl,type,
    hAPP_f234621849t_bool: fun_fu1534804551t_bool > fun_Pr2067565481t_bool > fun_Ar17477381t_bool ).

thf(hAPP_f449303873t_bool_decl,type,
    hAPP_f449303873t_bool: fun_fu1118734319t_bool > fun_Pr2067565481t_bool > fun_Ar331856045t_bool ).

thf(hAPP_f1550387441t_bool_decl,type,
    hAPP_f1550387441t_bool: fun_fu1287834969t_bool > fun_Pr2067565481t_bool > fun_Ar797671557t_bool ).

thf(hAPP_f1761571331t_bool_decl,type,
    hAPP_f1761571331t_bool: fun_fu1679793515t_bool > fun_Pr2067565481t_bool > fun_Ar1573071255t_bool ).

thf(hAPP_f1344464862t_bool_decl,type,
    hAPP_f1344464862t_bool: fun_fu230081932t_bool > fun_Pr2067565481t_bool > fun_Ar516759882t_bool ).

thf(hAPP_f480276746t_bool_decl,type,
    hAPP_f480276746t_bool: fun_fu1847201208t_bool > fun_Pr2067565481t_bool > fun_Ar274636406t_bool ).

thf(hAPP_f1723896209t_bool_decl,type,
    hAPP_f1723896209t_bool: fun_fu1414555455t_bool > fun_Pr2067565481t_bool > fun_bo1431306493t_bool ).

thf(hAPP_f15777819t_bool_decl,type,
    hAPP_f15777819t_bool: fun_fu1648543689t_bool > fun_Pr2067565481t_bool > fun_Pr1887398791t_bool ).

thf(hAPP_f1482930381l_bool_decl,type,
    hAPP_f1482930381l_bool: fun_fu864675765l_bool > fun_Pr2067565481t_bool > fun_fu2013733473l_bool ).

thf(hAPP_f930900275l_bool_decl,type,
    hAPP_f930900275l_bool: fun_fu643206625l_bool > fun_Pr2067565481t_bool > fun_fu638310559l_bool ).

thf(hAPP_f1299954409t_bool_decl,type,
    hAPP_f1299954409t_bool: fun_fu297564241t_bool > fun_Pr2067565481t_bool > fun_fu1550952061t_bool ).

thf(hAPP_f1356305429t_bool_decl,type,
    hAPP_f1356305429t_bool: fun_fu1550952061t_bool > fun_Pr2067565481t_bool > fun_Pr2067565481t_bool ).

thf(hAPP_f1700632141l_bool_decl,type,
    hAPP_f1700632141l_bool: fun_fu318801205l_bool > fun_Pr376858015t_unit > fun_fu627447383l_bool ).

thf(hAPP_f1033183015t_bool_decl,type,
    hAPP_f1033183015t_bool: fun_fu598681231t_bool > fun_Pr1085078251l_bool > fun_fu1550952061t_bool ).

thf(hAPP_P276596750e_indi_decl,type,
    hAPP_P276596750e_indi: fun_Pr1509342064e_indi > produc472769767le_alt > arrow_856714788e_indi ).

thf(hAPP_P1178790471t_bool_decl,type,
    hAPP_P1178790471t_bool: fun_Pr2067565481t_bool > produc472769767le_alt > bool ).

thf(hAPP_P1069491261t_unit_decl,type,
    hAPP_P1069491261t_unit: fun_Pr376858015t_unit > produc472769767le_alt > product_unit ).

thf(hAPP_P1859429372i_bool_decl,type,
    hAPP_P1859429372i_bool: fun_Pr895221296i_bool > produc472769767le_alt > fun_Ar1809396326i_bool ).

thf(hAPP_P1103642805l_bool_decl,type,
    hAPP_P1103642805l_bool: fun_Pr1780397033l_bool > produc472769767le_alt > fun_bool_bool ).

thf(hAPP_P2037731755t_bool_decl,type,
    hAPP_P2037731755t_bool: fun_Pr1069395679t_bool > produc472769767le_alt > fun_Pr1643180309t_bool ).

thf(hAPP_P38525833l_bool_decl,type,
    hAPP_P38525833l_bool: fun_Pr1085078251l_bool > produc472769767le_alt > fun_fu638310559l_bool ).

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

thf(member1479139729e_indi_decl,type,
    member1479139729e_indi: fun_Ar1047186533l_bool ).

thf(member_bool_decl,type,
    member_bool: fun_bo492988759l_bool ).

thf(member_Product_unit_decl,type,
    member_Product_unit: fun_Pr1863373635l_bool ).

thf(member933336803t_bool_decl,type,
    member933336803t_bool: fun_fu361117961l_bool ).

thf(member387840963le_alt_decl,type,
    member387840963le_alt: fun_fu2141985013l_bool ).

thf(member1133581546t_bool_decl,type,
    member1133581546t_bool: fun_fu827796887l_bool ).

thf(member684813948le_alt_decl,type,
    member684813948le_alt: fun_fu662095797l_bool ).

thf(member869664626le_alt_decl,type,
    member869664626le_alt: fun_fu323675445l_bool ).

thf(member173038353t_bool_decl,type,
    member173038353t_bool: fun_fu1383920485l_bool ).

thf(member1558233923e_indi_decl,type,
    member1558233923e_indi: fun_fu916781301l_bool ).

thf(member1069471740t_bool_decl,type,
    member1069471740t_bool: fun_fu864675765l_bool ).

thf(member1303779570t_unit_decl,type,
    member1303779570t_unit: fun_fu318801205l_bool ).

thf(member1333168212le_alt_decl,type,
    member1333168212le_alt: fun_Pr1085078251l_bool ).

thf(f_decl,type,
    f: fun_fu2114379172t_bool ).

thf(lab_decl,type,
    lab: fun_Pr2067565481t_bool ).

thf(lba_decl,type,
    lba: fun_Pr2067565481t_bool ).

thf(p_decl,type,
    p: fun_Ar274636406t_bool ).

thf(a_decl,type,
    a: arrow_1893660431le_alt ).

thf(b_decl,type,
    b: arrow_1893660431le_alt ).

thf(c_decl,type,
    c: arrow_1893660431le_alt ).

thf(d_decl,type,
    d: arrow_1893660431le_alt ).

thf(e_decl,type,
    e: arrow_1893660431le_alt ).

thf(h_decl,type,
    h: fun_Ar671024215di_nat ).

thf(n_decl,type,
    n: nat ).

thf(74,axiom,
    ! [A: nat,B: nat] :
      ( ( ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) )
        = ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
    <=> ( ( ( B
            = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) )
          & ( A = zero_zero_nat ) )
        | ( ( B = zero_zero_nat )
          & ( A
            = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1098_one__is__add) ).

thf(892,plain,
    ! [A: nat,B: nat] :
      ( ( ( ( ( B
              = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) )
            & ( A = zero_zero_nat ) )
          | ( ( B = zero_zero_nat )
            & ( A
              = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) ) ) )
       => ( ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) )
          = ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) )
      & ( ( ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) )
          = ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
       => ( ( ( B
              = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) )
            & ( A = zero_zero_nat ) )
          | ( ( B = zero_zero_nat )
            & ( A
              = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(288,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ~ ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_order__less__not__sym) ).

thf(1718,plain,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ~ ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(375,axiom,
    ! [A: arrow_856714788e_indi] : ( top_to788185952i_bool @ ( A @ ( member1479139729e_indi @ hAPP_A1597696899l_bool ) @ hAPP_f584385070l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_iso__tuple__UNIV__I) ).

thf(2094,plain,
    ! [A: arrow_856714788e_indi] : ( top_to788185952i_bool @ ( A @ ( member1479139729e_indi @ hAPP_A1597696899l_bool ) @ hAPP_f584385070l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(215,axiom,
    ! [A: fun_Ar535288606t_bool,B: fun_Ar274636406t_bool,C: arrow_856714788e_indi] :
      ( ( C @ ( B @ ( A @ cOMBS_1925466437t_bool @ hAPP_f1001205955t_bool ) @ hAPP_A834130326t_bool ) )
      = ( C @ ( B @ hAPP_A1646126530t_bool ) @ ( C @ ( A @ hAPP_A1395684458t_bool ) @ hAPP_f1299954409t_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000_427) ).

thf(1469,plain,
    ! [A: fun_Ar535288606t_bool,B: fun_Ar274636406t_bool,C: arrow_856714788e_indi] :
      ( ( C @ ( B @ ( A @ cOMBS_1925466437t_bool @ hAPP_f1001205955t_bool ) @ hAPP_A834130326t_bool ) )
      = ( C @ ( B @ hAPP_A1646126530t_bool ) @ ( C @ ( A @ hAPP_A1395684458t_bool ) @ hAPP_f1299954409t_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(515,axiom,
    ! [A: fun_Pr2067565481t_bool] : ( top_to1138392227t_bool @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_516_top__greatest) ).

thf(2744,plain,
    ! [A: fun_Pr2067565481t_bool] : ( top_to1138392227t_bool @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).

thf(142,axiom,
    ! [A: nat,B: nat] :
      ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
      <=> ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1079_not__less__less__Suc__eq) ).

thf(1168,plain,
    ! [A: nat,B: nat] :
      ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( ( A = B )
         => ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
        & ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(458,axiom,
    ! [A: nat,B: nat] :
      ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
      | ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_365_linorder__linear) ).

thf(2412,plain,
    ! [A: nat,B: nat] :
      ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
      | ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).

thf(465,axiom,
    ! [A: arrow_1893660431le_alt,B: arrow_1893660431le_alt,C: arrow_1893660431le_alt,D: arrow_1893660431le_alt] :
      ( ( ( B @ ( A @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) )
        = ( D @ ( C @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) ) )
    <=> ( ( B = D )
        & ( A = C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_Pair__eq) ).

thf(2463,plain,
    ! [A: arrow_1893660431le_alt,B: arrow_1893660431le_alt,C: arrow_1893660431le_alt,D: arrow_1893660431le_alt] :
      ( ( ( ( B = D )
          & ( A = C ) )
       => ( ( B @ ( A @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) )
          = ( D @ ( C @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) ) ) )
      & ( ( ( B @ ( A @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) )
          = ( D @ ( C @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) ) )
       => ( ( B = D )
          & ( A = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).

thf(173,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( C @ times_times_nat @ hAPP_nat_nat ) @ ( A @ ( B @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1159_mult__less__mono1) ).

thf(1315,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( C @ times_times_nat @ hAPP_nat_nat ) @ ( A @ ( B @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(84,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1102_less__eq__Suc__le) ).

thf(941,plain,
    ! [A: nat,B: nat] :
      ( ( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(439,axiom,
    ! [A: nat,B: nat] :
      ( ( A != B )
     => ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_419_order__neq__le__trans) ).

thf(2331,plain,
    ! [A: nat,B: nat] :
      ( ( A != B )
     => ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).

thf(336,axiom,
    arrow_1361987423le_Lin @ ( cOMBK_1701906001t_bool @ hAPP_f1104294872l_bool ) @ ( arrow_5070731e_Prof @ pi_fun1746584570t_bool ) @ ( f @ ( member173038353t_bool @ hAPP_f1714503811l_bool ) @ hAPP_f975209902l_bool ) @ hBOOL,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_assms_I1_J) ).

thf(1950,plain,
    arrow_1361987423le_Lin @ ( cOMBK_1701906001t_bool @ hAPP_f1104294872l_bool ) @ ( arrow_5070731e_Prof @ pi_fun1746584570t_bool ) @ ( f @ ( member173038353t_bool @ hAPP_f1714503811l_bool ) @ hAPP_f975209902l_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(127,axiom,
    ! [A: nat] :
      ~ ( A @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1092_Suc__n__not__le__n) ).

thf(1110,plain,
    ! [A: nat] :
      ~ ( A @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(406,axiom,
    ! [A: bool] :
      ( ( A = fFalse )
      | ( A = fTrue ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiq) ).

thf(2199,plain,
    ! [A: bool] :
      ( ( A = fFalse )
      | ( A = fTrue ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).

thf(176,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_745_add__strict__left__mono) ).

thf(1322,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(543,axiom,
    ! [A: fun_Ar338949104le_alt,B: fun_Ar274636406t_bool,C: fun_Ar1809396326i_bool] :
      ( ! [D: arrow_856714788e_indi] :
          ( ( C @ ( D @ ( member1479139729e_indi @ hAPP_A1597696899l_bool ) @ hAPP_f584385070l_bool ) @ hBOOL )
         => ( D @ ( B @ hAPP_A1646126530t_bool ) @ ( D @ ( A @ hAPP_A899858958le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
     => ( B @ ( C @ pi_Arr1460528004le_alt ) @ ( A @ ( member387840963le_alt @ hAPP_f766019597l_bool ) @ hAPP_f1754488902l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_634_Pi__I) ).

thf(2822,plain,
    ! [A: fun_Ar338949104le_alt,B: fun_Ar274636406t_bool,C: fun_Ar1809396326i_bool] :
      ( ! [D: arrow_856714788e_indi] :
          ( ( C @ ( D @ ( member1479139729e_indi @ hAPP_A1597696899l_bool ) @ hAPP_f584385070l_bool ) @ hBOOL )
         => ( D @ ( B @ hAPP_A1646126530t_bool ) @ ( D @ ( A @ hAPP_A899858958le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
     => ( B @ ( C @ pi_Arr1460528004le_alt ) @ ( A @ ( member387840963le_alt @ hAPP_f766019597l_bool ) @ hAPP_f1754488902l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).

thf(488,axiom,
    ! [A: fun_fu2114379172t_bool] : ( A @ ( top_to827110112l_bool @ hAPP_f1572141188l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_top1I) ).

thf(2630,plain,
    ! [A: fun_fu2114379172t_bool] : ( A @ ( top_to827110112l_bool @ hAPP_f1572141188l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).

thf(441,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( ( A != B )
        & ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1008_nat__less__le) ).

thf(2336,plain,
    ! [A: nat,B: nat] :
      ( ( ( ( A != B )
          & ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
       => ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ( A != B )
          & ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).

thf(379,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_order__less__trans) ).

thf(2109,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(387,axiom,
    ! [A: fun_Pr2067565481t_bool] :
      ( ( arrow_1361987423le_Lin @ ( A @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
     => ( arrow_5070731e_Prof @ ( A @ ( cOMBK_1650320063e_indi @ hAPP_f480276746t_bool ) @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_const__Lin__Prof) ).

thf(2131,plain,
    ! [A: fun_Pr2067565481t_bool] :
      ( ( arrow_1361987423le_Lin @ ( A @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
     => ( arrow_5070731e_Prof @ ( A @ ( cOMBK_1650320063e_indi @ hAPP_f480276746t_bool ) @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(360,axiom,
    ! [A: fun_fu2114379172t_bool,B: fun_fu2098777574l_bool] :
      ( ( B @ ( A @ ( member173038353t_bool @ hAPP_f1714503811l_bool ) @ hAPP_f975209902l_bool ) @ hBOOL )
    <=> ( A @ ( B @ hAPP_f1572141188l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_mem__def) ).

thf(2031,plain,
    ! [A: fun_fu2114379172t_bool,B: fun_fu2098777574l_bool] :
      ( ( ( A @ ( B @ hAPP_f1572141188l_bool ) @ hBOOL )
       => ( B @ ( A @ ( member173038353t_bool @ hAPP_f1714503811l_bool ) @ hAPP_f975209902l_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( member173038353t_bool @ hAPP_f1714503811l_bool ) @ hAPP_f975209902l_bool ) @ hBOOL )
       => ( A @ ( B @ hAPP_f1572141188l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(264,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B != zero_zero_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1047_gr__implies__not0) ).

thf(1633,plain,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B != zero_zero_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(527,axiom,
    ! [A: fun_Pr2090226719le_alt,B: fun_Pr1887398791t_bool,C: fun_Pr1643180309t_bool] :
      ( ! [D: product_unit] :
          ( ( C @ ( D @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
         => ( D @ ( B @ hAPP_P1914371027t_bool ) @ ( D @ ( A @ hAPP_P396106045le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
     => ( B @ ( C @ pi_Pro1820940723le_alt ) @ ( A @ ( member869664626le_alt @ hAPP_f41367117l_bool ) @ hAPP_f684683381l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_636_Pi__I) ).

thf(2778,plain,
    ! [A: fun_Pr2090226719le_alt,B: fun_Pr1887398791t_bool,C: fun_Pr1643180309t_bool] :
      ( ! [D: product_unit] :
          ( ( C @ ( D @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
         => ( D @ ( B @ hAPP_P1914371027t_bool ) @ ( D @ ( A @ hAPP_P396106045le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
     => ( B @ ( C @ pi_Pro1820940723le_alt ) @ ( A @ ( member869664626le_alt @ hAPP_f41367117l_bool ) @ hAPP_f684683381l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).

thf(75,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
      = ( C @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_990_nat__add__assoc) ).

thf(909,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
      = ( C @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(12,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) )
        = ( C @ ( A @ times_times_nat @ hAPP_nat_nat ) ) )
    <=> ( ( B = C )
        | ( A = zero_zero_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1179_nat__mult__eq__cancel__disj) ).

thf(628,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( ( B = C )
          | ( A = zero_zero_nat ) )
       => ( ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) )
          = ( C @ ( A @ times_times_nat @ hAPP_nat_nat ) ) ) )
      & ( ( ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) )
          = ( C @ ( A @ times_times_nat @ hAPP_nat_nat ) ) )
       => ( ( B = C )
          | ( A = zero_zero_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(92,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1088_le__SucI) ).

thf(977,plain,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(34,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
        = ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
    <=> ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_991_nat__add__left__cancel) ).

thf(730,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( B = C )
       => ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
          = ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) )
      & ( ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
          = ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
       => ( B = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(112,axiom,
    ! [A: nat] : ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1054_less__eq__nat_Osimps_I1_J) ).

thf(1068,plain,
    ! [A: nat] : ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(537,axiom,
    ~ ( fFalse @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).

thf(2808,plain,
    ~ ( fFalse @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).

thf(206,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
        = ( B @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
     => ( A = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_728_add__right__imp__eq) ).

thf(1443,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
        = ( B @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
     => ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(242,axiom,
    ! [A: fun_na699243463e_indi,B: fun_Ar671024215di_nat] :
      ( ( top_to788185952i_bool @ ( B @ inj_on1960344199di_nat @ hAPP_f584385070l_bool ) @ hBOOL )
     => ( ! [C: nat] :
            ( ( C @ ( A @ hAPP_n1937165849e_indi ) @ ( B @ hAPP_A376526755di_nat ) )
            = C )
       => ( ( B @ ( top_to788185952i_bool @ hilber1580028780di_nat ) )
          = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_651_inj__imp__inv__eq) ).

thf(1569,plain,
    ! [A: fun_na699243463e_indi,B: fun_Ar671024215di_nat] :
      ( ( top_to788185952i_bool @ ( B @ inj_on1960344199di_nat @ hAPP_f584385070l_bool ) @ hBOOL )
     => ( ! [C: nat] :
            ( ( C @ ( A @ hAPP_n1937165849e_indi ) @ ( B @ hAPP_A376526755di_nat ) )
            = C )
       => ( ( B @ ( top_to788185952i_bool @ hilber1580028780di_nat ) )
          = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(292,axiom,
    ! [A: fun_Ar516759882t_bool,B: fun_Ar274636406t_bool,C: arrow_856714788e_indi] :
      ( ( C @ ( B @ ( A @ cOMBS_1181656689t_bool @ hAPP_f1302887663t_bool ) @ hAPP_A1646126530t_bool ) )
      = ( C @ ( B @ hAPP_A1646126530t_bool ) @ ( C @ ( A @ hAPP_A834130326t_bool ) @ hAPP_f1356305429t_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000) ).

thf(1728,plain,
    ! [A: fun_Ar516759882t_bool,B: fun_Ar274636406t_bool,C: arrow_856714788e_indi] :
      ( ( C @ ( B @ ( A @ cOMBS_1181656689t_bool @ hAPP_f1302887663t_bool ) @ hAPP_A1646126530t_bool ) )
      = ( C @ ( B @ hAPP_A1646126530t_bool ) @ ( C @ ( A @ hAPP_A834130326t_bool ) @ hAPP_f1356305429t_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(344,axiom,
    ! [A: arrow_856714788e_indi,B: fun_Ar274636406t_bool,C: fun_Ar1809396326i_bool,D: fun_Ar1474557608l_bool] :
      ( ( D @ ( C @ pi_Arr959578316t_bool ) @ ( B @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_A897398598l_bool ) @ ( A @ ( B @ hAPP_A1646126530t_bool ) @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member1479139729e_indi @ hAPP_A1597696899l_bool ) @ hAPP_f584385070l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_PiE) ).

thf(1971,plain,
    ! [A: arrow_856714788e_indi,B: fun_Ar274636406t_bool,C: fun_Ar1809396326i_bool,D: fun_Ar1474557608l_bool] :
      ( ( D @ ( C @ pi_Arr959578316t_bool ) @ ( B @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_A897398598l_bool ) @ ( A @ ( B @ hAPP_A1646126530t_bool ) @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member1479139729e_indi @ hAPP_A1597696899l_bool ) @ hAPP_f584385070l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(477,axiom,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
      ( ( B @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
    <=> ( ( A = B )
        | ( B @ ( A @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_932_subset__iff__psubset__eq) ).

thf(2512,plain,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
      ( ( ( ( A = B )
          | ( B @ ( A @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
       => ( B @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( ( A = B )
          | ( B @ ( A @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).

thf(43,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
        = ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
    <=> ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_732_add__left__cancel) ).

thf(762,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( B = C )
       => ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
          = ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) )
      & ( ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
          = ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
       => ( B = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(100,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ~ ! [C: nat] :
            ( ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( B
             != ( C @ ( suc @ hAPP_nat_nat ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1122_Suc__lessE) ).

thf(1005,plain,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ~ ! [C: nat] :
            ( ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( B
             != ( C @ ( suc @ hAPP_nat_nat ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(408,axiom,
    ! [A: produc472769767le_alt,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool,D: fun_bool_bool] :
      ( ( D @ ( cOMBK_138598520le_alt @ hAPP_f699791347l_bool ) @ ( C @ pi_Pro1238944957t_bool ) @ ( B @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( D @ ( A @ ( B @ hAPP_P1178790471t_bool ) @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_581_funcset__mem) ).

thf(2210,plain,
    ! [A: produc472769767le_alt,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool,D: fun_bool_bool] :
      ( ( D @ ( cOMBK_138598520le_alt @ hAPP_f699791347l_bool ) @ ( C @ pi_Pro1238944957t_bool ) @ ( B @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( D @ ( A @ ( B @ hAPP_P1178790471t_bool ) @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(382,axiom,
    ! [A: nat,B: fun_Pr2067565481t_bool,C: fun_na998785244t_bool,D: nat] :
      ( ( D @ ( C @ hAPP_n1161265524t_bool ) @ ( B @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( ( A @ ( D @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [E: nat,F: nat] :
              ( ( F @ ( E @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( F @ ( C @ hAPP_n1161265524t_bool ) @ ( E @ ( C @ hAPP_n1161265524t_bool ) @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
         => ( A @ ( C @ hAPP_n1161265524t_bool ) @ ( B @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_815_order__le__less__subst1) ).

thf(2117,plain,
    ! [A: nat,B: fun_Pr2067565481t_bool,C: fun_na998785244t_bool,D: nat] :
      ( ( D @ ( C @ hAPP_n1161265524t_bool ) @ ( B @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( ( A @ ( D @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [E: nat,F: nat] :
              ( ( F @ ( E @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( F @ ( C @ hAPP_n1161265524t_bool ) @ ( E @ ( C @ hAPP_n1161265524t_bool ) @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
         => ( A @ ( C @ hAPP_n1161265524t_bool ) @ ( B @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(251,axiom,
    ! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool] :
      ( ( B @ ( A @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
     => ( ( A @ ( B @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
       => ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_xt1_I5_J) ).

thf(1596,plain,
    ! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool] :
      ( ( B @ ( A @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
     => ( ( A @ ( B @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(36,axiom,
    ! [A: nat] :
      ( ( A @ ( suc @ hAPP_nat_nat ) )
     != zero_zero_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1068_nat_Osimps_I3_J) ).

thf(741,plain,
    ! [A: nat] :
      ( ( A @ ( suc @ hAPP_nat_nat ) )
     != zero_zero_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(114,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1002_trans__less__add1) ).

thf(1073,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(377,axiom,
    ! [A: fun_fu2114379172t_bool] :
      ( ( A @ ( top_to827110112l_bool @ hAPP_f1572141188l_bool ) @ hBOOL )
    <=> ( top_top_bool @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_top__apply) ).

thf(2099,plain,
    ! [A: fun_fu2114379172t_bool] :
      ( ( ( top_top_bool @ hBOOL )
       => ( A @ ( top_to827110112l_bool @ hAPP_f1572141188l_bool ) @ hBOOL ) )
      & ( ( A @ ( top_to827110112l_bool @ hAPP_f1572141188l_bool ) @ hBOOL )
       => ( top_top_bool @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(427,axiom,
    ! [A: arrow_1893660431le_alt,B: fun_Pr2067565481t_bool] :
      ( ( arrow_1361987423le_Lin @ ( B @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
     => ( arrow_1361987423le_Lin @ ( A @ ( B @ ( arrow_1481558583_mkbot @ hAPP_f1761571331t_bool ) @ hAPP_A1601437999t_bool ) @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_mkbot__Lin) ).

thf(2282,plain,
    ! [A: arrow_1893660431le_alt,B: fun_Pr2067565481t_bool] :
      ( ( arrow_1361987423le_Lin @ ( B @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
     => ( arrow_1361987423le_Lin @ ( A @ ( B @ ( arrow_1481558583_mkbot @ hAPP_f1761571331t_bool ) @ hAPP_A1601437999t_bool ) @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).

thf(249,axiom,
    ! [A: nat] :
      ( ( A != zero_zero_nat )
     => ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1048_gr0I) ).

thf(1591,plain,
    ! [A: nat] :
      ( ( A != zero_zero_nat )
     => ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(10,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) )
        = ( C @ ( A @ times_times_nat @ hAPP_nat_nat ) ) )
    <=> ( ( A = zero_zero_nat )
        | ( B = C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1153_mult__cancel1) ).

thf(614,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( ( A = zero_zero_nat )
          | ( B = C ) )
       => ( ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) )
          = ( C @ ( A @ times_times_nat @ hAPP_nat_nat ) ) ) )
      & ( ( ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) )
          = ( C @ ( A @ times_times_nat @ hAPP_nat_nat ) ) )
       => ( ( A = zero_zero_nat )
          | ( B = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(281,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ~ ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_xt1_I9_J) ).

thf(1692,plain,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ~ ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(116,axiom,
    ! [A: nat,B: nat,C: fun_nat_nat] :
      ( ( top_top_fun_nat_bool @ ( C @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( ( A @ ( C @ hAPP_nat_nat ) )
          = B )
       => ( ( B @ ( C @ ( top_top_fun_nat_bool @ hilber195283148at_nat ) @ hAPP_nat_nat ) )
          = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_inv__f__eq) ).

thf(1078,plain,
    ! [A: nat,B: nat,C: fun_nat_nat] :
      ( ( top_top_fun_nat_bool @ ( C @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( ( A @ ( C @ hAPP_nat_nat ) )
          = B )
       => ( ( B @ ( C @ ( top_top_fun_nat_bool @ hilber195283148at_nat ) @ hAPP_nat_nat ) )
          = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(276,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ~ ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_order__less__asym_H) ).

thf(1671,plain,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ~ ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(270,axiom,
    ! [A: fun_bo1945492389t_bool,B: fun_Ar1809396326i_bool,C: arrow_856714788e_indi] :
      ( ( C @ ( B @ ( A @ cOMBB_1061985500e_indi @ hAPP_f668886383t_bool ) @ hAPP_A1395684458t_bool ) )
      = ( C @ ( B @ hAPP_A997847300i_bool ) @ ( A @ hAPP_b35146737t_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow_) ).

thf(1655,plain,
    ! [A: fun_bo1945492389t_bool,B: fun_Ar1809396326i_bool,C: arrow_856714788e_indi] :
      ( ( C @ ( B @ ( A @ cOMBB_1061985500e_indi @ hAPP_f668886383t_bool ) @ hAPP_A1395684458t_bool ) )
      = ( C @ ( B @ hAPP_A997847300i_bool ) @ ( A @ hAPP_b35146737t_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(134,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
        = ( B @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
    <=> ( A = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_731_add__right__cancel) ).

thf(1137,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( A = C )
       => ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
          = ( B @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) )
      & ( ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
          = ( B @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
       => ( A = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(497,axiom,
    ! [A: produc472769767le_alt,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
      ( ( C @ ( B @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_959_set__mp) ).

thf(2686,plain,
    ! [A: produc472769767le_alt,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
      ( ( C @ ( B @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).

thf(576,axiom,
    ! [A: produc472769767le_alt,B: fun_Pr2067565481t_bool] :
      ( ( B @ ( A @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
    <=> ( A @ ( B @ hAPP_P1178790471t_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_mem__def) ).

thf(3044,plain,
    ! [A: produc472769767le_alt,B: fun_Pr2067565481t_bool] :
      ( ( ( A @ ( B @ hAPP_P1178790471t_bool ) @ hBOOL )
       => ( B @ ( A @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( A @ ( B @ hAPP_P1178790471t_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).

thf(505,axiom,
    ! [A: arrow_1893660431le_alt,B: arrow_1893660431le_alt] :
      ( ( A != B )
     => ? [C: fun_Pr2067565481t_bool] :
          ( ( C @ ( B @ ( A @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
          & ( arrow_1361987423le_Lin @ ( C @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_complete__Lin) ).

thf(2712,plain,
    ! [A: arrow_1893660431le_alt,B: arrow_1893660431le_alt] :
      ( ( A != B )
     => ? [C: fun_Pr2067565481t_bool] :
          ( ( C @ ( B @ ( A @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
          & ( arrow_1361987423le_Lin @ ( C @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).

thf(487,axiom,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
      ( ( B @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( ( A != B )
       => ( B @ ( A @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_457_order__le__neq__trans) ).

thf(2627,plain,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
      ( ( B @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( ( A != B )
       => ( B @ ( A @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).

thf(482,axiom,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
      ( ( C @ ( B @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_xt1_I6_J) ).

thf(2580,plain,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
      ( ( C @ ( B @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).

thf(183,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1018_trans__le__add2) ).

thf(1354,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(141,axiom,
    ! [A: nat] :
      ( ( A != zero_zero_nat )
     => ~ ! [B: nat] :
            ( A
           != ( B @ ( suc @ hAPP_nat_nat ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1124_nat_Oexhaust) ).

thf(1164,plain,
    ! [A: nat] :
      ( ( A != zero_zero_nat )
     => ~ ! [B: nat] :
            ( A
           != ( B @ ( suc @ hAPP_nat_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(49,axiom,
    ! [A: nat] :
      ( ( A @ ( suc @ hAPP_nat_nat ) )
      = ( A @ ( one_one_nat @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1119_Suc__eq__plus1__left) ).

thf(797,plain,
    ! [A: nat] :
      ( ( A @ ( suc @ hAPP_nat_nat ) )
      = ( A @ ( one_one_nat @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(328,axiom,
    ! [A: fun_Pr1643180309t_bool,B: produc472769767le_alt] :
      ( ( B @ ( A @ ( cOMBK_751896174le_alt @ hAPP_f723483871t_bool ) @ hAPP_P2037731755t_bool ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_00_402) ).

thf(1919,plain,
    ! [A: fun_Pr1643180309t_bool,B: produc472769767le_alt] :
      ( ( B @ ( A @ ( cOMBK_751896174le_alt @ hAPP_f723483871t_bool ) @ hAPP_P2037731755t_bool ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(348,axiom,
    ! [A: nat] : ( A @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_993_le__refl) ).

thf(1988,plain,
    ! [A: nat] : ( A @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(300,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_order__trans) ).

thf(1761,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(38,axiom,
    ! [A: nat,B: nat] :
      ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1078_less__antisym) ).

thf(747,plain,
    ! [A: nat,B: nat] :
      ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(338,axiom,
    arrow_1361987423le_Lin @ ( lba @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75__096Lba_A_058_ALin_096) ).

thf(1954,plain,
    arrow_1361987423le_Lin @ ( lba @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(549,axiom,
    ! [A: produc472769767le_alt,B: fun_Pr1509342064e_indi,C: fun_Pr2067565481t_bool,D: fun_Pr895221296i_bool] :
      ( ( D @ ( C @ pi_Pro837265796e_indi ) @ ( B @ ( member1558233923e_indi @ hAPP_f1187850253l_bool ) @ hAPP_f2124588998l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_P1859429372i_bool ) @ ( A @ ( B @ hAPP_P276596750e_indi ) @ ( member1479139729e_indi @ hAPP_A1597696899l_bool ) @ hAPP_f584385070l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_PiE) ).

thf(2844,plain,
    ! [A: produc472769767le_alt,B: fun_Pr1509342064e_indi,C: fun_Pr2067565481t_bool,D: fun_Pr895221296i_bool] :
      ( ( D @ ( C @ pi_Pro837265796e_indi ) @ ( B @ ( member1558233923e_indi @ hAPP_f1187850253l_bool ) @ hAPP_f2124588998l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_P1859429372i_bool ) @ ( A @ ( B @ hAPP_P276596750e_indi ) @ ( member1479139729e_indi @ hAPP_A1597696899l_bool ) @ hAPP_f584385070l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).

thf(123,axiom,
    ! [A: fun_fu638310559l_bool] : ( top_to1312956197l_bool @ ( A @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_719_subset__UNIV) ).

thf(1095,plain,
    ! [A: fun_fu638310559l_bool] : ( top_to1312956197l_bool @ ( A @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(315,axiom,
    ! [A: fun_fu638310559l_bool,B: fun_fu638310559l_bool] :
      ( ( B @ ( member1069471740t_bool @ ( cOMBC_2133093654l_bool @ hAPP_f1776355587l_bool ) @ hAPP_f1060563265l_bool ) @ ( A @ ( member1069471740t_bool @ ( cOMBC_2133093654l_bool @ hAPP_f1776355587l_bool ) @ hAPP_f1060563265l_bool ) @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
    <=> ( B @ ( A @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_977_pred__subset__eq) ).

thf(1835,plain,
    ! [A: fun_fu638310559l_bool,B: fun_fu638310559l_bool] :
      ( ( ( B @ ( A @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
       => ( B @ ( member1069471740t_bool @ ( cOMBC_2133093654l_bool @ hAPP_f1776355587l_bool ) @ hAPP_f1060563265l_bool ) @ ( A @ ( member1069471740t_bool @ ( cOMBC_2133093654l_bool @ hAPP_f1776355587l_bool ) @ hAPP_f1060563265l_bool ) @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) )
      & ( ( B @ ( member1069471740t_bool @ ( cOMBC_2133093654l_bool @ hAPP_f1776355587l_bool ) @ hAPP_f1060563265l_bool ) @ ( A @ ( member1069471740t_bool @ ( cOMBC_2133093654l_bool @ hAPP_f1776355587l_bool ) @ hAPP_f1060563265l_bool ) @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(410,axiom,
    ! [A: arrow_856714788e_indi] : ( top_to788185952i_bool @ ( A @ ( member1479139729e_indi @ hAPP_A1597696899l_bool ) @ hAPP_f584385070l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_UNIV__I) ).

thf(2216,plain,
    ! [A: arrow_856714788e_indi] : ( top_to788185952i_bool @ ( A @ ( member1479139729e_indi @ hAPP_A1597696899l_bool ) @ hAPP_f584385070l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

thf(156,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
      = ( C @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_733_ab__semigroup__add__class_Oadd__ac_I1_J) ).

thf(1243,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
      = ( C @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(205,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1170_one__less__mult) ).

thf(1441,plain,
    ! [A: nat,B: nat] :
      ( ( B @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(31,axiom,
    ! [A: nat,B: nat] :
      ( ( one_one_nat
        = ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) ) )
    <=> ( ( B = one_one_nat )
        & ( A = one_one_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1147_nat__1__eq__mult__iff) ).

thf(709,plain,
    ! [A: nat,B: nat] :
      ( ( ( ( B = one_one_nat )
          & ( A = one_one_nat ) )
       => ( one_one_nat
          = ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) ) ) )
      & ( ( one_one_nat
          = ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) ) )
       => ( ( B = one_one_nat )
          & ( A = one_one_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(356,axiom,
    ! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool,C: fun_Ar331856045t_bool] :
      ( ( C @ ( B @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_xt1_I6_J) ).

thf(2010,plain,
    ! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool,C: fun_Ar331856045t_bool] :
      ( ( C @ ( B @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(267,axiom,
    ! [A: fun_fu1679793515t_bool,B: fun_Ar274636406t_bool,C: arrow_856714788e_indi] :
      ( ( C @ ( B @ ( A @ cOMBB_80760910e_indi @ hAPP_f831214557t_bool ) @ hAPP_A1309733808t_bool ) )
      = ( C @ ( B @ hAPP_A1646126530t_bool ) @ ( A @ hAPP_f1761571331t_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ef) ).

thf(1645,plain,
    ! [A: fun_fu1679793515t_bool,B: fun_Ar274636406t_bool,C: arrow_856714788e_indi] :
      ( ( C @ ( B @ ( A @ cOMBB_80760910e_indi @ hAPP_f831214557t_bool ) @ hAPP_A1309733808t_bool ) )
      = ( C @ ( B @ hAPP_A1646126530t_bool ) @ ( A @ hAPP_f1761571331t_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(290,axiom,
    ! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool,C: fun_Ar331856045t_bool] :
      ( ( C @ ( B @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_479_order__less__le__trans) ).

thf(1724,plain,
    ! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool,C: fun_Ar331856045t_bool] :
      ( ( C @ ( B @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(186,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1108_Suc__le__lessD) ).

thf(1366,plain,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(557,axiom,
    ! [A: produc472769767le_alt] : ( top_to1138392227t_bool @ ( A @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_iso__tuple__UNIV__I) ).

thf(2869,plain,
    ! [A: produc472769767le_alt] : ( top_to1138392227t_bool @ ( A @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).

thf(15,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ times_times_nat @ hAPP_nat_nat ) )
      = ( C @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1150_add__mult__distrib2) ).

thf(651,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ times_times_nat @ hAPP_nat_nat ) )
      = ( C @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(98,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_738_add__left__mono) ).

thf(1001,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(508,axiom,
    ! [A: arrow_1893660431le_alt,B: arrow_1893660431le_alt,C: arrow_1893660431le_alt,D: arrow_1893660431le_alt] :
      ( ( ( B @ ( A @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) )
        = ( D @ ( C @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_Pair__inject) ).

thf(2723,plain,
    ! [A: arrow_1893660431le_alt,B: arrow_1893660431le_alt,C: arrow_1893660431le_alt,D: arrow_1893660431le_alt] :
      ( ( ( B @ ( A @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) )
        = ( D @ ( C @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).

thf(91,axiom,
    ! [A: fun_fu638310559l_bool,B: fun_fu638310559l_bool,C: fun_fu638310559l_bool] :
      ( ( C @ ( B @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
     => ( ( C = A )
       => ( A @ ( B @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_ord__le__eq__trans) ).

thf(973,plain,
    ! [A: fun_fu638310559l_bool,B: fun_fu638310559l_bool,C: fun_fu638310559l_bool] :
      ( ( C @ ( B @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
     => ( ( C = A )
       => ( A @ ( B @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(108,axiom,
    ! [A: fun_Ar516759882t_bool,B: fun_Pr2067565481t_bool,C: arrow_856714788e_indi] :
      ( ( C @ ( B @ ( A @ ( cOMBC_750853729t_bool @ hAPP_f601594885t_bool ) @ hAPP_f480276746t_bool ) @ hAPP_A1646126530t_bool ) )
      = ( B @ ( C @ ( A @ hAPP_A834130326t_bool ) @ hAPP_f1356305429t_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000_418) ).

thf(1046,plain,
    ! [A: fun_Ar516759882t_bool,B: fun_Pr2067565481t_bool,C: arrow_856714788e_indi] :
      ( ( C @ ( B @ ( A @ ( cOMBC_750853729t_bool @ hAPP_f601594885t_bool ) @ hAPP_f480276746t_bool ) @ hAPP_A1646126530t_bool ) )
      = ( B @ ( C @ ( A @ hAPP_A834130326t_bool ) @ hAPP_f1356305429t_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(455,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_481_order__less__le__trans) ).

thf(2400,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).

thf(370,axiom,
    ! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool] :
      ( ( B @ ( A @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
     => ( ( A @ ( B @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
      <=> ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_order__antisym__conv) ).

thf(2067,plain,
    ! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool] :
      ( ( B @ ( A @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
     => ( ( ( B = A )
         => ( A @ ( B @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) )
        & ( ( A @ ( B @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
         => ( B = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(324,axiom,
    ( ( e @ ( p @ ( arrow_1481558583_mkbot @ cOMBB_80760910e_indi @ hAPP_f831214557t_bool ) @ ( cOMBC_1417338747t_bool @ hAPP_f1631649925t_bool ) @ hAPP_A425126512t_bool ) @ ( e @ ( c @ ( p @ ( arrow_216713899_above @ cOMBB_1876517692e_indi @ hAPP_f1751344075t_bool ) @ ( cOMBC_1486904681t_bool @ hAPP_f2102110817t_bool ) @ hAPP_A1889513822t_bool ) @ ( cOMBC_1417338747t_bool @ hAPP_f1631649925t_bool ) @ hAPP_A425126512t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_1869811296e_indi @ hAPP_f966656047t_bool ) @ ( cOMBC_722552198t_bool @ hAPP_f721434149i_bool ) @ hAPP_n34002993i_bool ) @ ( if_fun523439385t_bool @ cOMBB_1061985500e_indi @ hAPP_f668886383t_bool ) @ cOMBS_1925466437t_bool @ hAPP_f1001205955t_bool ) @ cOMBS_1181656689t_bool @ hAPP_f1302887663t_bool ) @ ( e @ ( p @ ( arrow_1630265669_mktop @ cOMBB_80760910e_indi @ hAPP_f831214557t_bool ) @ ( cOMBC_1417338747t_bool @ hAPP_f1631649925t_bool ) @ hAPP_A425126512t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_1869811296e_indi @ hAPP_f966656047t_bool ) @ ( cOMBC_722552198t_bool @ hAPP_f721434149i_bool ) @ hAPP_n34002993i_bool ) @ ( if_fun523439385t_bool @ cOMBB_1061985500e_indi @ hAPP_f668886383t_bool ) @ cOMBS_1925466437t_bool @ hAPP_f1001205955t_bool ) @ cOMBS_1181656689t_bool @ hAPP_f1302887663t_bool ) @ ( f @ hAPP_f2008608496t_bool ) @ ( e @ ( c @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
  <=> ( lba @ ( lab @ ( one_one_nat @ ( n @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( h @ ( ord_less_nat @ cOMBB_1869811296e_indi @ hAPP_f966656047t_bool ) @ ( cOMBC_722552198t_bool @ hAPP_f721434149i_bool ) @ hAPP_n34002993i_bool ) @ ( if_fun523439385t_bool @ cOMBB_1061985500e_indi @ hAPP_f668886383t_bool ) @ ( cOMBC_156709173t_bool @ hAPP_f1908974253t_bool ) @ hAPP_f1344464862t_bool ) @ ( cOMBC_750853729t_bool @ hAPP_f601594885t_bool ) @ hAPP_f480276746t_bool ) @ ( f @ hAPP_f2008608496t_bool ) @ ( b @ ( a @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184__096_Ic_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Am) ).

thf(1904,plain,
    ( ( ( lba @ ( lab @ ( one_one_nat @ ( n @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( h @ ( ord_less_nat @ cOMBB_1869811296e_indi @ hAPP_f966656047t_bool ) @ ( cOMBC_722552198t_bool @ hAPP_f721434149i_bool ) @ hAPP_n34002993i_bool ) @ ( if_fun523439385t_bool @ cOMBB_1061985500e_indi @ hAPP_f668886383t_bool ) @ ( cOMBC_156709173t_bool @ hAPP_f1908974253t_bool ) @ hAPP_f1344464862t_bool ) @ ( cOMBC_750853729t_bool @ hAPP_f601594885t_bool ) @ hAPP_f480276746t_bool ) @ ( f @ hAPP_f2008608496t_bool ) @ ( b @ ( a @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( e @ ( p @ ( arrow_1481558583_mkbot @ cOMBB_80760910e_indi @ hAPP_f831214557t_bool ) @ ( cOMBC_1417338747t_bool @ hAPP_f1631649925t_bool ) @ hAPP_A425126512t_bool ) @ ( e @ ( c @ ( p @ ( arrow_216713899_above @ cOMBB_1876517692e_indi @ hAPP_f1751344075t_bool ) @ ( cOMBC_1486904681t_bool @ hAPP_f2102110817t_bool ) @ hAPP_A1889513822t_bool ) @ ( cOMBC_1417338747t_bool @ hAPP_f1631649925t_bool ) @ hAPP_A425126512t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_1869811296e_indi @ hAPP_f966656047t_bool ) @ ( cOMBC_722552198t_bool @ hAPP_f721434149i_bool ) @ hAPP_n34002993i_bool ) @ ( if_fun523439385t_bool @ cOMBB_1061985500e_indi @ hAPP_f668886383t_bool ) @ cOMBS_1925466437t_bool @ hAPP_f1001205955t_bool ) @ cOMBS_1181656689t_bool @ hAPP_f1302887663t_bool ) @ ( e @ ( p @ ( arrow_1630265669_mktop @ cOMBB_80760910e_indi @ hAPP_f831214557t_bool ) @ ( cOMBC_1417338747t_bool @ hAPP_f1631649925t_bool ) @ hAPP_A425126512t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_1869811296e_indi @ hAPP_f966656047t_bool ) @ ( cOMBC_722552198t_bool @ hAPP_f721434149i_bool ) @ hAPP_n34002993i_bool ) @ ( if_fun523439385t_bool @ cOMBB_1061985500e_indi @ hAPP_f668886383t_bool ) @ cOMBS_1925466437t_bool @ hAPP_f1001205955t_bool ) @ cOMBS_1181656689t_bool @ hAPP_f1302887663t_bool ) @ ( f @ hAPP_f2008608496t_bool ) @ ( e @ ( c @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
    & ( ( e @ ( p @ ( arrow_1481558583_mkbot @ cOMBB_80760910e_indi @ hAPP_f831214557t_bool ) @ ( cOMBC_1417338747t_bool @ hAPP_f1631649925t_bool ) @ hAPP_A425126512t_bool ) @ ( e @ ( c @ ( p @ ( arrow_216713899_above @ cOMBB_1876517692e_indi @ hAPP_f1751344075t_bool ) @ ( cOMBC_1486904681t_bool @ hAPP_f2102110817t_bool ) @ hAPP_A1889513822t_bool ) @ ( cOMBC_1417338747t_bool @ hAPP_f1631649925t_bool ) @ hAPP_A425126512t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_1869811296e_indi @ hAPP_f966656047t_bool ) @ ( cOMBC_722552198t_bool @ hAPP_f721434149i_bool ) @ hAPP_n34002993i_bool ) @ ( if_fun523439385t_bool @ cOMBB_1061985500e_indi @ hAPP_f668886383t_bool ) @ cOMBS_1925466437t_bool @ hAPP_f1001205955t_bool ) @ cOMBS_1181656689t_bool @ hAPP_f1302887663t_bool ) @ ( e @ ( p @ ( arrow_1630265669_mktop @ cOMBB_80760910e_indi @ hAPP_f831214557t_bool ) @ ( cOMBC_1417338747t_bool @ hAPP_f1631649925t_bool ) @ hAPP_A425126512t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_1869811296e_indi @ hAPP_f966656047t_bool ) @ ( cOMBC_722552198t_bool @ hAPP_f721434149i_bool ) @ hAPP_n34002993i_bool ) @ ( if_fun523439385t_bool @ cOMBB_1061985500e_indi @ hAPP_f668886383t_bool ) @ cOMBS_1925466437t_bool @ hAPP_f1001205955t_bool ) @ cOMBS_1181656689t_bool @ hAPP_f1302887663t_bool ) @ ( f @ hAPP_f2008608496t_bool ) @ ( e @ ( c @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( lba @ ( lab @ ( one_one_nat @ ( n @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( h @ ( ord_less_nat @ cOMBB_1869811296e_indi @ hAPP_f966656047t_bool ) @ ( cOMBC_722552198t_bool @ hAPP_f721434149i_bool ) @ hAPP_n34002993i_bool ) @ ( if_fun523439385t_bool @ cOMBB_1061985500e_indi @ hAPP_f668886383t_bool ) @ ( cOMBC_156709173t_bool @ hAPP_f1908974253t_bool ) @ hAPP_f1344464862t_bool ) @ ( cOMBC_750853729t_bool @ hAPP_f601594885t_bool ) @ hAPP_f480276746t_bool ) @ ( f @ hAPP_f2008608496t_bool ) @ ( b @ ( a @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(229,axiom,
    ! [A: nat] :
      ( ( A @ ( top_top_fun_nat_bool @ hAPP_nat_bool ) @ hBOOL )
    <=> ( top_top_bool @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_top__apply) ).

thf(1518,plain,
    ! [A: nat] :
      ( ( ( top_top_bool @ hBOOL )
       => ( A @ ( top_top_fun_nat_bool @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( A @ ( top_top_fun_nat_bool @ hAPP_nat_bool ) @ hBOOL )
       => ( top_top_bool @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(260,axiom,
    ! [A: nat,B: nat] :
      ( ~ ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_linorder__le__cases) ).

thf(1623,plain,
    ! [A: nat,B: nat] :
      ( ~ ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(218,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1003_trans__less__add2) ).

thf(1482,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(362,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( fequal_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
      | ( A != B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Nat__Onat_T) ).

thf(2039,plain,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( fequal_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
      | ( A != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(32,axiom,
    ! [A: nat,B: nat] :
      ( ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
        = A )
     => ( B = zero_zero_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1052_add__eq__self__zero) ).

thf(719,plain,
    ! [A: nat,B: nat] :
      ( ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
        = A )
     => ( B = zero_zero_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(520,axiom,
    lab @ ( b @ ( a @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096) ).

thf(2755,plain,
    lab @ ( b @ ( a @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).

thf(504,axiom,
    ! [A: fun_Pr376858015t_unit,B: fun_Pr1069395679t_bool,C: fun_Pr2067565481t_bool] :
      ( ! [D: produc472769767le_alt] :
          ( ( C @ ( D @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
         => ( D @ ( B @ hAPP_P2037731755t_bool ) @ ( D @ ( A @ hAPP_P1069491261t_unit ) @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) )
     => ( B @ ( C @ pi_Pro346842291t_unit ) @ ( A @ ( member1303779570t_unit @ hAPP_f1700632141l_bool ) @ hAPP_f1159856629l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_621_Pi__I) ).

thf(2708,plain,
    ! [A: fun_Pr376858015t_unit,B: fun_Pr1069395679t_bool,C: fun_Pr2067565481t_bool] :
      ( ! [D: produc472769767le_alt] :
          ( ( C @ ( D @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
         => ( D @ ( B @ hAPP_P2037731755t_bool ) @ ( D @ ( A @ hAPP_P1069491261t_unit ) @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) )
     => ( B @ ( C @ pi_Pro346842291t_unit ) @ ( A @ ( member1303779570t_unit @ hAPP_f1700632141l_bool ) @ hAPP_f1159856629l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).

thf(321,axiom,
    ! [A: arrow_856714788e_indi] :
      ( ( ( ~ ( n @ ( A @ ( h @ hAPP_A376526755di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( ( ( ( A @ ( h @ hAPP_A376526755di_nat ) )
               != n )
             => ( e @ ( A @ ( p @ hAPP_A1646126530t_bool ) @ ( arrow_1481558583_mkbot @ hAPP_f1761571331t_bool ) @ hAPP_A1601437999t_bool ) @ ( e @ ( c @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
            & ( ( ( A @ ( h @ hAPP_A376526755di_nat ) )
                = n )
             => ( e @ ( c @ ( A @ ( p @ hAPP_A1646126530t_bool ) @ ( arrow_216713899_above @ hAPP_f1550387441t_bool ) @ hAPP_A1058422557t_bool ) @ hAPP_A1601437999t_bool ) @ ( e @ ( c @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ) )
        & ( ( n @ ( A @ ( h @ hAPP_A376526755di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( e @ ( A @ ( p @ hAPP_A1646126530t_bool ) @ ( arrow_1630265669_mktop @ hAPP_f1761571331t_bool ) @ hAPP_A1601437999t_bool ) @ ( e @ ( c @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) )
    <=> ( ( ~ ( one_one_nat @ ( n @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( h @ hAPP_A376526755di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( lba @ ( b @ ( a @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
        & ( ( one_one_nat @ ( n @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( h @ hAPP_A376526755di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( lab @ ( b @ ( a @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Am) ).

thf(1860,plain,
    ! [A: arrow_856714788e_indi] :
      ( ( ( ( ~ ( one_one_nat @ ( n @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( h @ hAPP_A376526755di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( lba @ ( b @ ( a @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
          & ( ( one_one_nat @ ( n @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( h @ hAPP_A376526755di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( lab @ ( b @ ( a @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) )
       => ( ( ~ ( n @ ( A @ ( h @ hAPP_A376526755di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( ( ( ( A @ ( h @ hAPP_A376526755di_nat ) )
                 != n )
               => ( e @ ( A @ ( p @ hAPP_A1646126530t_bool ) @ ( arrow_1481558583_mkbot @ hAPP_f1761571331t_bool ) @ hAPP_A1601437999t_bool ) @ ( e @ ( c @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
              & ( ( ( A @ ( h @ hAPP_A376526755di_nat ) )
                  = n )
               => ( e @ ( c @ ( A @ ( p @ hAPP_A1646126530t_bool ) @ ( arrow_216713899_above @ hAPP_f1550387441t_bool ) @ hAPP_A1058422557t_bool ) @ hAPP_A1601437999t_bool ) @ ( e @ ( c @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ) )
          & ( ( n @ ( A @ ( h @ hAPP_A376526755di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( e @ ( A @ ( p @ hAPP_A1646126530t_bool ) @ ( arrow_1630265669_mktop @ hAPP_f1761571331t_bool ) @ hAPP_A1601437999t_bool ) @ ( e @ ( c @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ) )
      & ( ( ( ~ ( n @ ( A @ ( h @ hAPP_A376526755di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( ( ( ( A @ ( h @ hAPP_A376526755di_nat ) )
                 != n )
               => ( e @ ( A @ ( p @ hAPP_A1646126530t_bool ) @ ( arrow_1481558583_mkbot @ hAPP_f1761571331t_bool ) @ hAPP_A1601437999t_bool ) @ ( e @ ( c @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
              & ( ( ( A @ ( h @ hAPP_A376526755di_nat ) )
                  = n )
               => ( e @ ( c @ ( A @ ( p @ hAPP_A1646126530t_bool ) @ ( arrow_216713899_above @ hAPP_f1550387441t_bool ) @ hAPP_A1058422557t_bool ) @ hAPP_A1601437999t_bool ) @ ( e @ ( c @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ) )
          & ( ( n @ ( A @ ( h @ hAPP_A376526755di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( e @ ( A @ ( p @ hAPP_A1646126530t_bool ) @ ( arrow_1630265669_mktop @ hAPP_f1761571331t_bool ) @ hAPP_A1601437999t_bool ) @ ( e @ ( c @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) )
       => ( ( ~ ( one_one_nat @ ( n @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( h @ hAPP_A376526755di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( lba @ ( b @ ( a @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
          & ( ( one_one_nat @ ( n @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( h @ hAPP_A376526755di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( lab @ ( b @ ( a @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(62,axiom,
    ! [A: fun_nat_bool,B: nat] :
      ( ( B @ ( A @ hAPP_nat_bool ) @ hBOOL )
     => ( ! [C: nat] :
            ( ( C @ ( suc @ hAPP_nat_nat ) @ ( A @ hAPP_nat_bool ) @ hBOOL )
           => ( C @ ( A @ hAPP_nat_bool ) @ hBOOL ) )
       => ( zero_zero_nat @ ( A @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1125_zero__induct) ).

thf(838,plain,
    ! [A: fun_nat_bool,B: nat] :
      ( ( B @ ( A @ hAPP_nat_bool ) @ hBOOL )
     => ( ! [C: nat] :
            ( ( C @ ( suc @ hAPP_nat_nat ) @ ( A @ hAPP_nat_bool ) @ hBOOL )
           => ( C @ ( A @ hAPP_nat_bool ) @ hBOOL ) )
       => ( zero_zero_nat @ ( A @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(227,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( B = C )
     => ( ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_xt1_I1_J) ).

thf(1511,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( B = C )
     => ( ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(313,axiom,
    ! [A: nat,B: nat] :
      ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_374_linorder__not__less) ).

thf(1826,plain,
    ! [A: nat,B: nat] :
      ( ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(172,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1019_add__le__mono1) ).

thf(1313,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(402,axiom,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
      ( ( B @ ( A @ ( fFalse @ ( if_fun523439385t_bool @ hAPP_b35146737t_bool ) @ hAPP_f1299954409t_bool ) @ hAPP_f1356305429t_bool ) )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiq) ).

thf(2185,plain,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
      ( ( B @ ( A @ ( fFalse @ ( if_fun523439385t_bool @ hAPP_b35146737t_bool ) @ hAPP_f1299954409t_bool ) @ hAPP_f1356305429t_bool ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(480,axiom,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
      ( ( A = B )
    <=> ( ( A @ ( B @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
        & ( B @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_358_order__eq__iff) ).

thf(2562,plain,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
      ( ( ( ( A @ ( B @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
          & ( B @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( ( A @ ( B @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
          & ( B @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).

thf(111,axiom,
    ! [A: nat] :
      ( ( one_one_nat = A )
    <=> ( A = one_one_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_734_one__reorient) ).

thf(1059,plain,
    ! [A: nat] :
      ( ( ( A = one_one_nat )
       => ( one_one_nat = A ) )
      & ( ( one_one_nat = A )
       => ( A = one_one_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(501,axiom,
    ~ ( lab @ ( a @ ( b @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80__096_Ib_M_Aa_J_A_126_058_ALab_096) ).

thf(2703,plain,
    ~ ( lab @ ( a @ ( b @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).

thf(540,axiom,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
      ( ( C @ ( B @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_497_order__le__less__trans) ).

thf(2814,plain,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
      ( ( C @ ( B @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).

thf(347,axiom,
    ! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool] :
      ( ( B @ ( A @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
     => ( ( B != A )
       => ( B @ ( A @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_469_xt1_I11_J) ).

thf(1985,plain,
    ! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool] :
      ( ( B @ ( A @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
     => ( ( B != A )
       => ( B @ ( A @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(499,axiom,
    ! [A: bool,B: fun_bool_bool,C: fun_bool_bool] :
      ( ( C @ ( B @ ( ord_le742797417l_bool @ hAPP_f612708895l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_913_subsetD) ).

thf(2698,plain,
    ! [A: bool,B: fun_bool_bool,C: fun_bool_bool] :
      ( ( C @ ( B @ ( ord_le742797417l_bool @ hAPP_f612708895l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).

thf(272,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( B = C )
     => ( ( A @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_ord__eq__less__trans) ).

thf(1660,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( B = C )
     => ( ( A @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(314,axiom,
    ! [A: bool] :
      ( ( A = fFalse )
      | ( A = fTrue ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).

thf(1832,plain,
    ! [A: bool] :
      ( ( A = fFalse )
      | ( A = fTrue ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(564,axiom,
    ! [A: fun_Pr1085078251l_bool,B: fun_Pr2067565481t_bool,C: produc472769767le_alt] :
      ( ( C @ ( B @ ( A @ ( cOMBC_593569186l_bool @ hAPP_f1033183015t_bool ) @ hAPP_f1356305429t_bool ) @ hAPP_P1178790471t_bool ) )
      = ( B @ ( C @ ( A @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs_) ).

thf(2897,plain,
    ! [A: fun_Pr1085078251l_bool,B: fun_Pr2067565481t_bool,C: produc472769767le_alt] :
      ( ( C @ ( B @ ( A @ ( cOMBC_593569186l_bool @ hAPP_f1033183015t_bool ) @ hAPP_f1356305429t_bool ) @ hAPP_P1178790471t_bool ) )
      = ( B @ ( C @ ( A @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).

thf(192,axiom,
    ! [A: nat] :
      ( ( A @ ( suc @ hAPP_nat_nat ) @ ( size_size_nat @ hAPP_nat_nat ) )
      = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( A @ ( size_size_nat @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1183_nat_Osize_I4_J) ).

thf(1379,plain,
    ! [A: nat] :
      ( ( A @ ( suc @ hAPP_nat_nat ) @ ( size_size_nat @ hAPP_nat_nat ) )
      = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( A @ ( size_size_nat @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(399,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( ( A != B )
        & ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_386_order__less__le) ).

thf(2169,plain,
    ! [A: nat,B: nat] :
      ( ( ( ( A != B )
          & ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
       => ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ( A != B )
          & ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(136,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1077_less__SucI) ).

thf(1147,plain,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(243,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_xt1_I6_J) ).

thf(1572,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(44,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( A @ ( suc @ hAPP_nat_nat ) @ times_times_nat @ hAPP_nat_nat ) @ ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1166_Suc__mult__le__cancel1) ).

thf(770,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( C @ ( A @ ( suc @ hAPP_nat_nat ) @ times_times_nat @ hAPP_nat_nat ) @ ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( C @ ( A @ ( suc @ hAPP_nat_nat ) @ times_times_nat @ hAPP_nat_nat ) @ ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(396,axiom,
    ! [A: arrow_856714788e_indi] :
      ( ( A @ ( top_to788185952i_bool @ hAPP_A997847300i_bool ) @ hBOOL )
    <=> ( top_top_bool @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_top__apply) ).

thf(2158,plain,
    ! [A: arrow_856714788e_indi] :
      ( ( ( top_top_bool @ hBOOL )
       => ( A @ ( top_to788185952i_bool @ hAPP_A997847300i_bool ) @ hBOOL ) )
      & ( ( A @ ( top_to788185952i_bool @ hAPP_A997847300i_bool ) @ hBOOL )
       => ( top_top_bool @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(358,axiom,
    ! [A: fun_Pr2067565481t_bool,B: nat,C: fun_fu841105374ol_nat,D: fun_Pr2067565481t_bool] :
      ( ( D @ ( C @ hAPP_f1842225014ol_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( D @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( ! [E: fun_Pr2067565481t_bool,F: fun_Pr2067565481t_bool] :
              ( ( F @ ( E @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
             => ( F @ ( C @ hAPP_f1842225014ol_nat ) @ ( E @ ( C @ hAPP_f1842225014ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
         => ( A @ ( C @ hAPP_f1842225014ol_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_850_order__less__le__subst1) ).

thf(2024,plain,
    ! [A: fun_Pr2067565481t_bool,B: nat,C: fun_fu841105374ol_nat,D: fun_Pr2067565481t_bool] :
      ( ( D @ ( C @ hAPP_f1842225014ol_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( D @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( ! [E: fun_Pr2067565481t_bool,F: fun_Pr2067565481t_bool] :
              ( ( F @ ( E @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
             => ( F @ ( C @ hAPP_f1842225014ol_nat ) @ ( E @ ( C @ hAPP_f1842225014ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
         => ( A @ ( C @ hAPP_f1842225014ol_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(303,axiom,
    ! [A: nat] :
      ( ( n @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( lba @ ( lab @ ( A @ ( h @ ( ord_less_nat @ cOMBB_1869811296e_indi @ hAPP_f966656047t_bool ) @ ( cOMBC_722552198t_bool @ hAPP_f721434149i_bool ) @ hAPP_n34002993i_bool ) @ ( if_fun523439385t_bool @ cOMBB_1061985500e_indi @ hAPP_f668886383t_bool ) @ ( cOMBC_156709173t_bool @ hAPP_f1908974253t_bool ) @ hAPP_f1344464862t_bool ) @ ( cOMBC_750853729t_bool @ hAPP_f601594885t_bool ) @ hAPP_f480276746t_bool ) @ ( f @ hAPP_f2008608496t_bool ) @ ( a @ ( b @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_n_I2_J) ).

thf(1773,plain,
    ! [A: nat] :
      ( ( n @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( lba @ ( lab @ ( A @ ( h @ ( ord_less_nat @ cOMBB_1869811296e_indi @ hAPP_f966656047t_bool ) @ ( cOMBC_722552198t_bool @ hAPP_f721434149i_bool ) @ hAPP_n34002993i_bool ) @ ( if_fun523439385t_bool @ cOMBB_1061985500e_indi @ hAPP_f668886383t_bool ) @ ( cOMBC_156709173t_bool @ hAPP_f1908974253t_bool ) @ hAPP_f1344464862t_bool ) @ ( cOMBC_750853729t_bool @ hAPP_f601594885t_bool ) @ hAPP_f480276746t_bool ) @ ( f @ hAPP_f2008608496t_bool ) @ ( a @ ( b @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(433,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B = A )
       => ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_xt1_I4_J) ).

thf(2301,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B = A )
       => ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).

thf(185,axiom,
    ! [A: nat,B: nat,C: fun_nat_nat] :
      ( ! [D: nat,E: nat] :
          ( ( E @ ( D @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( E @ ( C @ hAPP_nat_nat ) @ ( D @ ( C @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
     => ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( C @ hAPP_nat_nat ) @ ( B @ ( A @ ( C @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1023_mono__nat__linear__lb) ).

thf(1362,plain,
    ! [A: nat,B: nat,C: fun_nat_nat] :
      ( ! [D: nat,E: nat] :
          ( ( E @ ( D @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( E @ ( C @ hAPP_nat_nat ) @ ( D @ ( C @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
     => ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( C @ hAPP_nat_nat ) @ ( B @ ( A @ ( C @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(305,axiom,
    ! [A: product_unit] :
      ( ( A @ ( top_to1257323279t_bool @ hAPP_P1676879539t_bool ) @ hBOOL )
    <=> ( top_top_bool @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_top__apply) ).

thf(1778,plain,
    ! [A: product_unit] :
      ( ( ( top_top_bool @ hBOOL )
       => ( A @ ( top_to1257323279t_bool @ hAPP_P1676879539t_bool ) @ hBOOL ) )
      & ( ( A @ ( top_to1257323279t_bool @ hAPP_P1676879539t_bool ) @ hBOOL )
       => ( top_top_bool @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(553,axiom,
    e @ ( p @ ( arrow_1481558583_mkbot @ cOMBB_80760910e_indi @ hAPP_f831214557t_bool ) @ ( cOMBC_1417338747t_bool @ hAPP_f1631649925t_bool ) @ hAPP_A425126512t_bool ) @ ( e @ ( c @ ( p @ ( arrow_216713899_above @ cOMBB_1876517692e_indi @ hAPP_f1751344075t_bool ) @ ( cOMBC_1486904681t_bool @ hAPP_f2102110817t_bool ) @ hAPP_A1889513822t_bool ) @ ( cOMBC_1417338747t_bool @ hAPP_f1631649925t_bool ) @ hAPP_A425126512t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_1869811296e_indi @ hAPP_f966656047t_bool ) @ ( cOMBC_722552198t_bool @ hAPP_f721434149i_bool ) @ hAPP_n34002993i_bool ) @ ( if_fun523439385t_bool @ cOMBB_1061985500e_indi @ hAPP_f668886383t_bool ) @ cOMBS_1925466437t_bool @ hAPP_f1001205955t_bool ) @ cOMBS_1181656689t_bool @ hAPP_f1302887663t_bool ) @ ( e @ ( p @ ( arrow_1630265669_mktop @ cOMBB_80760910e_indi @ hAPP_f831214557t_bool ) @ ( cOMBC_1417338747t_bool @ hAPP_f1631649925t_bool ) @ hAPP_A425126512t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_1869811296e_indi @ hAPP_f966656047t_bool ) @ ( cOMBC_722552198t_bool @ hAPP_f721434149i_bool ) @ hAPP_n34002993i_bool ) @ ( if_fun523439385t_bool @ cOMBB_1061985500e_indi @ hAPP_f668886383t_bool ) @ cOMBS_1925466437t_bool @ hAPP_f1001205955t_bool ) @ cOMBS_1181656689t_bool @ hAPP_f1302887663t_bool ) @ ( f @ hAPP_f2008608496t_bool ) @ ( e @ ( c @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto) ).

thf(2852,plain,
    e @ ( p @ ( arrow_1481558583_mkbot @ cOMBB_80760910e_indi @ hAPP_f831214557t_bool ) @ ( cOMBC_1417338747t_bool @ hAPP_f1631649925t_bool ) @ hAPP_A425126512t_bool ) @ ( e @ ( c @ ( p @ ( arrow_216713899_above @ cOMBB_1876517692e_indi @ hAPP_f1751344075t_bool ) @ ( cOMBC_1486904681t_bool @ hAPP_f2102110817t_bool ) @ hAPP_A1889513822t_bool ) @ ( cOMBC_1417338747t_bool @ hAPP_f1631649925t_bool ) @ hAPP_A425126512t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_1869811296e_indi @ hAPP_f966656047t_bool ) @ ( cOMBC_722552198t_bool @ hAPP_f721434149i_bool ) @ hAPP_n34002993i_bool ) @ ( if_fun523439385t_bool @ cOMBB_1061985500e_indi @ hAPP_f668886383t_bool ) @ cOMBS_1925466437t_bool @ hAPP_f1001205955t_bool ) @ cOMBS_1181656689t_bool @ hAPP_f1302887663t_bool ) @ ( e @ ( p @ ( arrow_1630265669_mktop @ cOMBB_80760910e_indi @ hAPP_f831214557t_bool ) @ ( cOMBC_1417338747t_bool @ hAPP_f1631649925t_bool ) @ hAPP_A425126512t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_1869811296e_indi @ hAPP_f966656047t_bool ) @ ( cOMBC_722552198t_bool @ hAPP_f721434149i_bool ) @ hAPP_n34002993i_bool ) @ ( if_fun523439385t_bool @ cOMBB_1061985500e_indi @ hAPP_f668886383t_bool ) @ cOMBS_1925466437t_bool @ hAPP_f1001205955t_bool ) @ cOMBS_1181656689t_bool @ hAPP_f1302887663t_bool ) @ ( f @ hAPP_f2008608496t_bool ) @ ( e @ ( c @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).

thf(329,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A != B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_order__less__imp__not__eq) ).

thf(1922,plain,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(56,axiom,
    ! [A: nat,B: nat] :
      ~ ( A @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_999_not__add__less1) ).

thf(817,plain,
    ! [A: nat,B: nat] :
      ~ ( A @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(175,axiom,
    ! [A: fun_Pr2067565481t_bool] :
      ( ( top_to1647826457l_bool @ ( cOMBK_138598520le_alt @ hAPP_f699791347l_bool ) @ ( A @ pi_Pro1238944957t_bool ) )
      = top_to1312956197l_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_Pi__UNIV) ).

thf(1319,plain,
    ! [A: fun_Pr2067565481t_bool] :
      ( ( top_to1647826457l_bool @ ( cOMBK_138598520le_alt @ hAPP_f699791347l_bool ) @ ( A @ pi_Pro1238944957t_bool ) )
      = top_to1312956197l_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(284,axiom,
    ! [A: nat,B: fun_fu841105374ol_nat,C: fun_Pr2067565481t_bool,D: fun_Pr2067565481t_bool] :
      ( ( D @ ( C @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( ( C @ ( B @ hAPP_f1842225014ol_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [E: fun_Pr2067565481t_bool,F: fun_Pr2067565481t_bool] :
              ( ( E @ ( F @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
             => ( E @ ( B @ hAPP_f1842225014ol_nat ) @ ( F @ ( B @ hAPP_f1842225014ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
         => ( D @ ( B @ hAPP_f1842225014ol_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_702_xt7) ).

thf(1704,plain,
    ! [A: nat,B: fun_fu841105374ol_nat,C: fun_Pr2067565481t_bool,D: fun_Pr2067565481t_bool] :
      ( ( D @ ( C @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( ( C @ ( B @ hAPP_f1842225014ol_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [E: fun_Pr2067565481t_bool,F: fun_Pr2067565481t_bool] :
              ( ( E @ ( F @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
             => ( E @ ( B @ hAPP_f1842225014ol_nat ) @ ( F @ ( B @ hAPP_f1842225014ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
         => ( D @ ( B @ hAPP_f1842225014ol_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(69,axiom,
    ! [A: nat] :
      ( zero_zero_nat
     != ( A @ ( suc @ hAPP_nat_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1067_Zero__neq__Suc) ).

thf(870,plain,
    ! [A: nat] :
      ( zero_zero_nat
     != ( A @ ( suc @ hAPP_nat_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(295,axiom,
    ! [A: nat,B: nat] :
      ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
      <=> ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_409_linorder__antisym__conv1) ).

thf(1741,plain,
    ! [A: nat,B: nat] :
      ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( ( A = B )
         => ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
        & ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(71,axiom,
    ! [A: nat,B: fun_nat_bool] :
      ( ~ ( zero_zero_nat @ ( B @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( B @ hAPP_nat_bool ) @ hBOOL )
       => ? [C: nat] :
            ( ( one_one_nat @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ hAPP_nat_bool ) @ hBOOL )
            & ! [D: nat] :
                ( ( C @ ( D @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
               => ~ ( D @ ( B @ hAPP_nat_bool ) @ hBOOL ) )
            & ( A @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1056_ex__least__nat__less) ).

thf(881,plain,
    ! [A: nat,B: fun_nat_bool] :
      ( ~ ( zero_zero_nat @ ( B @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( B @ hAPP_nat_bool ) @ hBOOL )
       => ? [C: nat] :
            ( ( one_one_nat @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ hAPP_nat_bool ) @ hBOOL )
            & ! [D: nat] :
                ( ( C @ ( D @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
               => ~ ( D @ ( B @ hAPP_nat_bool ) @ hBOOL ) )
            & ( A @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(412,axiom,
    ( top_to1138392227t_bool
    = ( fTrue @ ( cOMBK_198697344le_alt @ hAPP_b128655177t_bool ) @ ( collec1988958098le_alt @ hAPP_f1356305429t_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_UNIV__def) ).

thf(2222,plain,
    ( top_to1138392227t_bool
    = ( fTrue @ ( cOMBK_198697344le_alt @ hAPP_b128655177t_bool ) @ ( collec1988958098le_alt @ hAPP_f1356305429t_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(287,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( B = C )
     => ( ( A @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_ord__eq__le__trans) ).

thf(1714,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( B = C )
     => ( ( A @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(179,axiom,
    ! [A: fun_Pr2067565481t_bool,B: fun_fu638310559l_bool,C: fun_fu638310559l_bool] :
      ( ( C @ ( B @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_967_in__mono) ).

thf(1334,plain,
    ! [A: fun_Pr2067565481t_bool,B: fun_fu638310559l_bool,C: fun_fu638310559l_bool] :
      ( ( C @ ( B @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(567,axiom,
    ! [A: fun_fu1572237755l_bool,B: fun_Ar2121501495le_alt,C: arrow_1893660431le_alt] :
      ( ( C @ ( B @ ( A @ cOMBB_1575576719le_alt @ hAPP_f184584489l_bool ) @ hAPP_A1608658241l_bool ) )
      = ( C @ ( B @ hAPP_A1146194953le_alt ) @ ( A @ hAPP_f1536341593l_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__) ).

thf(2925,plain,
    ! [A: fun_fu1572237755l_bool,B: fun_Ar2121501495le_alt,C: arrow_1893660431le_alt] :
      ( ( C @ ( B @ ( A @ cOMBB_1575576719le_alt @ hAPP_f184584489l_bool ) @ hAPP_A1608658241l_bool ) )
      = ( C @ ( B @ hAPP_A1146194953le_alt ) @ ( A @ hAPP_f1536341593l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).

thf(278,axiom,
    arrow_5070731e_Prof @ ( p @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3__096P_A_058_AProf_096) ).

thf(1677,plain,
    arrow_5070731e_Prof @ ( p @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(163,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1017_trans__le__add1) ).

thf(1283,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(110,axiom,
    ! [A: nat] :
      ( ( zero_zero_nat @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( A = zero_zero_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1053_le__0__eq) ).

thf(1051,plain,
    ! [A: nat] :
      ( ( ( A = zero_zero_nat )
       => ( zero_zero_nat @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( zero_zero_nat @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A = zero_zero_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(41,axiom,
    ! [A: fun_fu638310559l_bool,B: fun_fu638310559l_bool] :
      ( ( B @ ( A @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
     => ( ( A @ ( B @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
       => ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_xt1_I5_J) ).

thf(756,plain,
    ! [A: fun_fu638310559l_bool,B: fun_fu638310559l_bool] :
      ( ( B @ ( A @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
     => ( ( A @ ( B @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(273,axiom,
    ! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool] :
      ( ( B @ ( A @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
     => ( ( A @ ( B @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_order__antisym) ).

thf(1664,plain,
    ! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool] :
      ( ( B @ ( A @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
     => ( ( A @ ( B @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(531,axiom,
    ! [A: produc472769767le_alt,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
      ( ( C @ ( B @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_915_subsetD) ).

thf(2794,plain,
    ! [A: produc472769767le_alt,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
      ( ( C @ ( B @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).

thf(378,axiom,
    ! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool,C: fun_Ar331856045t_bool] :
      ( ( C @ ( B @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
     => ( ( B = A )
       => ( C @ ( A @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_xt1_I4_J) ).

thf(2105,plain,
    ! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool,C: fun_Ar331856045t_bool] :
      ( ( C @ ( B @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
     => ( ( B = A )
       => ( C @ ( A @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

thf(208,axiom,
    ! [A: nat,B: nat] : ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1014_le__add1) ).

thf(1450,plain,
    ! [A: nat,B: nat] : ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(189,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1026_termination__basic__simps_I4_J) ).

thf(1373,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(573,axiom,
    ! [A: fun_Ar274636406t_bool,B: fun_Ar274636406t_bool,C: arrow_1893660431le_alt,D: arrow_1893660431le_alt,E: arrow_1893660431le_alt] :
      ( ( D != E )
     => ( ( E != C )
       => ( ( D != C )
         => ( ( arrow_5070731e_Prof @ ( B @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL )
           => ( ( arrow_5070731e_Prof @ ( A @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL )
             => ( ! [F: arrow_856714788e_indi] :
                    ( ( F @ ( B @ hAPP_A1646126530t_bool ) @ ( E @ ( D @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
                  <=> ( F @ ( A @ hAPP_A1646126530t_bool ) @ ( C @ ( E @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
               => ( ( B @ ( f @ hAPP_f2008608496t_bool ) @ ( E @ ( D @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
                <=> ( A @ ( f @ hAPP_f2008608496t_bool ) @ ( C @ ( E @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8__C4_C) ).

thf(2996,plain,
    ! [A: fun_Ar274636406t_bool,B: fun_Ar274636406t_bool,C: arrow_1893660431le_alt,D: arrow_1893660431le_alt,E: arrow_1893660431le_alt] :
      ( ( D != E )
     => ( ( E != C )
       => ( ( D != C )
         => ( ( arrow_5070731e_Prof @ ( B @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL )
           => ( ( arrow_5070731e_Prof @ ( A @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL )
             => ( ! [F: arrow_856714788e_indi] :
                    ( ( ( F @ ( A @ hAPP_A1646126530t_bool ) @ ( C @ ( E @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
                     => ( F @ ( B @ hAPP_A1646126530t_bool ) @ ( E @ ( D @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
                    & ( ( F @ ( B @ hAPP_A1646126530t_bool ) @ ( E @ ( D @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
                     => ( F @ ( A @ hAPP_A1646126530t_bool ) @ ( C @ ( E @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) )
               => ( ( ( A @ ( f @ hAPP_f2008608496t_bool ) @ ( C @ ( E @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
                   => ( B @ ( f @ hAPP_f2008608496t_bool ) @ ( E @ ( D @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
                  & ( ( B @ ( f @ hAPP_f2008608496t_bool ) @ ( E @ ( D @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
                   => ( A @ ( f @ hAPP_f2008608496t_bool ) @ ( C @ ( E @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).

thf(326,axiom,
    ! [A: nat,B: nat] :
      ( ( ( A = B )
        | ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
     => ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1012_less__or__eq__imp__le) ).

thf(1911,plain,
    ! [A: nat,B: nat] :
      ( ( ( A = B )
        | ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
     => ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(528,axiom,
    ! [A: produc472769767le_alt,B: fun_Pr1509342064e_indi,C: fun_Pr2067565481t_bool,D: fun_Pr895221296i_bool] :
      ( ( D @ ( C @ pi_Pro837265796e_indi ) @ ( B @ ( member1558233923e_indi @ hAPP_f1187850253l_bool ) @ hAPP_f2124588998l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( A @ ( D @ hAPP_P1859429372i_bool ) @ ( A @ ( B @ hAPP_P276596750e_indi ) @ ( member1479139729e_indi @ hAPP_A1597696899l_bool ) @ hAPP_f584385070l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_548_Pi__mem) ).

thf(2782,plain,
    ! [A: produc472769767le_alt,B: fun_Pr1509342064e_indi,C: fun_Pr2067565481t_bool,D: fun_Pr895221296i_bool] :
      ( ( D @ ( C @ pi_Pro837265796e_indi ) @ ( B @ ( member1558233923e_indi @ hAPP_f1187850253l_bool ) @ hAPP_f2124588998l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( A @ ( D @ hAPP_P1859429372i_bool ) @ ( A @ ( B @ hAPP_P276596750e_indi ) @ ( member1479139729e_indi @ hAPP_A1597696899l_bool ) @ hAPP_f584385070l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).

thf(191,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( D @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( D @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1020_add__le__mono) ).

thf(1377,plain,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( D @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( D @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(484,axiom,
    f @ ( arrow_320876018nimity @ hAPP_f1572141188l_bool ) @ hBOOL,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_u) ).

thf(2618,plain,
    f @ ( arrow_320876018nimity @ hAPP_f1572141188l_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).

thf(68,axiom,
    ! [A: fun_fu638310559l_bool,B: fun_fu638310559l_bool] :
      ( ( A = B )
     => ( B @ ( A @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_order__eq__refl) ).

thf(866,plain,
    ! [A: fun_fu638310559l_bool,B: fun_fu638310559l_bool] :
      ( ( A = B )
     => ( B @ ( A @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(130,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1168_n__less__m__mult__n) ).

thf(1119,plain,
    ! [A: nat,B: nat] :
      ( ( B @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(203,axiom,
    ! [A: nat,B: nat] :
      ( ~ ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( A @ ( B @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1091_not__less__eq__eq) ).

thf(1433,plain,
    ! [A: nat,B: nat] :
      ( ( ( A @ ( B @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ~ ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ~ ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( B @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(334,axiom,
    ! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool,C: fun_Ar331856045t_bool] :
      ( ( B = C )
     => ( ( A @ ( C @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_ord__eq__le__trans) ).

thf(1943,plain,
    ! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool,C: fun_Ar331856045t_bool] :
      ( ( B = C )
     => ( ( A @ ( C @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(506,axiom,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
      ( ( B @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( ( B != A )
       => ( B @ ( A @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_467_xt1_I11_J) ).

thf(2718,plain,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
      ( ( B @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( ( B != A )
       => ( B @ ( A @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).

thf(523,axiom,
    ( ( p @ ( f @ hAPP_f2008608496t_bool ) @ ( d @ ( c @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
  <=> ( e @ ( p @ ( arrow_1481558583_mkbot @ cOMBB_80760910e_indi @ hAPP_f831214557t_bool ) @ ( cOMBC_1417338747t_bool @ hAPP_f1631649925t_bool ) @ hAPP_A425126512t_bool ) @ ( e @ ( c @ ( p @ ( arrow_216713899_above @ cOMBB_1876517692e_indi @ hAPP_f1751344075t_bool ) @ ( cOMBC_1486904681t_bool @ hAPP_f2102110817t_bool ) @ hAPP_A1889513822t_bool ) @ ( cOMBC_1417338747t_bool @ hAPP_f1631649925t_bool ) @ hAPP_A425126512t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_1869811296e_indi @ hAPP_f966656047t_bool ) @ ( cOMBC_722552198t_bool @ hAPP_f721434149i_bool ) @ hAPP_n34002993i_bool ) @ ( if_fun523439385t_bool @ cOMBB_1061985500e_indi @ hAPP_f668886383t_bool ) @ cOMBS_1925466437t_bool @ hAPP_f1001205955t_bool ) @ cOMBS_1181656689t_bool @ hAPP_f1302887663t_bool ) @ ( e @ ( p @ ( arrow_1630265669_mktop @ cOMBB_80760910e_indi @ hAPP_f831214557t_bool ) @ ( cOMBC_1417338747t_bool @ hAPP_f1631649925t_bool ) @ hAPP_A425126512t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_1869811296e_indi @ hAPP_f966656047t_bool ) @ ( cOMBC_722552198t_bool @ hAPP_f721434149i_bool ) @ hAPP_n34002993i_bool ) @ ( if_fun523439385t_bool @ cOMBB_1061985500e_indi @ hAPP_f668886383t_bool ) @ cOMBS_1925466437t_bool @ hAPP_f1001205955t_bool ) @ cOMBS_1181656689t_bool @ hAPP_f1302887663t_bool ) @ ( f @ hAPP_f2008608496t_bool ) @ ( d @ ( c @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_PW) ).

thf(2762,plain,
    ( ( ( e @ ( p @ ( arrow_1481558583_mkbot @ cOMBB_80760910e_indi @ hAPP_f831214557t_bool ) @ ( cOMBC_1417338747t_bool @ hAPP_f1631649925t_bool ) @ hAPP_A425126512t_bool ) @ ( e @ ( c @ ( p @ ( arrow_216713899_above @ cOMBB_1876517692e_indi @ hAPP_f1751344075t_bool ) @ ( cOMBC_1486904681t_bool @ hAPP_f2102110817t_bool ) @ hAPP_A1889513822t_bool ) @ ( cOMBC_1417338747t_bool @ hAPP_f1631649925t_bool ) @ hAPP_A425126512t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_1869811296e_indi @ hAPP_f966656047t_bool ) @ ( cOMBC_722552198t_bool @ hAPP_f721434149i_bool ) @ hAPP_n34002993i_bool ) @ ( if_fun523439385t_bool @ cOMBB_1061985500e_indi @ hAPP_f668886383t_bool ) @ cOMBS_1925466437t_bool @ hAPP_f1001205955t_bool ) @ cOMBS_1181656689t_bool @ hAPP_f1302887663t_bool ) @ ( e @ ( p @ ( arrow_1630265669_mktop @ cOMBB_80760910e_indi @ hAPP_f831214557t_bool ) @ ( cOMBC_1417338747t_bool @ hAPP_f1631649925t_bool ) @ hAPP_A425126512t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_1869811296e_indi @ hAPP_f966656047t_bool ) @ ( cOMBC_722552198t_bool @ hAPP_f721434149i_bool ) @ hAPP_n34002993i_bool ) @ ( if_fun523439385t_bool @ cOMBB_1061985500e_indi @ hAPP_f668886383t_bool ) @ cOMBS_1925466437t_bool @ hAPP_f1001205955t_bool ) @ cOMBS_1181656689t_bool @ hAPP_f1302887663t_bool ) @ ( f @ hAPP_f2008608496t_bool ) @ ( d @ ( c @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( p @ ( f @ hAPP_f2008608496t_bool ) @ ( d @ ( c @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
    & ( ( p @ ( f @ hAPP_f2008608496t_bool ) @ ( d @ ( c @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( e @ ( p @ ( arrow_1481558583_mkbot @ cOMBB_80760910e_indi @ hAPP_f831214557t_bool ) @ ( cOMBC_1417338747t_bool @ hAPP_f1631649925t_bool ) @ hAPP_A425126512t_bool ) @ ( e @ ( c @ ( p @ ( arrow_216713899_above @ cOMBB_1876517692e_indi @ hAPP_f1751344075t_bool ) @ ( cOMBC_1486904681t_bool @ hAPP_f2102110817t_bool ) @ hAPP_A1889513822t_bool ) @ ( cOMBC_1417338747t_bool @ hAPP_f1631649925t_bool ) @ hAPP_A425126512t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_1869811296e_indi @ hAPP_f966656047t_bool ) @ ( cOMBC_722552198t_bool @ hAPP_f721434149i_bool ) @ hAPP_n34002993i_bool ) @ ( if_fun523439385t_bool @ cOMBB_1061985500e_indi @ hAPP_f668886383t_bool ) @ cOMBS_1925466437t_bool @ hAPP_f1001205955t_bool ) @ cOMBS_1181656689t_bool @ hAPP_f1302887663t_bool ) @ ( e @ ( p @ ( arrow_1630265669_mktop @ cOMBB_80760910e_indi @ hAPP_f831214557t_bool ) @ ( cOMBC_1417338747t_bool @ hAPP_f1631649925t_bool ) @ hAPP_A425126512t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_1869811296e_indi @ hAPP_f966656047t_bool ) @ ( cOMBC_722552198t_bool @ hAPP_f721434149i_bool ) @ hAPP_n34002993i_bool ) @ ( if_fun523439385t_bool @ cOMBB_1061985500e_indi @ hAPP_f668886383t_bool ) @ cOMBS_1925466437t_bool @ hAPP_f1001205955t_bool ) @ cOMBS_1181656689t_bool @ hAPP_f1302887663t_bool ) @ ( f @ hAPP_f2008608496t_bool ) @ ( d @ ( c @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).

thf(474,axiom,
    fTrue @ hBOOL,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fTrue_1_1_U) ).

thf(2508,plain,
    fTrue @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).

thf(94,axiom,
    ! [A: fun_Pr2067565481t_bool,B: fun_fu638310559l_bool,C: fun_fu638310559l_bool] :
      ( ( C @ ( B @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_956_set__mp) ).

thf(981,plain,
    ! [A: fun_Pr2067565481t_bool,B: fun_fu638310559l_bool,C: fun_fu638310559l_bool] :
      ( ( C @ ( B @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(231,axiom,
    ! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool] :
      ( ( B @ ( A @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
    <=> ( ( A != B )
        & ( B @ ( A @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_384_order__less__le) ).

thf(1526,plain,
    ! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool] :
      ( ( ( ( A != B )
          & ( B @ ( A @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) )
       => ( B @ ( A @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
       => ( ( A != B )
          & ( B @ ( A @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(390,axiom,
    ! [A: bool,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_order__less__imp__triv) ).

thf(2137,plain,
    ! [A: bool,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(533,axiom,
    ! [A: fun_Pr2067565481t_bool] : ( top_to1138392227t_bool @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_722_subset__UNIV) ).

thf(2799,plain,
    ! [A: fun_Pr2067565481t_bool] : ( top_to1138392227t_bool @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).

thf(429,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A != B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_less__imp__neq) ).

thf(2286,plain,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).

thf(490,axiom,
    ! [A: arrow_1893660431le_alt,B: arrow_1893660431le_alt,C: fun_Pr2067565481t_bool] :
      ( ( arrow_1361987423le_Lin @ ( C @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
     => ( ( A != B )
       => ( ~ ( C @ ( B @ ( A @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
        <=> ( C @ ( A @ ( B @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_notin__Lin__iff) ).

thf(2639,plain,
    ! [A: arrow_1893660431le_alt,B: arrow_1893660431le_alt,C: fun_Pr2067565481t_bool] :
      ( ( arrow_1361987423le_Lin @ ( C @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
     => ( ( A != B )
       => ( ( ( C @ ( A @ ( B @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
           => ~ ( C @ ( B @ ( A @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
          & ( ~ ( C @ ( B @ ( A @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
           => ( C @ ( A @ ( B @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).

thf(269,axiom,
    ! [A: fun_Ar331856045t_bool,B: fun_fu1677555470ol_nat,C: fun_Ar331856045t_bool,D: nat] :
      ( ( D @ ( C @ ( B @ hAPP_f1403773274ol_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
       => ( ! [E: fun_Ar331856045t_bool,F: fun_Ar331856045t_bool] :
              ( ( E @ ( F @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
             => ( E @ ( B @ hAPP_f1403773274ol_nat ) @ ( F @ ( B @ hAPP_f1403773274ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
         => ( D @ ( A @ ( B @ hAPP_f1403773274ol_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_805_xt4) ).

thf(1651,plain,
    ! [A: fun_Ar331856045t_bool,B: fun_fu1677555470ol_nat,C: fun_Ar331856045t_bool,D: nat] :
      ( ( D @ ( C @ ( B @ hAPP_f1403773274ol_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
       => ( ! [E: fun_Ar331856045t_bool,F: fun_Ar331856045t_bool] :
              ( ( E @ ( F @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
             => ( E @ ( B @ hAPP_f1403773274ol_nat ) @ ( F @ ( B @ hAPP_f1403773274ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
         => ( D @ ( A @ ( B @ hAPP_f1403773274ol_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(574,axiom,
    ! [A: arrow_1893660431le_alt,B: arrow_1893660431le_alt,C: fun_Pr2067565481t_bool,D: arrow_1893660431le_alt] :
      ( ( D @ ( C @ ( arrow_1481558583_mkbot @ hAPP_f1761571331t_bool ) @ hAPP_A1601437999t_bool ) @ ( B @ ( A @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
    <=> ( ( ( A != D )
         => ( C @ ( B @ ( A @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
        & ( ( A = D )
         => ( A != B ) )
        & ( B != D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_in__mkbot) ).

thf(3011,plain,
    ! [A: arrow_1893660431le_alt,B: arrow_1893660431le_alt,C: fun_Pr2067565481t_bool,D: arrow_1893660431le_alt] :
      ( ( ( ( ( A != D )
           => ( C @ ( B @ ( A @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
          & ( ( A = D )
           => ( A != B ) )
          & ( B != D ) )
       => ( D @ ( C @ ( arrow_1481558583_mkbot @ hAPP_f1761571331t_bool ) @ hAPP_A1601437999t_bool ) @ ( B @ ( A @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
      & ( ( D @ ( C @ ( arrow_1481558583_mkbot @ hAPP_f1761571331t_bool ) @ hAPP_A1601437999t_bool ) @ ( B @ ( A @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( ( ( A != D )
           => ( C @ ( B @ ( A @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
          & ( ( A = D )
           => ( A != B ) )
          & ( B != D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).

thf(466,axiom,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
      ( ( C @ ( B @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( ( B = A )
       => ( C @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_xt1_I4_J) ).

thf(2473,plain,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
      ( ( C @ ( B @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( ( B = A )
       => ( C @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).

thf(48,axiom,
    ! [A: fun_na300967376t_bool,B: fun_Ar331856045t_bool,C: nat,D: nat] :
      ( ( D @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( D @ ( A @ hAPP_n1312530466t_bool ) @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
       => ( ! [E: nat,F: nat] :
              ( ( F @ ( E @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( F @ ( A @ hAPP_n1312530466t_bool ) @ ( E @ ( A @ hAPP_n1312530466t_bool ) @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) )
         => ( B @ ( C @ ( A @ hAPP_n1312530466t_bool ) @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_863_order__le__less__subst2) ).

thf(793,plain,
    ! [A: fun_na300967376t_bool,B: fun_Ar331856045t_bool,C: nat,D: nat] :
      ( ( D @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( D @ ( A @ hAPP_n1312530466t_bool ) @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
       => ( ! [E: nat,F: nat] :
              ( ( F @ ( E @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( F @ ( A @ hAPP_n1312530466t_bool ) @ ( E @ ( A @ hAPP_n1312530466t_bool ) @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) )
         => ( B @ ( C @ ( A @ hAPP_n1312530466t_bool ) @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(170,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( ( A @ ( suc @ hAPP_nat_nat ) )
         != B )
       => ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1076_Suc__lessI) ).

thf(1306,plain,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( ( A @ ( suc @ hAPP_nat_nat ) )
         != B )
       => ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(54,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ? [C: nat] :
          ( B
          = ( C @ ( suc @ hAPP_nat_nat ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1120_Suc__le__D) ).

thf(810,plain,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ? [C: nat] :
          ( B
          = ( C @ ( suc @ hAPP_nat_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(364,axiom,
    ! [A: bool] :
      ( ( A = fFalse )
      | ( A = fTrue ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fTrue_1_1_T) ).

thf(2047,plain,
    ! [A: bool] :
      ( ( A = fFalse )
      | ( A = fTrue ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(285,axiom,
    ! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool,C: fun_Ar331856045t_bool] :
      ( ( C @ ( B @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_order__trans) ).

thf(1708,plain,
    ! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool,C: fun_Ar331856045t_bool] :
      ( ( C @ ( B @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(512,axiom,
    ! [A: arrow_856714788e_indi,B: fun_Ar338949104le_alt,C: fun_Ar1809396326i_bool,D: fun_Ar274636406t_bool] :
      ( ( D @ ( C @ pi_Arr1460528004le_alt ) @ ( B @ ( member387840963le_alt @ hAPP_f766019597l_bool ) @ hAPP_f1754488902l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member1479139729e_indi @ hAPP_A1597696899l_bool ) @ hAPP_f584385070l_bool ) @ hBOOL )
       => ( A @ ( D @ hAPP_A1646126530t_bool ) @ ( A @ ( B @ hAPP_A899858958le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_562_Pi__mem) ).

thf(2737,plain,
    ! [A: arrow_856714788e_indi,B: fun_Ar338949104le_alt,C: fun_Ar1809396326i_bool,D: fun_Ar274636406t_bool] :
      ( ( D @ ( C @ pi_Arr1460528004le_alt ) @ ( B @ ( member387840963le_alt @ hAPP_f766019597l_bool ) @ hAPP_f1754488902l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member1479139729e_indi @ hAPP_A1597696899l_bool ) @ hAPP_f584385070l_bool ) @ hBOOL )
       => ( A @ ( D @ hAPP_A1646126530t_bool ) @ ( A @ ( B @ hAPP_A899858958le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).

thf(470,axiom,
    ! [A: fun_Pr2067565481t_bool] :
      ( ! [B: produc472769767le_alt] : ( B @ ( A @ hAPP_P1178790471t_bool ) @ hBOOL )
    <=> ! [B: arrow_1893660431le_alt,C: arrow_1893660431le_alt] : ( C @ ( B @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( A @ hAPP_P1178790471t_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_split__paired__All) ).

thf(2496,plain,
    ! [A: fun_Pr2067565481t_bool] :
      ( ( ! [B: arrow_1893660431le_alt,C: arrow_1893660431le_alt] : ( C @ ( B @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( A @ hAPP_P1178790471t_bool ) @ hBOOL )
       => ! [B: produc472769767le_alt] : ( B @ ( A @ hAPP_P1178790471t_bool ) @ hBOOL ) )
      & ( ! [B: produc472769767le_alt] : ( B @ ( A @ hAPP_P1178790471t_bool ) @ hBOOL )
       => ! [B: arrow_1893660431le_alt,C: arrow_1893660431le_alt] : ( C @ ( B @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( A @ hAPP_P1178790471t_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).

thf(481,axiom,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
      ( ( B @ ( produc1590937303le_alt @ ( member1333168212le_alt @ cOMBB_1660064607le_alt @ cOMBB_1575576719le_alt @ hAPP_f184584489l_bool ) @ ( cOMBC_395465908l_bool @ cOMBB_652885079le_alt @ hAPP_f105674721t_bool ) @ ( cOMBC_557453916t_bool @ hAPP_f1081591777t_bool ) @ hAPP_f449303873t_bool ) @ ( A @ ( produc1590937303le_alt @ ( member1333168212le_alt @ cOMBB_1660064607le_alt @ cOMBB_1575576719le_alt @ hAPP_f184584489l_bool ) @ ( cOMBC_395465908l_bool @ cOMBB_652885079le_alt @ hAPP_f105674721t_bool ) @ ( cOMBC_557453916t_bool @ hAPP_f1081591777t_bool ) @ hAPP_f449303873t_bool ) @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
    <=> ( B @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_718_pred__subset__eq2) ).

thf(2574,plain,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
      ( ( ( B @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( B @ ( produc1590937303le_alt @ ( member1333168212le_alt @ cOMBB_1660064607le_alt @ cOMBB_1575576719le_alt @ hAPP_f184584489l_bool ) @ ( cOMBC_395465908l_bool @ cOMBB_652885079le_alt @ hAPP_f105674721t_bool ) @ ( cOMBC_557453916t_bool @ hAPP_f1081591777t_bool ) @ hAPP_f449303873t_bool ) @ ( A @ ( produc1590937303le_alt @ ( member1333168212le_alt @ cOMBB_1660064607le_alt @ cOMBB_1575576719le_alt @ hAPP_f184584489l_bool ) @ ( cOMBC_395465908l_bool @ cOMBB_652885079le_alt @ hAPP_f105674721t_bool ) @ ( cOMBC_557453916t_bool @ hAPP_f1081591777t_bool ) @ hAPP_f449303873t_bool ) @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) )
      & ( ( B @ ( produc1590937303le_alt @ ( member1333168212le_alt @ cOMBB_1660064607le_alt @ cOMBB_1575576719le_alt @ hAPP_f184584489l_bool ) @ ( cOMBC_395465908l_bool @ cOMBB_652885079le_alt @ hAPP_f105674721t_bool ) @ ( cOMBC_557453916t_bool @ hAPP_f1081591777t_bool ) @ hAPP_f449303873t_bool ) @ ( A @ ( produc1590937303le_alt @ ( member1333168212le_alt @ cOMBB_1660064607le_alt @ cOMBB_1575576719le_alt @ hAPP_f184584489l_bool ) @ ( cOMBC_395465908l_bool @ cOMBB_652885079le_alt @ hAPP_f105674721t_bool ) @ ( cOMBC_557453916t_bool @ hAPP_f1081591777t_bool ) @ hAPP_f449303873t_bool ) @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).

thf(19,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ times_times_nat @ hAPP_nat_nat ) )
      = ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1165_mult__Suc) ).

thf(661,plain,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ times_times_nat @ hAPP_nat_nat ) )
      = ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(448,axiom,
    ! [A: fun_fu2114379172t_bool] : ( top_to827110112l_bool @ ( A @ ( member173038353t_bool @ hAPP_f1714503811l_bool ) @ hAPP_f975209902l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_iso__tuple__UNIV__I) ).

thf(2364,plain,
    ! [A: fun_fu2114379172t_bool] : ( top_to827110112l_bool @ ( A @ ( member173038353t_bool @ hAPP_f1714503811l_bool ) @ hAPP_f975209902l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).

thf(397,axiom,
    ! [A: nat,B: nat] :
      ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
      | ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_994_nat__le__linear) ).

thf(2164,plain,
    ! [A: nat,B: nat] :
      ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
      | ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(368,axiom,
    ! [A: nat,B: fun_na998785244t_bool,C: nat,D: fun_Pr2067565481t_bool] :
      ( ( D @ ( C @ ( B @ hAPP_n1161265524t_bool ) @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [E: nat,F: nat] :
              ( ( E @ ( F @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( E @ ( B @ hAPP_n1161265524t_bool ) @ ( F @ ( B @ hAPP_n1161265524t_bool ) @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
         => ( D @ ( A @ ( B @ hAPP_n1161265524t_bool ) @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_778_xt4) ).

thf(2061,plain,
    ! [A: nat,B: fun_na998785244t_bool,C: nat,D: fun_Pr2067565481t_bool] :
      ( ( D @ ( C @ ( B @ hAPP_n1161265524t_bool ) @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [E: nat,F: nat] :
              ( ( E @ ( F @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( E @ ( B @ hAPP_n1161265524t_bool ) @ ( F @ ( B @ hAPP_n1161265524t_bool ) @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
         => ( D @ ( A @ ( B @ hAPP_n1161265524t_bool ) @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(525,axiom,
    ! [A: arrow_856714788e_indi,B: fun_Ar338949104le_alt,C: fun_Ar1809396326i_bool,D: fun_Ar274636406t_bool] :
      ( ( D @ ( C @ pi_Arr1460528004le_alt ) @ ( B @ ( member387840963le_alt @ hAPP_f766019597l_bool ) @ hAPP_f1754488902l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_A1646126530t_bool ) @ ( A @ ( B @ hAPP_A899858958le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member1479139729e_indi @ hAPP_A1597696899l_bool ) @ hAPP_f584385070l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_PiE) ).

thf(2773,plain,
    ! [A: arrow_856714788e_indi,B: fun_Ar338949104le_alt,C: fun_Ar1809396326i_bool,D: fun_Ar274636406t_bool] :
      ( ( D @ ( C @ pi_Arr1460528004le_alt ) @ ( B @ ( member387840963le_alt @ hAPP_f766019597l_bool ) @ hAPP_f1754488902l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_A1646126530t_bool ) @ ( A @ ( B @ hAPP_A899858958le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member1479139729e_indi @ hAPP_A1597696899l_bool ) @ hAPP_f584385070l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).

thf(502,axiom,
    e @ ( p @ ( arrow_1481558583_mkbot @ cOMBB_80760910e_indi @ hAPP_f831214557t_bool ) @ ( cOMBC_1417338747t_bool @ hAPP_f1631649925t_bool ) @ hAPP_A425126512t_bool ) @ ( e @ ( c @ ( p @ ( arrow_216713899_above @ cOMBB_1876517692e_indi @ hAPP_f1751344075t_bool ) @ ( cOMBC_1486904681t_bool @ hAPP_f2102110817t_bool ) @ hAPP_A1889513822t_bool ) @ ( cOMBC_1417338747t_bool @ hAPP_f1631649925t_bool ) @ hAPP_A425126512t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_1869811296e_indi @ hAPP_f966656047t_bool ) @ ( cOMBC_722552198t_bool @ hAPP_f721434149i_bool ) @ hAPP_n34002993i_bool ) @ ( if_fun523439385t_bool @ cOMBB_1061985500e_indi @ hAPP_f668886383t_bool ) @ cOMBS_1925466437t_bool @ hAPP_f1001205955t_bool ) @ cOMBS_1181656689t_bool @ hAPP_f1302887663t_bool ) @ ( e @ ( p @ ( arrow_1630265669_mktop @ cOMBB_80760910e_indi @ hAPP_f831214557t_bool ) @ ( cOMBC_1417338747t_bool @ hAPP_f1631649925t_bool ) @ hAPP_A425126512t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_1869811296e_indi @ hAPP_f966656047t_bool ) @ ( cOMBC_722552198t_bool @ hAPP_f721434149i_bool ) @ hAPP_n34002993i_bool ) @ ( if_fun523439385t_bool @ cOMBB_1061985500e_indi @ hAPP_f668886383t_bool ) @ cOMBS_1925466437t_bool @ hAPP_f1001205955t_bool ) @ cOMBS_1181656689t_bool @ hAPP_f1302887663t_bool ) @ ( f @ hAPP_f2008608496t_bool ) @ ( d @ ( e @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18__096e_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto) ).

thf(2705,plain,
    e @ ( p @ ( arrow_1481558583_mkbot @ cOMBB_80760910e_indi @ hAPP_f831214557t_bool ) @ ( cOMBC_1417338747t_bool @ hAPP_f1631649925t_bool ) @ hAPP_A425126512t_bool ) @ ( e @ ( c @ ( p @ ( arrow_216713899_above @ cOMBB_1876517692e_indi @ hAPP_f1751344075t_bool ) @ ( cOMBC_1486904681t_bool @ hAPP_f2102110817t_bool ) @ hAPP_A1889513822t_bool ) @ ( cOMBC_1417338747t_bool @ hAPP_f1631649925t_bool ) @ hAPP_A425126512t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_1869811296e_indi @ hAPP_f966656047t_bool ) @ ( cOMBC_722552198t_bool @ hAPP_f721434149i_bool ) @ hAPP_n34002993i_bool ) @ ( if_fun523439385t_bool @ cOMBB_1061985500e_indi @ hAPP_f668886383t_bool ) @ cOMBS_1925466437t_bool @ hAPP_f1001205955t_bool ) @ cOMBS_1181656689t_bool @ hAPP_f1302887663t_bool ) @ ( e @ ( p @ ( arrow_1630265669_mktop @ cOMBB_80760910e_indi @ hAPP_f831214557t_bool ) @ ( cOMBC_1417338747t_bool @ hAPP_f1631649925t_bool ) @ hAPP_A425126512t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_1869811296e_indi @ hAPP_f966656047t_bool ) @ ( cOMBC_722552198t_bool @ hAPP_f721434149i_bool ) @ hAPP_n34002993i_bool ) @ ( if_fun523439385t_bool @ cOMBB_1061985500e_indi @ hAPP_f668886383t_bool ) @ cOMBS_1925466437t_bool @ hAPP_f1001205955t_bool ) @ cOMBS_1181656689t_bool @ hAPP_f1302887663t_bool ) @ ( f @ hAPP_f2008608496t_bool ) @ ( d @ ( e @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).

thf(88,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
        | ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1055_add__gr__0) ).

thf(957,plain,
    ! [A: nat,B: nat] :
      ( ( ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
          | ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
       => ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
          | ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(121,axiom,
    ! [A: fun_fu638310559l_bool,B: fun_fu638310559l_bool,C: fun_fu638310559l_bool] :
      ( ( C @ ( B @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_order__trans) ).

thf(1091,plain,
    ! [A: fun_fu638310559l_bool,B: fun_fu638310559l_bool,C: fun_fu638310559l_bool] :
      ( ( C @ ( B @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(46,axiom,
    ! [A: fun_fu638310559l_bool] :
      ( ( A @ ( top_to1312956197l_bool @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
    <=> ( A = top_to1312956197l_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_521_top__unique) ).

thf(778,plain,
    ! [A: fun_fu638310559l_bool] :
      ( ( ( A = top_to1312956197l_bool )
       => ( A @ ( top_to1312956197l_bool @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) )
      & ( ( A @ ( top_to1312956197l_bool @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
       => ( A = top_to1312956197l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(107,axiom,
    ! [A: nat] :
      ( ( A @ ( suc @ hAPP_nat_nat ) )
     != zero_zero_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1066_Suc__neq__Zero) ).

thf(1042,plain,
    ! [A: nat] :
      ( ( A @ ( suc @ hAPP_nat_nat ) )
     != zero_zero_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(245,axiom,
    ! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool] :
      ( ( A != B )
     => ( ( B @ ( A @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_417_order__neq__le__trans) ).

thf(1580,plain,
    ! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool] :
      ( ( A != B )
     => ( ( B @ ( A @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(388,axiom,
    ! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool,C: fun_Ar331856045t_bool] :
      ( ( C @ ( B @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_489_xt1_I7_J) ).

thf(2133,plain,
    ! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool,C: fun_Ar331856045t_bool] :
      ( ( C @ ( B @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(57,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ? [C: nat] :
          ( B
          = ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1116_less__imp__Suc__add) ).

thf(820,plain,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ? [C: nat] :
          ( B
          = ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(579,axiom,
    ~ ! [A: fun_Pr2067565481t_bool] :
        ( ( A @ ( b @ ( a @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ~ ( arrow_1361987423le_Lin @ ( A @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_) ).

thf(3069,plain,
    ~ ! [A: fun_Pr2067565481t_bool] :
        ( ( A @ ( b @ ( a @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ~ ( arrow_1361987423le_Lin @ ( A @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).

thf(25,axiom,
    ( ( zero_zero_nat @ ( size_size_nat @ hAPP_nat_nat ) )
    = zero_zero_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1185_nat_Osize_I3_J) ).

thf(693,plain,
    ( ( zero_zero_nat @ ( size_size_nat @ hAPP_nat_nat ) )
    = zero_zero_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(154,axiom,
    ! [A: fun_Ar1809396326i_bool] :
      ( ( top_to1312956197l_bool @ ( cOMBK_1520063231e_indi @ hAPP_f1717907078l_bool ) @ ( A @ pi_Arr959578316t_bool ) )
      = top_to553140914l_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_Pi__UNIV) ).

thf(1238,plain,
    ! [A: fun_Ar1809396326i_bool] :
      ( ( top_to1312956197l_bool @ ( cOMBK_1520063231e_indi @ hAPP_f1717907078l_bool ) @ ( A @ pi_Arr959578316t_bool ) )
      = top_to553140914l_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(59,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_742_add__less__imp__less__left) ).

thf(825,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(536,axiom,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
      ( ( B @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( ( A @ ( B @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_908_equalityI) ).

thf(2805,plain,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
      ( ( B @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( ( A @ ( B @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).

thf(258,axiom,
    ! [A: fun_Pr2067565481t_bool] : ( top_to1312956197l_bool @ ( A @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_iso__tuple__UNIV__I) ).

thf(1619,plain,
    ! [A: fun_Pr2067565481t_bool] : ( top_to1312956197l_bool @ ( A @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(188,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ~ ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A
          = ( B @ ( suc @ hAPP_nat_nat ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1087_le__SucE) ).

thf(1370,plain,
    ! [A: nat,B: nat] :
      ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ~ ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A
          = ( B @ ( suc @ hAPP_nat_nat ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(562,axiom,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
      ( ( C @ ( B @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( ( C = A )
       => ( A @ ( B @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_ord__le__eq__trans) ).

thf(2890,plain,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
      ( ( C @ ( B @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( ( C = A )
       => ( A @ ( B @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).

thf(459,axiom,
    ! [A: produc472769767le_alt,B: fun_Pr1509342064e_indi,C: fun_Pr2067565481t_bool,D: fun_Ar1809396326i_bool] :
      ( ( D @ ( cOMBK_1987648063le_alt @ hAPP_f359069313i_bool ) @ ( C @ pi_Pro837265796e_indi ) @ ( B @ ( member1558233923e_indi @ hAPP_f1187850253l_bool ) @ hAPP_f2124588998l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( D @ ( A @ ( B @ hAPP_P276596750e_indi ) @ ( member1479139729e_indi @ hAPP_A1597696899l_bool ) @ hAPP_f584385070l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_582_funcset__mem) ).

thf(2414,plain,
    ! [A: produc472769767le_alt,B: fun_Pr1509342064e_indi,C: fun_Pr2067565481t_bool,D: fun_Ar1809396326i_bool] :
      ( ( D @ ( cOMBK_1987648063le_alt @ hAPP_f359069313i_bool ) @ ( C @ pi_Pro837265796e_indi ) @ ( B @ ( member1558233923e_indi @ hAPP_f1187850253l_bool ) @ hAPP_f2124588998l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( D @ ( A @ ( B @ hAPP_P276596750e_indi ) @ ( member1479139729e_indi @ hAPP_A1597696899l_bool ) @ hAPP_f584385070l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).

thf(201,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_747_add__less__cancel__left) ).

thf(1423,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(77,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1025_termination__basic__simps_I3_J) ).

thf(916,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(253,axiom,
    ! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool,C: fun_Ar331856045t_bool] :
      ( ( B = C )
     => ( ( C @ ( A @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_xt1_I3_J) ).

thf(1602,plain,
    ! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool,C: fun_Ar331856045t_bool] :
      ( ( B = C )
     => ( ( C @ ( A @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(343,axiom,
    ! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool] :
      ( ( A != B )
     => ( ( A @ ( B @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_427_xt1_I12_J) ).

thf(1968,plain,
    ! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool] :
      ( ( A != B )
     => ( ( A @ ( B @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(144,axiom,
    ! [A: nat,B: nat] :
      ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( A @ ( suc @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1082_not__less__eq) ).

thf(1178,plain,
    ! [A: nat,B: nat] :
      ( ( ( A @ ( suc @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( suc @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(337,axiom,
    ! [A: nat] :
      ~ ( A @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_order__less__irrefl) ).

thf(1951,plain,
    ! [A: nat] :
      ~ ( A @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(210,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1105_le__imp__less__Suc) ).

thf(1457,plain,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(400,axiom,
    ! [A: arrow_856714788e_indi,B: fun_Ar671024215di_nat] :
      ( ( top_to788185952i_bool @ ( B @ inj_on1960344199di_nat @ hAPP_f584385070l_bool ) @ hBOOL )
     => ( ( A @ ( B @ hAPP_A376526755di_nat ) @ ( B @ ( top_to788185952i_bool @ hilber1580028780di_nat ) @ hAPP_n1937165849e_indi ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_inv__f__f) ).

thf(2179,plain,
    ! [A: arrow_856714788e_indi,B: fun_Ar671024215di_nat] :
      ( ( top_to788185952i_bool @ ( B @ inj_on1960344199di_nat @ hAPP_f584385070l_bool ) @ hBOOL )
     => ( ( A @ ( B @ hAPP_A376526755di_nat ) @ ( B @ ( top_to788185952i_bool @ hilber1580028780di_nat ) @ hAPP_n1937165849e_indi ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).

thf(139,axiom,
    ! [A: nat,B: nat] :
      ~ ( B @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1000_not__add__less2) ).

thf(1159,plain,
    ! [A: nat,B: nat] :
      ~ ( B @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(577,axiom,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
      ( ( C @ ( B @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_477_order__less__le__trans) ).

thf(3050,plain,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
      ( ( C @ ( B @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).

thf(514,axiom,
    ! [A: fun_Ar339057223l_bool,B: fun_Pr2067565481t_bool,C: arrow_1893660431le_alt] :
      ( ( C @ ( B @ ( A @ ( cOMBC_395465908l_bool @ hAPP_f1689397393t_bool ) @ hAPP_f234621849t_bool ) @ hAPP_A1748732503t_bool ) )
      = ( B @ ( C @ ( A @ hAPP_A442239897l_bool ) @ hAPP_f52567537l_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_000t) ).

thf(2741,plain,
    ! [A: fun_Ar339057223l_bool,B: fun_Pr2067565481t_bool,C: arrow_1893660431le_alt] :
      ( ( C @ ( B @ ( A @ ( cOMBC_395465908l_bool @ hAPP_f1689397393t_bool ) @ hAPP_f234621849t_bool ) @ hAPP_A1748732503t_bool ) )
      = ( B @ ( C @ ( A @ hAPP_A442239897l_bool ) @ hAPP_f52567537l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).

thf(415,axiom,
    ! [A: fun_Ar331856045t_bool] : ( A @ ( A @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_order__refl) ).

thf(2228,plain,
    ! [A: fun_Ar331856045t_bool] : ( A @ ( A @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

thf(166,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_740_add__le__cancel__left) ).

thf(1291,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(102,axiom,
    ! [A: nat] :
      ( ( A != zero_zero_nat )
     => ? [B: nat] :
          ( A
          = ( B @ ( suc @ hAPP_nat_nat ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1123_not0__implies__Suc) ).

thf(1012,plain,
    ! [A: nat] :
      ( ( A != zero_zero_nat )
     => ? [B: nat] :
          ( A
          = ( B @ ( suc @ hAPP_nat_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(11,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( D @ ( B @ ( C @ times_times_nat @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
      = ( D @ ( B @ ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ times_times_nat @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1180_left__add__mult__distrib) ).

thf(625,plain,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( D @ ( B @ ( C @ times_times_nat @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
      = ( D @ ( B @ ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ times_times_nat @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(467,axiom,
    ! [A: produc472769767le_alt] : ( A @ ( top_to1138392227t_bool @ hAPP_P1178790471t_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_top1I) ).

thf(2477,plain,
    ! [A: produc472769767le_alt] : ( A @ ( top_to1138392227t_bool @ hAPP_P1178790471t_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).

thf(239,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( ~ ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
        & ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_396_less__le__not__le) ).

thf(1555,plain,
    ! [A: nat,B: nat] :
      ( ( ( ~ ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
          & ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
       => ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ~ ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
          & ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(544,axiom,
    ! [A: produc472769767le_alt] : ( top_to1138392227t_bool @ ( A @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_UNIV__I) ).

thf(2826,plain,
    ! [A: produc472769767le_alt] : ( top_to1138392227t_bool @ ( A @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).

thf(197,axiom,
    ! [A: nat,B: nat] :
      ( ( ( A @ ( suc @ hAPP_nat_nat ) )
        = ( B @ ( suc @ hAPP_nat_nat ) ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1063_nat_Oinject) ).

thf(1402,plain,
    ! [A: nat,B: nat] :
      ( ( ( A = B )
       => ( ( A @ ( suc @ hAPP_nat_nat ) )
          = ( B @ ( suc @ hAPP_nat_nat ) ) ) )
      & ( ( ( A @ ( suc @ hAPP_nat_nat ) )
          = ( B @ ( suc @ hAPP_nat_nat ) ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(534,axiom,
    ! [A: fun_Pr2067565481t_bool] : ( A @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_order__refl) ).

thf(2801,plain,
    ! [A: fun_Pr2067565481t_bool] : ( A @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).

thf(104,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1173_mult__le__cancel1) ).

thf(1017,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
       => ( C @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( C @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(475,axiom,
    ! [A: produc472769767le_alt,B: fun_Pr376858015t_unit,C: fun_Pr2067565481t_bool,D: fun_Pr1643180309t_bool] :
      ( ( D @ ( cOMBK_751896174le_alt @ hAPP_f723483871t_bool ) @ ( C @ pi_Pro346842291t_unit ) @ ( B @ ( member1303779570t_unit @ hAPP_f1700632141l_bool ) @ hAPP_f1159856629l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( D @ ( A @ ( B @ hAPP_P1069491261t_unit ) @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_583_funcset__mem) ).

thf(2509,plain,
    ! [A: produc472769767le_alt,B: fun_Pr376858015t_unit,C: fun_Pr2067565481t_bool,D: fun_Pr1643180309t_bool] :
      ( ( D @ ( cOMBK_751896174le_alt @ hAPP_f723483871t_bool ) @ ( C @ pi_Pro346842291t_unit ) @ ( B @ ( member1303779570t_unit @ hAPP_f1700632141l_bool ) @ hAPP_f1159856629l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( D @ ( A @ ( B @ hAPP_P1069491261t_unit ) @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).

thf(479,axiom,
    ! [A: arrow_856714788e_indi] :
      ( ( A @ ( p @ hAPP_A1646126530t_bool ) @ ( d @ ( c @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
    <=> ( ( ~ ( n @ ( A @ ( h @ hAPP_A376526755di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( ( ( ( A @ ( h @ hAPP_A376526755di_nat ) )
               != n )
             => ( e @ ( A @ ( p @ hAPP_A1646126530t_bool ) @ ( arrow_1481558583_mkbot @ hAPP_f1761571331t_bool ) @ hAPP_A1601437999t_bool ) @ ( d @ ( c @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
            & ( ( ( A @ ( h @ hAPP_A376526755di_nat ) )
                = n )
             => ( e @ ( c @ ( A @ ( p @ hAPP_A1646126530t_bool ) @ ( arrow_216713899_above @ hAPP_f1550387441t_bool ) @ hAPP_A1058422557t_bool ) @ hAPP_A1601437999t_bool ) @ ( d @ ( c @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ) )
        & ( ( n @ ( A @ ( h @ hAPP_A376526755di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( e @ ( A @ ( p @ hAPP_A1646126530t_bool ) @ ( arrow_1630265669_mktop @ hAPP_f1761571331t_bool ) @ hAPP_A1601437999t_bool ) @ ( d @ ( c @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ad_J) ).

thf(2537,plain,
    ! [A: arrow_856714788e_indi] :
      ( ( ( ( ~ ( n @ ( A @ ( h @ hAPP_A376526755di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( ( ( ( A @ ( h @ hAPP_A376526755di_nat ) )
                 != n )
               => ( e @ ( A @ ( p @ hAPP_A1646126530t_bool ) @ ( arrow_1481558583_mkbot @ hAPP_f1761571331t_bool ) @ hAPP_A1601437999t_bool ) @ ( d @ ( c @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
              & ( ( ( A @ ( h @ hAPP_A376526755di_nat ) )
                  = n )
               => ( e @ ( c @ ( A @ ( p @ hAPP_A1646126530t_bool ) @ ( arrow_216713899_above @ hAPP_f1550387441t_bool ) @ hAPP_A1058422557t_bool ) @ hAPP_A1601437999t_bool ) @ ( d @ ( c @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ) )
          & ( ( n @ ( A @ ( h @ hAPP_A376526755di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( e @ ( A @ ( p @ hAPP_A1646126530t_bool ) @ ( arrow_1630265669_mktop @ hAPP_f1761571331t_bool ) @ hAPP_A1601437999t_bool ) @ ( d @ ( c @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) )
       => ( A @ ( p @ hAPP_A1646126530t_bool ) @ ( d @ ( c @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
      & ( ( A @ ( p @ hAPP_A1646126530t_bool ) @ ( d @ ( c @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( ( ~ ( n @ ( A @ ( h @ hAPP_A376526755di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( ( ( ( A @ ( h @ hAPP_A376526755di_nat ) )
                 != n )
               => ( e @ ( A @ ( p @ hAPP_A1646126530t_bool ) @ ( arrow_1481558583_mkbot @ hAPP_f1761571331t_bool ) @ hAPP_A1601437999t_bool ) @ ( d @ ( c @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
              & ( ( ( A @ ( h @ hAPP_A376526755di_nat ) )
                  = n )
               => ( e @ ( c @ ( A @ ( p @ hAPP_A1646126530t_bool ) @ ( arrow_216713899_above @ hAPP_f1550387441t_bool ) @ hAPP_A1058422557t_bool ) @ hAPP_A1601437999t_bool ) @ ( d @ ( c @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ) )
          & ( ( n @ ( A @ ( h @ hAPP_A376526755di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( e @ ( A @ ( p @ hAPP_A1646126530t_bool ) @ ( arrow_1630265669_mktop @ hAPP_f1761571331t_bool ) @ hAPP_A1601437999t_bool ) @ ( d @ ( c @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).

thf(298,axiom,
    ! [A: fun_fu3835832l_bool] :
      ( ( top_to1312956197l_bool @ ( cOMBK_1701906001t_bool @ hAPP_f1104294872l_bool ) @ ( A @ pi_fun1746584570t_bool ) )
      = top_to827110112l_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_Pi__UNIV) ).

thf(1755,plain,
    ! [A: fun_fu3835832l_bool] :
      ( ( top_to1312956197l_bool @ ( cOMBK_1701906001t_bool @ hAPP_f1104294872l_bool ) @ ( A @ pi_fun1746584570t_bool ) )
      = top_to827110112l_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(419,axiom,
    ! [A: product_unit] : ( top_to1257323279t_bool @ ( A @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_UNIV__I) ).

thf(2245,plain,
    ! [A: product_unit] : ( top_to1257323279t_bool @ ( A @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

thf(182,axiom,
    ! [A: nat] :
      ( ( A @ ( suc @ hAPP_nat_nat ) )
     != A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1064_Suc__n__not__n) ).

thf(1350,plain,
    ! [A: nat] :
      ( ( A @ ( suc @ hAPP_nat_nat ) )
     != A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(27,axiom,
    ! [A: fun_fu638310559l_bool,B: bool] :
      ( ( B @ ( A @ ( cOMBK_650639032l_bool @ hAPP_f86272063l_bool ) @ hAPP_b1272691967l_bool ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe) ).

thf(697,plain,
    ! [A: fun_fu638310559l_bool,B: bool] :
      ( ( B @ ( A @ ( cOMBK_650639032l_bool @ hAPP_f86272063l_bool ) @ hAPP_b1272691967l_bool ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(234,axiom,
    ! [A: arrow_856714788e_indi,B: fun_Ar274636406t_bool,C: fun_Ar1809396326i_bool,D: fun_Ar1474557608l_bool] :
      ( ( D @ ( C @ pi_Arr959578316t_bool ) @ ( B @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member1479139729e_indi @ hAPP_A1597696899l_bool ) @ hAPP_f584385070l_bool ) @ hBOOL )
       => ( A @ ( D @ hAPP_A897398598l_bool ) @ ( A @ ( B @ hAPP_A1646126530t_bool ) @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_577_Pi__mem) ).

thf(1541,plain,
    ! [A: arrow_856714788e_indi,B: fun_Ar274636406t_bool,C: fun_Ar1809396326i_bool,D: fun_Ar1474557608l_bool] :
      ( ( D @ ( C @ pi_Arr959578316t_bool ) @ ( B @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member1479139729e_indi @ hAPP_A1597696899l_bool ) @ hAPP_f584385070l_bool ) @ hBOOL )
       => ( A @ ( D @ hAPP_A897398598l_bool ) @ ( A @ ( B @ hAPP_A1646126530t_bool ) @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(70,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( ( B @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
        & ( A @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1171_one__le__mult__iff) ).

thf(874,plain,
    ! [A: nat,B: nat] :
      ( ( ( ( B @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
          & ( A @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
       => ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ( B @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
          & ( A @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(381,axiom,
    ! [A: fun_fu2114379172t_bool] : ( top_to827110112l_bool @ ( A @ ( member173038353t_bool @ hAPP_f1714503811l_bool ) @ hAPP_f975209902l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_UNIV__I) ).

thf(2115,plain,
    ! [A: fun_fu2114379172t_bool] : ( top_to827110112l_bool @ ( A @ ( member173038353t_bool @ hAPP_f1714503811l_bool ) @ hAPP_f975209902l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(319,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ~ ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_430_leD) ).

thf(1851,plain,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ~ ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(160,axiom,
    ! [A: nat,B: fun_Ar331856045t_bool,C: fun_na300967376t_bool,D: nat] :
      ( ( D @ ( C @ hAPP_n1312530466t_bool ) @ ( B @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
     => ( ( A @ ( D @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [E: nat,F: nat] :
              ( ( F @ ( E @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( F @ ( C @ hAPP_n1312530466t_bool ) @ ( E @ ( C @ hAPP_n1312530466t_bool ) @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) )
         => ( A @ ( C @ hAPP_n1312530466t_bool ) @ ( B @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_829_order__less__le__subst1) ).

thf(1259,plain,
    ! [A: nat,B: fun_Ar331856045t_bool,C: fun_na300967376t_bool,D: nat] :
      ( ( D @ ( C @ hAPP_n1312530466t_bool ) @ ( B @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
     => ( ( A @ ( D @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [E: nat,F: nat] :
              ( ( F @ ( E @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( F @ ( C @ hAPP_n1312530466t_bool ) @ ( E @ ( C @ hAPP_n1312530466t_bool ) @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) )
         => ( A @ ( C @ hAPP_n1312530466t_bool ) @ ( B @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(131,axiom,
    ! [A: fun_fu638310559l_bool,B: fun_fu638310559l_bool,C: fun_fu638310559l_bool] :
      ( ( B = C )
     => ( ( C @ ( A @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_xt1_I3_J) ).

thf(1121,plain,
    ! [A: fun_fu638310559l_bool,B: fun_fu638310559l_bool,C: fun_fu638310559l_bool] :
      ( ( B = C )
     => ( ( C @ ( A @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(446,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ~ ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_order__less__imp__not__less) ).

thf(2359,plain,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ~ ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(190,axiom,
    ! [A: nat] : ( A @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1059_lessI) ).

thf(1375,plain,
    ! [A: nat] : ( A @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(222,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
        & ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1162_nat__0__less__mult__iff) ).

thf(1493,plain,
    ! [A: nat,B: nat] :
      ( ( ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
          & ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
       => ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
          & ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(117,axiom,
    ! [A: fun_fu638310559l_bool,B: fun_fu638310559l_bool,C: fun_fu638310559l_bool] :
      ( ( C @ ( B @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_xt1_I6_J) ).

thf(1082,plain,
    ! [A: fun_fu638310559l_bool,B: fun_fu638310559l_bool,C: fun_fu638310559l_bool] :
      ( ( C @ ( B @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(82,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1103_less__Suc__eq__le) ).

thf(933,plain,
    ! [A: nat,B: nat] :
      ( ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(40,axiom,
    ! [A: fun_nat_nat] :
      ( ! [B: nat] : ( B @ ( A @ hAPP_nat_nat ) @ ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ? [B: nat] :
        ! [C: nat] :
          ( ( C @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ hAPP_nat_nat ) )
          = ( B @ ( A @ hAPP_nat_nat ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1186_weak__decr__stable) ).

thf(753,plain,
    ! [A: fun_nat_nat] :
      ( ! [B: nat] : ( B @ ( A @ hAPP_nat_nat ) @ ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ? [B: nat] :
        ! [C: nat] :
          ( ( C @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ hAPP_nat_nat ) )
          = ( B @ ( A @ hAPP_nat_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(546,axiom,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
      ( ( C @ ( B @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_487_xt1_I7_J) ).

thf(2830,plain,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
      ( ( C @ ( B @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).

thf(212,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( D @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( D @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_655_add__le__less__mono) ).

thf(1461,plain,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( D @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( D @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(22,axiom,
    ! [A: nat,B: nat] :
      ( ( ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) )
        = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) )
    <=> ( ( B
          = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) )
        & ( A
          = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1157_mult__eq__1__iff) ).

thf(669,plain,
    ! [A: nat,B: nat] :
      ( ( ( ( B
            = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) )
          & ( A
            = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) ) )
       => ( ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) )
          = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) ) )
      & ( ( ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) )
          = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) )
       => ( ( B
            = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) )
          & ( A
            = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(115,axiom,
    ! [A: nat,B: fun_nat_nat] :
      ( ( top_top_fun_nat_bool @ ( B @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( A @ ( B @ hAPP_nat_nat ) @ ( B @ ( top_top_fun_nat_bool @ hilber195283148at_nat ) @ hAPP_nat_nat ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_inv__f__f) ).

thf(1075,plain,
    ! [A: nat,B: fun_nat_nat] :
      ( ( top_top_fun_nat_bool @ ( B @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( A @ ( B @ hAPP_nat_nat ) @ ( B @ ( top_top_fun_nat_bool @ hilber195283148at_nat ) @ hAPP_nat_nat ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(435,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_xt1_I10_J) ).

thf(2312,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).

thf(207,axiom,
    ! [A: fun_fu638310559l_bool,B: fun_fu638310559l_bool,C: fun_fu638310559l_bool] :
      ( ( B = C )
     => ( ( A @ ( C @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_ord__eq__le__trans) ).

thf(1446,plain,
    ! [A: fun_fu638310559l_bool,B: fun_fu638310559l_bool,C: fun_fu638310559l_bool] :
      ( ( B = C )
     => ( ( A @ ( C @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(23,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) )
        = ( B @ ( C @ times_times_nat @ hAPP_nat_nat ) ) )
    <=> ( ( B = zero_zero_nat )
        | ( A = C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1152_mult__cancel2) ).

thf(679,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( ( B = zero_zero_nat )
          | ( A = C ) )
       => ( ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) )
          = ( B @ ( C @ times_times_nat @ hAPP_nat_nat ) ) ) )
      & ( ( ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) )
          = ( B @ ( C @ times_times_nat @ hAPP_nat_nat ) ) )
       => ( ( B = zero_zero_nat )
          | ( A = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(30,axiom,
    ! [A: nat] :
      ( ( one_one_nat @ ( A @ times_times_nat @ hAPP_nat_nat ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1146_nat__mult__1__right) ).

thf(706,plain,
    ! [A: nat] :
      ( ( one_one_nat @ ( A @ times_times_nat @ hAPP_nat_nat ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(150,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1089_Suc__le__mono) ).

thf(1214,plain,
    ! [A: nat,B: nat] :
      ( ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(443,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( C = A )
       => ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_ord__less__eq__trans) ).

thf(2349,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( C = A )
       => ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).

thf(437,axiom,
    ! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool,C: fun_Ar331856045t_bool] :
      ( ( C @ ( B @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_509_xt1_I8_J) ).

thf(2317,plain,
    ! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool,C: fun_Ar331856045t_bool] :
      ( ( C @ ( B @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).

thf(138,axiom,
    ! [A: fun_fu638310559l_bool,B: fun_fu638310559l_bool,C: fun_fu638310559l_bool] :
      ( ( C @ ( B @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
     => ( ( B = A )
       => ( C @ ( A @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_xt1_I4_J) ).

thf(1155,plain,
    ! [A: fun_fu638310559l_bool,B: fun_fu638310559l_bool,C: fun_fu638310559l_bool] :
      ( ( C @ ( B @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
     => ( ( B = A )
       => ( C @ ( A @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(161,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1074_less__SucE) ).

thf(1263,plain,
    ! [A: nat,B: nat] :
      ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(158,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( B @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_736_add__le__imp__le__right) ).

thf(1249,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( B @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(167,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
      = ( A @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_988_nat__add__commute) ).

thf(1297,plain,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
      = ( A @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(35,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
      = ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1084_add__Suc) ).

thf(738,plain,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
      = ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(16,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ times_times_nat @ hAPP_nat_nat ) )
      = ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1164_mult__Suc__right) ).

thf(654,plain,
    ! [A: nat,B: nat] :
      ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ times_times_nat @ hAPP_nat_nat ) )
      = ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(147,axiom,
    ! [A: nat,B: nat] :
      ( ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
        = zero_zero_nat )
    <=> ( ( B = zero_zero_nat )
        & ( A = zero_zero_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1051_add__is__0) ).

thf(1192,plain,
    ! [A: nat,B: nat] :
      ( ( ( ( B = zero_zero_nat )
          & ( A = zero_zero_nat ) )
       => ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
          = zero_zero_nat ) )
      & ( ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
          = zero_zero_nat )
       => ( ( B = zero_zero_nat )
          & ( A = zero_zero_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(355,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( B = C )
     => ( ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_xt1_I3_J) ).

thf(2006,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( B = C )
     => ( ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(309,axiom,
    ! [A: fun_Ar274636406t_bool] : ( top_to553140914l_bool @ ( A @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_UNIV__I) ).

thf(1799,plain,
    ! [A: fun_Ar274636406t_bool] : ( top_to553140914l_bool @ ( A @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(335,axiom,
    ! [A: fun_Ar636018671t_bool,B: fun_Pr2067565481t_bool,C: arrow_1893660431le_alt] :
      ( ( C @ ( B @ ( A @ ( cOMBC_557453916t_bool @ hAPP_f1081591777t_bool ) @ hAPP_f449303873t_bool ) @ hAPP_A2063800319t_bool ) )
      = ( B @ ( C @ ( A @ hAPP_A656921921t_bool ) @ hAPP_f234621849t_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_000t_414) ).

thf(1947,plain,
    ! [A: fun_Ar636018671t_bool,B: fun_Pr2067565481t_bool,C: arrow_1893660431le_alt] :
      ( ( C @ ( B @ ( A @ ( cOMBC_557453916t_bool @ hAPP_f1081591777t_bool ) @ hAPP_f449303873t_bool ) @ hAPP_A2063800319t_bool ) )
      = ( B @ ( C @ ( A @ hAPP_A656921921t_bool ) @ hAPP_f234621849t_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(346,axiom,
    arrow_5070731e_Prof @ ( e @ ( p @ ( arrow_1481558583_mkbot @ cOMBB_80760910e_indi @ hAPP_f831214557t_bool ) @ ( cOMBC_1417338747t_bool @ hAPP_f1631649925t_bool ) @ hAPP_A425126512t_bool ) @ ( e @ ( c @ ( p @ ( arrow_216713899_above @ cOMBB_1876517692e_indi @ hAPP_f1751344075t_bool ) @ ( cOMBC_1486904681t_bool @ hAPP_f2102110817t_bool ) @ hAPP_A1889513822t_bool ) @ ( cOMBC_1417338747t_bool @ hAPP_f1631649925t_bool ) @ hAPP_A425126512t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_1869811296e_indi @ hAPP_f966656047t_bool ) @ ( cOMBC_722552198t_bool @ hAPP_f721434149i_bool ) @ hAPP_n34002993i_bool ) @ ( if_fun523439385t_bool @ cOMBB_1061985500e_indi @ hAPP_f668886383t_bool ) @ cOMBS_1925466437t_bool @ hAPP_f1001205955t_bool ) @ cOMBS_1181656689t_bool @ hAPP_f1302887663t_bool ) @ ( e @ ( p @ ( arrow_1630265669_mktop @ cOMBB_80760910e_indi @ hAPP_f831214557t_bool ) @ ( cOMBC_1417338747t_bool @ hAPP_f1631649925t_bool ) @ hAPP_A425126512t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_1869811296e_indi @ hAPP_f966656047t_bool ) @ ( cOMBC_722552198t_bool @ hAPP_f721434149i_bool ) @ hAPP_n34002993i_bool ) @ ( if_fun523439385t_bool @ cOMBB_1061985500e_indi @ hAPP_f668886383t_bool ) @ cOMBS_1925466437t_bool @ hAPP_f1001205955t_bool ) @ cOMBS_1181656689t_bool @ hAPP_f1302887663t_bool ) @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16__096_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai) ).

thf(1984,plain,
    arrow_5070731e_Prof @ ( e @ ( p @ ( arrow_1481558583_mkbot @ cOMBB_80760910e_indi @ hAPP_f831214557t_bool ) @ ( cOMBC_1417338747t_bool @ hAPP_f1631649925t_bool ) @ hAPP_A425126512t_bool ) @ ( e @ ( c @ ( p @ ( arrow_216713899_above @ cOMBB_1876517692e_indi @ hAPP_f1751344075t_bool ) @ ( cOMBC_1486904681t_bool @ hAPP_f2102110817t_bool ) @ hAPP_A1889513822t_bool ) @ ( cOMBC_1417338747t_bool @ hAPP_f1631649925t_bool ) @ hAPP_A425126512t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_1869811296e_indi @ hAPP_f966656047t_bool ) @ ( cOMBC_722552198t_bool @ hAPP_f721434149i_bool ) @ hAPP_n34002993i_bool ) @ ( if_fun523439385t_bool @ cOMBB_1061985500e_indi @ hAPP_f668886383t_bool ) @ cOMBS_1925466437t_bool @ hAPP_f1001205955t_bool ) @ cOMBS_1181656689t_bool @ hAPP_f1302887663t_bool ) @ ( e @ ( p @ ( arrow_1630265669_mktop @ cOMBB_80760910e_indi @ hAPP_f831214557t_bool ) @ ( cOMBC_1417338747t_bool @ hAPP_f1631649925t_bool ) @ hAPP_A425126512t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_1869811296e_indi @ hAPP_f966656047t_bool ) @ ( cOMBC_722552198t_bool @ hAPP_f721434149i_bool ) @ hAPP_n34002993i_bool ) @ ( if_fun523439385t_bool @ cOMBB_1061985500e_indi @ hAPP_f668886383t_bool ) @ cOMBS_1925466437t_bool @ hAPP_f1001205955t_bool ) @ cOMBS_1181656689t_bool @ hAPP_f1302887663t_bool ) @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(202,axiom,
    ! [A: fun_fu955147676ol_nat,B: nat,C: fun_fu638310559l_bool,D: fun_fu638310559l_bool] :
      ( ( D @ ( C @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
     => ( ( B @ ( D @ ( A @ hAPP_f1487854056ol_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [E: fun_fu638310559l_bool,F: fun_fu638310559l_bool] :
              ( ( F @ ( E @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
             => ( F @ ( A @ hAPP_f1487854056ol_nat ) @ ( E @ ( A @ hAPP_f1487854056ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
         => ( B @ ( C @ ( A @ hAPP_f1487854056ol_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_881_order__le__less__subst2) ).

thf(1429,plain,
    ! [A: fun_fu955147676ol_nat,B: nat,C: fun_fu638310559l_bool,D: fun_fu638310559l_bool] :
      ( ( D @ ( C @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
     => ( ( B @ ( D @ ( A @ hAPP_f1487854056ol_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [E: fun_fu638310559l_bool,F: fun_fu638310559l_bool] :
              ( ( F @ ( E @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
             => ( F @ ( A @ hAPP_f1487854056ol_nat ) @ ( E @ ( A @ hAPP_f1487854056ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
         => ( B @ ( C @ ( A @ hAPP_f1487854056ol_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(289,axiom,
    ! [A: fun_Ar331856045t_bool,B: nat,C: fun_fu1677555470ol_nat,D: fun_Ar331856045t_bool] :
      ( ( D @ ( C @ hAPP_f1403773274ol_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( D @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
       => ( ! [E: fun_Ar331856045t_bool,F: fun_Ar331856045t_bool] :
              ( ( F @ ( E @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
             => ( F @ ( C @ hAPP_f1403773274ol_nat ) @ ( E @ ( C @ hAPP_f1403773274ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
         => ( A @ ( C @ hAPP_f1403773274ol_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_854_order__less__le__subst1) ).

thf(1720,plain,
    ! [A: fun_Ar331856045t_bool,B: nat,C: fun_fu1677555470ol_nat,D: fun_Ar331856045t_bool] :
      ( ( D @ ( C @ hAPP_f1403773274ol_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( D @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
       => ( ! [E: fun_Ar331856045t_bool,F: fun_Ar331856045t_bool] :
              ( ( F @ ( E @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
             => ( F @ ( C @ hAPP_f1403773274ol_nat ) @ ( E @ ( C @ hAPP_f1403773274ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
         => ( A @ ( C @ hAPP_f1403773274ol_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(521,axiom,
    ! [A: fun_Pr1085078251l_bool,B: fun_Ar245737999le_alt,C: arrow_1893660431le_alt] :
      ( ( C @ ( B @ ( A @ cOMBB_1660064607le_alt @ hAPP_f1536341593l_bool ) @ hAPP_A442239897l_bool ) )
      = ( C @ ( B @ hAPP_A1299015393le_alt ) @ ( A @ hAPP_P38525833l_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs_) ).

thf(2756,plain,
    ! [A: fun_Pr1085078251l_bool,B: fun_Ar245737999le_alt,C: arrow_1893660431le_alt] :
      ( ( C @ ( B @ ( A @ cOMBB_1660064607le_alt @ hAPP_f1536341593l_bool ) @ hAPP_A442239897l_bool ) )
      = ( C @ ( B @ hAPP_A1299015393le_alt ) @ ( A @ hAPP_P38525833l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).

thf(7,axiom,
    ! [A: nat] :
      ( ( A @ ( size_size_nat @ hAPP_nat_nat ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1184_nat__size) ).

thf(605,plain,
    ! [A: nat] :
      ( ( A @ ( size_size_nat @ hAPP_nat_nat ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(262,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B != A )
       => ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_471_xt1_I11_J) ).

thf(1627,plain,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B != A )
       => ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(177,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( B @ ( C @ times_times_nat @ hAPP_nat_nat ) @ ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
        & ( B @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1160_mult__less__cancel2) ).

thf(1324,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
          & ( B @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
       => ( B @ ( C @ times_times_nat @ hAPP_nat_nat ) @ ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( B @ ( C @ times_times_nat @ hAPP_nat_nat ) @ ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
          & ( B @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(472,axiom,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
      ( ( C @ ( B @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_951_subset__psubset__trans) ).

thf(2504,plain,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
      ( ( C @ ( B @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).

thf(384,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1010_less__imp__le__nat) ).

thf(2125,plain,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(248,axiom,
    ! [A: nat] :
      ~ ( A @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_984_less__irrefl__nat) ).

thf(1588,plain,
    ! [A: nat] :
      ~ ( A @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(548,axiom,
    ! [A: fun_Pr2067565481t_bool] :
      ( ( A != top_to1138392227t_bool )
    <=> ( top_to1138392227t_bool @ ( A @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_less__top) ).

thf(2836,plain,
    ! [A: fun_Pr2067565481t_bool] :
      ( ( ( top_to1138392227t_bool @ ( A @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( A != top_to1138392227t_bool ) )
      & ( ( A != top_to1138392227t_bool )
       => ( top_to1138392227t_bool @ ( A @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).

thf(193,axiom,
    ! [A: fun_nat_nat,B: fun_nat_nat] :
      ( ( top_top_fun_nat_bool @ ( B @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ! [C: nat] :
            ( ( C @ ( A @ hAPP_nat_nat ) @ ( B @ hAPP_nat_nat ) )
            = C )
       => ( ( B @ ( top_top_fun_nat_bool @ hilber195283148at_nat ) )
          = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_652_inj__imp__inv__eq) ).

thf(1382,plain,
    ! [A: fun_nat_nat,B: fun_nat_nat] :
      ( ( top_top_fun_nat_bool @ ( B @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ! [C: nat] :
            ( ( C @ ( A @ hAPP_nat_nat ) @ ( B @ hAPP_nat_nat ) )
            = C )
       => ( ( B @ ( top_top_fun_nat_bool @ hilber195283148at_nat ) )
          = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(162,axiom,
    ! [A: nat,B: nat] :
      ( ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
        = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) )
    <=> ( ( ( B
            = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) )
          & ( A = zero_zero_nat ) )
        | ( ( B = zero_zero_nat )
          & ( A
            = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1097_add__is__1) ).

thf(1266,plain,
    ! [A: nat,B: nat] :
      ( ( ( ( ( B
              = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) )
            & ( A = zero_zero_nat ) )
          | ( ( B = zero_zero_nat )
            & ( A
              = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) ) ) )
       => ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
          = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) ) )
      & ( ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
          = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) )
       => ( ( ( B
              = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) )
            & ( A = zero_zero_nat ) )
          | ( ( B = zero_zero_nat )
            & ( A
              = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(565,axiom,
    ! [A: arrow_1893660431le_alt,B: arrow_1893660431le_alt,C: fun_Pr2067565481t_bool,D: arrow_1893660431le_alt] :
      ( ( D @ ( C @ ( arrow_1630265669_mktop @ hAPP_f1761571331t_bool ) @ hAPP_A1601437999t_bool ) @ ( B @ ( A @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
    <=> ( ( ( B != D )
         => ( C @ ( B @ ( A @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
        & ( ( B = D )
         => ( A != B ) )
        & ( A != D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_in__mktop) ).

thf(2900,plain,
    ! [A: arrow_1893660431le_alt,B: arrow_1893660431le_alt,C: fun_Pr2067565481t_bool,D: arrow_1893660431le_alt] :
      ( ( ( ( ( B != D )
           => ( C @ ( B @ ( A @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
          & ( ( B = D )
           => ( A != B ) )
          & ( A != D ) )
       => ( D @ ( C @ ( arrow_1630265669_mktop @ hAPP_f1761571331t_bool ) @ hAPP_A1601437999t_bool ) @ ( B @ ( A @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
      & ( ( D @ ( C @ ( arrow_1630265669_mktop @ hAPP_f1761571331t_bool ) @ hAPP_A1601437999t_bool ) @ ( B @ ( A @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( ( ( B != D )
           => ( C @ ( B @ ( A @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
          & ( ( B = D )
           => ( A != B ) )
          & ( A != D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).

thf(451,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A != B )
       => ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_461_order__le__neq__trans) ).

thf(2387,plain,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A != B )
       => ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).

thf(153,axiom,
    ! [A: fun_fu638310559l_bool,B: fun_fu638310559l_bool] :
      ( ( B @ ( A @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
     => ( ( A @ ( B @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
      <=> ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_order__antisym__conv) ).

thf(1231,plain,
    ! [A: fun_fu638310559l_bool,B: fun_fu638310559l_bool] :
      ( ( B @ ( A @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
     => ( ( ( B = A )
         => ( A @ ( B @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) )
        & ( ( A @ ( B @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
         => ( B = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(238,axiom,
    ! [A: nat,B: nat] :
      ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A != B )
       => ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_linorder__cases) ).

thf(1552,plain,
    ! [A: nat,B: nat] :
      ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A != B )
       => ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(418,axiom,
    ! [A: nat] : ( A @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_order__refl) ).

thf(2243,plain,
    ! [A: nat] : ( A @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

thf(524,axiom,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
      ( ( B @ ( A @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
    <=> ( ~ ( A @ ( B @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
        & ( B @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_712_less__fun__def) ).

thf(2766,plain,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
      ( ( ( ~ ( A @ ( B @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
          & ( B @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
       => ( B @ ( A @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( ~ ( A @ ( B @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
          & ( B @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).

thf(252,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_order__antisym) ).

thf(1599,plain,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(157,axiom,
    ! [A: nat,B: nat,C: fun_nat_nat] :
      ( ( top_top_fun_nat_bool @ ( C @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( ( A @ ( C @ hAPP_nat_nat ) )
          = ( B @ ( C @ hAPP_nat_nat ) ) )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_615_injD) ).

thf(1246,plain,
    ! [A: nat,B: nat,C: fun_nat_nat] :
      ( ( top_top_fun_nat_bool @ ( C @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( ( A @ ( C @ hAPP_nat_nat ) )
          = ( B @ ( C @ hAPP_nat_nat ) ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(148,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( ( A
          = ( B @ ( suc @ hAPP_nat_nat ) ) )
        | ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1090_le__Suc__eq) ).

thf(1202,plain,
    ! [A: nat,B: nat] :
      ( ( ( ( A
            = ( B @ ( suc @ hAPP_nat_nat ) ) )
          | ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
       => ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ( A
            = ( B @ ( suc @ hAPP_nat_nat ) ) )
          | ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(119,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( B @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_743_add__less__imp__less__right) ).

thf(1086,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( B @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(155,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1004_add__less__mono1) ).

thf(1241,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(52,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( D @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( D @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_737_add__mono) ).

thf(805,plain,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( D @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( D @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(363,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( C = A )
       => ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_ord__le__eq__trans) ).

thf(2043,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( C = A )
       => ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(560,axiom,
    ~ ! [A: fun_Pr2067565481t_bool] :
        ( ( A @ ( a @ ( b @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ~ ( arrow_1361987423le_Lin @ ( A @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_) ).

thf(2883,plain,
    ~ ! [A: fun_Pr2067565481t_bool] :
        ( ( A @ ( a @ ( b @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ~ ( arrow_1361987423le_Lin @ ( A @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).

thf(17,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( D @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( D @ times_times_nat @ hAPP_nat_nat ) @ ( A @ ( C @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1144_mult__le__mono) ).

thf(657,plain,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( D @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( D @ times_times_nat @ hAPP_nat_nat ) @ ( A @ ( C @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(366,axiom,
    ! [A: fun_Pr2067565481t_bool] : ( top_to1312956197l_bool @ ( A @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_UNIV__I) ).

thf(2057,plain,
    ! [A: fun_Pr2067565481t_bool] : ( top_to1312956197l_bool @ ( A @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(456,axiom,
    ! [A: produc472769767le_alt] :
      ( ( A @ ( top_to1138392227t_bool @ hAPP_P1178790471t_bool ) @ hBOOL )
    <=> ( top_top_bool @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_top__apply) ).

thf(2402,plain,
    ! [A: produc472769767le_alt] :
      ( ( ( top_top_bool @ hBOOL )
       => ( A @ ( top_to1138392227t_bool @ hAPP_P1178790471t_bool ) @ hBOOL ) )
      & ( ( A @ ( top_to1138392227t_bool @ hAPP_P1178790471t_bool ) @ hBOOL )
       => ( top_top_bool @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).

thf(457,axiom,
    ! [A: fun_Pr2067565481t_bool,B: fun_na998785244t_bool,C: nat,D: nat] :
      ( ( D @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( C @ ( B @ hAPP_n1161265524t_bool ) @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( ! [E: nat,F: nat] :
              ( ( E @ ( F @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( E @ ( B @ hAPP_n1161265524t_bool ) @ ( F @ ( B @ hAPP_n1161265524t_bool ) @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
         => ( D @ ( B @ hAPP_n1161265524t_bool ) @ ( A @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_667_xt5) ).

thf(2408,plain,
    ! [A: fun_Pr2067565481t_bool,B: fun_na998785244t_bool,C: nat,D: nat] :
      ( ( D @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( C @ ( B @ hAPP_n1161265524t_bool ) @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( ! [E: nat,F: nat] :
              ( ( E @ ( F @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( E @ ( B @ hAPP_n1161265524t_bool ) @ ( F @ ( B @ hAPP_n1161265524t_bool ) @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
         => ( D @ ( B @ hAPP_n1161265524t_bool ) @ ( A @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).

thf(228,axiom,
    ! [A: fun_Pr2067565481t_bool,B: arrow_856714788e_indi] :
      ( ( B @ ( A @ ( cOMBK_1650320063e_indi @ hAPP_f480276746t_bool ) @ hAPP_A1646126530t_bool ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ef_405) ).

thf(1515,plain,
    ! [A: fun_Pr2067565481t_bool,B: arrow_856714788e_indi] :
      ( ( B @ ( A @ ( cOMBK_1650320063e_indi @ hAPP_f480276746t_bool ) @ hAPP_A1646126530t_bool ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(86,axiom,
    ! [A: fun_Pr1780397033l_bool,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
      ( ( C @ ( B @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( A @ ( B @ pi_Pro1238944957t_bool ) @ ( A @ ( C @ pi_Pro1238944957t_bool ) @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_715_Pi__anti__mono) ).

thf(953,plain,
    ! [A: fun_Pr1780397033l_bool,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
      ( ( C @ ( B @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( A @ ( B @ pi_Pro1238944957t_bool ) @ ( A @ ( C @ pi_Pro1238944957t_bool ) @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(351,axiom,
    ! [A: nat,B: nat] :
      ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_407_leI) ).

thf(1996,plain,
    ! [A: nat,B: nat] :
      ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(79,axiom,
    ! [A: fun_fu638310559l_bool,B: fun_fu638310559l_bool] :
      ( ( B @ ( A @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
     => ( ( A @ ( B @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_905_equalityI) ).

thf(926,plain,
    ! [A: fun_fu638310559l_bool,B: fun_fu638310559l_bool] :
      ( ( B @ ( A @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
     => ( ( A @ ( B @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(372,axiom,
    ! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool] :
      ( ( B @ ( A @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
    <=> ( ( A = B )
        | ( B @ ( A @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_404_order__le__less) ).

thf(2076,plain,
    ! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool] :
      ( ( ( ( A = B )
          | ( B @ ( A @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) )
       => ( B @ ( A @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
       => ( ( A = B )
          | ( B @ ( A @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(517,axiom,
    ! [A: fun_Pr1509342064e_indi,B: fun_Pr895221296i_bool,C: fun_Pr2067565481t_bool] :
      ( ! [D: produc472769767le_alt] :
          ( ( C @ ( D @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
         => ( D @ ( B @ hAPP_P1859429372i_bool ) @ ( D @ ( A @ hAPP_P276596750e_indi ) @ ( member1479139729e_indi @ hAPP_A1597696899l_bool ) @ hAPP_f584385070l_bool ) @ hBOOL ) )
     => ( B @ ( C @ pi_Pro837265796e_indi ) @ ( A @ ( member1558233923e_indi @ hAPP_f1187850253l_bool ) @ hAPP_f2124588998l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_620_Pi__I) ).

thf(2748,plain,
    ! [A: fun_Pr1509342064e_indi,B: fun_Pr895221296i_bool,C: fun_Pr2067565481t_bool] :
      ( ! [D: produc472769767le_alt] :
          ( ( C @ ( D @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
         => ( D @ ( B @ hAPP_P1859429372i_bool ) @ ( D @ ( A @ hAPP_P276596750e_indi ) @ ( member1479139729e_indi @ hAPP_A1597696899l_bool ) @ hAPP_f584385070l_bool ) @ hBOOL ) )
     => ( B @ ( C @ pi_Pro837265796e_indi ) @ ( A @ ( member1558233923e_indi @ hAPP_f1187850253l_bool ) @ hAPP_f2124588998l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).

thf(491,axiom,
    ! [A: fun_Ar274636406t_bool] : ( A @ ( top_to553140914l_bool @ hAPP_f995490902l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_top1I) ).

thf(2645,plain,
    ! [A: fun_Ar274636406t_bool] : ( A @ ( top_to553140914l_bool @ hAPP_f995490902l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).

thf(257,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A != B )
       => ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1011_le__neq__implies__less) ).

thf(1616,plain,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A != B )
       => ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(461,axiom,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
      ( ( B @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( ( A = B )
        | ( B @ ( A @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_447_order__le__imp__less__or__eq) ).

thf(2423,plain,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
      ( ( B @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( ( A = B )
        | ( B @ ( A @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).

thf(73,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ~ ( ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ~ ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_904_add__leE) ).

thf(888,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ~ ( ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ~ ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(383,axiom,
    ! [A: fun_bo1431306493t_bool,B: fun_bo377688929l_bool,C: fun_bool_bool] :
      ( ! [D: bool] :
          ( ( C @ ( D @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
         => ( D @ ( B @ hAPP_b1272691967l_bool ) @ ( D @ ( A @ hAPP_b128655177t_bool ) @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) )
     => ( B @ ( C @ pi_boo1111177555t_bool ) @ ( A @ ( member1133581546t_bool @ hAPP_f416878261l_bool ) @ hAPP_f398210311l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_643_Pi__I) ).

thf(2121,plain,
    ! [A: fun_bo1431306493t_bool,B: fun_bo377688929l_bool,C: fun_bool_bool] :
      ( ! [D: bool] :
          ( ( C @ ( D @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
         => ( D @ ( B @ hAPP_b1272691967l_bool ) @ ( D @ ( A @ hAPP_b128655177t_bool ) @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) )
     => ( B @ ( C @ pi_boo1111177555t_bool ) @ ( A @ ( member1133581546t_bool @ hAPP_f416878261l_bool ) @ hAPP_f398210311l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(353,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_440_order__less__imp__le) ).

thf(2001,plain,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(159,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
        = ( B @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
    <=> ( A = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_992_nat__add__right__cancel) ).

thf(1251,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( A = C )
       => ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
          = ( B @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) )
      & ( ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
          = ( B @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
       => ( A = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(66,axiom,
    ! [A: nat] :
      ( zero_zero_nat
     != ( A @ ( suc @ hAPP_nat_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1070_nat_Osimps_I2_J) ).

thf(856,plain,
    ! [A: nat] :
      ( zero_zero_nat
     != ( A @ ( suc @ hAPP_nat_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(37,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( D @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( D @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1005_add__less__mono) ).

thf(745,plain,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( D @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( D @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(563,axiom,
    ! [A: fun_fu864675765l_bool,B: fun_fu638310559l_bool,C: fun_Pr2067565481t_bool] :
      ( ( C @ ( B @ ( A @ ( cOMBC_2133093654l_bool @ hAPP_f1776355587l_bool ) @ hAPP_f1060563265l_bool ) @ hAPP_f52567537l_bool ) )
      = ( B @ ( C @ ( A @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ef) ).

thf(2894,plain,
    ! [A: fun_fu864675765l_bool,B: fun_fu638310559l_bool,C: fun_Pr2067565481t_bool] :
      ( ( C @ ( B @ ( A @ ( cOMBC_2133093654l_bool @ hAPP_f1776355587l_bool ) @ hAPP_f1060563265l_bool ) @ hAPP_f52567537l_bool ) )
      = ( B @ ( C @ ( A @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).

thf(424,axiom,
    ! [A: nat,B: nat] :
      ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ~ ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
      <=> ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_linorder__antisym__conv3) ).

thf(2260,plain,
    ! [A: nat,B: nat] :
      ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( ( B = A )
         => ~ ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
        & ( ~ ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( B = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).

thf(509,axiom,
    ! [A: product_unit,B: fun_Pr2090226719le_alt,C: fun_Pr1643180309t_bool,D: fun_Pr1887398791t_bool] :
      ( ( D @ ( C @ pi_Pro1820940723le_alt ) @ ( B @ ( member869664626le_alt @ hAPP_f41367117l_bool ) @ hAPP_f684683381l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ( A @ ( D @ hAPP_P1914371027t_bool ) @ ( A @ ( B @ hAPP_P396106045le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_564_Pi__mem) ).

thf(2729,plain,
    ! [A: product_unit,B: fun_Pr2090226719le_alt,C: fun_Pr1643180309t_bool,D: fun_Pr1887398791t_bool] :
      ( ( D @ ( C @ pi_Pro1820940723le_alt ) @ ( B @ ( member869664626le_alt @ hAPP_f41367117l_bool ) @ hAPP_f684683381l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ( A @ ( D @ hAPP_P1914371027t_bool ) @ ( A @ ( B @ hAPP_P396106045le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).

thf(268,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_xt1_I5_J) ).

thf(1648,plain,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(89,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_735_add__le__imp__le__left) ).

thf(965,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(39,axiom,
    ! [A: fun_Ar535288606t_bool,B: fun_Pr2067565481t_bool,C: arrow_856714788e_indi] :
      ( ( C @ ( B @ ( A @ ( cOMBC_156709173t_bool @ hAPP_f1908974253t_bool ) @ hAPP_f1344464862t_bool ) @ hAPP_A834130326t_bool ) )
      = ( B @ ( C @ ( A @ hAPP_A1395684458t_bool ) @ hAPP_f1299954409t_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000_426) ).

thf(750,plain,
    ! [A: fun_Ar535288606t_bool,B: fun_Pr2067565481t_bool,C: arrow_856714788e_indi] :
      ( ( C @ ( B @ ( A @ ( cOMBC_156709173t_bool @ hAPP_f1908974253t_bool ) @ hAPP_f1344464862t_bool ) @ hAPP_A834130326t_bool ) )
      = ( B @ ( C @ ( A @ hAPP_A1395684458t_bool ) @ hAPP_f1299954409t_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(359,axiom,
    ! [A: nat,B: nat] :
      ( ( A = B )
      | ~ ( B @ ( A @ ( fequal_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Nat__Onat_T) ).

thf(2028,plain,
    ! [A: nat,B: nat] :
      ( ( A = B )
      | ~ ( B @ ( A @ ( fequal_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(511,axiom,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
      ( ( A != B )
     => ( ( A @ ( B @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_425_xt1_I12_J) ).

thf(2734,plain,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
      ( ( A != B )
     => ( ( A @ ( B @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).

thf(569,axiom,
    ! [A: arrow_1893660431le_alt,B: arrow_1893660431le_alt,C: fun_Pr2067565481t_bool,D: arrow_1893660431le_alt,E: arrow_1893660431le_alt] :
      ( ( D != E )
     => ( ( arrow_1361987423le_Lin @ ( C @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
       => ( ( E @ ( D @ ( C @ ( arrow_216713899_above @ hAPP_f1550387441t_bool ) @ hAPP_A1058422557t_bool ) @ hAPP_A1601437999t_bool ) @ ( B @ ( A @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
        <=> ( ( ( A != E )
             => ( ( ( B != E )
                 => ( C @ ( B @ ( A @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
                & ( ( B = E )
                 => ( ( C @ ( D @ ( A @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
                    | ( A = D ) ) ) ) )
            & ( ( A = E )
             => ( C @ ( B @ ( D @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
            & ( A != B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_in__above) ).

thf(2938,plain,
    ! [A: arrow_1893660431le_alt,B: arrow_1893660431le_alt,C: fun_Pr2067565481t_bool,D: arrow_1893660431le_alt,E: arrow_1893660431le_alt] :
      ( ( D != E )
     => ( ( arrow_1361987423le_Lin @ ( C @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
       => ( ( ( ( ( A != E )
               => ( ( ( B != E )
                   => ( C @ ( B @ ( A @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
                  & ( ( B = E )
                   => ( ( C @ ( D @ ( A @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
                      | ( A = D ) ) ) ) )
              & ( ( A = E )
               => ( C @ ( B @ ( D @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
              & ( A != B ) )
           => ( E @ ( D @ ( C @ ( arrow_216713899_above @ hAPP_f1550387441t_bool ) @ hAPP_A1058422557t_bool ) @ hAPP_A1601437999t_bool ) @ ( B @ ( A @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
          & ( ( E @ ( D @ ( C @ ( arrow_216713899_above @ hAPP_f1550387441t_bool ) @ hAPP_A1058422557t_bool ) @ hAPP_A1601437999t_bool ) @ ( B @ ( A @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
           => ( ( ( A != E )
               => ( ( ( B != E )
                   => ( C @ ( B @ ( A @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
                  & ( ( B = E )
                   => ( ( C @ ( D @ ( A @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
                      | ( A = D ) ) ) ) )
              & ( ( A = E )
               => ( C @ ( B @ ( D @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
              & ( A != B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).

thf(297,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_997_le__antisym) ).

thf(1752,plain,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(494,axiom,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
      ( ( B @ ( member1333168212le_alt @ ( cOMBC_593569186l_bool @ hAPP_f1033183015t_bool ) @ hAPP_f1356305429t_bool ) @ ( A @ ( member1333168212le_alt @ ( cOMBC_593569186l_bool @ hAPP_f1033183015t_bool ) @ hAPP_f1356305429t_bool ) @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
    <=> ( B @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_980_pred__subset__eq) ).

thf(2674,plain,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
      ( ( ( B @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( B @ ( member1333168212le_alt @ ( cOMBC_593569186l_bool @ hAPP_f1033183015t_bool ) @ hAPP_f1356305429t_bool ) @ ( A @ ( member1333168212le_alt @ ( cOMBC_593569186l_bool @ hAPP_f1033183015t_bool ) @ hAPP_f1356305429t_bool ) @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
      & ( ( B @ ( member1333168212le_alt @ ( cOMBC_593569186l_bool @ hAPP_f1033183015t_bool ) @ hAPP_f1356305429t_bool ) @ ( A @ ( member1333168212le_alt @ ( cOMBC_593569186l_bool @ hAPP_f1033183015t_bool ) @ hAPP_f1356305429t_bool ) @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).

thf(454,axiom,
    ! [A: bool,B: fun_bo1431306493t_bool,C: fun_bool_bool,D: fun_bo377688929l_bool] :
      ( ( D @ ( C @ pi_boo1111177555t_bool ) @ ( B @ ( member1133581546t_bool @ hAPP_f416878261l_bool ) @ hAPP_f398210311l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_b1272691967l_bool ) @ ( A @ ( B @ hAPP_b128655177t_bool ) @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_PiE) ).

thf(2398,plain,
    ! [A: bool,B: fun_bo1431306493t_bool,C: fun_bool_bool,D: fun_bo377688929l_bool] :
      ( ( D @ ( C @ pi_boo1111177555t_bool ) @ ( B @ ( member1133581546t_bool @ hAPP_f416878261l_bool ) @ hAPP_f398210311l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_b1272691967l_bool ) @ ( A @ ( B @ hAPP_b128655177t_bool ) @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).

thf(342,axiom,
    ! [A: nat,B: nat] :
      ( ( A != B )
     => ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_429_xt1_I12_J) ).

thf(1965,plain,
    ! [A: nat,B: nat] :
      ( ( A != B )
     => ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(220,axiom,
    ! [A: nat,B: nat] :
      ( ( ( A @ ( suc @ hAPP_nat_nat ) )
        = ( B @ ( suc @ hAPP_nat_nat ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1062_Suc__inject) ).

thf(1488,plain,
    ! [A: nat,B: nat] :
      ( ( ( A @ ( suc @ hAPP_nat_nat ) )
        = ( B @ ( suc @ hAPP_nat_nat ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(306,axiom,
    top_to788185952i_bool @ ( h @ inj_on1960344199di_nat @ hAPP_f584385070l_bool ) @ hBOOL,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_injh) ).

thf(1784,plain,
    top_to788185952i_bool @ ( h @ inj_on1960344199di_nat @ hAPP_f584385070l_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(195,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( ( A = B )
        | ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1081_less__Suc__eq) ).

thf(1389,plain,
    ! [A: nat,B: nat] :
      ( ( ( ( A = B )
          | ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
       => ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ( A = B )
          | ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(63,axiom,
    ( arrow_5070731e_Prof
    = ( arrow_1361987423le_Lin @ ( cOMBK_1520063231e_indi @ hAPP_f1717907078l_bool ) @ ( top_to788185952i_bool @ pi_Arr959578316t_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_579_Prof__def) ).

thf(843,plain,
    ( arrow_5070731e_Prof
    = ( arrow_1361987423le_Lin @ ( cOMBK_1520063231e_indi @ hAPP_f1717907078l_bool ) @ ( top_to788185952i_bool @ pi_Arr959578316t_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(132,axiom,
    ! [A: nat,B: fun_nat_bool] :
      ( ~ ( zero_zero_nat @ ( B @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( B @ hAPP_nat_bool ) @ hBOOL )
       => ? [C: nat] :
            ( ( C @ ( B @ hAPP_nat_bool ) @ hBOOL )
            & ! [D: nat] :
                ( ( C @ ( D @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
               => ~ ( D @ ( B @ hAPP_nat_bool ) @ hBOOL ) )
            & ( A @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1057_ex__least__nat__le) ).

thf(1125,plain,
    ! [A: nat,B: fun_nat_bool] :
      ( ~ ( zero_zero_nat @ ( B @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( B @ hAPP_nat_bool ) @ hBOOL )
       => ? [C: nat] :
            ( ( C @ ( B @ hAPP_nat_bool ) @ hBOOL )
            & ! [D: nat] :
                ( ( C @ ( D @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
               => ~ ( D @ ( B @ hAPP_nat_bool ) @ hBOOL ) )
            & ( A @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(403,axiom,
    ! [A: fun_Pr2067565481t_bool,B: product_unit] :
      ( ( B @ ( A @ ( cOMBK_681766254t_unit @ hAPP_f15777819t_bool ) @ hAPP_P1914371027t_bool ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ef_403) ).

thf(2188,plain,
    ! [A: fun_Pr2067565481t_bool,B: product_unit] :
      ( ( B @ ( A @ ( cOMBK_681766254t_unit @ hAPP_f15777819t_bool ) @ hAPP_P1914371027t_bool ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(572,axiom,
    ! [A: fun_Ar274636406t_bool,B: fun_Ar274636406t_bool,C: arrow_1893660431le_alt,D: arrow_1893660431le_alt] :
      ( ( C != D )
     => ( ( arrow_5070731e_Prof @ ( B @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL )
       => ( ( arrow_5070731e_Prof @ ( A @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL )
         => ( ! [E: arrow_856714788e_indi] :
                ( ( E @ ( B @ hAPP_A1646126530t_bool ) @ ( D @ ( C @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
              <=> ( E @ ( A @ hAPP_A1646126530t_bool ) @ ( C @ ( D @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
           => ( ( B @ ( f @ hAPP_f2008608496t_bool ) @ ( D @ ( C @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
            <=> ( A @ ( f @ hAPP_f2008608496t_bool ) @ ( C @ ( D @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10__C3_C) ).

thf(2981,plain,
    ! [A: fun_Ar274636406t_bool,B: fun_Ar274636406t_bool,C: arrow_1893660431le_alt,D: arrow_1893660431le_alt] :
      ( ( C != D )
     => ( ( arrow_5070731e_Prof @ ( B @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL )
       => ( ( arrow_5070731e_Prof @ ( A @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL )
         => ( ! [E: arrow_856714788e_indi] :
                ( ( ( E @ ( A @ hAPP_A1646126530t_bool ) @ ( C @ ( D @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
                 => ( E @ ( B @ hAPP_A1646126530t_bool ) @ ( D @ ( C @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
                & ( ( E @ ( B @ hAPP_A1646126530t_bool ) @ ( D @ ( C @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
                 => ( E @ ( A @ hAPP_A1646126530t_bool ) @ ( C @ ( D @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) )
           => ( ( ( A @ ( f @ hAPP_f2008608496t_bool ) @ ( C @ ( D @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
               => ( B @ ( f @ hAPP_f2008608496t_bool ) @ ( D @ ( C @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
              & ( ( B @ ( f @ hAPP_f2008608496t_bool ) @ ( D @ ( C @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
               => ( A @ ( f @ hAPP_f2008608496t_bool ) @ ( C @ ( D @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).

thf(14,axiom,
    ! [A: nat,B: nat] :
      ( ( ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) )
        = one_one_nat )
    <=> ( ( B = one_one_nat )
        & ( A = one_one_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1145_nat__mult__eq__1__iff) ).

thf(641,plain,
    ! [A: nat,B: nat] :
      ( ( ( ( B = one_one_nat )
          & ( A = one_one_nat ) )
       => ( ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) )
          = one_one_nat ) )
      & ( ( ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) )
          = one_one_nat )
       => ( ( B = one_one_nat )
          & ( A = one_one_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(275,axiom,
    ! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool,C: fun_Ar331856045t_bool] :
      ( ( C @ ( B @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_499_order__le__less__trans) ).

thf(1669,plain,
    ! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool,C: fun_Ar331856045t_bool] :
      ( ( C @ ( B @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(431,axiom,
    ? [A: nat] :
      ( ( lba @ ( lab @ ( one_one_nat @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( h @ ( ord_less_nat @ cOMBB_1869811296e_indi @ hAPP_f966656047t_bool ) @ ( cOMBC_722552198t_bool @ hAPP_f721434149i_bool ) @ hAPP_n34002993i_bool ) @ ( if_fun523439385t_bool @ cOMBB_1061985500e_indi @ hAPP_f668886383t_bool ) @ ( cOMBC_156709173t_bool @ hAPP_f1908974253t_bool ) @ hAPP_f1344464862t_bool ) @ ( cOMBC_750853729t_bool @ hAPP_f601594885t_bool ) @ hAPP_f480276746t_bool ) @ ( f @ hAPP_f2008608496t_bool ) @ ( b @ ( a @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
      & ! [B: nat] :
          ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( lba @ ( lab @ ( B @ ( h @ ( ord_less_nat @ cOMBB_1869811296e_indi @ hAPP_f966656047t_bool ) @ ( cOMBC_722552198t_bool @ hAPP_f721434149i_bool ) @ hAPP_n34002993i_bool ) @ ( if_fun523439385t_bool @ cOMBB_1061985500e_indi @ hAPP_f668886383t_bool ) @ ( cOMBC_156709173t_bool @ hAPP_f1908974253t_bool ) @ hAPP_f1344464862t_bool ) @ ( cOMBC_750853729t_bool @ hAPP_f601594885t_bool ) @ hAPP_f480276746t_bool ) @ ( f @ hAPP_f2008608496t_bool ) @ ( a @ ( b @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
      & ( top_to788185952i_bool @ ( finite1672073426e_indi @ hAPP_f846027769ol_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I) ).

thf(2293,plain,
    ? [A: nat] :
      ( ( lba @ ( lab @ ( one_one_nat @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( h @ ( ord_less_nat @ cOMBB_1869811296e_indi @ hAPP_f966656047t_bool ) @ ( cOMBC_722552198t_bool @ hAPP_f721434149i_bool ) @ hAPP_n34002993i_bool ) @ ( if_fun523439385t_bool @ cOMBB_1061985500e_indi @ hAPP_f668886383t_bool ) @ ( cOMBC_156709173t_bool @ hAPP_f1908974253t_bool ) @ hAPP_f1344464862t_bool ) @ ( cOMBC_750853729t_bool @ hAPP_f601594885t_bool ) @ hAPP_f480276746t_bool ) @ ( f @ hAPP_f2008608496t_bool ) @ ( b @ ( a @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
      & ! [B: nat] :
          ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( lba @ ( lab @ ( B @ ( h @ ( ord_less_nat @ cOMBB_1869811296e_indi @ hAPP_f966656047t_bool ) @ ( cOMBC_722552198t_bool @ hAPP_f721434149i_bool ) @ hAPP_n34002993i_bool ) @ ( if_fun523439385t_bool @ cOMBB_1061985500e_indi @ hAPP_f668886383t_bool ) @ ( cOMBC_156709173t_bool @ hAPP_f1908974253t_bool ) @ hAPP_f1344464862t_bool ) @ ( cOMBC_750853729t_bool @ hAPP_f601594885t_bool ) @ hAPP_f480276746t_bool ) @ ( f @ hAPP_f2008608496t_bool ) @ ( a @ ( b @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
      & ( top_to788185952i_bool @ ( finite1672073426e_indi @ hAPP_f846027769ol_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).

thf(9,axiom,
    ! [A: nat,B: nat] :
      ( ( A
        = ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) ) )
     => ( ( A = zero_zero_nat )
        | ( B = one_one_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1167_mult__eq__self__implies__10) ).

thf(611,plain,
    ! [A: nat,B: nat] :
      ( ( A
        = ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) ) )
     => ( ( A = zero_zero_nat )
        | ( B = one_one_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(126,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
        = ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
     => ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_729_add__imp__eq) ).

thf(1107,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
        = ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
     => ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(522,axiom,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
      ( ( B @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( ( A @ ( B @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_order__antisym) ).

thf(2759,plain,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
      ( ( B @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( ( A @ ( B @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).

thf(503,axiom,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
      ( ( B @ ( A @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( B @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_939_psubset__imp__subset) ).

thf(2706,plain,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
      ( ( B @ ( A @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( B @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).

thf(398,axiom,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
      ( ( B @ ( A @ ( fTrue @ ( if_fun523439385t_bool @ hAPP_b35146737t_bool ) @ hAPP_f1299954409t_bool ) @ hAPP_f1356305429t_bool ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiq) ).

thf(2166,plain,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
      ( ( B @ ( A @ ( fTrue @ ( if_fun523439385t_bool @ hAPP_b35146737t_bool ) @ hAPP_f1299954409t_bool ) @ hAPP_f1356305429t_bool ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

thf(85,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1016_nat__add__left__cancel__le) ).

thf(947,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(152,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( ( A @ ( C @ times_times_nat @ hAPP_nat_nat ) )
          = ( B @ ( C @ times_times_nat @ hAPP_nat_nat ) ) )
      <=> ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1178_nat__mult__eq__cancel1) ).

thf(1224,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( ( A = B )
         => ( ( A @ ( C @ times_times_nat @ hAPP_nat_nat ) )
            = ( B @ ( C @ times_times_nat @ hAPP_nat_nat ) ) ) )
        & ( ( ( A @ ( C @ times_times_nat @ hAPP_nat_nat ) )
            = ( B @ ( C @ times_times_nat @ hAPP_nat_nat ) ) )
         => ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(393,axiom,
    ! [A: arrow_856714788e_indi,B: arrow_856714788e_indi,C: fun_Ar671024215di_nat] :
      ( ( top_to788185952i_bool @ ( C @ inj_on1960344199di_nat @ hAPP_f584385070l_bool ) @ hBOOL )
     => ( ( ( A @ ( C @ hAPP_A376526755di_nat ) )
          = ( B @ ( C @ hAPP_A376526755di_nat ) ) )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_614_injD) ).

thf(2148,plain,
    ! [A: arrow_856714788e_indi,B: arrow_856714788e_indi,C: fun_Ar671024215di_nat] :
      ( ( top_to788185952i_bool @ ( C @ inj_on1960344199di_nat @ hAPP_f584385070l_bool ) @ hBOOL )
     => ( ( ( A @ ( C @ hAPP_A376526755di_nat ) )
          = ( B @ ( C @ hAPP_A376526755di_nat ) ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(438,axiom,
    ! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool] :
      ( ( A = B )
    <=> ( ( A @ ( B @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
        & ( B @ ( A @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_362_order__eq__iff) ).

thf(2319,plain,
    ! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool] :
      ( ( ( ( A @ ( B @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
          & ( B @ ( A @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( ( A @ ( B @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
          & ( B @ ( A @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).

thf(184,axiom,
    ! [A: fun_nat_nat] :
      ( ! [B: nat,C: nat] :
          ( ( ( B @ ( A @ hAPP_nat_nat ) )
            = ( C @ ( A @ hAPP_nat_nat ) ) )
         => ( B = C ) )
     => ( top_top_fun_nat_bool @ ( A @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_657_injI) ).

thf(1356,plain,
    ! [A: fun_nat_nat] :
      ( ! [B: nat,C: nat] :
          ( ( ( B @ ( A @ hAPP_nat_nat ) )
            = ( C @ ( A @ hAPP_nat_nat ) ) )
         => ( B = C ) )
     => ( top_top_fun_nat_bool @ ( A @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(93,axiom,
    ! [A: bool,B: fun_bo1431306493t_bool,C: fun_bool_bool,D: fun_fu638310559l_bool] :
      ( ( D @ ( cOMBK_650639032l_bool @ hAPP_f86272063l_bool ) @ ( C @ pi_boo1111177555t_bool ) @ ( B @ ( member1133581546t_bool @ hAPP_f416878261l_bool ) @ hAPP_f398210311l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
       => ( D @ ( A @ ( B @ hAPP_b128655177t_bool ) @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_605_funcset__mem) ).

thf(979,plain,
    ! [A: bool,B: fun_bo1431306493t_bool,C: fun_bool_bool,D: fun_fu638310559l_bool] :
      ( ( D @ ( cOMBK_650639032l_bool @ hAPP_f86272063l_bool ) @ ( C @ pi_boo1111177555t_bool ) @ ( B @ ( member1133581546t_bool @ hAPP_f416878261l_bool ) @ hAPP_f398210311l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
       => ( D @ ( A @ ( B @ hAPP_b128655177t_bool ) @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(442,axiom,
    ! [A: fun_Pr2067565481t_bool,B: bool] :
      ( ( B @ ( A @ ( cOMBK_5056120l_bool @ hAPP_f1723896209t_bool ) @ hAPP_b128655177t_bool ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ef) ).

thf(2346,plain,
    ! [A: fun_Pr2067565481t_bool,B: bool] :
      ( ( B @ ( A @ ( cOMBK_5056120l_bool @ hAPP_f1723896209t_bool ) @ hAPP_b128655177t_bool ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).

thf(447,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A = B )
        | ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_451_order__le__imp__less__or__eq) ).

thf(2361,plain,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A = B )
        | ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).

thf(507,axiom,
    ! [A: fun_nat_bool] : ( A @ ( cOMBI_nat @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_580_inj__on__id2) ).

thf(2721,plain,
    ! [A: fun_nat_bool] : ( A @ ( cOMBI_nat @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).

thf(61,axiom,
    ! [A: nat,B: nat,C: fun_nat_nat] :
      ( ( top_top_fun_nat_bool @ ( C @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( ( A @ ( C @ hAPP_nat_nat ) )
          = ( B @ ( C @ hAPP_nat_nat ) ) )
      <=> ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_613_inj__eq) ).

thf(831,plain,
    ! [A: nat,B: nat,C: fun_nat_nat] :
      ( ( top_top_fun_nat_bool @ ( C @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( ( A = B )
         => ( ( A @ ( C @ hAPP_nat_nat ) )
            = ( B @ ( C @ hAPP_nat_nat ) ) ) )
        & ( ( ( A @ ( C @ hAPP_nat_nat ) )
            = ( B @ ( C @ hAPP_nat_nat ) ) )
         => ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(320,axiom,
    ! [A: arrow_856714788e_indi,B: arrow_856714788e_indi,C: fun_Ar671024215di_nat] :
      ( ( top_to788185952i_bool @ ( C @ inj_on1960344199di_nat @ hAPP_f584385070l_bool ) @ hBOOL )
     => ( ( ( A @ ( C @ hAPP_A376526755di_nat ) )
          = ( B @ ( C @ hAPP_A376526755di_nat ) ) )
      <=> ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_612_inj__eq) ).

thf(1853,plain,
    ! [A: arrow_856714788e_indi,B: arrow_856714788e_indi,C: fun_Ar671024215di_nat] :
      ( ( top_to788185952i_bool @ ( C @ inj_on1960344199di_nat @ hAPP_f584385070l_bool ) @ hBOOL )
     => ( ( ( A = B )
         => ( ( A @ ( C @ hAPP_A376526755di_nat ) )
            = ( B @ ( C @ hAPP_A376526755di_nat ) ) ) )
        & ( ( ( A @ ( C @ hAPP_A376526755di_nat ) )
            = ( B @ ( C @ hAPP_A376526755di_nat ) ) )
         => ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(394,axiom,
    ! [A: nat,B: arrow_856714788e_indi,C: fun_Ar671024215di_nat,D: fun_Ar1809396326i_bool] :
      ( ( D @ ( C @ inj_on1960344199di_nat @ hAPP_f584385070l_bool ) @ hBOOL )
     => ( ( D @ ( B @ ( member1479139729e_indi @ hAPP_A1597696899l_bool ) @ hAPP_f584385070l_bool ) @ hBOOL )
       => ( ( ( B @ ( C @ hAPP_A376526755di_nat ) )
            = A )
         => ( ( A @ ( C @ ( D @ hilber1580028780di_nat ) @ hAPP_n1937165849e_indi ) )
            = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_618_inv__into__f__eq) ).

thf(2151,plain,
    ! [A: nat,B: arrow_856714788e_indi,C: fun_Ar671024215di_nat,D: fun_Ar1809396326i_bool] :
      ( ( D @ ( C @ inj_on1960344199di_nat @ hAPP_f584385070l_bool ) @ hBOOL )
     => ( ( D @ ( B @ ( member1479139729e_indi @ hAPP_A1597696899l_bool ) @ hAPP_f584385070l_bool ) @ hBOOL )
       => ( ( ( B @ ( C @ hAPP_A376526755di_nat ) )
            = A )
         => ( ( A @ ( C @ ( D @ hilber1580028780di_nat ) @ hAPP_n1937165849e_indi ) )
            = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).

thf(323,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( ( A = B )
        | ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_406_order__le__less) ).

thf(1894,plain,
    ! [A: nat,B: nat] :
      ( ( ( ( A = B )
          | ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
       => ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ( A = B )
          | ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(244,axiom,
    ! [A: fun_Ar671024215di_nat] :
      ( ! [B: arrow_856714788e_indi,C: arrow_856714788e_indi] :
          ( ( ( B @ ( A @ hAPP_A376526755di_nat ) )
            = ( C @ ( A @ hAPP_A376526755di_nat ) ) )
         => ( B = C ) )
     => ( top_to788185952i_bool @ ( A @ inj_on1960344199di_nat @ hAPP_f584385070l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_656_injI) ).

thf(1574,plain,
    ! [A: fun_Ar671024215di_nat] :
      ( ! [B: arrow_856714788e_indi,C: arrow_856714788e_indi] :
          ( ( ( B @ ( A @ hAPP_A376526755di_nat ) )
            = ( C @ ( A @ hAPP_A376526755di_nat ) ) )
         => ( B = C ) )
     => ( top_to788185952i_bool @ ( A @ inj_on1960344199di_nat @ hAPP_f584385070l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(230,axiom,
    ! [A: arrow_1893660431le_alt,B: fun_Pr2067565481t_bool] :
      ( ( arrow_1361987423le_Lin @ ( B @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
     => ( arrow_1361987423le_Lin @ ( A @ ( B @ ( arrow_1630265669_mktop @ hAPP_f1761571331t_bool ) @ hAPP_A1601437999t_bool ) @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_mktop__Lin) ).

thf(1524,plain,
    ! [A: arrow_1893660431le_alt,B: fun_Pr2067565481t_bool] :
      ( ( arrow_1361987423le_Lin @ ( B @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
     => ( arrow_1361987423le_Lin @ ( A @ ( B @ ( arrow_1630265669_mktop @ hAPP_f1761571331t_bool ) @ hAPP_A1601437999t_bool ) @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(428,axiom,
    ? [A: fun_Pr2067565481t_bool] : ( arrow_1361987423le_Lin @ ( A @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1030_linear__alt) ).

thf(2284,plain,
    ? [A: fun_Pr2067565481t_bool] : ( arrow_1361987423le_Lin @ ( A @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).

thf(310,axiom,
    ! [A: nat,B: nat] :
      ( ( A != B )
    <=> ( ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
        | ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_linorder__neq__iff) ).

thf(1801,plain,
    ! [A: nat,B: nat] :
      ( ( ( ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
          | ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
       => ( A != B ) )
      & ( ( A != B )
       => ( ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
          | ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(405,axiom,
    ! [A: arrow_856714788e_indi,B: fun_Ar274636406t_bool,C: fun_Ar1809396326i_bool,D: fun_fu638310559l_bool] :
      ( ( D @ ( cOMBK_1520063231e_indi @ hAPP_f1717907078l_bool ) @ ( C @ pi_Arr959578316t_bool ) @ ( B @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member1479139729e_indi @ hAPP_A1597696899l_bool ) @ hAPP_f584385070l_bool ) @ hBOOL )
       => ( D @ ( A @ ( B @ hAPP_A1646126530t_bool ) @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_611_funcset__mem) ).

thf(2197,plain,
    ! [A: arrow_856714788e_indi,B: fun_Ar274636406t_bool,C: fun_Ar1809396326i_bool,D: fun_fu638310559l_bool] :
      ( ( D @ ( cOMBK_1520063231e_indi @ hAPP_f1717907078l_bool ) @ ( C @ pi_Arr959578316t_bool ) @ ( B @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member1479139729e_indi @ hAPP_A1597696899l_bool ) @ hAPP_f584385070l_bool ) @ hBOOL )
       => ( D @ ( A @ ( B @ hAPP_A1646126530t_bool ) @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(558,axiom,
    ! [A: fun_Ar274636406t_bool,B: fun_Ar274636406t_bool,C: arrow_1893660431le_alt,D: arrow_1893660431le_alt,E: arrow_1893660431le_alt,F: arrow_1893660431le_alt] :
      ( ( E != F )
     => ( ( C != D )
       => ( ( E != D )
         => ( ( F != C )
           => ( ( arrow_5070731e_Prof @ ( B @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL )
             => ( ( arrow_5070731e_Prof @ ( A @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL )
               => ( ! [G: arrow_856714788e_indi] :
                      ( ( G @ ( B @ hAPP_A1646126530t_bool ) @ ( F @ ( E @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
                    <=> ( G @ ( A @ hAPP_A1646126530t_bool ) @ ( D @ ( C @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
                 => ( ( B @ ( f @ hAPP_f2008608496t_bool ) @ ( F @ ( E @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
                   => ( A @ ( f @ hAPP_f2008608496t_bool ) @ ( D @ ( C @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7__C1_C) ).

thf(2871,plain,
    ! [A: fun_Ar274636406t_bool,B: fun_Ar274636406t_bool,C: arrow_1893660431le_alt,D: arrow_1893660431le_alt,E: arrow_1893660431le_alt,F: arrow_1893660431le_alt] :
      ( ( E != F )
     => ( ( C != D )
       => ( ( E != D )
         => ( ( F != C )
           => ( ( arrow_5070731e_Prof @ ( B @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL )
             => ( ( arrow_5070731e_Prof @ ( A @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL )
               => ( ! [G: arrow_856714788e_indi] :
                      ( ( ( G @ ( A @ hAPP_A1646126530t_bool ) @ ( D @ ( C @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
                       => ( G @ ( B @ hAPP_A1646126530t_bool ) @ ( F @ ( E @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
                      & ( ( G @ ( B @ hAPP_A1646126530t_bool ) @ ( F @ ( E @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
                       => ( G @ ( A @ hAPP_A1646126530t_bool ) @ ( D @ ( C @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) )
                 => ( ( B @ ( f @ hAPP_f2008608496t_bool ) @ ( F @ ( E @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
                   => ( A @ ( f @ hAPP_f2008608496t_bool ) @ ( D @ ( C @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).

thf(204,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1029_termination__basic__simps_I1_J) ).

thf(1439,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(369,axiom,
    ! [A: product_unit] : ( top_to1257323279t_bool @ ( A @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_iso__tuple__UNIV__I) ).

thf(2065,plain,
    ! [A: product_unit] : ( top_to1257323279t_bool @ ( A @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(143,axiom,
    ! [A: nat] :
      ( ( zero_zero_nat @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1050_Nat_Oadd__0__right) ).

thf(1175,plain,
    ! [A: nat] :
      ( ( zero_zero_nat @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(274,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ~ ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_order__less__asym) ).

thf(1667,plain,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ~ ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(401,axiom,
    ! [A: fun_Ar603939593t_bool,B: nat,C: arrow_856714788e_indi] :
      ( ( C @ ( B @ ( A @ ( cOMBC_722552198t_bool @ hAPP_f721434149i_bool ) @ hAPP_n34002993i_bool ) @ hAPP_A997847300i_bool ) )
      = ( B @ ( C @ ( A @ hAPP_A1686943911t_bool ) @ hAPP_nat_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000) ).

thf(2182,plain,
    ! [A: fun_Ar603939593t_bool,B: nat,C: arrow_856714788e_indi] :
      ( ( C @ ( B @ ( A @ ( cOMBC_722552198t_bool @ hAPP_f721434149i_bool ) @ hAPP_n34002993i_bool ) @ hAPP_A997847300i_bool ) )
      = ( B @ ( C @ ( A @ hAPP_A1686943911t_bool ) @ hAPP_nat_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

thf(380,axiom,
    ! [A: fun_na998785244t_bool,B: fun_Pr2067565481t_bool,C: nat,D: nat] :
      ( ( D @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( D @ ( A @ hAPP_n1161265524t_bool ) @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( ! [E: nat,F: nat] :
              ( ( F @ ( E @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( F @ ( A @ hAPP_n1161265524t_bool ) @ ( E @ ( A @ hAPP_n1161265524t_bool ) @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
         => ( B @ ( C @ ( A @ hAPP_n1161265524t_bool ) @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_898_order__less__le__subst2) ).

thf(2111,plain,
    ! [A: fun_na998785244t_bool,B: fun_Pr2067565481t_bool,C: nat,D: nat] :
      ( ( D @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( D @ ( A @ hAPP_n1161265524t_bool ) @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( ! [E: nat,F: nat] :
              ( ( F @ ( E @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( F @ ( A @ hAPP_n1161265524t_bool ) @ ( E @ ( A @ hAPP_n1161265524t_bool ) @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
         => ( B @ ( C @ ( A @ hAPP_n1161265524t_bool ) @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

thf(425,axiom,
    ! [A: nat,B: fun_Ar331856045t_bool,C: fun_na300967376t_bool,D: nat] :
      ( ( D @ ( C @ hAPP_n1312530466t_bool ) @ ( B @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
     => ( ( A @ ( D @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [E: nat,F: nat] :
              ( ( F @ ( E @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( F @ ( C @ hAPP_n1312530466t_bool ) @ ( E @ ( C @ hAPP_n1312530466t_bool ) @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) )
         => ( A @ ( C @ hAPP_n1312530466t_bool ) @ ( B @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_817_order__le__less__subst1) ).

thf(2267,plain,
    ! [A: nat,B: fun_Ar331856045t_bool,C: fun_na300967376t_bool,D: nat] :
      ( ( D @ ( C @ hAPP_n1312530466t_bool ) @ ( B @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
     => ( ( A @ ( D @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [E: nat,F: nat] :
              ( ( F @ ( E @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( F @ ( C @ hAPP_n1312530466t_bool ) @ ( E @ ( C @ hAPP_n1312530466t_bool ) @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) )
         => ( A @ ( C @ hAPP_n1312530466t_bool ) @ ( B @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).

thf(140,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1007_add__lessD1) ).

thf(1162,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(28,axiom,
    ! [A: nat] :
      ( ( A @ ( one_one_nat @ times_times_nat @ hAPP_nat_nat ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1148_nat__mult__1) ).

thf(700,plain,
    ! [A: nat] :
      ( ( A @ ( one_one_nat @ times_times_nat @ hAPP_nat_nat ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(106,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( ? [C: nat] :
            ( ( B @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
            & ( A
              = ( C @ ( suc @ hAPP_nat_nat ) ) ) )
        | ( A = zero_zero_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1096_less__Suc__eq__0__disj) ).

thf(1029,plain,
    ! [A: nat,B: nat] :
      ( ( ( ? [C: nat] :
              ( ( B @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
              & ( A
                = ( C @ ( suc @ hAPP_nat_nat ) ) ) )
          | ( A = zero_zero_nat ) )
       => ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ? [C: nat] :
              ( ( B @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
              & ( A
                = ( C @ ( suc @ hAPP_nat_nat ) ) ) )
          | ( A = zero_zero_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(137,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( B @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_741_add__le__cancel__right) ).

thf(1149,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( B @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(492,axiom,
    ! [A: fun_fu2114379172t_bool] :
      ( ( A @ ( arrow_1335103695le_IIA @ hAPP_f1572141188l_bool ) @ hBOOL )
    <=> ! [B: fun_Ar274636406t_bool] :
          ( ( arrow_5070731e_Prof @ ( B @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL )
         => ! [C: fun_Ar274636406t_bool] :
              ( ( arrow_5070731e_Prof @ ( C @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL )
             => ! [D: arrow_1893660431le_alt,E: arrow_1893660431le_alt] :
                  ( ! [F: arrow_856714788e_indi] :
                      ( ( F @ ( B @ hAPP_A1646126530t_bool ) @ ( E @ ( D @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
                    <=> ( F @ ( C @ hAPP_A1646126530t_bool ) @ ( E @ ( D @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
                 => ( ( B @ ( A @ hAPP_f2008608496t_bool ) @ ( E @ ( D @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
                  <=> ( C @ ( A @ hAPP_f2008608496t_bool ) @ ( E @ ( D @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_IIA__def) ).

thf(2647,plain,
    ! [A: fun_fu2114379172t_bool] :
      ( ( ! [B: fun_Ar274636406t_bool] :
            ( ( arrow_5070731e_Prof @ ( B @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL )
           => ! [C: fun_Ar274636406t_bool] :
                ( ( arrow_5070731e_Prof @ ( C @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL )
               => ! [D: arrow_1893660431le_alt,E: arrow_1893660431le_alt] :
                    ( ! [F: arrow_856714788e_indi] :
                        ( ( ( F @ ( C @ hAPP_A1646126530t_bool ) @ ( E @ ( D @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
                         => ( F @ ( B @ hAPP_A1646126530t_bool ) @ ( E @ ( D @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
                        & ( ( F @ ( B @ hAPP_A1646126530t_bool ) @ ( E @ ( D @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
                         => ( F @ ( C @ hAPP_A1646126530t_bool ) @ ( E @ ( D @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) )
                   => ( ( ( C @ ( A @ hAPP_f2008608496t_bool ) @ ( E @ ( D @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
                       => ( B @ ( A @ hAPP_f2008608496t_bool ) @ ( E @ ( D @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
                      & ( ( B @ ( A @ hAPP_f2008608496t_bool ) @ ( E @ ( D @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
                       => ( C @ ( A @ hAPP_f2008608496t_bool ) @ ( E @ ( D @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ) ) ) )
       => ( A @ ( arrow_1335103695le_IIA @ hAPP_f1572141188l_bool ) @ hBOOL ) )
      & ( ( A @ ( arrow_1335103695le_IIA @ hAPP_f1572141188l_bool ) @ hBOOL )
       => ! [B: fun_Ar274636406t_bool] :
            ( ( arrow_5070731e_Prof @ ( B @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL )
           => ! [C: fun_Ar274636406t_bool] :
                ( ( arrow_5070731e_Prof @ ( C @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL )
               => ! [D: arrow_1893660431le_alt,E: arrow_1893660431le_alt] :
                    ( ! [F: arrow_856714788e_indi] :
                        ( ( ( F @ ( C @ hAPP_A1646126530t_bool ) @ ( E @ ( D @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
                         => ( F @ ( B @ hAPP_A1646126530t_bool ) @ ( E @ ( D @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
                        & ( ( F @ ( B @ hAPP_A1646126530t_bool ) @ ( E @ ( D @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
                         => ( F @ ( C @ hAPP_A1646126530t_bool ) @ ( E @ ( D @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) )
                   => ( ( ( C @ ( A @ hAPP_f2008608496t_bool ) @ ( E @ ( D @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
                       => ( B @ ( A @ hAPP_f2008608496t_bool ) @ ( E @ ( D @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
                      & ( ( B @ ( A @ hAPP_f2008608496t_bool ) @ ( E @ ( D @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
                       => ( C @ ( A @ hAPP_f2008608496t_bool ) @ ( E @ ( D @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).

thf(568,axiom,
    ! [A: fun_fu2114379172t_bool] :
      ( ( A @ ( arrow_320876018nimity @ hAPP_f1572141188l_bool ) @ hBOOL )
    <=> ! [B: fun_Ar274636406t_bool] :
          ( ( arrow_5070731e_Prof @ ( B @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL )
         => ! [C: arrow_1893660431le_alt,D: arrow_1893660431le_alt] :
              ( ! [E: arrow_856714788e_indi] : ( E @ ( B @ hAPP_A1646126530t_bool ) @ ( D @ ( C @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
             => ( B @ ( A @ hAPP_f2008608496t_bool ) @ ( D @ ( C @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_unanimity__def) ).

thf(2928,plain,
    ! [A: fun_fu2114379172t_bool] :
      ( ( ! [B: fun_Ar274636406t_bool] :
            ( ( arrow_5070731e_Prof @ ( B @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL )
           => ! [C: arrow_1893660431le_alt,D: arrow_1893660431le_alt] :
                ( ! [E: arrow_856714788e_indi] : ( E @ ( B @ hAPP_A1646126530t_bool ) @ ( D @ ( C @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
               => ( B @ ( A @ hAPP_f2008608496t_bool ) @ ( D @ ( C @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) )
       => ( A @ ( arrow_320876018nimity @ hAPP_f1572141188l_bool ) @ hBOOL ) )
      & ( ( A @ ( arrow_320876018nimity @ hAPP_f1572141188l_bool ) @ hBOOL )
       => ! [B: fun_Ar274636406t_bool] :
            ( ( arrow_5070731e_Prof @ ( B @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL )
           => ! [C: arrow_1893660431le_alt,D: arrow_1893660431le_alt] :
                ( ! [E: arrow_856714788e_indi] : ( E @ ( B @ hAPP_A1646126530t_bool ) @ ( D @ ( C @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
               => ( B @ ( A @ hAPP_f2008608496t_bool ) @ ( D @ ( C @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).

thf(539,axiom,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
      ( ( B @ ( A @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( B @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_436_order__less__imp__le) ).

thf(2812,plain,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
      ( ( B @ ( A @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( B @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).

thf(489,axiom,
    ! [A: arrow_856714788e_indi,B: fun_fu2114379172t_bool] :
      ( ( arrow_1361987423le_Lin @ ( cOMBK_1701906001t_bool @ hAPP_f1104294872l_bool ) @ ( arrow_5070731e_Prof @ pi_fun1746584570t_bool ) @ ( B @ ( member173038353t_bool @ hAPP_f1714503811l_bool ) @ hAPP_f975209902l_bool ) @ hBOOL )
     => ( ! [C: fun_Ar274636406t_bool] :
            ( ( arrow_5070731e_Prof @ ( C @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL )
           => ! [D: arrow_1893660431le_alt,E: arrow_1893660431le_alt] :
                ( ( D != E )
               => ( ( A @ ( C @ hAPP_A1646126530t_bool ) @ ( E @ ( D @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
                 => ( C @ ( B @ hAPP_f2008608496t_bool ) @ ( E @ ( D @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ) )
       => ( A @ ( B @ ( arrow_1765888670ctator @ hAPP_f399308031i_bool ) @ hAPP_A997847300i_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_dictatorI) ).

thf(2632,plain,
    ! [A: arrow_856714788e_indi,B: fun_fu2114379172t_bool] :
      ( ( arrow_1361987423le_Lin @ ( cOMBK_1701906001t_bool @ hAPP_f1104294872l_bool ) @ ( arrow_5070731e_Prof @ pi_fun1746584570t_bool ) @ ( B @ ( member173038353t_bool @ hAPP_f1714503811l_bool ) @ hAPP_f975209902l_bool ) @ hBOOL )
     => ( ! [C: fun_Ar274636406t_bool] :
            ( ( arrow_5070731e_Prof @ ( C @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL )
           => ! [D: arrow_1893660431le_alt,E: arrow_1893660431le_alt] :
                ( ( D != E )
               => ( ( A @ ( C @ hAPP_A1646126530t_bool ) @ ( E @ ( D @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
                 => ( C @ ( B @ hAPP_f2008608496t_bool ) @ ( E @ ( D @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ) )
       => ( A @ ( B @ ( arrow_1765888670ctator @ hAPP_f399308031i_bool ) @ hAPP_A997847300i_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).

thf(436,axiom,
    ! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool] :
      ( ( B @ ( A @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
     => ( ( A = B )
        | ( B @ ( A @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_449_order__le__imp__less__or__eq) ).

thf(2314,plain,
    ! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool] :
      ( ( B @ ( A @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
     => ( ( A = B )
        | ( B @ ( A @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).

thf(486,axiom,
    ! [A: bool,B: fun_bo1682907689le_alt,C: fun_bool_bool,D: fun_Pr2067565481t_bool] :
      ( ( D @ ( cOMBK_5056120l_bool @ hAPP_f1723896209t_bool ) @ ( C @ pi_boo7125949le_alt ) @ ( B @ ( member684813948le_alt @ hAPP_f334747853l_bool ) @ hAPP_f1620711039l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
       => ( D @ ( A @ ( B @ hAPP_b2094455111le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_597_funcset__mem) ).

thf(2625,plain,
    ! [A: bool,B: fun_bo1682907689le_alt,C: fun_bool_bool,D: fun_Pr2067565481t_bool] :
      ( ( D @ ( cOMBK_5056120l_bool @ hAPP_f1723896209t_bool ) @ ( C @ pi_boo7125949le_alt ) @ ( B @ ( member684813948le_alt @ hAPP_f334747853l_bool ) @ hAPP_f1620711039l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
       => ( D @ ( A @ ( B @ hAPP_b2094455111le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).

thf(263,axiom,
    a != b,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76__096a_A_126_061_Ab_096) ).

thf(1630,plain,
    a != b,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(350,axiom,
    ! [A: nat] :
      ~ ( A @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_981_less__not__refl) ).

thf(1993,plain,
    ! [A: nat] :
      ~ ( A @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(293,axiom,
    ! [A: nat,B: nat] :
      ( ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
      | ( A = B )
      | ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_linorder__less__linear) ).

thf(1731,plain,
    ! [A: nat,B: nat] :
      ( ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
      | ( A = B )
      | ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(6,axiom,
    ! [A: nat,B: nat] :
      ( ( ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) )
        = zero_zero_nat )
    <=> ( ( B = zero_zero_nat )
        | ( A = zero_zero_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1154_mult__is__0) ).

thf(594,plain,
    ! [A: nat,B: nat] :
      ( ( ( ( B = zero_zero_nat )
          | ( A = zero_zero_nat ) )
       => ( ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) )
          = zero_zero_nat ) )
      & ( ( ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) )
          = zero_zero_nat )
       => ( ( B = zero_zero_nat )
          | ( A = zero_zero_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(575,axiom,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
      ( ( B @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
    <=> ( ( A = B )
        | ( B @ ( A @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_402_order__le__less) ).

thf(3034,plain,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
      ( ( ( ( A = B )
          | ( B @ ( A @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
       => ( B @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( ( A = B )
          | ( B @ ( A @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).

thf(566,axiom,
    ! [A: product_unit,B: fun_Pr2090226719le_alt,C: fun_Pr1643180309t_bool,D: fun_Pr2067565481t_bool] :
      ( ( D @ ( cOMBK_681766254t_unit @ hAPP_f15777819t_bool ) @ ( C @ pi_Pro1820940723le_alt ) @ ( B @ ( member869664626le_alt @ hAPP_f41367117l_bool ) @ hAPP_f684683381l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ( D @ ( A @ ( B @ hAPP_P396106045le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_598_funcset__mem) ).

thf(2923,plain,
    ! [A: product_unit,B: fun_Pr2090226719le_alt,C: fun_Pr1643180309t_bool,D: fun_Pr2067565481t_bool] :
      ( ( D @ ( cOMBK_681766254t_unit @ hAPP_f15777819t_bool ) @ ( C @ pi_Pro1820940723le_alt ) @ ( B @ ( member869664626le_alt @ hAPP_f41367117l_bool ) @ hAPP_f684683381l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ( D @ ( A @ ( B @ hAPP_P396106045le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).

thf(464,axiom,
    ! [A: produc472769767le_alt,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
      ( ( C @ ( B @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_970_in__mono) ).

thf(2461,plain,
    ! [A: produc472769767le_alt,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
      ( ( C @ ( B @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).

thf(570,axiom,
    ! [A: fun_Pr2067565481t_bool,B: fun_fu638310559l_bool] :
      ( ( B @ ( A @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
    <=> ( A @ ( B @ hAPP_f52567537l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_mem__def) ).

thf(2974,plain,
    ! [A: fun_Pr2067565481t_bool,B: fun_fu638310559l_bool] :
      ( ( ( A @ ( B @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( B @ ( A @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
       => ( A @ ( B @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).

thf(76,axiom,
    ! [A: fun_fu638310559l_bool,B: fun_fu955147676ol_nat,C: fun_fu638310559l_bool,D: nat] :
      ( ( D @ ( C @ ( B @ hAPP_f1487854056ol_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
       => ( ! [E: fun_fu638310559l_bool,F: fun_fu638310559l_bool] :
              ( ( E @ ( F @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
             => ( E @ ( B @ hAPP_f1487854056ol_nat ) @ ( F @ ( B @ hAPP_f1487854056ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
         => ( D @ ( A @ ( B @ hAPP_f1487854056ol_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_798_xt4) ).

thf(912,plain,
    ! [A: fun_fu638310559l_bool,B: fun_fu955147676ol_nat,C: fun_fu638310559l_bool,D: nat] :
      ( ( D @ ( C @ ( B @ hAPP_f1487854056ol_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
       => ( ! [E: fun_fu638310559l_bool,F: fun_fu638310559l_bool] :
              ( ( E @ ( F @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
             => ( E @ ( B @ hAPP_f1487854056ol_nat ) @ ( F @ ( B @ hAPP_f1487854056ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
         => ( D @ ( A @ ( B @ hAPP_f1487854056ol_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(95,axiom,
    ! [A: nat,B: fun_na300967376t_bool,C: nat,D: fun_Ar331856045t_bool] :
      ( ( D @ ( C @ ( B @ hAPP_n1312530466t_bool ) @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [E: nat,F: nat] :
              ( ( E @ ( F @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( E @ ( B @ hAPP_n1312530466t_bool ) @ ( F @ ( B @ hAPP_n1312530466t_bool ) @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) )
         => ( D @ ( A @ ( B @ hAPP_n1312530466t_bool ) @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_780_xt4) ).

thf(983,plain,
    ! [A: nat,B: fun_na300967376t_bool,C: nat,D: fun_Ar331856045t_bool] :
      ( ( D @ ( C @ ( B @ hAPP_n1312530466t_bool ) @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [E: nat,F: nat] :
              ( ( E @ ( F @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( E @ ( B @ hAPP_n1312530466t_bool ) @ ( F @ ( B @ hAPP_n1312530466t_bool ) @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) )
         => ( D @ ( A @ ( B @ hAPP_n1312530466t_bool ) @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(316,axiom,
    ! [A: nat,B: fun_na300967376t_bool,C: nat,D: fun_Ar331856045t_bool] :
      ( ( D @ ( C @ ( B @ hAPP_n1312530466t_bool ) @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [E: nat,F: nat] :
              ( ( E @ ( F @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( E @ ( B @ hAPP_n1312530466t_bool ) @ ( F @ ( B @ hAPP_n1312530466t_bool ) @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) )
         => ( D @ ( A @ ( B @ hAPP_n1312530466t_bool ) @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_768_xt6) ).

thf(1841,plain,
    ! [A: nat,B: fun_na300967376t_bool,C: nat,D: fun_Ar331856045t_bool] :
      ( ( D @ ( C @ ( B @ hAPP_n1312530466t_bool ) @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [E: nat,F: nat] :
              ( ( E @ ( F @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( E @ ( B @ hAPP_n1312530466t_bool ) @ ( F @ ( B @ hAPP_n1312530466t_bool ) @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) )
         => ( D @ ( A @ ( B @ hAPP_n1312530466t_bool ) @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(330,axiom,
    ! [A: arrow_856714788e_indi,B: nat,C: fun_Ar671024215di_nat] :
      ( ( top_to788185952i_bool @ ( C @ inj_on1960344199di_nat @ hAPP_f584385070l_bool ) @ hBOOL )
     => ( ( ( A @ ( C @ hAPP_A376526755di_nat ) )
          = B )
       => ( ( B @ ( C @ ( top_to788185952i_bool @ hilber1580028780di_nat ) @ hAPP_n1937165849e_indi ) )
          = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_inv__f__eq) ).

thf(1926,plain,
    ! [A: arrow_856714788e_indi,B: nat,C: fun_Ar671024215di_nat] :
      ( ( top_to788185952i_bool @ ( C @ inj_on1960344199di_nat @ hAPP_f584385070l_bool ) @ hBOOL )
     => ( ( ( A @ ( C @ hAPP_A376526755di_nat ) )
          = B )
       => ( ( B @ ( C @ ( top_to788185952i_bool @ hilber1580028780di_nat ) @ hAPP_n1937165849e_indi ) )
          = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(250,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_501_order__le__less__trans) ).

thf(1594,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(409,axiom,
    ! [A: nat,B: nat] :
      ( ( A = B )
     => ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_995_eq__imp__le) ).

thf(2212,plain,
    ! [A: nat,B: nat] :
      ( ( A = B )
     => ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(60,axiom,
    ! [A: fun_fu638310559l_bool,B: nat,C: fun_fu955147676ol_nat,D: fun_fu638310559l_bool] :
      ( ( D @ ( C @ hAPP_f1487854056ol_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( D @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
       => ( ! [E: fun_fu638310559l_bool,F: fun_fu638310559l_bool] :
              ( ( F @ ( E @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
             => ( F @ ( C @ hAPP_f1487854056ol_nat ) @ ( E @ ( C @ hAPP_f1487854056ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
         => ( A @ ( C @ hAPP_f1487854056ol_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_847_order__less__le__subst1) ).

thf(827,plain,
    ! [A: fun_fu638310559l_bool,B: nat,C: fun_fu955147676ol_nat,D: fun_fu638310559l_bool] :
      ( ( D @ ( C @ hAPP_f1487854056ol_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( D @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
       => ( ! [E: fun_fu638310559l_bool,F: fun_fu638310559l_bool] :
              ( ( F @ ( E @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
             => ( F @ ( C @ hAPP_f1487854056ol_nat ) @ ( E @ ( C @ hAPP_f1487854056ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
         => ( A @ ( C @ hAPP_f1487854056ol_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(26,axiom,
    ! [A: nat] : ( A @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1140_le__square) ).

thf(695,plain,
    ! [A: nat] : ( A @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(373,axiom,
    ! [A: bool,B: fun_bool_bool] :
      ( ( B @ ( A @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
    <=> ( A @ ( B @ hAPP_bool_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_mem__def) ).

thf(2086,plain,
    ! [A: bool,B: fun_bool_bool] :
      ( ( ( A @ ( B @ hAPP_bool_bool ) @ hBOOL )
       => ( B @ ( A @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
       => ( A @ ( B @ hAPP_bool_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(266,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_511_xt1_I8_J) ).

thf(1643,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(391,axiom,
    ! [A: fun_fu1287834969t_bool,B: fun_Ar274636406t_bool,C: arrow_856714788e_indi] :
      ( ( C @ ( B @ ( A @ cOMBB_1876517692e_indi @ hAPP_f1751344075t_bool ) @ hAPP_A38124190t_bool ) )
      = ( C @ ( B @ hAPP_A1646126530t_bool ) @ ( A @ hAPP_f1550387441t_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ef_425) ).

thf(2139,plain,
    ! [A: fun_fu1287834969t_bool,B: fun_Ar274636406t_bool,C: arrow_856714788e_indi] :
      ( ( C @ ( B @ ( A @ cOMBB_1876517692e_indi @ hAPP_f1751344075t_bool ) @ hAPP_A38124190t_bool ) )
      = ( C @ ( B @ hAPP_A1646126530t_bool ) @ ( A @ hAPP_f1550387441t_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(103,axiom,
    ! [A: nat] : ( A @ ( top_top_fun_nat_bool @ hAPP_nat_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_top1I) ).

thf(1015,plain,
    ! [A: nat] : ( A @ ( top_top_fun_nat_bool @ hAPP_nat_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(8,axiom,
    ! [A: nat] :
      ( ( A @ ( zero_zero_nat @ times_times_nat @ hAPP_nat_nat ) )
      = zero_zero_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1156_mult__0) ).

thf(608,plain,
    ! [A: nat] :
      ( ( A @ ( zero_zero_nat @ times_times_nat @ hAPP_nat_nat ) )
      = zero_zero_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(128,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
        = ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
     => ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_730_add__left__imp__eq) ).

thf(1113,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
        = ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
     => ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(65,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ? [C: nat] :
          ( ( ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
            = B )
          & ( C @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1058_less__imp__add__positive) ).

thf(851,plain,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ? [C: nat] :
          ( ( ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
            = B )
          & ( C @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(282,axiom,
    ! [A: fun_Ar331856045t_bool] :
      ( ( A @ ( top_to951839027t_bool @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
    <=> ( A = top_to951839027t_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_526_top__unique) ).

thf(1694,plain,
    ! [A: fun_Ar331856045t_bool] :
      ( ( ( A = top_to951839027t_bool )
       => ( A @ ( top_to951839027t_bool @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) )
      & ( ( A @ ( top_to951839027t_bool @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
       => ( A = top_to951839027t_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(345,axiom,
    ! [A: nat,B: nat] :
      ( ( A != B )
    <=> ( ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
        | ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_982_nat__neq__iff) ).

thf(1973,plain,
    ! [A: nat,B: nat] :
      ( ( ( ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
          | ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
       => ( A != B ) )
      & ( ( A != B )
       => ( ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
          | ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(304,axiom,
    ! [A: arrow_856714788e_indi,B: fun_Ar671024215di_nat,C: fun_Ar1809396326i_bool] :
      ( ( C @ ( B @ inj_on1960344199di_nat @ hAPP_f584385070l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member1479139729e_indi @ hAPP_A1597696899l_bool ) @ hAPP_f584385070l_bool ) @ hBOOL )
       => ( ( A @ ( B @ hAPP_A376526755di_nat ) @ ( B @ ( C @ hilber1580028780di_nat ) @ hAPP_n1937165849e_indi ) )
          = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_616_inv__into__f__f) ).

thf(1775,plain,
    ! [A: arrow_856714788e_indi,B: fun_Ar671024215di_nat,C: fun_Ar1809396326i_bool] :
      ( ( C @ ( B @ inj_on1960344199di_nat @ hAPP_f584385070l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member1479139729e_indi @ hAPP_A1597696899l_bool ) @ hAPP_f584385070l_bool ) @ hBOOL )
       => ( ( A @ ( B @ hAPP_A376526755di_nat ) @ ( B @ ( C @ hilber1580028780di_nat ) @ hAPP_n1937165849e_indi ) )
          = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(518,axiom,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
      ( ( C @ ( B @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_507_xt1_I8_J) ).

thf(2752,plain,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
      ( ( C @ ( B @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).

thf(291,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_996_le__trans) ).

thf(1726,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(452,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B = A )
       => ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_xt1_I2_J) ).

thf(2390,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B = A )
       => ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).

thf(473,axiom,
    ! [A: produc472769767le_alt,B: fun_Pr376858015t_unit,C: fun_Pr2067565481t_bool,D: fun_Pr1069395679t_bool] :
      ( ( D @ ( C @ pi_Pro346842291t_unit ) @ ( B @ ( member1303779570t_unit @ hAPP_f1700632141l_bool ) @ hAPP_f1159856629l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( A @ ( D @ hAPP_P2037731755t_bool ) @ ( A @ ( B @ hAPP_P1069491261t_unit ) @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_549_Pi__mem) ).

thf(2506,plain,
    ! [A: produc472769767le_alt,B: fun_Pr376858015t_unit,C: fun_Pr2067565481t_bool,D: fun_Pr1069395679t_bool] :
      ( ( D @ ( C @ pi_Pro346842291t_unit ) @ ( B @ ( member1303779570t_unit @ hAPP_f1700632141l_bool ) @ hAPP_f1159856629l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( A @ ( D @ hAPP_P2037731755t_bool ) @ ( A @ ( B @ hAPP_P1069491261t_unit ) @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).

thf(240,axiom,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr1780397033l_bool,C: fun_Pr2067565481t_bool] :
      ( ! [D: produc472769767le_alt] :
          ( ( C @ ( D @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
         => ( D @ ( B @ hAPP_P1103642805l_bool ) @ ( D @ ( A @ hAPP_P1178790471t_bool ) @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) )
     => ( B @ ( C @ pi_Pro1238944957t_bool ) @ ( A @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_648_Pi__I) ).

thf(1562,plain,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr1780397033l_bool,C: fun_Pr2067565481t_bool] :
      ( ! [D: produc472769767le_alt] :
          ( ( C @ ( D @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
         => ( D @ ( B @ hAPP_P1103642805l_bool ) @ ( D @ ( A @ hAPP_P1178790471t_bool ) @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) )
     => ( B @ ( C @ pi_Pro1238944957t_bool ) @ ( A @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(33,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ? [C: nat] :
          ( B
          = ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1015_le__iff__add) ).

thf(722,plain,
    ! [A: nat,B: nat] :
      ( ( ? [C: nat] :
            ( B
            = ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
       => ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ? [C: nat] :
            ( B
            = ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(376,axiom,
    ! [A: fun_fu696673523t_bool,B: fun_Ar1995913199l_bool,C: arrow_1893660431le_alt] :
      ( ( C @ ( B @ ( A @ cOMBB_652885079le_alt @ hAPP_f105674721t_bool ) @ hAPP_A656921921t_bool ) )
      = ( C @ ( B @ hAPP_A1608658241l_bool ) @ ( A @ hAPP_f1689397393t_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs___428) ).

thf(2096,plain,
    ! [A: fun_fu696673523t_bool,B: fun_Ar1995913199l_bool,C: arrow_1893660431le_alt] :
      ( ( C @ ( B @ ( A @ cOMBB_652885079le_alt @ hAPP_f105674721t_bool ) @ hAPP_A656921921t_bool ) )
      = ( C @ ( B @ hAPP_A1608658241l_bool ) @ ( A @ hAPP_f1689397393t_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(299,axiom,
    ! [A: fun_Ar290235730t_bool,B: arrow_1893660431le_alt,C: arrow_856714788e_indi] :
      ( ( C @ ( B @ ( A @ ( cOMBC_1486904681t_bool @ hAPP_f2102110817t_bool ) @ hAPP_A1889513822t_bool ) @ hAPP_A1309733808t_bool ) )
      = ( B @ ( C @ ( A @ hAPP_A38124190t_bool ) @ hAPP_A1058422557t_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000_417) ).

thf(1758,plain,
    ! [A: fun_Ar290235730t_bool,B: arrow_1893660431le_alt,C: arrow_856714788e_indi] :
      ( ( C @ ( B @ ( A @ ( cOMBC_1486904681t_bool @ hAPP_f2102110817t_bool ) @ hAPP_A1889513822t_bool ) @ hAPP_A1309733808t_bool ) )
      = ( B @ ( C @ ( A @ hAPP_A38124190t_bool ) @ hAPP_A1058422557t_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(4,axiom,
    ! [A: nat] :
      ( ( zero_zero_nat @ ( A @ times_times_nat @ hAPP_nat_nat ) )
      = zero_zero_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1155_mult__0__right) ).

thf(589,plain,
    ! [A: nat] :
      ( ( zero_zero_nat @ ( A @ times_times_nat @ hAPP_nat_nat ) )
      = zero_zero_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(214,axiom,
    ! [A: fun_fu638310559l_bool] : ( top_to1312956197l_bool @ ( A @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_512_top__greatest) ).

thf(1467,plain,
    ! [A: fun_fu638310559l_bool] : ( top_to1312956197l_bool @ ( A @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(200,axiom,
    ! [A: fun_fu638310559l_bool,B: fun_fu638310559l_bool] :
      ( ( B @ ( A @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
     => ( ( A @ ( B @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_order__antisym) ).

thf(1420,plain,
    ! [A: fun_fu638310559l_bool,B: fun_fu638310559l_bool] :
      ( ( B @ ( A @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
     => ( ( A @ ( B @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(361,axiom,
    ! [A: bool] : ( top_to1647826457l_bool @ ( A @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_UNIV__I) ).

thf(2037,plain,
    ! [A: bool] : ( top_to1647826457l_bool @ ( A @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(226,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1072_Suc__less__SucD) ).

thf(1509,plain,
    ! [A: nat,B: nat] :
      ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(83,axiom,
    ! [A: fun_Pr2067565481t_bool,B: fun_fu638310559l_bool,C: fun_fu638310559l_bool] :
      ( ( C @ ( B @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_918_subsetD) ).

thf(939,plain,
    ! [A: fun_Pr2067565481t_bool,B: fun_fu638310559l_bool,C: fun_fu638310559l_bool] :
      ( ( C @ ( B @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(216,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ? [C: nat] :
          ( B
          = ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1101_less__iff__Suc__add) ).

thf(1472,plain,
    ! [A: nat,B: nat] :
      ( ( ? [C: nat] :
            ( B
            = ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) ) )
       => ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ? [C: nat] :
            ( B
            = ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(58,axiom,
    ! [A: nat] : ( A @ ( suc @ hAPP_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1061_zero__less__Suc) ).

thf(823,plain,
    ! [A: nat] : ( A @ ( suc @ hAPP_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(483,axiom,
    ! [A: arrow_1893660431le_alt,B: arrow_1893660431le_alt,C: fun_Pr2067565481t_bool,D: arrow_1893660431le_alt,E: arrow_1893660431le_alt] :
      ( ( D != E )
     => ( ( arrow_1361987423le_Lin @ ( C @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
       => ( ( E @ ( D @ ( C @ arrow_1525312447_below ) ) @ ( B @ ( A @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
        <=> ( ( ( B != D )
             => ( ( ( A != D )
                 => ( C @ ( B @ ( A @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
                & ( ( A = D )
                 => ( ( C @ ( B @ ( E @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
                    | ( B = E ) ) ) ) )
            & ( ( B = D )
             => ( C @ ( E @ ( A @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
            & ( A != B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_in__below) ).

thf(2582,plain,
    ! [A: arrow_1893660431le_alt,B: arrow_1893660431le_alt,C: fun_Pr2067565481t_bool,D: arrow_1893660431le_alt,E: arrow_1893660431le_alt] :
      ( ( D != E )
     => ( ( arrow_1361987423le_Lin @ ( C @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
       => ( ( ( ( ( B != D )
               => ( ( ( A != D )
                   => ( C @ ( B @ ( A @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
                  & ( ( A = D )
                   => ( ( C @ ( B @ ( E @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
                      | ( B = E ) ) ) ) )
              & ( ( B = D )
               => ( C @ ( E @ ( A @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
              & ( A != B ) )
           => ( E @ ( D @ ( C @ arrow_1525312447_below ) ) @ ( B @ ( A @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
          & ( ( E @ ( D @ ( C @ arrow_1525312447_below ) ) @ ( B @ ( A @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
           => ( ( ( B != D )
               => ( ( ( A != D )
                   => ( C @ ( B @ ( A @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
                  & ( ( A = D )
                   => ( ( C @ ( B @ ( E @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
                      | ( B = E ) ) ) ) )
              & ( ( B = D )
               => ( C @ ( E @ ( A @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
              & ( A != B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).

thf(109,axiom,
    ! [A: nat,B: nat] : ( A @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1100_less__add__Suc2) ).

thf(1049,plain,
    ! [A: nat,B: nat] : ( A @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(541,axiom,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
      ( ( C @ ( B @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_order__trans) ).

thf(2816,plain,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
      ( ( C @ ( B @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).

thf(246,axiom,
    ! [A: produc472769767le_alt,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool,D: fun_Pr1780397033l_bool] :
      ( ( D @ ( C @ pi_Pro1238944957t_bool ) @ ( B @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( A @ ( D @ hAPP_P1103642805l_bool ) @ ( A @ ( B @ hAPP_P1178790471t_bool ) @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_547_Pi__mem) ).

thf(1583,plain,
    ! [A: produc472769767le_alt,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool,D: fun_Pr1780397033l_bool] :
      ( ( D @ ( C @ pi_Pro1238944957t_bool ) @ ( B @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( A @ ( D @ hAPP_P1103642805l_bool ) @ ( A @ ( B @ hAPP_P1178790471t_bool ) @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(529,axiom,
    ! [A: fun_Pr2067565481t_bool] :
      ( ( A @ ( top_to1138392227t_bool @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
    <=> ( A = top_to1138392227t_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_525_top__unique) ).

thf(2784,plain,
    ! [A: fun_Pr2067565481t_bool] :
      ( ( ( A = top_to1138392227t_bool )
       => ( A @ ( top_to1138392227t_bool @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
      & ( ( A @ ( top_to1138392227t_bool @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( A = top_to1138392227t_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).

thf(426,axiom,
    ! [A: fun_nat_fun_nat_bool,B: nat,C: nat] :
      ( ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( C @ ( A @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
     => ( ( ( B = C )
         => ( B @ ( C @ ( A @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
       => ( ( ( B @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( B @ ( C @ ( A @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
         => ( B @ ( C @ ( A @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_987_nat__less__cases) ).

thf(2271,plain,
    ! [A: fun_nat_fun_nat_bool,B: nat,C: nat] :
      ( ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( C @ ( A @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
     => ( ( ( B = C )
         => ( B @ ( C @ ( A @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
       => ( ( ( B @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( B @ ( C @ ( A @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
         => ( B @ ( C @ ( A @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).

thf(349,axiom,
    ! [A: arrow_856714788e_indi,B: arrow_856714788e_indi,C: fun_Ar671024215di_nat,D: fun_Ar1809396326i_bool] :
      ( ( D @ ( C @ inj_on1960344199di_nat @ hAPP_f584385070l_bool ) @ hBOOL )
     => ( ( ( A @ ( C @ hAPP_A376526755di_nat ) )
          = ( B @ ( C @ hAPP_A376526755di_nat ) ) )
       => ( ( D @ ( A @ ( member1479139729e_indi @ hAPP_A1597696899l_bool ) @ hAPP_f584385070l_bool ) @ hBOOL )
         => ( ( D @ ( B @ ( member1479139729e_indi @ hAPP_A1597696899l_bool ) @ hAPP_f584385070l_bool ) @ hBOOL )
           => ( A = B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_545_inj__onD) ).

thf(1990,plain,
    ! [A: arrow_856714788e_indi,B: arrow_856714788e_indi,C: fun_Ar671024215di_nat,D: fun_Ar1809396326i_bool] :
      ( ( D @ ( C @ inj_on1960344199di_nat @ hAPP_f584385070l_bool ) @ hBOOL )
     => ( ( ( A @ ( C @ hAPP_A376526755di_nat ) )
          = ( B @ ( C @ hAPP_A376526755di_nat ) ) )
       => ( ( D @ ( A @ ( member1479139729e_indi @ hAPP_A1597696899l_bool ) @ hAPP_f584385070l_bool ) @ hBOOL )
         => ( ( D @ ( B @ ( member1479139729e_indi @ hAPP_A1597696899l_bool ) @ hAPP_f584385070l_bool ) @ hBOOL )
           => ( A = B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(496,axiom,
    ! [A: bool,B: fun_bo1682907689le_alt,C: fun_bool_bool,D: fun_bo1431306493t_bool] :
      ( ( D @ ( C @ pi_boo7125949le_alt ) @ ( B @ ( member684813948le_alt @ hAPP_f334747853l_bool ) @ hAPP_f1620711039l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
       => ( A @ ( D @ hAPP_b128655177t_bool ) @ ( A @ ( B @ hAPP_b2094455111le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_563_Pi__mem) ).

thf(2684,plain,
    ! [A: bool,B: fun_bo1682907689le_alt,C: fun_bool_bool,D: fun_bo1431306493t_bool] :
      ( ( D @ ( C @ pi_boo7125949le_alt ) @ ( B @ ( member684813948le_alt @ hAPP_f334747853l_bool ) @ hAPP_f1620711039l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
       => ( A @ ( D @ hAPP_b128655177t_bool ) @ ( A @ ( B @ hAPP_b2094455111le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).

thf(407,axiom,
    ! [A: nat] :
      ( ( A != zero_zero_nat )
    <=> ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1045_neq0__conv) ).

thf(2202,plain,
    ! [A: nat] :
      ( ( ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A != zero_zero_nat ) )
      & ( ( A != zero_zero_nat )
       => ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

thf(135,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( B @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1075_less__trans__Suc) ).

thf(1145,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( B @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(550,axiom,
    top_to788185952i_bool @ ( finite92092049e_indi @ hAPP_f584385070l_bool ) @ hBOOL,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1031_finite__indi) ).

thf(2846,plain,
    top_to788185952i_bool @ ( finite92092049e_indi @ hAPP_f584385070l_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).

thf(423,axiom,
    ! [A: fun_fu841105374ol_nat,B: nat,C: fun_Pr2067565481t_bool,D: fun_Pr2067565481t_bool] :
      ( ( D @ ( C @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( ( B @ ( D @ ( A @ hAPP_f1842225014ol_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [E: fun_Pr2067565481t_bool,F: fun_Pr2067565481t_bool] :
              ( ( F @ ( E @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
             => ( F @ ( A @ hAPP_f1842225014ol_nat ) @ ( E @ ( A @ hAPP_f1842225014ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
         => ( B @ ( C @ ( A @ hAPP_f1842225014ol_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_884_order__le__less__subst2) ).

thf(2256,plain,
    ! [A: fun_fu841105374ol_nat,B: nat,C: fun_Pr2067565481t_bool,D: fun_Pr2067565481t_bool] :
      ( ( D @ ( C @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( ( B @ ( D @ ( A @ hAPP_f1842225014ol_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [E: fun_Pr2067565481t_bool,F: fun_Pr2067565481t_bool] :
              ( ( F @ ( E @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
             => ( F @ ( A @ hAPP_f1842225014ol_nat ) @ ( E @ ( A @ hAPP_f1842225014ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
         => ( B @ ( C @ ( A @ hAPP_f1842225014ol_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).

thf(317,axiom,
    ! [A: fun_nat_fun_nat_bool,B: fun_Ar671024215di_nat,C: arrow_856714788e_indi] :
      ( ( C @ ( B @ ( A @ cOMBB_1869811296e_indi @ hAPP_f966656047t_bool ) @ hAPP_A1686943911t_bool ) )
      = ( C @ ( B @ hAPP_A376526755di_nat ) @ ( A @ hAPP_n1699378549t_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__401) ).

thf(1845,plain,
    ! [A: fun_nat_fun_nat_bool,B: fun_Ar671024215di_nat,C: arrow_856714788e_indi] :
      ( ( C @ ( B @ ( A @ cOMBB_1869811296e_indi @ hAPP_f966656047t_bool ) @ hAPP_A1686943911t_bool ) )
      = ( C @ ( B @ hAPP_A376526755di_nat ) @ ( A @ hAPP_n1699378549t_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(432,axiom,
    ! [A: fun_Ar1809396326i_bool,B: produc472769767le_alt] :
      ( ( B @ ( A @ ( cOMBK_1987648063le_alt @ hAPP_f359069313i_bool ) @ hAPP_P1859429372i_bool ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs___404) ).

thf(2298,plain,
    ! [A: fun_Ar1809396326i_bool,B: produc472769767le_alt] :
      ( ( B @ ( A @ ( cOMBK_1987648063le_alt @ hAPP_f359069313i_bool ) @ hAPP_P1859429372i_bool ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

thf(99,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( D @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( D @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_654_add__less__le__mono) ).

thf(1003,plain,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( D @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( D @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(1,conjecture,
    p @ ( f @ hAPP_f2008608496t_bool ) @ ( d @ ( c @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

thf(2,negated_conjecture,
    ~ ( p @ ( f @ hAPP_f2008608496t_bool ) @ ( d @ ( c @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(580,plain,
    ~ ( p @ ( f @ hAPP_f2008608496t_bool ) @ ( d @ ( c @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(24,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ times_times_nat @ hAPP_nat_nat ) )
      = ( C @ ( B @ times_times_nat @ hAPP_nat_nat ) @ ( C @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1149_add__mult__distrib) ).

thf(690,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ times_times_nat @ hAPP_nat_nat ) )
      = ( C @ ( B @ times_times_nat @ hAPP_nat_nat ) @ ( C @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(341,axiom,
    ! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool,C: fun_Ar331856045t_bool] :
      ( ( C @ ( B @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
     => ( ( C = A )
       => ( A @ ( B @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_ord__le__eq__trans) ).

thf(1961,plain,
    ! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool,C: fun_Ar331856045t_bool] :
      ( ( C @ ( B @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
     => ( ( C = A )
       => ( A @ ( B @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(105,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( C @ times_times_nat @ hAPP_nat_nat ) @ ( A @ ( C @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
      <=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1176_nat__mult__le__cancel1) ).

thf(1025,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( B @ ( C @ times_times_nat @ hAPP_nat_nat ) @ ( A @ ( C @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
        & ( ( B @ ( C @ times_times_nat @ hAPP_nat_nat ) @ ( A @ ( C @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(113,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
      = ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_989_nat__add__left__commute) ).

thf(1070,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
      = ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(187,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_739_add__right__mono) ).

thf(1368,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(561,axiom,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
      ( ( C @ ( B @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_946_psubset__subset__trans) ).

thf(2888,plain,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
      ( ( C @ ( B @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).

thf(559,axiom,
    n @ ( h @ ( top_to788185952i_bool @ hilber1580028780di_nat ) @ hAPP_n1937165849e_indi ) @ ( p @ hAPP_A1646126530t_bool ) @ ( d @ ( c @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12__096c_A_060_092_060_094bsub_062P_A_Iinv_Ah_An_J_092_060_094esub_062_Ad_0) ).

thf(2882,plain,
    n @ ( h @ ( top_to788185952i_bool @ hilber1580028780di_nat ) @ hAPP_n1937165849e_indi ) @ ( p @ hAPP_A1646126530t_bool ) @ ( d @ ( c @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).

thf(97,axiom,
    ! [A: nat] :
      ( ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( A = zero_zero_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1095_less__Suc0) ).

thf(993,plain,
    ! [A: nat] :
      ( ( ( A = zero_zero_nat )
       => ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A = zero_zero_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(45,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1060_Suc__mono) ).

thf(776,plain,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(296,axiom,
    ! [A: fun_na998785244t_bool,B: fun_Pr2067565481t_bool,C: nat,D: nat] :
      ( ( D @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( D @ ( A @ hAPP_n1161265524t_bool ) @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( ! [E: nat,F: nat] :
              ( ( F @ ( E @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( F @ ( A @ hAPP_n1161265524t_bool ) @ ( E @ ( A @ hAPP_n1161265524t_bool ) @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
         => ( B @ ( C @ ( A @ hAPP_n1161265524t_bool ) @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_861_order__le__less__subst2) ).

thf(1748,plain,
    ! [A: fun_na998785244t_bool,B: fun_Pr2067565481t_bool,C: nat,D: nat] :
      ( ( D @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( D @ ( A @ hAPP_n1161265524t_bool ) @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( ! [E: nat,F: nat] :
              ( ( F @ ( E @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( F @ ( A @ hAPP_n1161265524t_bool ) @ ( E @ ( A @ hAPP_n1161265524t_bool ) @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
         => ( B @ ( C @ ( A @ hAPP_n1161265524t_bool ) @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(241,axiom,
    ! [A: nat] :
      ~ ( zero_zero_nat @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1044_not__less0) ).

thf(1566,plain,
    ! [A: nat] :
      ~ ( zero_zero_nat @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(357,axiom,
    ! [A: nat,B: nat] :
      ( ( A = B )
    <=> ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
        & ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_363_order__eq__iff) ).

thf(2012,plain,
    ! [A: nat,B: nat] :
      ( ( ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
          & ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
          & ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(552,axiom,
    ! [A: fun_Pr2067565481t_bool] : ( A @ ( top_to1312956197l_bool @ hAPP_f52567537l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_top1I) ).

thf(2850,plain,
    ! [A: fun_Pr2067565481t_bool] : ( A @ ( top_to1312956197l_bool @ hAPP_f52567537l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).

thf(219,axiom,
    ! [A: nat,B: fun_nat_bool] :
      ( ( zero_zero_nat @ ( B @ hAPP_nat_bool ) @ hBOOL )
     => ( ! [C: nat] :
            ( ( C @ ( B @ hAPP_nat_bool ) @ hBOOL )
           => ( C @ ( suc @ hAPP_nat_nat ) @ ( B @ hAPP_nat_bool ) @ hBOOL ) )
       => ( A @ ( B @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1126_nat__induct) ).

thf(1484,plain,
    ! [A: nat,B: fun_nat_bool] :
      ( ( zero_zero_nat @ ( B @ hAPP_nat_bool ) @ hBOOL )
     => ( ! [C: nat] :
            ( ( C @ ( B @ hAPP_nat_bool ) @ hBOOL )
           => ( C @ ( suc @ hAPP_nat_nat ) @ ( B @ hAPP_nat_bool ) @ hBOOL ) )
       => ( A @ ( B @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(374,axiom,
    ! [A: fun_nat_bool] : ( A @ ( suc @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1093_inj__Suc) ).

thf(2092,plain,
    ! [A: fun_nat_bool] : ( A @ ( suc @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(413,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1027_termination__basic__simps_I5_J) ).

thf(2224,plain,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(307,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A != B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_986_less__not__refl3) ).

thf(1785,plain,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(271,axiom,
    ! [A: produc472769767le_alt,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool,D: fun_Pr1780397033l_bool] :
      ( ( D @ ( C @ pi_Pro1238944957t_bool ) @ ( B @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_P1103642805l_bool ) @ ( A @ ( B @ hAPP_P1178790471t_bool ) @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_PiE) ).

thf(1658,plain,
    ! [A: produc472769767le_alt,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool,D: fun_Pr1780397033l_bool] :
      ( ( D @ ( C @ pi_Pro1238944957t_bool ) @ ( B @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_P1103642805l_bool ) @ ( A @ ( B @ hAPP_P1178790471t_bool ) @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(469,axiom,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
      ( ( B @ ( A @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
    <=> ( ( A != B )
        & ( B @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_925_psubset__eq) ).

thf(2486,plain,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
      ( ( ( ( A != B )
          & ( B @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
       => ( B @ ( A @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( ( A != B )
          & ( B @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).

thf(133,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
        & ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1161_mult__less__cancel1) ).

thf(1130,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
          & ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
       => ( C @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( C @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
          & ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(164,axiom,
    ! [A: nat] :
      ( ( A @ ( suc @ hAPP_nat_nat ) )
      = ( one_one_nat @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1118_Suc__eq__plus1) ).

thf(1285,plain,
    ! [A: nat] :
      ( ( A @ ( suc @ hAPP_nat_nat ) )
      = ( one_one_nat @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(180,axiom,
    ! [A: fun_fu638310559l_bool,B: fun_fu638310559l_bool] :
      ( ( A = B )
    <=> ( ( A @ ( B @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
        & ( B @ ( A @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_355_order__eq__iff) ).

thf(1336,plain,
    ! [A: fun_fu638310559l_bool,B: fun_fu638310559l_bool] :
      ( ( ( ( A @ ( B @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
          & ( B @ ( A @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( ( A @ ( B @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
          & ( B @ ( A @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(151,axiom,
    ! [A: fun_Ar331856045t_bool,B: fun_na300967376t_bool,C: nat,D: nat] :
      ( ( D @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( C @ ( B @ hAPP_n1312530466t_bool ) @ ( A @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
       => ( ! [E: nat,F: nat] :
              ( ( E @ ( F @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( E @ ( B @ hAPP_n1312530466t_bool ) @ ( F @ ( B @ hAPP_n1312530466t_bool ) @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) )
         => ( D @ ( B @ hAPP_n1312530466t_bool ) @ ( A @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_681_xt7) ).

thf(1220,plain,
    ! [A: fun_Ar331856045t_bool,B: fun_na300967376t_bool,C: nat,D: nat] :
      ( ( D @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( C @ ( B @ hAPP_n1312530466t_bool ) @ ( A @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
       => ( ! [E: nat,F: nat] :
              ( ( E @ ( F @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( E @ ( B @ hAPP_n1312530466t_bool ) @ ( F @ ( B @ hAPP_n1312530466t_bool ) @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) )
         => ( D @ ( B @ hAPP_n1312530466t_bool ) @ ( A @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(168,axiom,
    ! [A: nat] :
      ( ( A @ ( suc @ hAPP_nat_nat ) @ ( nat_size @ hAPP_nat_nat ) )
      = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( A @ ( nat_size @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1181_nat_Osize_I2_J) ).

thf(1300,plain,
    ! [A: nat] :
      ( ( A @ ( suc @ hAPP_nat_nat ) @ ( nat_size @ hAPP_nat_nat ) )
      = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( A @ ( nat_size @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(209,axiom,
    ! [A: fun_nat_bool,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( C @ ( A @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [D: nat] :
              ( ( C @ ( D @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( ( D @ ( suc @ hAPP_nat_nat ) @ ( A @ hAPP_nat_bool ) @ hBOOL )
               => ( D @ ( A @ hAPP_nat_bool ) @ hBOOL ) ) )
         => ( B @ ( A @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1115_inc__induct) ).

thf(1452,plain,
    ! [A: fun_nat_bool,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( C @ ( A @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [D: nat] :
              ( ( C @ ( D @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( ( D @ ( suc @ hAPP_nat_nat ) @ ( A @ hAPP_nat_bool ) @ hBOOL )
               => ( D @ ( A @ hAPP_nat_bool ) @ hBOOL ) ) )
         => ( B @ ( A @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(265,axiom,
    ! [A: arrow_856714788e_indi,B: fun_Ar1809396326i_bool] :
      ( ( B @ ( A @ ( member1479139729e_indi @ hAPP_A1597696899l_bool ) @ hAPP_f584385070l_bool ) @ hBOOL )
    <=> ( A @ ( B @ hAPP_A997847300i_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_mem__def) ).

thf(1637,plain,
    ! [A: arrow_856714788e_indi,B: fun_Ar1809396326i_bool] :
      ( ( ( A @ ( B @ hAPP_A997847300i_bool ) @ hBOOL )
       => ( B @ ( A @ ( member1479139729e_indi @ hAPP_A1597696899l_bool ) @ hAPP_f584385070l_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( member1479139729e_indi @ hAPP_A1597696899l_bool ) @ hAPP_f584385070l_bool ) @ hBOOL )
       => ( A @ ( B @ hAPP_A997847300i_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(498,axiom,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
      ( ( B @ ( A @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
    <=> ( ( A != B )
        & ( B @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_382_order__less__le) ).

thf(2688,plain,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
      ( ( ( ( A != B )
          & ( B @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
       => ( B @ ( A @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( ( A != B )
          & ( B @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).

thf(500,axiom,
    ! [A: bool,B: fun_Pr2067565481t_bool] :
      ( ( B @ ( A @ ( cOMBK_81143760t_bool @ hAPP_b1272691967l_bool ) @ hAPP_f52567537l_bool ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__prod_Itc__Arrow____Order_) ).

thf(2700,plain,
    ! [A: bool,B: fun_Pr2067565481t_bool] :
      ( ( B @ ( A @ ( cOMBK_81143760t_bool @ hAPP_b1272691967l_bool ) @ hAPP_f52567537l_bool ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).

thf(146,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1104_Suc__le__eq) ).

thf(1186,plain,
    ! [A: nat,B: nat] :
      ( ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(174,axiom,
    ! [A: nat] : ( one_one_nat @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_653_less__add__one) ).

thf(1317,plain,
    ! [A: nat] : ( one_one_nat @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(301,axiom,
    ! [A: fun_Ar274636406t_bool] :
      ( ( A @ ( top_to553140914l_bool @ hAPP_f995490902l_bool ) @ hBOOL )
    <=> ( top_top_bool @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_top__apply) ).

thf(1763,plain,
    ! [A: fun_Ar274636406t_bool] :
      ( ( ( top_top_bool @ hBOOL )
       => ( A @ ( top_to553140914l_bool @ hAPP_f995490902l_bool ) @ hBOOL ) )
      & ( ( A @ ( top_to553140914l_bool @ hAPP_f995490902l_bool ) @ hBOOL )
       => ( top_top_bool @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(420,axiom,
    ! [A: nat,B: nat] :
      ( ( A = B )
     => ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_353_order__eq__refl) ).

thf(2247,plain,
    ! [A: nat,B: nat] :
      ( ( A = B )
     => ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).

thf(332,axiom,
    ~ ! [A: nat] :
        ( ( top_to788185952i_bool @ ( finite1672073426e_indi @ hAPP_f846027769ol_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [B: nat] :
              ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( lba @ ( lab @ ( B @ ( h @ ( ord_less_nat @ cOMBB_1869811296e_indi @ hAPP_f966656047t_bool ) @ ( cOMBC_722552198t_bool @ hAPP_f721434149i_bool ) @ hAPP_n34002993i_bool ) @ ( if_fun523439385t_bool @ cOMBB_1061985500e_indi @ hAPP_f668886383t_bool ) @ ( cOMBC_156709173t_bool @ hAPP_f1908974253t_bool ) @ hAPP_f1344464862t_bool ) @ ( cOMBC_750853729t_bool @ hAPP_f601594885t_bool ) @ hAPP_f480276746t_bool ) @ ( f @ hAPP_f2008608496t_bool ) @ ( a @ ( b @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
         => ~ ( lba @ ( lab @ ( one_one_nat @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( h @ ( ord_less_nat @ cOMBB_1869811296e_indi @ hAPP_f966656047t_bool ) @ ( cOMBC_722552198t_bool @ hAPP_f721434149i_bool ) @ hAPP_n34002993i_bool ) @ ( if_fun523439385t_bool @ cOMBB_1061985500e_indi @ hAPP_f668886383t_bool ) @ ( cOMBC_156709173t_bool @ hAPP_f1908974253t_bool ) @ hAPP_f1344464862t_bool ) @ ( cOMBC_750853729t_bool @ hAPP_f601594885t_bool ) @ hAPP_f480276746t_bool ) @ ( f @ hAPP_f2008608496t_bool ) @ ( b @ ( a @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237__096_B_Bthesis_O_A_I_B_Bn_O_A_091_124_An_A_060_AN_059_AALL_Am_060_061n_) ).

thf(1934,plain,
    ~ ! [A: nat] :
        ( ( top_to788185952i_bool @ ( finite1672073426e_indi @ hAPP_f846027769ol_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [B: nat] :
              ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( lba @ ( lab @ ( B @ ( h @ ( ord_less_nat @ cOMBB_1869811296e_indi @ hAPP_f966656047t_bool ) @ ( cOMBC_722552198t_bool @ hAPP_f721434149i_bool ) @ hAPP_n34002993i_bool ) @ ( if_fun523439385t_bool @ cOMBB_1061985500e_indi @ hAPP_f668886383t_bool ) @ ( cOMBC_156709173t_bool @ hAPP_f1908974253t_bool ) @ hAPP_f1344464862t_bool ) @ ( cOMBC_750853729t_bool @ hAPP_f601594885t_bool ) @ hAPP_f480276746t_bool ) @ ( f @ hAPP_f2008608496t_bool ) @ ( a @ ( b @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
         => ~ ( lba @ ( lab @ ( one_one_nat @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( h @ ( ord_less_nat @ cOMBB_1869811296e_indi @ hAPP_f966656047t_bool ) @ ( cOMBC_722552198t_bool @ hAPP_f721434149i_bool ) @ hAPP_n34002993i_bool ) @ ( if_fun523439385t_bool @ cOMBB_1061985500e_indi @ hAPP_f668886383t_bool ) @ ( cOMBC_156709173t_bool @ hAPP_f1908974253t_bool ) @ hAPP_f1344464862t_bool ) @ ( cOMBC_750853729t_bool @ hAPP_f601594885t_bool ) @ hAPP_f480276746t_bool ) @ ( f @ hAPP_f2008608496t_bool ) @ ( b @ ( a @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(235,axiom,
    ! [A: nat] :
      ~ ( zero_zero_nat @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1042_less__zeroE) ).

thf(1543,plain,
    ! [A: nat] :
      ~ ( zero_zero_nat @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(29,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) )
      = ( A @ ( B @ times_times_nat @ hAPP_nat_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1174_nat__mult__commute) ).

thf(703,plain,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) )
      = ( A @ ( B @ times_times_nat @ hAPP_nat_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(283,axiom,
    ! [A: nat] : ( arrow_5070731e_Prof @ ( lba @ ( lab @ ( A @ ( h @ ( ord_less_nat @ cOMBB_1869811296e_indi @ hAPP_f966656047t_bool ) @ ( cOMBC_722552198t_bool @ hAPP_f721434149i_bool ) @ hAPP_n34002993i_bool ) @ ( if_fun523439385t_bool @ cOMBB_1061985500e_indi @ hAPP_f668886383t_bool ) @ ( cOMBC_156709173t_bool @ hAPP_f1908974253t_bool ) @ hAPP_f1344464862t_bool ) @ ( cOMBC_750853729t_bool @ hAPP_f601594885t_bool ) @ hAPP_f480276746t_bool ) @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_PiProf) ).

thf(1702,plain,
    ! [A: nat] : ( arrow_5070731e_Prof @ ( lba @ ( lab @ ( A @ ( h @ ( ord_less_nat @ cOMBB_1869811296e_indi @ hAPP_f966656047t_bool ) @ ( cOMBC_722552198t_bool @ hAPP_f721434149i_bool ) @ hAPP_n34002993i_bool ) @ ( if_fun523439385t_bool @ cOMBB_1061985500e_indi @ hAPP_f668886383t_bool ) @ ( cOMBC_156709173t_bool @ hAPP_f1908974253t_bool ) @ hAPP_f1344464862t_bool ) @ ( cOMBC_750853729t_bool @ hAPP_f601594885t_bool ) @ hAPP_f480276746t_bool ) @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(225,axiom,
    ! [A: fun_fu638310559l_bool,B: arrow_856714788e_indi] :
      ( ( B @ ( A @ ( cOMBK_1520063231e_indi @ hAPP_f1717907078l_bool ) @ hAPP_A897398598l_bool ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_409) ).

thf(1506,plain,
    ! [A: fun_fu638310559l_bool,B: arrow_856714788e_indi] :
      ( ( B @ ( A @ ( cOMBK_1520063231e_indi @ hAPP_f1717907078l_bool ) @ hAPP_A897398598l_bool ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(224,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1022_add__leD1) ).

thf(1504,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(462,axiom,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
      ( ( A = B )
     => ( B @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_order__eq__refl) ).

thf(2426,plain,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
      ( ( A = B )
     => ( B @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).

thf(232,axiom,
    lba @ ( lab @ ( one_one_nat @ ( n @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( h @ ( ord_less_nat @ cOMBB_1869811296e_indi @ hAPP_f966656047t_bool ) @ ( cOMBC_722552198t_bool @ hAPP_f721434149i_bool ) @ hAPP_n34002993i_bool ) @ ( if_fun523439385t_bool @ cOMBB_1061985500e_indi @ hAPP_f668886383t_bool ) @ ( cOMBC_156709173t_bool @ hAPP_f1908974253t_bool ) @ hAPP_f1344464862t_bool ) @ ( cOMBC_750853729t_bool @ hAPP_f601594885t_bool ) @ hAPP_f480276746t_bool ) @ ( f @ hAPP_f2008608496t_bool ) @ ( b @ ( a @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_n_I3_J) ).

thf(1536,plain,
    lba @ ( lab @ ( one_one_nat @ ( n @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( h @ ( ord_less_nat @ cOMBB_1869811296e_indi @ hAPP_f966656047t_bool ) @ ( cOMBC_722552198t_bool @ hAPP_f721434149i_bool ) @ hAPP_n34002993i_bool ) @ ( if_fun523439385t_bool @ cOMBB_1061985500e_indi @ hAPP_f668886383t_bool ) @ ( cOMBC_156709173t_bool @ hAPP_f1908974253t_bool ) @ hAPP_f1344464862t_bool ) @ ( cOMBC_750853729t_bool @ hAPP_f601594885t_bool ) @ hAPP_f480276746t_bool ) @ ( f @ hAPP_f2008608496t_bool ) @ ( b @ ( a @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(445,axiom,
    ! [A: nat,B: nat] :
      ( ~ ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_408_not__leE) ).

thf(2357,plain,
    ! [A: nat,B: nat] :
      ( ~ ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).

thf(339,axiom,
    ! [A: fun_Ar274636406t_bool,B: fun_fu2114379172t_bool,C: fun_fu3835832l_bool,D: fun_fu638310559l_bool] :
      ( ( D @ ( cOMBK_1701906001t_bool @ hAPP_f1104294872l_bool ) @ ( C @ pi_fun1746584570t_bool ) @ ( B @ ( member173038353t_bool @ hAPP_f1714503811l_bool ) @ hAPP_f975209902l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL )
       => ( D @ ( A @ ( B @ hAPP_f2008608496t_bool ) @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_610_funcset__mem) ).

thf(1955,plain,
    ! [A: fun_Ar274636406t_bool,B: fun_fu2114379172t_bool,C: fun_fu3835832l_bool,D: fun_fu638310559l_bool] :
      ( ( D @ ( cOMBK_1701906001t_bool @ hAPP_f1104294872l_bool ) @ ( C @ pi_fun1746584570t_bool ) @ ( B @ ( member173038353t_bool @ hAPP_f1714503811l_bool ) @ hAPP_f975209902l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL )
       => ( D @ ( A @ ( B @ hAPP_f2008608496t_bool ) @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(247,axiom,
    ! [A: fun_Ar331856045t_bool] :
      ( ( A @ ( top_to951839027t_bool @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
     => ( A = top_to951839027t_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_535_top__le) ).

thf(1585,plain,
    ! [A: fun_Ar331856045t_bool] :
      ( ( A @ ( top_to951839027t_bool @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
     => ( A = top_to951839027t_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(476,axiom,
    e @ ( p @ ( arrow_1481558583_mkbot @ cOMBB_80760910e_indi @ hAPP_f831214557t_bool ) @ ( cOMBC_1417338747t_bool @ hAPP_f1631649925t_bool ) @ hAPP_A425126512t_bool ) @ ( e @ ( c @ ( p @ ( arrow_216713899_above @ cOMBB_1876517692e_indi @ hAPP_f1751344075t_bool ) @ ( cOMBC_1486904681t_bool @ hAPP_f2102110817t_bool ) @ hAPP_A1889513822t_bool ) @ ( cOMBC_1417338747t_bool @ hAPP_f1631649925t_bool ) @ hAPP_A425126512t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_1869811296e_indi @ hAPP_f966656047t_bool ) @ ( cOMBC_722552198t_bool @ hAPP_f721434149i_bool ) @ hAPP_n34002993i_bool ) @ ( if_fun523439385t_bool @ cOMBB_1061985500e_indi @ hAPP_f668886383t_bool ) @ cOMBS_1925466437t_bool @ hAPP_f1001205955t_bool ) @ cOMBS_1181656689t_bool @ hAPP_f1302887663t_bool ) @ ( e @ ( p @ ( arrow_1630265669_mktop @ cOMBB_80760910e_indi @ hAPP_f831214557t_bool ) @ ( cOMBC_1417338747t_bool @ hAPP_f1631649925t_bool ) @ hAPP_A425126512t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_1869811296e_indi @ hAPP_f966656047t_bool ) @ ( cOMBC_722552198t_bool @ hAPP_f721434149i_bool ) @ hAPP_n34002993i_bool ) @ ( if_fun523439385t_bool @ cOMBB_1061985500e_indi @ hAPP_f668886383t_bool ) @ cOMBS_1925466437t_bool @ hAPP_f1001205955t_bool ) @ cOMBS_1181656689t_bool @ hAPP_f1302887663t_bool ) @ ( f @ hAPP_f2008608496t_bool ) @ ( d @ ( c @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto) ).

thf(2511,plain,
    e @ ( p @ ( arrow_1481558583_mkbot @ cOMBB_80760910e_indi @ hAPP_f831214557t_bool ) @ ( cOMBC_1417338747t_bool @ hAPP_f1631649925t_bool ) @ hAPP_A425126512t_bool ) @ ( e @ ( c @ ( p @ ( arrow_216713899_above @ cOMBB_1876517692e_indi @ hAPP_f1751344075t_bool ) @ ( cOMBC_1486904681t_bool @ hAPP_f2102110817t_bool ) @ hAPP_A1889513822t_bool ) @ ( cOMBC_1417338747t_bool @ hAPP_f1631649925t_bool ) @ hAPP_A425126512t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_1869811296e_indi @ hAPP_f966656047t_bool ) @ ( cOMBC_722552198t_bool @ hAPP_f721434149i_bool ) @ hAPP_n34002993i_bool ) @ ( if_fun523439385t_bool @ cOMBB_1061985500e_indi @ hAPP_f668886383t_bool ) @ cOMBS_1925466437t_bool @ hAPP_f1001205955t_bool ) @ cOMBS_1181656689t_bool @ hAPP_f1302887663t_bool ) @ ( e @ ( p @ ( arrow_1630265669_mktop @ cOMBB_80760910e_indi @ hAPP_f831214557t_bool ) @ ( cOMBC_1417338747t_bool @ hAPP_f1631649925t_bool ) @ hAPP_A425126512t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_1869811296e_indi @ hAPP_f966656047t_bool ) @ ( cOMBC_722552198t_bool @ hAPP_f721434149i_bool ) @ hAPP_n34002993i_bool ) @ ( if_fun523439385t_bool @ cOMBB_1061985500e_indi @ hAPP_f668886383t_bool ) @ cOMBS_1925466437t_bool @ hAPP_f1001205955t_bool ) @ cOMBS_1181656689t_bool @ hAPP_f1302887663t_bool ) @ ( f @ hAPP_f2008608496t_bool ) @ ( d @ ( c @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).

thf(333,axiom,
    ! [A: fun_Pr2067565481t_bool,B: arrow_1893660431le_alt,C: arrow_1893660431le_alt] :
      ( ( B != C )
     => ( ( arrow_1361987423le_Lin @ ( A @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
       => ( arrow_1361987423le_Lin @ ( C @ ( B @ ( A @ arrow_1525312447_below ) ) @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_578_below__Lin) ).

thf(1940,plain,
    ! [A: fun_Pr2067565481t_bool,B: arrow_1893660431le_alt,C: arrow_1893660431le_alt] :
      ( ( B != C )
     => ( ( arrow_1361987423le_Lin @ ( A @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
       => ( arrow_1361987423le_Lin @ ( C @ ( B @ ( A @ arrow_1525312447_below ) ) @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(64,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( A @ ( suc @ hAPP_nat_nat ) @ times_times_nat @ hAPP_nat_nat ) @ ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1163_Suc__mult__less__cancel1) ).

thf(845,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( C @ ( A @ ( suc @ hAPP_nat_nat ) @ times_times_nat @ hAPP_nat_nat ) @ ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( C @ ( A @ ( suc @ hAPP_nat_nat ) @ times_times_nat @ hAPP_nat_nat ) @ ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(118,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1106_Suc__leI) ).

thf(1084,plain,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(468,axiom,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
      ( ( B @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( ( A @ ( B @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
      <=> ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_order__antisym__conv) ).

thf(2479,plain,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
      ( ( B @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( ( ( B = A )
         => ( A @ ( B @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
        & ( ( A @ ( B @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
         => ( B = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).

thf(211,axiom,
    ! [A: fun_fu638310559l_bool,B: fun_Pr2067565481t_bool,C: fun_fu638310559l_bool] :
      ( ( C @ ( B @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
       => ( A @ ( B @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_961_set__rev__mp) ).

thf(1459,plain,
    ! [A: fun_fu638310559l_bool,B: fun_Pr2067565481t_bool,C: fun_fu638310559l_bool] :
      ( ( C @ ( B @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
       => ( A @ ( B @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(542,axiom,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
      ( ( B = C )
     => ( ( A @ ( C @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_ord__eq__le__trans) ).

thf(2818,plain,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
      ( ( B = C )
     => ( ( A @ ( C @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).

thf(545,axiom,
    ! [A: product_unit] : ( A @ ( top_to1257323279t_bool @ hAPP_P1676879539t_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_top1I) ).

thf(2828,plain,
    ! [A: product_unit] : ( A @ ( top_to1257323279t_bool @ hAPP_P1676879539t_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).

thf(3,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ times_times_nat @ hAPP_nat_nat ) )
        = ( C @ ( A @ ( suc @ hAPP_nat_nat ) @ times_times_nat @ hAPP_nat_nat ) ) )
    <=> ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1151_Suc__mult__cancel1) ).

thf(581,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( B = C )
       => ( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ times_times_nat @ hAPP_nat_nat ) )
          = ( C @ ( A @ ( suc @ hAPP_nat_nat ) @ times_times_nat @ hAPP_nat_nat ) ) ) )
      & ( ( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ times_times_nat @ hAPP_nat_nat ) )
          = ( C @ ( A @ ( suc @ hAPP_nat_nat ) @ times_times_nat @ hAPP_nat_nat ) ) )
       => ( B = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(199,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( B @ ( C @ times_times_nat @ hAPP_nat_nat ) @ ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1172_mult__le__cancel2) ).

thf(1412,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
       => ( B @ ( C @ times_times_nat @ hAPP_nat_nat ) @ ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( B @ ( C @ times_times_nat @ hAPP_nat_nat ) @ ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(42,axiom,
    ! [A: nat] :
      ( ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ? [B: nat] :
          ( A
          = ( B @ ( suc @ hAPP_nat_nat ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1117_gr0__implies__Suc) ).

thf(759,plain,
    ! [A: nat] :
      ( ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ? [B: nat] :
          ( A
          = ( B @ ( suc @ hAPP_nat_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(414,axiom,
    ! [A: fun_Ar274636406t_bool,B: fun_fu2114379172t_bool,C: fun_fu3835832l_bool,D: fun_fu1863781882l_bool] :
      ( ( D @ ( C @ pi_fun1746584570t_bool ) @ ( B @ ( member173038353t_bool @ hAPP_f1714503811l_bool ) @ hAPP_f975209902l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL )
       => ( A @ ( D @ hAPP_f1915815064l_bool ) @ ( A @ ( B @ hAPP_f2008608496t_bool ) @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_576_Pi__mem) ).

thf(2226,plain,
    ! [A: fun_Ar274636406t_bool,B: fun_fu2114379172t_bool,C: fun_fu3835832l_bool,D: fun_fu1863781882l_bool] :
      ( ( D @ ( C @ pi_fun1746584570t_bool ) @ ( B @ ( member173038353t_bool @ hAPP_f1714503811l_bool ) @ hAPP_f975209902l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL )
       => ( A @ ( D @ hAPP_f1915815064l_bool ) @ ( A @ ( B @ hAPP_f2008608496t_bool ) @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).

thf(526,axiom,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
      ( ( B @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( ( A @ ( B @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_xt1_I5_J) ).

thf(2775,plain,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
      ( ( B @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( ( A @ ( B @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).

thf(352,axiom,
    ! [A: bool,B: produc472769767le_alt] :
      ( ( B @ ( A @ ( cOMBK_198697344le_alt @ hAPP_b128655177t_bool ) @ hAPP_P1178790471t_bool ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__prod_Itc__Arrow____Order____Mirabe) ).

thf(1998,plain,
    ! [A: bool,B: produc472769767le_alt] :
      ( ( B @ ( A @ ( cOMBK_198697344le_alt @ hAPP_b128655177t_bool ) @ hAPP_P1178790471t_bool ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(81,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1086_Suc__leD) ).

thf(931,plain,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(280,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
      <=> ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_order__antisym__conv) ).

thf(1685,plain,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( ( B = A )
         => ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
        & ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( B = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(101,axiom,
    ! [A: fun_fu638310559l_bool] : ( A @ ( A @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_order__refl) ).

thf(1010,plain,
    ! [A: fun_fu638310559l_bool] : ( A @ ( A @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(434,axiom,
    ! [A: arrow_856714788e_indi,B: arrow_856714788e_indi,C: fun_Ar671024215di_nat,D: fun_Ar1809396326i_bool] :
      ( ( D @ ( C @ inj_on1960344199di_nat @ hAPP_f584385070l_bool ) @ hBOOL )
     => ( ( D @ ( B @ ( member1479139729e_indi @ hAPP_A1597696899l_bool ) @ hAPP_f584385070l_bool ) @ hBOOL )
       => ( ( D @ ( A @ ( member1479139729e_indi @ hAPP_A1597696899l_bool ) @ hAPP_f584385070l_bool ) @ hBOOL )
         => ( ( ( B @ ( C @ hAPP_A376526755di_nat ) )
              = ( A @ ( C @ hAPP_A376526755di_nat ) ) )
          <=> ( B = A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_543_inj__on__iff) ).

thf(2305,plain,
    ! [A: arrow_856714788e_indi,B: arrow_856714788e_indi,C: fun_Ar671024215di_nat,D: fun_Ar1809396326i_bool] :
      ( ( D @ ( C @ inj_on1960344199di_nat @ hAPP_f584385070l_bool ) @ hBOOL )
     => ( ( D @ ( B @ ( member1479139729e_indi @ hAPP_A1597696899l_bool ) @ hAPP_f584385070l_bool ) @ hBOOL )
       => ( ( D @ ( A @ ( member1479139729e_indi @ hAPP_A1597696899l_bool ) @ hAPP_f584385070l_bool ) @ hBOOL )
         => ( ( ( B = A )
             => ( ( B @ ( C @ hAPP_A376526755di_nat ) )
                = ( A @ ( C @ hAPP_A376526755di_nat ) ) ) )
            & ( ( ( B @ ( C @ hAPP_A376526755di_nat ) )
                = ( A @ ( C @ hAPP_A376526755di_nat ) ) )
             => ( B = A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).

thf(294,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
      <=> ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_441_linorder__antisym__conv2) ).

thf(1734,plain,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( ( A = B )
         => ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
        & ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(530,axiom,
    ! [A: arrow_856714788e_indi] : ( A @ ( top_to788185952i_bool @ hAPP_A997847300i_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_top1I) ).

thf(2792,plain,
    ! [A: arrow_856714788e_indi] : ( A @ ( top_to788185952i_bool @ hAPP_A997847300i_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).

thf(389,axiom,
    ! [A: fun_Ar274636406t_bool] : ( top_to553140914l_bool @ ( A @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_iso__tuple__UNIV__I) ).

thf(2135,plain,
    ! [A: fun_Ar274636406t_bool] : ( top_to553140914l_bool @ ( A @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(125,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( B @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_748_add__less__cancel__right) ).

thf(1101,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( B @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(386,axiom,
    arrow_1361987423le_Lin @ ( lab @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74__096Lab_A_058_ALin_096) ).

thf(2130,plain,
    arrow_1361987423le_Lin @ ( lab @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(47,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( suc @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
      <=> ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1107_le__less__Suc__eq) ).

thf(786,plain,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( ( B = A )
         => ( A @ ( suc @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
        & ( ( A @ ( suc @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( B = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(460,axiom,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
      ( ( B @ ( A @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
    <=> ( ~ ( A @ ( B @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
        & ( B @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_392_less__le__not__le) ).

thf(2416,plain,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
      ( ( ( ~ ( A @ ( B @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
          & ( B @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
       => ( B @ ( A @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( ~ ( A @ ( B @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
          & ( B @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).

thf(453,axiom,
    ! [A: fun_na300967376t_bool,B: fun_Ar331856045t_bool,C: nat,D: nat] :
      ( ( D @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( D @ ( A @ hAPP_n1312530466t_bool ) @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
       => ( ! [E: nat,F: nat] :
              ( ( F @ ( E @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( F @ ( A @ hAPP_n1312530466t_bool ) @ ( E @ ( A @ hAPP_n1312530466t_bool ) @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) )
         => ( B @ ( C @ ( A @ hAPP_n1312530466t_bool ) @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_900_order__less__le__subst2) ).

thf(2394,plain,
    ! [A: fun_na300967376t_bool,B: fun_Ar331856045t_bool,C: nat,D: nat] :
      ( ( D @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( D @ ( A @ hAPP_n1312530466t_bool ) @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
       => ( ! [E: nat,F: nat] :
              ( ( F @ ( E @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( F @ ( A @ hAPP_n1312530466t_bool ) @ ( E @ ( A @ hAPP_n1312530466t_bool ) @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) )
         => ( B @ ( C @ ( A @ hAPP_n1312530466t_bool ) @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).

thf(55,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( C @ times_times_nat @ hAPP_nat_nat ) @ ( A @ ( C @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
      <=> ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1177_nat__mult__less__cancel1) ).

thf(813,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( B @ ( C @ times_times_nat @ hAPP_nat_nat ) @ ( A @ ( C @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
        & ( ( B @ ( C @ times_times_nat @ hAPP_nat_nat ) @ ( A @ ( C @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(194,axiom,
    ! [A: nat,B: nat,C: fun_nat_nat] :
      ( ! [D: nat,E: nat] :
          ( ( E @ ( D @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( E @ ( C @ hAPP_nat_nat ) @ ( D @ ( C @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
     => ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( C @ hAPP_nat_nat ) @ ( A @ ( C @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1024_less__mono__imp__le__mono) ).

thf(1385,plain,
    ! [A: nat,B: nat,C: fun_nat_nat] :
      ( ! [D: nat,E: nat] :
          ( ( E @ ( D @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( E @ ( C @ hAPP_nat_nat ) @ ( D @ ( C @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
     => ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( C @ hAPP_nat_nat ) @ ( A @ ( C @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(554,axiom,
    ! [A: fun_Ar274636406t_bool,B: fun_Ar274636406t_bool,C: arrow_1893660431le_alt,D: arrow_1893660431le_alt,E: arrow_1893660431le_alt,F: arrow_1893660431le_alt] :
      ( ( E != F )
     => ( ( C != D )
       => ( ( E != D )
         => ( ( F != C )
           => ( ( arrow_5070731e_Prof @ ( B @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL )
             => ( ( arrow_5070731e_Prof @ ( A @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL )
               => ( ! [G: arrow_856714788e_indi] :
                      ( ( G @ ( B @ hAPP_A1646126530t_bool ) @ ( F @ ( E @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
                    <=> ( G @ ( A @ hAPP_A1646126530t_bool ) @ ( D @ ( C @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
                 => ( ( B @ ( f @ hAPP_f2008608496t_bool ) @ ( F @ ( E @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
                  <=> ( A @ ( f @ hAPP_f2008608496t_bool ) @ ( D @ ( C @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6__C2_C) ).

thf(2853,plain,
    ! [A: fun_Ar274636406t_bool,B: fun_Ar274636406t_bool,C: arrow_1893660431le_alt,D: arrow_1893660431le_alt,E: arrow_1893660431le_alt,F: arrow_1893660431le_alt] :
      ( ( E != F )
     => ( ( C != D )
       => ( ( E != D )
         => ( ( F != C )
           => ( ( arrow_5070731e_Prof @ ( B @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL )
             => ( ( arrow_5070731e_Prof @ ( A @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL )
               => ( ! [G: arrow_856714788e_indi] :
                      ( ( ( G @ ( A @ hAPP_A1646126530t_bool ) @ ( D @ ( C @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
                       => ( G @ ( B @ hAPP_A1646126530t_bool ) @ ( F @ ( E @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
                      & ( ( G @ ( B @ hAPP_A1646126530t_bool ) @ ( F @ ( E @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
                       => ( G @ ( A @ hAPP_A1646126530t_bool ) @ ( D @ ( C @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) )
                 => ( ( ( A @ ( f @ hAPP_f2008608496t_bool ) @ ( D @ ( C @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
                     => ( B @ ( f @ hAPP_f2008608496t_bool ) @ ( F @ ( E @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
                    & ( ( B @ ( f @ hAPP_f2008608496t_bool ) @ ( F @ ( E @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
                     => ( A @ ( f @ hAPP_f2008608496t_bool ) @ ( D @ ( C @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).

thf(430,axiom,
    ! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool] :
      ( ( B @ ( A @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
     => ( ( A != B )
       => ( B @ ( A @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_459_order__le__neq__trans) ).

thf(2290,plain,
    ! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool] :
      ( ( B @ ( A @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
     => ( ( A != B )
       => ( B @ ( A @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).

thf(421,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B != A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_order__less__imp__not__eq2) ).

thf(2251,plain,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).

thf(221,axiom,
    ! [A: nat,B: nat] : ( A @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1013_le__add2) ).

thf(1491,plain,
    ! [A: nat,B: nat] : ( A @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(532,axiom,
    ! [A: fun_Pr2067565481t_bool] :
      ( ( A @ ( top_to1138392227t_bool @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( A = top_to1138392227t_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_534_top__le) ).

thf(2796,plain,
    ! [A: fun_Pr2067565481t_bool] :
      ( ( A @ ( top_to1138392227t_bool @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( A = top_to1138392227t_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).

thf(21,axiom,
    ! [A: nat] : ( A @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1141_le__cube) ).

thf(667,plain,
    ! [A: nat] : ( A @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(80,axiom,
    ( one_one_nat
    = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1109_One__nat__def) ).

thf(929,plain,
    ( one_one_nat
    = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(513,axiom,
    ! [A: arrow_1893660431le_alt,B: arrow_1893660431le_alt,C: fun_Pr2067565481t_bool] :
      ( ( arrow_1361987423le_Lin @ ( C @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
     => ( ( C @ ( B @ ( A @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( B @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_Lin__irrefl) ).

thf(2739,plain,
    ! [A: arrow_1893660431le_alt,B: arrow_1893660431le_alt,C: fun_Pr2067565481t_bool] :
      ( ( arrow_1361987423le_Lin @ ( C @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
     => ( ( C @ ( B @ ( A @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( B @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).

thf(495,axiom,
    ! [A: fun_bo1682907689le_alt,B: fun_bo1431306493t_bool,C: fun_bool_bool] :
      ( ! [D: bool] :
          ( ( C @ ( D @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
         => ( D @ ( B @ hAPP_b128655177t_bool ) @ ( D @ ( A @ hAPP_b2094455111le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
     => ( B @ ( C @ pi_boo7125949le_alt ) @ ( A @ ( member684813948le_alt @ hAPP_f334747853l_bool ) @ hAPP_f1620711039l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_635_Pi__I) ).

thf(2680,plain,
    ! [A: fun_bo1682907689le_alt,B: fun_bo1431306493t_bool,C: fun_bool_bool] :
      ( ! [D: bool] :
          ( ( C @ ( D @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
         => ( D @ ( B @ hAPP_b128655177t_bool ) @ ( D @ ( A @ hAPP_b2094455111le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
     => ( B @ ( C @ pi_boo7125949le_alt ) @ ( A @ ( member684813948le_alt @ hAPP_f334747853l_bool ) @ hAPP_f1620711039l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).

thf(149,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1073_Suc__lessD) ).

thf(1212,plain,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(416,axiom,
    ! [A: fun_fu638310559l_bool,B: fun_Ar274636406t_bool] :
      ( ( B @ ( A @ ( cOMBK_1701906001t_bool @ hAPP_f1104294872l_bool ) @ hAPP_f1915815064l_bool ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_419) ).

thf(2230,plain,
    ! [A: fun_fu638310559l_bool,B: fun_Ar274636406t_bool] :
      ( ( B @ ( A @ ( cOMBK_1701906001t_bool @ hAPP_f1104294872l_bool ) @ hAPP_f1915815064l_bool ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).

thf(171,axiom,
    ! [A: nat] :
      ( zero_zero_nat
     != ( A @ ( suc @ hAPP_nat_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1071_Zero__not__Suc) ).

thf(1309,plain,
    ! [A: nat] :
      ( zero_zero_nat
     != ( A @ ( suc @ hAPP_nat_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(256,axiom,
    ! [A: bool] : ( top_to1647826457l_bool @ ( A @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_iso__tuple__UNIV__I) ).

thf(1614,plain,
    ! [A: bool] : ( top_to1647826457l_bool @ ( A @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(50,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
      = ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1085_add__Suc__right) ).

thf(800,plain,
    ! [A: nat,B: nat] :
      ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
      = ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(411,axiom,
    ! [A: nat,B: fun_na998785244t_bool,C: nat,D: fun_Pr2067565481t_bool] :
      ( ( D @ ( C @ ( B @ hAPP_n1161265524t_bool ) @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [E: nat,F: nat] :
              ( ( E @ ( F @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( E @ ( B @ hAPP_n1161265524t_bool ) @ ( F @ ( B @ hAPP_n1161265524t_bool ) @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
         => ( D @ ( A @ ( B @ hAPP_n1161265524t_bool ) @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_766_xt6) ).

thf(2218,plain,
    ! [A: nat,B: fun_na998785244t_bool,C: nat,D: fun_Pr2067565481t_bool] :
      ( ( D @ ( C @ ( B @ hAPP_n1161265524t_bool ) @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [E: nat,F: nat] :
              ( ( E @ ( F @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( E @ ( B @ hAPP_n1161265524t_bool ) @ ( F @ ( B @ hAPP_n1161265524t_bool ) @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
         => ( D @ ( A @ ( B @ hAPP_n1161265524t_bool ) @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(181,axiom,
    ! [A: nat,B: nat] : ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1099_less__add__Suc1) ).

thf(1348,plain,
    ! [A: nat,B: nat] : ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(340,axiom,
    ! [A: nat,B: fun_Pr2067565481t_bool,C: fun_na998785244t_bool,D: nat] :
      ( ( D @ ( C @ hAPP_n1161265524t_bool ) @ ( B @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( ( A @ ( D @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [E: nat,F: nat] :
              ( ( F @ ( E @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( F @ ( C @ hAPP_n1161265524t_bool ) @ ( E @ ( C @ hAPP_n1161265524t_bool ) @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
         => ( A @ ( C @ hAPP_n1161265524t_bool ) @ ( B @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_827_order__less__le__subst1) ).

thf(1957,plain,
    ! [A: nat,B: fun_Pr2067565481t_bool,C: fun_na998785244t_bool,D: nat] :
      ( ( D @ ( C @ hAPP_n1161265524t_bool ) @ ( B @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( ( A @ ( D @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [E: nat,F: nat] :
              ( ( F @ ( E @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( F @ ( C @ hAPP_n1161265524t_bool ) @ ( E @ ( C @ hAPP_n1161265524t_bool ) @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
         => ( A @ ( C @ hAPP_n1161265524t_bool ) @ ( B @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(279,axiom,
    ! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool] :
      ( ( B @ ( A @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
    <=> ( ~ ( A @ ( B @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
        & ( B @ ( A @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_394_less__le__not__le) ).

thf(1678,plain,
    ! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool] :
      ( ( ( ~ ( A @ ( B @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
          & ( B @ ( A @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) )
       => ( B @ ( A @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
       => ( ~ ( A @ ( B @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
          & ( B @ ( A @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(90,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1080_Suc__less__eq) ).

thf(967,plain,
    ! [A: nat,B: nat] :
      ( ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(124,axiom,
    ! [A: nat] :
      ( ( A @ ( suc @ hAPP_nat_nat ) )
     != zero_zero_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1069_Suc__not__Zero) ).

thf(1097,plain,
    ! [A: nat] :
      ( ( A @ ( suc @ hAPP_nat_nat ) )
     != zero_zero_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(417,axiom,
    ! [A: fun_fu2114379172t_bool,B: arrow_856714788e_indi] :
      ( ( B @ ( A @ ( arrow_1765888670ctator @ hAPP_f399308031i_bool ) @ hAPP_A997847300i_bool ) @ hBOOL )
    <=> ! [C: fun_Ar274636406t_bool] :
          ( ( arrow_5070731e_Prof @ ( C @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL )
         => ( ( C @ ( A @ hAPP_f2008608496t_bool ) )
            = ( B @ ( C @ hAPP_A1646126530t_bool ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_dictator__def) ).

thf(2233,plain,
    ! [A: fun_fu2114379172t_bool,B: arrow_856714788e_indi] :
      ( ( ! [C: fun_Ar274636406t_bool] :
            ( ( arrow_5070731e_Prof @ ( C @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL )
           => ( ( C @ ( A @ hAPP_f2008608496t_bool ) )
              = ( B @ ( C @ hAPP_A1646126530t_bool ) ) ) )
       => ( B @ ( A @ ( arrow_1765888670ctator @ hAPP_f399308031i_bool ) @ hAPP_A997847300i_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( arrow_1765888670ctator @ hAPP_f399308031i_bool ) @ hAPP_A997847300i_bool ) @ hBOOL )
       => ! [C: fun_Ar274636406t_bool] :
            ( ( arrow_5070731e_Prof @ ( C @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL )
           => ( ( C @ ( A @ hAPP_f2008608496t_bool ) )
              = ( B @ ( C @ hAPP_A1646126530t_bool ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

thf(236,axiom,
    ! [A: fun_Pr2067565481t_bool,B: fun_na998785244t_bool,C: nat,D: nat] :
      ( ( D @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( C @ ( B @ hAPP_n1161265524t_bool ) @ ( A @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( ! [E: nat,F: nat] :
              ( ( E @ ( F @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( E @ ( B @ hAPP_n1161265524t_bool ) @ ( F @ ( B @ hAPP_n1161265524t_bool ) @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
         => ( D @ ( B @ hAPP_n1161265524t_bool ) @ ( A @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_679_xt7) ).

thf(1546,plain,
    ! [A: fun_Pr2067565481t_bool,B: fun_na998785244t_bool,C: nat,D: nat] :
      ( ( D @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( C @ ( B @ hAPP_n1161265524t_bool ) @ ( A @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( ! [E: nat,F: nat] :
              ( ( E @ ( F @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( E @ ( B @ hAPP_n1161265524t_bool ) @ ( F @ ( B @ hAPP_n1161265524t_bool ) @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
         => ( D @ ( B @ hAPP_n1161265524t_bool ) @ ( A @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(261,axiom,
    ! [A: fun_Ar274636406t_bool,B: fun_fu2114379172t_bool,C: fun_fu3835832l_bool,D: fun_fu1863781882l_bool] :
      ( ( D @ ( C @ pi_fun1746584570t_bool ) @ ( B @ ( member173038353t_bool @ hAPP_f1714503811l_bool ) @ hAPP_f975209902l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_f1915815064l_bool ) @ ( A @ ( B @ hAPP_f2008608496t_bool ) @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_PiE) ).

thf(1625,plain,
    ! [A: fun_Ar274636406t_bool,B: fun_fu2114379172t_bool,C: fun_fu3835832l_bool,D: fun_fu1863781882l_bool] :
      ( ( D @ ( C @ pi_fun1746584570t_bool ) @ ( B @ ( member173038353t_bool @ hAPP_f1714503811l_bool ) @ hAPP_f975209902l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_f1915815064l_bool ) @ ( A @ ( B @ hAPP_f2008608496t_bool ) @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(478,axiom,
    ! [A: fun_Ar274636406t_bool,B: fun_Ar274636406t_bool,C: arrow_1893660431le_alt,D: arrow_1893660431le_alt,E: arrow_1893660431le_alt,F: arrow_1893660431le_alt] :
      ( ( E != F )
     => ( ( C != D )
       => ( ( arrow_5070731e_Prof @ ( B @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL )
         => ( ( arrow_5070731e_Prof @ ( A @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL )
           => ( ! [G: arrow_856714788e_indi] :
                  ( ( G @ ( B @ hAPP_A1646126530t_bool ) @ ( F @ ( E @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
                <=> ( G @ ( A @ hAPP_A1646126530t_bool ) @ ( D @ ( C @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
             => ( ( B @ ( f @ hAPP_f2008608496t_bool ) @ ( F @ ( E @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
              <=> ( A @ ( f @ hAPP_f2008608496t_bool ) @ ( D @ ( C @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_pairwise__neutrality) ).

thf(2522,plain,
    ! [A: fun_Ar274636406t_bool,B: fun_Ar274636406t_bool,C: arrow_1893660431le_alt,D: arrow_1893660431le_alt,E: arrow_1893660431le_alt,F: arrow_1893660431le_alt] :
      ( ( E != F )
     => ( ( C != D )
       => ( ( arrow_5070731e_Prof @ ( B @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL )
         => ( ( arrow_5070731e_Prof @ ( A @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL )
           => ( ! [G: arrow_856714788e_indi] :
                  ( ( ( G @ ( A @ hAPP_A1646126530t_bool ) @ ( D @ ( C @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
                   => ( G @ ( B @ hAPP_A1646126530t_bool ) @ ( F @ ( E @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
                  & ( ( G @ ( B @ hAPP_A1646126530t_bool ) @ ( F @ ( E @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
                   => ( G @ ( A @ hAPP_A1646126530t_bool ) @ ( D @ ( C @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) )
             => ( ( ( A @ ( f @ hAPP_f2008608496t_bool ) @ ( D @ ( C @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
                 => ( B @ ( f @ hAPP_f2008608496t_bool ) @ ( F @ ( E @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
                & ( ( B @ ( f @ hAPP_f2008608496t_bool ) @ ( F @ ( E @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
                 => ( A @ ( f @ hAPP_f2008608496t_bool ) @ ( D @ ( C @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).

thf(169,axiom,
    ! [A: nat] :
      ( ( A @ ( zero_zero_nat @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1049_plus__nat_Oadd__0) ).

thf(1303,plain,
    ! [A: nat] :
      ( ( A @ ( zero_zero_nat @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(277,axiom,
    ! [A: fun_fu2114379172t_bool,B: fun_fu1863781882l_bool,C: fun_fu3835832l_bool] :
      ( ! [D: fun_Ar274636406t_bool] :
          ( ( C @ ( D @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL )
         => ( D @ ( B @ hAPP_f1915815064l_bool ) @ ( D @ ( A @ hAPP_f2008608496t_bool ) @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) )
     => ( B @ ( C @ pi_fun1746584570t_bool ) @ ( A @ ( member173038353t_bool @ hAPP_f1714503811l_bool ) @ hAPP_f975209902l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_649_Pi__I) ).

thf(1673,plain,
    ! [A: fun_fu2114379172t_bool,B: fun_fu1863781882l_bool,C: fun_fu3835832l_bool] :
      ( ! [D: fun_Ar274636406t_bool] :
          ( ( C @ ( D @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL )
         => ( D @ ( B @ hAPP_f1915815064l_bool ) @ ( D @ ( A @ hAPP_f2008608496t_bool ) @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) )
     => ( B @ ( C @ pi_fun1746584570t_bool ) @ ( A @ ( member173038353t_bool @ hAPP_f1714503811l_bool ) @ hAPP_f975209902l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(365,axiom,
    ! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool] :
      ( ( B @ ( A @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
    <=> ( ~ ( A @ ( B @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
        & ( B @ ( A @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_713_less__fun__def) ).

thf(2050,plain,
    ! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool] :
      ( ( ( ~ ( A @ ( B @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
          & ( B @ ( A @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) )
       => ( B @ ( A @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
       => ( ~ ( A @ ( B @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
          & ( B @ ( A @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(217,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1021_add__leD2) ).

thf(1480,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(354,axiom,
    ! [A: nat] :
      ~ ( zero_zero_nat @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1046_less__nat__zero__code) ).

thf(2003,plain,
    ! [A: nat] :
      ~ ( zero_zero_nat @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(392,axiom,
    ! [A: nat,B: nat] :
      ( ~ ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_375_linorder__not__le) ).

thf(2142,plain,
    ! [A: nat,B: nat] :
      ( ( ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ~ ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ~ ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(129,axiom,
    ! [A: fun_bool_bool,B: produc472769767le_alt] :
      ( ( B @ ( A @ ( cOMBK_138598520le_alt @ hAPP_f699791347l_bool ) @ hAPP_P1103642805l_bool ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__prod_It) ).

thf(1116,plain,
    ! [A: fun_bool_bool,B: produc472769767le_alt] :
      ( ( B @ ( A @ ( cOMBK_138598520le_alt @ hAPP_f699791347l_bool ) @ hAPP_P1103642805l_bool ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(325,axiom,
    ! [A: nat,B: nat] :
      ( ( A != B )
     => ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_983_linorder__neqE__nat) ).

thf(1908,plain,
    ! [A: nat,B: nat] :
      ( ( A != B )
     => ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(395,axiom,
    ! [A: nat,B: nat] :
      ( ( A != B )
     => ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_linorder__neqE) ).

thf(2155,plain,
    ! [A: nat,B: nat] :
      ( ( A != B )
     => ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).

thf(422,axiom,
    top_to788185952i_bool @ ( finite1672073426e_indi @ hAPP_f846027769ol_nat ) @ ( n @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_n_I1_J) ).

thf(2255,plain,
    top_to788185952i_bool @ ( finite1672073426e_indi @ hAPP_f846027769ol_nat ) @ ( n @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).

thf(78,axiom,
    ! [A: nat] :
      ( ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ? [B: nat] :
          ( A
          = ( B @ ( suc @ hAPP_nat_nat ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1094_gr0__conv__Suc) ).

thf(918,plain,
    ! [A: nat] :
      ( ( ? [B: nat] :
            ( A
            = ( B @ ( suc @ hAPP_nat_nat ) ) )
       => ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ? [B: nat] :
            ( A
            = ( B @ ( suc @ hAPP_nat_nat ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(312,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( ( A = B )
        | ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1009_le__eq__less__or__eq) ).

thf(1816,plain,
    ! [A: nat,B: nat] :
      ( ( ( ( A = B )
          | ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
       => ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ( A = B )
          | ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(440,axiom,
    ( top_to1312956197l_bool
    = ( fTrue @ ( cOMBK_81143760t_bool @ hAPP_b1272691967l_bool ) @ ( collec2125531966t_bool @ hAPP_f1060563265l_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_UNIV__def) ).

thf(2334,plain,
    ( top_to1312956197l_bool
    = ( fTrue @ ( cOMBK_81143760t_bool @ hAPP_b1272691967l_bool ) @ ( collec2125531966t_bool @ hAPP_f1060563265l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).

thf(53,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( D @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( ( D @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
          = ( B @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
       => ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1006_less__add__eq__less) ).

thf(807,plain,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( D @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( ( D @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
          = ( B @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
       => ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(516,axiom,
    ! [A: fun_Pr2067565481t_bool,B: produc472769767le_alt,C: fun_Pr2067565481t_bool] :
      ( ( C @ ( B @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( A @ ( B @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_964_set__rev__mp) ).

thf(2746,plain,
    ! [A: fun_Pr2067565481t_bool,B: produc472769767le_alt,C: fun_Pr2067565481t_bool] :
      ( ( C @ ( B @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( A @ ( B @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).

thf(198,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_746_add__strict__right__mono) ).

thf(1410,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(449,axiom,
    ! [A: fun_Ar274636406t_bool,B: fun_fu3835832l_bool] :
      ( ( B @ ( A @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL )
    <=> ( A @ ( B @ hAPP_f995490902l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_mem__def) ).

thf(2366,plain,
    ! [A: fun_Ar274636406t_bool,B: fun_fu3835832l_bool] :
      ( ( ( A @ ( B @ hAPP_f995490902l_bool ) @ hBOOL )
       => ( B @ ( A @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL )
       => ( A @ ( B @ hAPP_f995490902l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).

thf(322,axiom,
    ! [A: fun_Ar64685412t_bool,B: arrow_1893660431le_alt,C: arrow_856714788e_indi] :
      ( ( C @ ( B @ ( A @ ( cOMBC_1417338747t_bool @ hAPP_f1631649925t_bool ) @ hAPP_A425126512t_bool ) @ hAPP_A1646126530t_bool ) )
      = ( B @ ( C @ ( A @ hAPP_A1309733808t_bool ) @ hAPP_A1601437999t_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000_411) ).

thf(1891,plain,
    ! [A: fun_Ar64685412t_bool,B: arrow_1893660431le_alt,C: arrow_856714788e_indi] :
      ( ( C @ ( B @ ( A @ ( cOMBC_1417338747t_bool @ hAPP_f1631649925t_bool ) @ hAPP_A425126512t_bool ) @ hAPP_A1646126530t_bool ) )
      = ( B @ ( C @ ( A @ hAPP_A1309733808t_bool ) @ hAPP_A1601437999t_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(485,axiom,
    ! [A: fun_Pr2067565481t_bool] :
      ( ( A @ ( top_to1312956197l_bool @ hAPP_f52567537l_bool ) @ hBOOL )
    <=> ( top_top_bool @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_top__apply) ).

thf(2619,plain,
    ! [A: fun_Pr2067565481t_bool] :
      ( ( ( top_top_bool @ hBOOL )
       => ( A @ ( top_to1312956197l_bool @ hAPP_f52567537l_bool ) @ hBOOL ) )
      & ( ( A @ ( top_to1312956197l_bool @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( top_top_bool @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).

thf(87,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( D @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( D @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_744_add__strict__mono) ).

thf(955,plain,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( D @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( D @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(255,axiom,
    ! [A: fun_Ar331856045t_bool,B: fun_na300967376t_bool,C: nat,D: nat] :
      ( ( D @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( C @ ( B @ hAPP_n1312530466t_bool ) @ ( A @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
       => ( ! [E: nat,F: nat] :
              ( ( E @ ( F @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( E @ ( B @ hAPP_n1312530466t_bool ) @ ( F @ ( B @ hAPP_n1312530466t_bool ) @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) )
         => ( D @ ( B @ hAPP_n1312530466t_bool ) @ ( A @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_669_xt5) ).

thf(1610,plain,
    ! [A: fun_Ar331856045t_bool,B: fun_na300967376t_bool,C: nat,D: nat] :
      ( ( D @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( C @ ( B @ hAPP_n1312530466t_bool ) @ ( A @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
       => ( ! [E: nat,F: nat] :
              ( ( E @ ( F @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( E @ ( B @ hAPP_n1312530466t_bool ) @ ( F @ ( B @ hAPP_n1312530466t_bool ) @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) )
         => ( D @ ( B @ hAPP_n1312530466t_bool ) @ ( A @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(72,axiom,
    ! [A: nat] : ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1043_le0) ).

thf(886,plain,
    ! [A: nat] : ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(308,axiom,
    ! [A: nat,B: nat] :
      ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( ( A = B )
        | ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_not__less__iff__gr__or__eq) ).

thf(1789,plain,
    ! [A: nat,B: nat] :
      ( ( ( ( A = B )
          | ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
       => ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ( A = B )
          | ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(20,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ times_times_nat @ hAPP_nat_nat ) )
      = ( C @ ( B @ times_times_nat @ hAPP_nat_nat ) @ ( A @ times_times_nat @ hAPP_nat_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1175_nat__mult__assoc) ).

thf(664,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ times_times_nat @ hAPP_nat_nat ) )
      = ( C @ ( B @ times_times_nat @ hAPP_nat_nat ) @ ( A @ times_times_nat @ hAPP_nat_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(165,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
      = ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1083_add__Suc__shift) ).

thf(1288,plain,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
      = ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(286,axiom,
    ! [A: fun_Ar274636406t_bool,B: fun_Ar1474557608l_bool,C: fun_Ar1809396326i_bool] :
      ( ! [D: arrow_856714788e_indi] :
          ( ( C @ ( D @ ( member1479139729e_indi @ hAPP_A1597696899l_bool ) @ hAPP_f584385070l_bool ) @ hBOOL )
         => ( D @ ( B @ hAPP_A897398598l_bool ) @ ( D @ ( A @ hAPP_A1646126530t_bool ) @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) )
     => ( B @ ( C @ pi_Arr959578316t_bool ) @ ( A @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_650_Pi__I) ).

thf(1710,plain,
    ! [A: fun_Ar274636406t_bool,B: fun_Ar1474557608l_bool,C: fun_Ar1809396326i_bool] :
      ( ! [D: arrow_856714788e_indi] :
          ( ( C @ ( D @ ( member1479139729e_indi @ hAPP_A1597696899l_bool ) @ hAPP_f584385070l_bool ) @ hBOOL )
         => ( D @ ( B @ hAPP_A897398598l_bool ) @ ( D @ ( A @ hAPP_A1646126530t_bool ) @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) )
     => ( B @ ( C @ pi_Arr959578316t_bool ) @ ( A @ ( member933336803t_bool @ hAPP_f1225332775l_bool ) @ hAPP_f73423488l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(463,axiom,
    ! [A: arrow_856714788e_indi] :
      ( ( ( ~ ( n @ ( A @ ( h @ hAPP_A376526755di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( ( ( ( A @ ( h @ hAPP_A376526755di_nat ) )
               != n )
             => ( e @ ( A @ ( p @ hAPP_A1646126530t_bool ) @ ( arrow_1481558583_mkbot @ hAPP_f1761571331t_bool ) @ hAPP_A1601437999t_bool ) @ ( d @ ( e @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
            & ( ( ( A @ ( h @ hAPP_A376526755di_nat ) )
                = n )
             => ( e @ ( c @ ( A @ ( p @ hAPP_A1646126530t_bool ) @ ( arrow_216713899_above @ hAPP_f1550387441t_bool ) @ hAPP_A1058422557t_bool ) @ hAPP_A1601437999t_bool ) @ ( d @ ( e @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ) )
        & ( ( n @ ( A @ ( h @ hAPP_A376526755di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( e @ ( A @ ( p @ hAPP_A1646126530t_bool ) @ ( arrow_1630265669_mktop @ hAPP_f1761571331t_bool ) @ hAPP_A1601437999t_bool ) @ ( d @ ( e @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) )
    <=> ( ( ~ ( n @ ( A @ ( h @ hAPP_A376526755di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( lba @ ( a @ ( b @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
        & ( ( n @ ( A @ ( h @ hAPP_A376526755di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( lab @ ( a @ ( b @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amk) ).

thf(2430,plain,
    ! [A: arrow_856714788e_indi] :
      ( ( ( ( ~ ( n @ ( A @ ( h @ hAPP_A376526755di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( lba @ ( a @ ( b @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
          & ( ( n @ ( A @ ( h @ hAPP_A376526755di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( lab @ ( a @ ( b @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) )
       => ( ( ~ ( n @ ( A @ ( h @ hAPP_A376526755di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( ( ( ( A @ ( h @ hAPP_A376526755di_nat ) )
                 != n )
               => ( e @ ( A @ ( p @ hAPP_A1646126530t_bool ) @ ( arrow_1481558583_mkbot @ hAPP_f1761571331t_bool ) @ hAPP_A1601437999t_bool ) @ ( d @ ( e @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
              & ( ( ( A @ ( h @ hAPP_A376526755di_nat ) )
                  = n )
               => ( e @ ( c @ ( A @ ( p @ hAPP_A1646126530t_bool ) @ ( arrow_216713899_above @ hAPP_f1550387441t_bool ) @ hAPP_A1058422557t_bool ) @ hAPP_A1601437999t_bool ) @ ( d @ ( e @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ) )
          & ( ( n @ ( A @ ( h @ hAPP_A376526755di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( e @ ( A @ ( p @ hAPP_A1646126530t_bool ) @ ( arrow_1630265669_mktop @ hAPP_f1761571331t_bool ) @ hAPP_A1601437999t_bool ) @ ( d @ ( e @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ) )
      & ( ( ( ~ ( n @ ( A @ ( h @ hAPP_A376526755di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( ( ( ( A @ ( h @ hAPP_A376526755di_nat ) )
                 != n )
               => ( e @ ( A @ ( p @ hAPP_A1646126530t_bool ) @ ( arrow_1481558583_mkbot @ hAPP_f1761571331t_bool ) @ hAPP_A1601437999t_bool ) @ ( d @ ( e @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
              & ( ( ( A @ ( h @ hAPP_A376526755di_nat ) )
                  = n )
               => ( e @ ( c @ ( A @ ( p @ hAPP_A1646126530t_bool ) @ ( arrow_216713899_above @ hAPP_f1550387441t_bool ) @ hAPP_A1058422557t_bool ) @ hAPP_A1601437999t_bool ) @ ( d @ ( e @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ) )
          & ( ( n @ ( A @ ( h @ hAPP_A376526755di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( e @ ( A @ ( p @ hAPP_A1646126530t_bool ) @ ( arrow_1630265669_mktop @ hAPP_f1761571331t_bool ) @ hAPP_A1601437999t_bool ) @ ( d @ ( e @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) )
       => ( ( ~ ( n @ ( A @ ( h @ hAPP_A376526755di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( lba @ ( a @ ( b @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
          & ( ( n @ ( A @ ( h @ hAPP_A376526755di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( lab @ ( a @ ( b @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).

thf(233,axiom,
    ! [A: nat,B: fun_fu1677555470ol_nat,C: fun_Ar331856045t_bool,D: fun_Ar331856045t_bool] :
      ( ( D @ ( C @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
     => ( ( C @ ( B @ hAPP_f1403773274ol_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [E: fun_Ar331856045t_bool,F: fun_Ar331856045t_bool] :
              ( ( E @ ( F @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
             => ( E @ ( B @ hAPP_f1403773274ol_nat ) @ ( F @ ( B @ hAPP_f1403773274ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
         => ( D @ ( B @ hAPP_f1403773274ol_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_706_xt7) ).

thf(1537,plain,
    ! [A: nat,B: fun_fu1677555470ol_nat,C: fun_Ar331856045t_bool,D: fun_Ar331856045t_bool] :
      ( ( D @ ( C @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
     => ( ( C @ ( B @ hAPP_f1403773274ol_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [E: fun_Ar331856045t_bool,F: fun_Ar331856045t_bool] :
              ( ( E @ ( F @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
             => ( E @ ( B @ hAPP_f1403773274ol_nat ) @ ( F @ ( B @ hAPP_f1403773274ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
         => ( D @ ( B @ hAPP_f1403773274ol_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(237,axiom,
    ! [A: nat,B: nat] :
      ( ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
      | ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_376_linorder__le__less__linear) ).

thf(1550,plain,
    ! [A: nat,B: nat] :
      ( ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
      | ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(223,axiom,
    ! [A: nat,B: fun_fu955147676ol_nat,C: fun_fu638310559l_bool,D: fun_fu638310559l_bool] :
      ( ( D @ ( C @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
     => ( ( C @ ( B @ hAPP_f1487854056ol_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [E: fun_fu638310559l_bool,F: fun_fu638310559l_bool] :
              ( ( E @ ( F @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
             => ( E @ ( B @ hAPP_f1487854056ol_nat ) @ ( F @ ( B @ hAPP_f1487854056ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
         => ( D @ ( B @ hAPP_f1487854056ol_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_699_xt7) ).

thf(1500,plain,
    ! [A: nat,B: fun_fu955147676ol_nat,C: fun_fu638310559l_bool,D: fun_fu638310559l_bool] :
      ( ( D @ ( C @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
     => ( ( C @ ( B @ hAPP_f1487854056ol_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [E: fun_fu638310559l_bool,F: fun_fu638310559l_bool] :
              ( ( E @ ( F @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
             => ( E @ ( B @ hAPP_f1487854056ol_nat ) @ ( F @ ( B @ hAPP_f1487854056ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
         => ( D @ ( B @ hAPP_f1487854056ol_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(555,axiom,
    ! [A: arrow_856714788e_indi,B: fun_Ar338949104le_alt,C: fun_Ar1809396326i_bool,D: fun_Pr2067565481t_bool] :
      ( ( D @ ( cOMBK_1650320063e_indi @ hAPP_f480276746t_bool ) @ ( C @ pi_Arr1460528004le_alt ) @ ( B @ ( member387840963le_alt @ hAPP_f766019597l_bool ) @ hAPP_f1754488902l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member1479139729e_indi @ hAPP_A1597696899l_bool ) @ hAPP_f584385070l_bool ) @ hBOOL )
       => ( D @ ( A @ ( B @ hAPP_A899858958le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_596_funcset__mem) ).

thf(2864,plain,
    ! [A: arrow_856714788e_indi,B: fun_Ar338949104le_alt,C: fun_Ar1809396326i_bool,D: fun_Pr2067565481t_bool] :
      ( ( D @ ( cOMBK_1650320063e_indi @ hAPP_f480276746t_bool ) @ ( C @ pi_Arr1460528004le_alt ) @ ( B @ ( member387840963le_alt @ hAPP_f766019597l_bool ) @ hAPP_f1754488902l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member1479139729e_indi @ hAPP_A1597696899l_bool ) @ hAPP_f584385070l_bool ) @ hBOOL )
       => ( D @ ( A @ ( B @ hAPP_A899858958le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).

thf(450,axiom,
    ! [A: fun_Ar671024215di_nat,B: fun_Ar1809396326i_bool] :
      ( ( B @ ( A @ inj_on1960344199di_nat @ hAPP_f584385070l_bool ) @ hBOOL )
    <=> ! [C: arrow_856714788e_indi] :
          ( ( B @ ( C @ ( member1479139729e_indi @ hAPP_A1597696899l_bool ) @ hAPP_f584385070l_bool ) @ hBOOL )
         => ! [D: arrow_856714788e_indi] :
              ( ( B @ ( D @ ( member1479139729e_indi @ hAPP_A1597696899l_bool ) @ hAPP_f584385070l_bool ) @ hBOOL )
             => ( ( ( C @ ( A @ hAPP_A376526755di_nat ) )
                  = ( D @ ( A @ hAPP_A376526755di_nat ) ) )
               => ( C = D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_539_inj__on__def) ).

thf(2372,plain,
    ! [A: fun_Ar671024215di_nat,B: fun_Ar1809396326i_bool] :
      ( ( ! [C: arrow_856714788e_indi] :
            ( ( B @ ( C @ ( member1479139729e_indi @ hAPP_A1597696899l_bool ) @ hAPP_f584385070l_bool ) @ hBOOL )
           => ! [D: arrow_856714788e_indi] :
                ( ( B @ ( D @ ( member1479139729e_indi @ hAPP_A1597696899l_bool ) @ hAPP_f584385070l_bool ) @ hBOOL )
               => ( ( ( C @ ( A @ hAPP_A376526755di_nat ) )
                    = ( D @ ( A @ hAPP_A376526755di_nat ) ) )
                 => ( C = D ) ) ) )
       => ( B @ ( A @ inj_on1960344199di_nat @ hAPP_f584385070l_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ inj_on1960344199di_nat @ hAPP_f584385070l_bool ) @ hBOOL )
       => ! [C: arrow_856714788e_indi] :
            ( ( B @ ( C @ ( member1479139729e_indi @ hAPP_A1597696899l_bool ) @ hAPP_f584385070l_bool ) @ hBOOL )
           => ! [D: arrow_856714788e_indi] :
                ( ( B @ ( D @ ( member1479139729e_indi @ hAPP_A1597696899l_bool ) @ hAPP_f584385070l_bool ) @ hBOOL )
               => ( ( ( C @ ( A @ hAPP_A376526755di_nat ) )
                    = ( D @ ( A @ hAPP_A376526755di_nat ) ) )
                 => ( C = D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).

thf(122,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1028_termination__basic__simps_I2_J) ).

thf(1093,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(331,axiom,
    ! [A: fun_Pr2067565481t_bool,B: fun_fu841105374ol_nat,C: fun_Pr2067565481t_bool,D: nat] :
      ( ( D @ ( C @ ( B @ hAPP_f1842225014ol_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( ! [E: fun_Pr2067565481t_bool,F: fun_Pr2067565481t_bool] :
              ( ( E @ ( F @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
             => ( E @ ( B @ hAPP_f1842225014ol_nat ) @ ( F @ ( B @ hAPP_f1842225014ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
         => ( D @ ( A @ ( B @ hAPP_f1842225014ol_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_801_xt4) ).

thf(1930,plain,
    ! [A: fun_Pr2067565481t_bool,B: fun_fu841105374ol_nat,C: fun_Pr2067565481t_bool,D: nat] :
      ( ( D @ ( C @ ( B @ hAPP_f1842225014ol_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( ! [E: fun_Pr2067565481t_bool,F: fun_Pr2067565481t_bool] :
              ( ( E @ ( F @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
             => ( E @ ( B @ hAPP_f1842225014ol_nat ) @ ( F @ ( B @ hAPP_f1842225014ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
         => ( D @ ( A @ ( B @ hAPP_f1842225014ol_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(444,axiom,
    ( ( e @ ( p @ ( arrow_1481558583_mkbot @ cOMBB_80760910e_indi @ hAPP_f831214557t_bool ) @ ( cOMBC_1417338747t_bool @ hAPP_f1631649925t_bool ) @ hAPP_A425126512t_bool ) @ ( e @ ( c @ ( p @ ( arrow_216713899_above @ cOMBB_1876517692e_indi @ hAPP_f1751344075t_bool ) @ ( cOMBC_1486904681t_bool @ hAPP_f2102110817t_bool ) @ hAPP_A1889513822t_bool ) @ ( cOMBC_1417338747t_bool @ hAPP_f1631649925t_bool ) @ hAPP_A425126512t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_1869811296e_indi @ hAPP_f966656047t_bool ) @ ( cOMBC_722552198t_bool @ hAPP_f721434149i_bool ) @ hAPP_n34002993i_bool ) @ ( if_fun523439385t_bool @ cOMBB_1061985500e_indi @ hAPP_f668886383t_bool ) @ cOMBS_1925466437t_bool @ hAPP_f1001205955t_bool ) @ cOMBS_1181656689t_bool @ hAPP_f1302887663t_bool ) @ ( e @ ( p @ ( arrow_1630265669_mktop @ cOMBB_80760910e_indi @ hAPP_f831214557t_bool ) @ ( cOMBC_1417338747t_bool @ hAPP_f1631649925t_bool ) @ hAPP_A425126512t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_1869811296e_indi @ hAPP_f966656047t_bool ) @ ( cOMBC_722552198t_bool @ hAPP_f721434149i_bool ) @ hAPP_n34002993i_bool ) @ ( if_fun523439385t_bool @ cOMBB_1061985500e_indi @ hAPP_f668886383t_bool ) @ cOMBS_1925466437t_bool @ hAPP_f1001205955t_bool ) @ cOMBS_1181656689t_bool @ hAPP_f1302887663t_bool ) @ ( f @ hAPP_f2008608496t_bool ) @ ( d @ ( e @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
  <=> ( lba @ ( lab @ ( n @ ( h @ ( ord_less_nat @ cOMBB_1869811296e_indi @ hAPP_f966656047t_bool ) @ ( cOMBC_722552198t_bool @ hAPP_f721434149i_bool ) @ hAPP_n34002993i_bool ) @ ( if_fun523439385t_bool @ cOMBB_1061985500e_indi @ hAPP_f668886383t_bool ) @ ( cOMBC_156709173t_bool @ hAPP_f1908974253t_bool ) @ hAPP_f1344464862t_bool ) @ ( cOMBC_750853729t_bool @ hAPP_f601594885t_bool ) @ hAPP_f480276746t_bool ) @ ( f @ hAPP_f2008608496t_bool ) @ ( a @ ( b @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/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(2353,plain,
    ( ( ( lba @ ( lab @ ( n @ ( h @ ( ord_less_nat @ cOMBB_1869811296e_indi @ hAPP_f966656047t_bool ) @ ( cOMBC_722552198t_bool @ hAPP_f721434149i_bool ) @ hAPP_n34002993i_bool ) @ ( if_fun523439385t_bool @ cOMBB_1061985500e_indi @ hAPP_f668886383t_bool ) @ ( cOMBC_156709173t_bool @ hAPP_f1908974253t_bool ) @ hAPP_f1344464862t_bool ) @ ( cOMBC_750853729t_bool @ hAPP_f601594885t_bool ) @ hAPP_f480276746t_bool ) @ ( f @ hAPP_f2008608496t_bool ) @ ( a @ ( b @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( e @ ( p @ ( arrow_1481558583_mkbot @ cOMBB_80760910e_indi @ hAPP_f831214557t_bool ) @ ( cOMBC_1417338747t_bool @ hAPP_f1631649925t_bool ) @ hAPP_A425126512t_bool ) @ ( e @ ( c @ ( p @ ( arrow_216713899_above @ cOMBB_1876517692e_indi @ hAPP_f1751344075t_bool ) @ ( cOMBC_1486904681t_bool @ hAPP_f2102110817t_bool ) @ hAPP_A1889513822t_bool ) @ ( cOMBC_1417338747t_bool @ hAPP_f1631649925t_bool ) @ hAPP_A425126512t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_1869811296e_indi @ hAPP_f966656047t_bool ) @ ( cOMBC_722552198t_bool @ hAPP_f721434149i_bool ) @ hAPP_n34002993i_bool ) @ ( if_fun523439385t_bool @ cOMBB_1061985500e_indi @ hAPP_f668886383t_bool ) @ cOMBS_1925466437t_bool @ hAPP_f1001205955t_bool ) @ cOMBS_1181656689t_bool @ hAPP_f1302887663t_bool ) @ ( e @ ( p @ ( arrow_1630265669_mktop @ cOMBB_80760910e_indi @ hAPP_f831214557t_bool ) @ ( cOMBC_1417338747t_bool @ hAPP_f1631649925t_bool ) @ hAPP_A425126512t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_1869811296e_indi @ hAPP_f966656047t_bool ) @ ( cOMBC_722552198t_bool @ hAPP_f721434149i_bool ) @ hAPP_n34002993i_bool ) @ ( if_fun523439385t_bool @ cOMBB_1061985500e_indi @ hAPP_f668886383t_bool ) @ cOMBS_1925466437t_bool @ hAPP_f1001205955t_bool ) @ cOMBS_1181656689t_bool @ hAPP_f1302887663t_bool ) @ ( f @ hAPP_f2008608496t_bool ) @ ( d @ ( e @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
    & ( ( e @ ( p @ ( arrow_1481558583_mkbot @ cOMBB_80760910e_indi @ hAPP_f831214557t_bool ) @ ( cOMBC_1417338747t_bool @ hAPP_f1631649925t_bool ) @ hAPP_A425126512t_bool ) @ ( e @ ( c @ ( p @ ( arrow_216713899_above @ cOMBB_1876517692e_indi @ hAPP_f1751344075t_bool ) @ ( cOMBC_1486904681t_bool @ hAPP_f2102110817t_bool ) @ hAPP_A1889513822t_bool ) @ ( cOMBC_1417338747t_bool @ hAPP_f1631649925t_bool ) @ hAPP_A425126512t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_1869811296e_indi @ hAPP_f966656047t_bool ) @ ( cOMBC_722552198t_bool @ hAPP_f721434149i_bool ) @ hAPP_n34002993i_bool ) @ ( if_fun523439385t_bool @ cOMBB_1061985500e_indi @ hAPP_f668886383t_bool ) @ cOMBS_1925466437t_bool @ hAPP_f1001205955t_bool ) @ cOMBS_1181656689t_bool @ hAPP_f1302887663t_bool ) @ ( e @ ( p @ ( arrow_1630265669_mktop @ cOMBB_80760910e_indi @ hAPP_f831214557t_bool ) @ ( cOMBC_1417338747t_bool @ hAPP_f1631649925t_bool ) @ hAPP_A425126512t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_1869811296e_indi @ hAPP_f966656047t_bool ) @ ( cOMBC_722552198t_bool @ hAPP_f721434149i_bool ) @ hAPP_n34002993i_bool ) @ ( if_fun523439385t_bool @ cOMBB_1061985500e_indi @ hAPP_f668886383t_bool ) @ cOMBS_1925466437t_bool @ hAPP_f1001205955t_bool ) @ cOMBS_1181656689t_bool @ hAPP_f1302887663t_bool ) @ ( f @ hAPP_f2008608496t_bool ) @ ( d @ ( e @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
     => ( lba @ ( lab @ ( n @ ( h @ ( ord_less_nat @ cOMBB_1869811296e_indi @ hAPP_f966656047t_bool ) @ ( cOMBC_722552198t_bool @ hAPP_f721434149i_bool ) @ hAPP_n34002993i_bool ) @ ( if_fun523439385t_bool @ cOMBB_1061985500e_indi @ hAPP_f668886383t_bool ) @ ( cOMBC_156709173t_bool @ hAPP_f1908974253t_bool ) @ hAPP_f1344464862t_bool ) @ ( cOMBC_750853729t_bool @ hAPP_f601594885t_bool ) @ hAPP_f480276746t_bool ) @ ( f @ hAPP_f2008608496t_bool ) @ ( a @ ( b @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).

thf(471,axiom,
    ! [A: product_unit,B: fun_Pr2090226719le_alt,C: fun_Pr1643180309t_bool,D: fun_Pr1887398791t_bool] :
      ( ( D @ ( C @ pi_Pro1820940723le_alt ) @ ( B @ ( member869664626le_alt @ hAPP_f41367117l_bool ) @ hAPP_f684683381l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_P1914371027t_bool ) @ ( A @ ( B @ hAPP_P396106045le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_PiE) ).

thf(2502,plain,
    ! [A: product_unit,B: fun_Pr2090226719le_alt,C: fun_Pr1643180309t_bool,D: fun_Pr1887398791t_bool] :
      ( ( D @ ( C @ pi_Pro1820940723le_alt ) @ ( B @ ( member869664626le_alt @ hAPP_f41367117l_bool ) @ hAPP_f684683381l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_P1914371027t_bool ) @ ( A @ ( B @ hAPP_P396106045le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).

thf(96,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B
         != ( A @ ( suc @ hAPP_nat_nat ) ) )
       => ~ ! [C: nat] :
              ( ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( B
               != ( C @ ( suc @ hAPP_nat_nat ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1121_lessE) ).

thf(987,plain,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B
         != ( A @ ( suc @ hAPP_nat_nat ) ) )
       => ~ ! [C: nat] :
              ( ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( B
               != ( C @ ( suc @ hAPP_nat_nat ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(385,axiom,
    ! [A: fun_Pr2067565481t_bool,B: arrow_1893660431le_alt,C: arrow_1893660431le_alt] :
      ( ( B != C )
     => ( ( arrow_1361987423le_Lin @ ( A @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
       => ( arrow_1361987423le_Lin @ ( C @ ( B @ ( A @ ( arrow_216713899_above @ hAPP_f1550387441t_bool ) @ hAPP_A1058422557t_bool ) @ hAPP_A1601437999t_bool ) @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_above__Lin) ).

thf(2127,plain,
    ! [A: fun_Pr2067565481t_bool,B: arrow_1893660431le_alt,C: arrow_1893660431le_alt] :
      ( ( B != C )
     => ( ( arrow_1361987423le_Lin @ ( A @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
       => ( arrow_1361987423le_Lin @ ( C @ ( B @ ( A @ ( arrow_216713899_above @ hAPP_f1550387441t_bool ) @ hAPP_A1058422557t_bool ) @ hAPP_A1601437999t_bool ) @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(538,axiom,
    ! [A: bool,B: fun_bo1682907689le_alt,C: fun_bool_bool,D: fun_bo1431306493t_bool] :
      ( ( D @ ( C @ pi_boo7125949le_alt ) @ ( B @ ( member684813948le_alt @ hAPP_f334747853l_bool ) @ hAPP_f1620711039l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_b128655177t_bool ) @ ( A @ ( B @ hAPP_b2094455111le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_PiE) ).

thf(2810,plain,
    ! [A: bool,B: fun_bo1682907689le_alt,C: fun_bool_bool,D: fun_bo1431306493t_bool] :
      ( ( D @ ( C @ pi_boo7125949le_alt ) @ ( B @ ( member684813948le_alt @ hAPP_f334747853l_bool ) @ hAPP_f1620711039l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_b128655177t_bool ) @ ( A @ ( B @ hAPP_b2094455111le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).

thf(510,axiom,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
      ( ( A != B )
     => ( ( B @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_415_order__neq__le__trans) ).

thf(2731,plain,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
      ( ( A != B )
     => ( ( B @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).

thf(535,axiom,
    ! [A: produc472769767le_alt,B: fun_Pr376858015t_unit,C: fun_Pr2067565481t_bool,D: fun_Pr1069395679t_bool] :
      ( ( D @ ( C @ pi_Pro346842291t_unit ) @ ( B @ ( member1303779570t_unit @ hAPP_f1700632141l_bool ) @ hAPP_f1159856629l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_P2037731755t_bool ) @ ( A @ ( B @ hAPP_P1069491261t_unit ) @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_PiE) ).

thf(2803,plain,
    ! [A: produc472769767le_alt,B: fun_Pr376858015t_unit,C: fun_Pr2067565481t_bool,D: fun_Pr1069395679t_bool] :
      ( ( D @ ( C @ pi_Pro346842291t_unit ) @ ( B @ ( member1303779570t_unit @ hAPP_f1700632141l_bool ) @ hAPP_f1159856629l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_P2037731755t_bool ) @ ( A @ ( B @ hAPP_P1069491261t_unit ) @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).

thf(67,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1001_nat__add__left__cancel__less) ).

thf(860,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(551,axiom,
    c != d,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__096c_A_126_061_Ad_096) ).

thf(2847,plain,
    c != d,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).

thf(196,axiom,
    ! [A: nat] :
      ( ( A @ ( cOMBI_nat @ hAPP_nat_nat ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBI_1_1_COMBI_000tc__Nat__Onat_U) ).

thf(1399,plain,
    ! [A: nat] :
      ( ( A @ ( cOMBI_nat @ hAPP_nat_nat ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(259,axiom,
    ! [A: bool,B: fun_bo1431306493t_bool,C: fun_bool_bool,D: fun_bo377688929l_bool] :
      ( ( D @ ( C @ pi_boo1111177555t_bool ) @ ( B @ ( member1133581546t_bool @ hAPP_f416878261l_bool ) @ hAPP_f398210311l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
       => ( A @ ( D @ hAPP_b1272691967l_bool ) @ ( A @ ( B @ hAPP_b128655177t_bool ) @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_571_Pi__mem) ).

thf(1621,plain,
    ! [A: bool,B: fun_bo1431306493t_bool,C: fun_bool_bool,D: fun_bo377688929l_bool] :
      ( ( D @ ( C @ pi_boo1111177555t_bool ) @ ( B @ ( member1133581546t_bool @ hAPP_f416878261l_bool ) @ hAPP_f398210311l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
       => ( A @ ( D @ hAPP_b1272691967l_bool ) @ ( A @ ( B @ hAPP_b128655177t_bool ) @ ( member1069471740t_bool @ hAPP_f1482930381l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(519,axiom,
    f @ ( arrow_1335103695le_IIA @ hAPP_f1572141188l_bool ) @ hBOOL,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_assms_I3_J) ).

thf(2754,plain,
    f @ ( arrow_1335103695le_IIA @ hAPP_f1572141188l_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).

thf(493,axiom,
    ~ ( lba @ ( b @ ( a @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79__096_Ia_M_Ab_J_A_126_058_ALba_096) ).

thf(2672,plain,
    ~ ( lba @ ( b @ ( a @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).

thf(51,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( C @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1158_mult__less__mono2) ).

thf(803,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( C @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(13,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( C @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1143_mult__le__mono2) ).

thf(639,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( C @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(578,axiom,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
      ( ! [C: arrow_1893660431le_alt,D: arrow_1893660431le_alt] :
          ( ( B @ ( D @ ( C @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
        <=> ( A @ ( D @ ( C @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_pred__equals__eq2) ).

thf(3052,plain,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
      ( ( ( B = A )
       => ! [C: arrow_1893660431le_alt,D: arrow_1893660431le_alt] :
            ( ( ( A @ ( D @ ( C @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
             => ( B @ ( D @ ( C @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
            & ( ( B @ ( D @ ( C @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
             => ( A @ ( D @ ( C @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ) )
      & ( ! [C: arrow_1893660431le_alt,D: arrow_1893660431le_alt] :
            ( ( ( A @ ( D @ ( C @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
             => ( B @ ( D @ ( C @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) )
            & ( ( B @ ( D @ ( C @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
             => ( A @ ( D @ ( C @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).

thf(120,axiom,
    ! [A: fun_fu638310559l_bool] :
      ( ( A @ ( top_to1312956197l_bool @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
     => ( A = top_to1312956197l_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_530_top__le) ).

thf(1088,plain,
    ! [A: fun_fu638310559l_bool] :
      ( ( A @ ( top_to1312956197l_bool @ ( ord_le1545885909l_bool @ hAPP_f1722316607l_bool ) @ hAPP_f182583295l_bool ) @ hBOOL )
     => ( A = top_to1312956197l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(5,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A @ ( C @ times_times_nat @ hAPP_nat_nat ) @ ( A @ ( B @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1142_mult__le__mono1) ).

thf(592,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A @ ( C @ times_times_nat @ hAPP_nat_nat ) @ ( A @ ( B @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(571,axiom,
    lba @ ( a @ ( b @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096) ).

thf(2980,plain,
    lba @ ( a @ ( b @ ( produc1590937303le_alt @ hAPP_A1146194953le_alt ) @ hAPP_A1299015393le_alt ) @ ( member1333168212le_alt @ hAPP_P38525833l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).

thf(178,axiom,
    ! [A: nat] :
      ( ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) )
      = ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1110_less__eq__Suc__le__raw) ).

thf(1331,plain,
    ! [A: nat] :
      ( ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) )
      = ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(254,axiom,
    ! [A: fun_fu1677555470ol_nat,B: nat,C: fun_Ar331856045t_bool,D: fun_Ar331856045t_bool] :
      ( ( D @ ( C @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
     => ( ( B @ ( D @ ( A @ hAPP_f1403773274ol_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [E: fun_Ar331856045t_bool,F: fun_Ar331856045t_bool] :
              ( ( F @ ( E @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
             => ( F @ ( A @ hAPP_f1403773274ol_nat ) @ ( E @ ( A @ hAPP_f1403773274ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
         => ( B @ ( C @ ( A @ hAPP_f1403773274ol_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_888_order__le__less__subst2) ).

thf(1606,plain,
    ! [A: fun_fu1677555470ol_nat,B: nat,C: fun_Ar331856045t_bool,D: fun_Ar331856045t_bool] :
      ( ( D @ ( C @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
     => ( ( B @ ( D @ ( A @ hAPP_f1403773274ol_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [E: fun_Ar331856045t_bool,F: fun_Ar331856045t_bool] :
              ( ( F @ ( E @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
             => ( F @ ( A @ hAPP_f1403773274ol_nat ) @ ( E @ ( A @ hAPP_f1403773274ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
         => ( B @ ( C @ ( A @ hAPP_f1403773274ol_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(145,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( B @ times_times_nat @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1169_n__less__n__mult__m) ).

thf(1184,plain,
    ! [A: nat,B: nat] :
      ( ( B @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( B @ times_times_nat @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(371,axiom,
    ! [A: fun_Ar331856045t_bool] : ( top_to951839027t_bool @ ( A @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_517_top__greatest) ).

thf(2074,plain,
    ! [A: fun_Ar331856045t_bool] : ( top_to951839027t_bool @ ( A @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(213,axiom,
    ! [A: nat] :
      ( A
     != ( A @ ( suc @ hAPP_nat_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1065_n__not__Suc__n) ).

thf(1463,plain,
    ! [A: nat] :
      ( A
     != ( A @ ( suc @ hAPP_nat_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(18,axiom,
    ( ( zero_zero_nat @ ( nat_size @ hAPP_nat_nat ) )
    = zero_zero_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1182_nat_Osize_I1_J) ).

thf(659,plain,
    ( ( zero_zero_nat @ ( nat_size @ hAPP_nat_nat ) )
    = zero_zero_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(556,axiom,
    ! [A: fun_Pr2067565481t_bool] :
      ~ ( A @ ( top_to1138392227t_bool @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_not__top__less) ).

thf(2866,plain,
    ! [A: fun_Pr2067565481t_bool] :
      ~ ( A @ ( top_to1138392227t_bool @ ( ord_le1478665215t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).

thf(547,axiom,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
      ( ( B = C )
     => ( ( C @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_xt1_I3_J) ).

thf(2832,plain,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
      ( ( B = C )
     => ( ( C @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_le1577377523t_bool @ hAPP_f930900275l_bool ) @ hAPP_f52567537l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).

thf(318,axiom,
    ! [A: arrow_856714788e_indi,B: arrow_856714788e_indi,C: fun_Ar671024215di_nat,D: fun_Ar1809396326i_bool] :
      ( ( D @ ( C @ inj_on1960344199di_nat @ hAPP_f584385070l_bool ) @ hBOOL )
     => ( ( A != B )
       => ( ( D @ ( A @ ( member1479139729e_indi @ hAPP_A1597696899l_bool ) @ hAPP_f584385070l_bool ) @ hBOOL )
         => ( ( D @ ( B @ ( member1479139729e_indi @ hAPP_A1597696899l_bool ) @ hAPP_f584385070l_bool ) @ hBOOL )
           => ( ( A @ ( C @ hAPP_A376526755di_nat ) )
             != ( B @ ( C @ hAPP_A376526755di_nat ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_541_inj__on__contraD) ).

thf(1848,plain,
    ! [A: arrow_856714788e_indi,B: arrow_856714788e_indi,C: fun_Ar671024215di_nat,D: fun_Ar1809396326i_bool] :
      ( ( D @ ( C @ inj_on1960344199di_nat @ hAPP_f584385070l_bool ) @ hBOOL )
     => ( ( A != B )
       => ( ( D @ ( A @ ( member1479139729e_indi @ hAPP_A1597696899l_bool ) @ hAPP_f584385070l_bool ) @ hBOOL )
         => ( ( D @ ( B @ ( member1479139729e_indi @ hAPP_A1597696899l_bool ) @ hAPP_f584385070l_bool ) @ hBOOL )
           => ( ( A @ ( C @ hAPP_A376526755di_nat ) )
             != ( B @ ( C @ hAPP_A376526755di_nat ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(367,axiom,
    ! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool] :
      ( ( B @ ( A @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
     => ( B @ ( A @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_438_order__less__imp__le) ).

thf(2059,plain,
    ! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool] :
      ( ( B @ ( A @ ( ord_le19409623t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL )
     => ( B @ ( A @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(302,axiom,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B != A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_985_less__not__refl2) ).

thf(1769,plain,
    ! [A: nat,B: nat] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(327,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_491_xt1_I7_J) ).

thf(1917,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(404,axiom,
    ! [A: product_unit,B: fun_Pr1643180309t_bool] :
      ( ( B @ ( A @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
    <=> ( A @ ( B @ hAPP_P1676879539t_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_mem__def) ).

thf(2191,plain,
    ! [A: product_unit,B: fun_Pr1643180309t_bool] :
      ( ( ( A @ ( B @ hAPP_P1676879539t_bool ) @ hBOOL )
       => ( B @ ( A @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ( A @ ( B @ hAPP_P1676879539t_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(311,axiom,
    ! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool] :
      ( ( A = B )
     => ( B @ ( A @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_352_order__eq__refl) ).

thf(1812,plain,
    ! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool] :
      ( ( A = B )
     => ( B @ ( A @ ( ord_le172225251t_bool @ hAPP_f1055587775l_bool ) @ hAPP_f1452856589l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(3129,plain,
    $false,
    inference(e,[status(thm)],[892,1718,2094,1469,2744,1168,2412,2463,1315,941,2331,1950,1110,2199,1322,2822,2630,2336,2109,2131,2031,1633,2778,909,628,977,730,1068,2808,1443,1569,1728,1971,2512,762,1005,2210,2117,1596,741,1073,2099,2282,1591,614,1692,1078,1671,1655,1137,2686,3044,2712,2627,2580,1354,1164,797,1919,1988,1761,747,1954,2844,1095,1835,2216,1243,1441,709,2010,1645,1724,1366,2869,651,1001,2723,973,1046,2400,2067,1904,1518,1623,1482,2039,719,2755,2708,1860,838,1511,1826,1313,2185,2562,1059,2703,2814,1985,2698,1660,1832,2897,1379,2169,1147,1572,770,2158,2024,1773,2301,1362,1778,2852,1922,817,1319,1704,870,1741,881,2222,1714,1334,2925,1677,1283,1051,756,1664,2794,2105,1450,1373,2996,1911,2782,1377,2618,866,1119,1433,1943,2718,2762,2508,981,1526,2137,2799,2286,2639,1651,3011,2473,793,1306,810,2047,1708,2737,2496,2574,661,2364,2164,2061,2773,2705,957,1091,778,1042,1580,2133,820,3069,693,1238,825,2805,1619,1370,2890,2414,1423,916,1602,1968,1178,1951,1457,2179,1159,3050,2741,2228,1291,1012,625,2477,1555,2826,1402,2801,1017,2509,2537,1755,2245,1350,697,1541,874,2115,1851,1259,1121,2359,1375,1493,1082,933,753,2830,1461,669,1075,2312,1446,679,706,1214,2349,2317,1155,1263,1249,1297,738,654,1192,2006,1799,1947,1984,1429,1720,2756,605,1627,1324,2504,2125,1588,2836,1382,1266,2900,2387,1231,1552,2243,2766,1599,1246,1202,1086,1241,805,2043,2883,657,2057,2402,2408,1515,953,1996,926,2076,2748,2645,1616,2423,888,2121,2001,1251,856,745,2894,2260,2729,1648,965,750,2028,2734,2938,1752,2674,2398,1965,1488,1784,1389,843,1125,2188,2981,641,1669,2293,611,1107,2759,2706,2166,947,1224,2148,2319,1356,979,2346,2361,2721,831,1853,2151,1894,1574,1524,2284,1801,2197,2871,1439,2065,1175,1667,2182,2111,2267,1162,700,1029,1149,2647,2928,2812,2632,2314,2625,1630,1993,1731,594,3034,2923,2461,2974,912,983,1841,1926,1594,2212,827,695,2086,1643,2139,1015,608,1113,851,1694,1973,1775,2752,1726,2390,2506,1562,722,2096,1758,589,1467,1420,2037,1509,939,1472,823,2582,1049,2816,1583,2784,2271,1990,2684,2202,1145,2846,2256,1845,2298,1003,580,690,1961,1025,1070,1368,2888,2882,993,776,1748,1566,2012,2850,1484,2092,2224,1785,1658,2486,1130,1285,1336,1220,1300,1452,1637,2688,2700,1186,1317,1763,2247,1934,1543,703,1702,1506,1504,2426,1536,2357,1955,1585,2511,1940,845,1084,2479,1459,2818,2828,581,1412,759,2226,2775,1998,931,1685,1010,2305,1734,2792,2135,1101,2130,786,2416,2394,813,1385,2853,2290,2251,1491,2796,667,929,2739,2680,1212,2230,1309,1614,800,2218,1348,1957,1678,967,1097,2233,1546,1625,2522,1303,1673,2050,1480,2003,2142,1116,1908,2155,2255,918,1816,2334,807,2746,1410,2366,1891,2619,955,1610,886,1789,664,1288,1710,2430,1537,1550,1500,2864,2372,1093,1930,2353,2502,987,2127,2810,2731,2803,860,2847,1399,1621,2754,2672,803,639,3052,1088,592,2980,1331,1606,1184,2074,1463,659,2866,2832,1848,2059,1769,1917,2191,1812]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SCT171_3 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.08  % Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.13/0.40  % Computer : n017.cluster.edu
% 0.13/0.40  % Model    : x86_64 x86_64
% 0.13/0.40  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40  % Memory   : 8046.5625MB
% 0.13/0.40  % OS       : Linux 6.8.0-71-generic
% 0.13/0.40  % CPULimit : 300
% 0.13/0.40  % WCLimit  : 300
% 0.13/0.40  % DateTime : Sat Sep 26 06:34:18 UTC 2026
% 0.13/0.40  % CPUTime  : 
% 0.13/0.40  Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.88/0.99  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 3.36/1.63  % [INFO] 	 Parsing done (635ms). 
% 3.36/1.64  % [INFO] 	 Running in sequential loop mode. 
% 4.41/2.05  % [INFO] 	 eprover registered as external prover. 
% 4.41/2.06  % [INFO] 	 Scanning for conjecture ... 
% 5.45/2.49  % [INFO] 	 Found a conjecture (or negated_conjecture) and 1278 axioms. Running axiom selection ... 
% 7.33/3.00  % [INFO] 	 Axiom selection finished. Selected 577 axioms (removed 701 axioms). 
% 8.90/3.42  % [INFO] 	 Problem is typed first-order (TPTP TFF). 
% 8.90/3.45  % [INFO] 	 Type checking passed. 
% 8.90/3.46  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 17.08/5.98  % [INFO] 	 [Domain constraints] Detected constraint on bool 
% 17.08/5.99  % [INFO] 	 [Domain constraints] dom(bool) ⊆ {fTrue,fFalse} 
% 18.03/6.20  % [INFO] 	 [Domain constraints] Detected constraint on bool 
% 18.03/6.20  % [INFO] 	 [Domain constraints] dom(bool) ⊆ {fTrue,fFalse} 
% 18.75/6.32  % [INFO] 	 [Domain constraints] Detected constraint on bool 
% 18.75/6.32  % [INFO] 	 [Domain constraints] dom(bool) ⊆ {fTrue,fFalse} 
% 27.36/8.38  % External prover 'e' found a proof!
% 27.36/8.38  % [INFO] 	 Killing All external provers ... 
% 27.36/8.38  % Time passed: 7826ms (effective reasoning time: 6728ms)
% 27.36/8.38  % 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)>
% 27.36/8.39  % Axioms used in derivation (577): fact_1001_nat__add__left__cancel__less, fact_78__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096, fact_222_Pi__UNIV, fact_983_linorder__neqE__nat, fact_1099_less__add__Suc1, fact_402_order__le__less, fact_815_order__le__less__subst1, fact_706_xt7, fact_730_add__left__imp__eq, fact_1170_one__less__mult, fact_25_top1I, fact_780_xt4, fact_827_order__less__le__subst1, fact_908_equalityI, fact_1177_nat__mult__less__cancel1, fact_459_order__le__neq__trans, fact_614_injD, fact_1073_Suc__lessD, fact_1180_left__add__mult__distrib, fact_850_order__less__le__subst1, fact_1044_not__less0, fact_1115_inc__induct, fact_415_order__neq__le__trans, fact_650_Pi__I, fact_1070_nat_Osimps_I2_J, fact_220_PiE, fact_176_UNIV__def, fact_1071_Zero__not__Suc, fact_651_inj__imp__inv__eq, fact_1013_le__add2, fact_578_below__Lin, fact_67_less__top, fact_613_inj__eq, fact_386_order__less__le, fact_108_xt1_I2_J, fact_970_in__mono, fact_718_pred__subset__eq2, fact_1053_le__0__eq, fact_847_order__less__le__subst1, fact_1083_add__Suc__shift, fact_52_top__apply, fact_1173_mult__le__cancel1, fact_491_xt1_I7_J, fact_153_linorder__neqE, fact_1125_zero__induct, fact_430_leD, fact_140_order__less__imp__not__eq, fact_854_order__less__le__subst1, fact_1072_Suc__less__SucD, fact_406_order__le__less, fact_1108_Suc__le__lessD, fact_985_less__not__refl2, fact_363_order__eq__iff, fact_225_in__below, fact_267_order__trans, fact_1119_Suc__eq__plus1__left, fact_1143_mult__le__mono2, fact_250_xt1_I6_J, fact_1021_add__leD2, fact_1144_mult__le__mono, fact_1051_add__is__0, fact_656_injI, fact_596_funcset__mem, help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__401, fact_382_order__less__le, fact_547_Pi__mem, help_fequal_2_1_fequal_000tc__Nat__Onat_T, fact_989_nat__add__left__commute, fact_1056_ex__least__nat__less, fact_1060_Suc__mono, fact_545_inj__onD, fact_334_order__antisym__conv, fact_409_linorder__antisym__conv1, fact_635_Pi__I, fact_1018_trans__le__add2, fact_1059_lessI, fact_1012_less__or__eq__imp__le, fact_224_Pi__UNIV, fact_582_funcset__mem, fact_1074_less__SucE, fact_925_psubset__eq, fact_564_Pi__mem, fact_1183_nat_Osize_I4_J, fact_128_order__less__asym_H, fact_735_add__le__imp__le__left, fact_307_xt1_I3_J, fact_526_top__unique, fact_1052_add__eq__self__zero, fact_353_order__eq__refl, fact_1103_less__Suc__eq__le, fact_1179_nat__mult__eq__cancel__disj, fact_188_inv__f__f, fact_1152_mult__cancel2, fact_1068_nat_Osimps_I3_J, fact_254_xt1_I6_J, fact_1176_nat__mult__le__cancel1, help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000_411, fact_1047_gr__implies__not0, fact_535_top__le, fact_648_Pi__I, fact_530_top__le, fact_50_top__apply, fact_85_n_I2_J, fact_22_Pair__eq, fact_576_Pi__mem, fact_734_one__reorient, fact_1123_not0__implies__Suc, fact_900_order__less__le__subst2, fact_1141_le__cube, fact_30_top1I, fact_6__C2_C, fact_991_nat__add__left__cancel, fact_489_xt1_I7_J, fact_275_order__trans, fact_161_order__less__irrefl, help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ef_405, fact_615_injD, help_fTrue_1_1_T, fact_0_assms_I3_J, fact_374_linorder__not__less, fact_499_order__le__less__trans, fact_112_ord__less__eq__trans, fact_257_xt1_I5_J, fact_86_notin__Lin__iff, fact_290_xt1_I4_J, fact_79__096_Ia_M_Ab_J_A_126_058_ALba_096, fact_1182_nat_Osize_I1_J, fact_264_xt1_I5_J, fact_1017_trans__le__add1, fact_317_ord__eq__le__trans, fact_1094_gr0__conv__Suc, fact_1003_trans__less__add2, fact_888_order__le__less__subst2, fact_655_add__le__less__mono, fact_1008_nat__less__le, fact_461_order__le__neq__trans, fact_737_add__mono, fact_41_iso__tuple__UNIV__I, fact_247_xt1_I6_J, fact_3__096P_A_058_AProf_096, fact_191_PiE, fact_1042_less__zeroE, help_COMBC_1_1_COMBC_000tc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs_, fact_408_not__leE, fact_96_order__less__asym, fact_315_xt1_I3_J, fact_1086_Suc__leD, fact_562_Pi__mem, fact_719_subset__UNIV, fact_18__096e_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto, fact_994_nat__le__linear, fact_297_ord__le__eq__trans, fact_407_leI, fact_40_iso__tuple__UNIV__I, fact_657_injI, fact_1181_nat_Osize_I2_J, fact_1162_nat__0__less__mult__iff, fact_1185_nat_Osize_I3_J, help_fTrue_1_1_U, fact_653_less__add__one, fact_1031_finite__indi, fact_345_order__eq__refl, fact_741_add__le__cancel__right, fact_29_top1I, fact_425_xt1_I12_J, fact_304_ord__le__eq__trans, fact_1142_mult__le__mono1, fact_183_n_I3_J, fact_1007_add__lessD1, fact_999_not__add__less1, fact_605_funcset__mem, fact_440_order__less__imp__le, help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000, fact_539_inj__on__def, fact_1100_less__add__Suc2, fact_438_order__less__imp__le, fact_1030_linear__alt, fact_732_add__left__cancel, fact_1004_add__less__mono1, fact_746_add__strict__right__mono, fact_441_linorder__antisym__conv2, fact_1025_termination__basic__simps_I3_J, fact_1148_nat__mult__1, fact_1172_mult__le__cancel2, fact_541_inj__on__contraD, fact_28_top1I, fact_612_inj__eq, fact_801_xt4, fact_229_order__refl, fact_1155_mult__0__right, fact_1026_termination__basic__simps_I4_J, fact_1160_mult__less__cancel2, fact_1150_add__mult__distrib2, fact_325_ord__eq__le__trans, fact_449_order__le__imp__less__or__eq, fact_681_xt7, fact_1159_mult__less__mono1, fact_1122_Suc__lessE, fact_479_order__less__le__trans, fact_20_injh, fact_43_iso__tuple__UNIV__I, fact_563_Pi__mem, fact_1106_Suc__leI, fact_959_set__mp, fact_21_Pair__inject, help_fFalse_1_1_T, fact_525_top__unique, fact_457_order__le__neq__trans, fact_1010_less__imp__le__nat, fact_163_mem__def, fact_92_linorder__cases, fact_168_mem__def, fact_988_nat__add__commute, fact_722_subset__UNIV, fact_1078_less__antisym, fact_964_set__rev__mp, help_COMBI_1_1_COMBI_000tc__Nat__Onat_U, fact_620_Pi__I, fact_1097_add__is__1, fact_136_order__less__imp__not__eq2, fact_1067_Zero__neq__Suc, fact_193_PiE, fact_736_add__le__imp__le__right, fact_1093_inj__Suc, fact_1015_le__iff__add, help_COMBS_1_1_COMBS_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000, help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__prod_It, help_COMBC_1_1_COMBC_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ef, fact_91_const__Lin__Prof, fact_1153_mult__cancel1, fact_375_linorder__not__le, help_COMBK_1_1_COMBK_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_00_402, help_COMBB_1_1_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__, fact_71_assms_I1_J, fact_951_subset__psubset__trans, help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_000t, fact_100_xt1_I10_J, fact_237__096_B_Bthesis_O_A_I_B_Bn_O_A_091_124_An_A_060_AN_059_AALL_Am_060_061n_, fact_1076_Suc__lessI, fact_1101_less__iff__Suc__add, fact_152_less__imp__neq, fact_798_xt4, fact_993_le__refl, fact_990_nat__add__assoc, fact_54_top__apply, fact_295_xt1_I4_J, fact_898_order__less__le__subst2, fact_132_order__less__imp__triv, fact_23_IIA__def, help_If_1_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiq, fact_1118_Suc__eq__plus1, fact_742_add__less__imp__less__left, fact_512_top__greatest, fact_305_ord__le__eq__trans, help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_409, fact_223_Pi__UNIV, fact_481_order__less__le__trans, fact_1154_mult__is__0, fact_162_mem__def, fact_77__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096, fact_74__096Lab_A_058_ALin_096, fact_1064_Suc__n__not__n, fact_904_add__leE, fact_120_ord__eq__less__trans, fact_634_Pi__I, fact_863_order__le__less__subst2, fact_447_order__le__imp__less__or__eq, fact_1157_mult__eq__1__iff, fact_348_order__eq__refl, fact_1149_add__mult__distrib, fact_48_top__apply, fact_744_add__strict__mono, fact_362_order__eq__iff, help_fequal_1_1_fequal_000tc__Nat__Onat_T, help_If_2_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiq, help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000_418, fact_1175_nat__mult__assoc, fact_32_UNIV__I, fact_1107_le__less__Suc__eq, fact_1087_le__SucE, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow_, fact_1085_add__Suc__right, fact_1126_nat__induct, fact_274_order__trans, fact_89_mkbot__Lin, fact_961_set__rev__mp, fact_932_subset__iff__psubset__eq, fact_165_mem__def, help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs___404, fact_610_funcset__mem, help_COMBS_1_1_COMBS_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000_427, fact_116_xt1_I1_J, fact_1169_n__less__n__mult__m, fact_1048_gr0I, help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__prod_Itc__Arrow____Order____Mirabe, fact_173_UNIV__def, fact_1006_less__add__eq__less, fact_355_order__eq__iff, fact_516_top__greatest, fact_548_Pi__mem, fact_219_PiE, fact_59_not__top__less, fact_699_xt7, fact_946_psubset__subset__trans, fact_517_top__greatest, fact_206_PiE, fact_636_Pi__I, fact_715_Pi__anti__mono, fact_167_mem__def, fact_189_inv__f__f, fact_365_linorder__linear, fact_186_inv__f__eq, help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_000t_414, fact_1171_one__le__mult__iff, fact_1079_not__less__less__Suc__eq, fact_1069_Suc__not__Zero, fact_1105_le__imp__less__Suc, fact_1016_nat__add__left__cancel__le, fact_1147_nat__1__eq__mult__iff, fact_396_less__le__not__le, fact_618_inv__into__f__eq, fact_233_order__refl, fact_83__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_, fact_1043_le0, help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_419, fact_270_order__trans, fact_577_Pi__mem, fact_1110_less__eq__Suc__le__raw, fact_649_Pi__I, fact_1151_Suc__mult__cancel1, fact_881_order__le__less__subst2, fact_1063_nat_Oinject, fact_1061_zero__less__Suc, fact_192_PiE, fact_330_order__antisym__conv, fact_1158_mult__less__mono2, fact_1055_add__gr__0, fact_88_mktop__Lin, fact_11__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ad_J, fact_1081_less__Suc__eq, fact_87_Lin__irrefl, fact_166_mem__def, fact_51_top__apply, fact_2__096c_A_126_061_Ad_096, fact_748_add__less__cancel__right, fact_154_linorder__antisym__conv3, fact_731_add__right__cancel, fact_8__C4_C, fact_419_order__neq__le__trans, fact_181_pred__equals__eq2, fact_1014_le__add1, fact_255_xt1_I6_J, fact_26_top1I, fact_579_Prof__def, fact_182_dictatorI, fact_4_in__mkbot, fact_1166_Suc__mult__le__cancel1, fact_1027_termination__basic__simps_I5_J, fact_180_in__above, fact_1062_Suc__inject, help_If_3_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiq, fact_376_linorder__le__less__linear, fact_1089_Suc__le__mono, fact_42_iso__tuple__UNIV__I, fact_394_less__le__not__le, fact_745_add__strict__left__mono, help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000_417, fact_35_UNIV__I, fact_300_ord__le__eq__trans, fact_205_PiE, fact_82__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_, fact_543_inj__on__iff, fact_471_xt1_I11_J, fact_611_funcset__mem, fact_616_inv__into__f__f, fact_1168_n__less__m__mult__n, fact_1046_less__nat__zero__code, fact_1121_lessE, fact_285_order__antisym, fact_1098_one__is__add, fact_1117_gr0__implies__Suc, fact_31_top1I, fact_469_xt1_I11_J, fact_1124_nat_Oexhaust, fact_1000_not__add__less2, fact_915_subsetD, fact_583_funcset__mem, fact_236__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I, fact_1146_nat__mult__1__right, fact_1116_less__imp__Suc__add, fact_164_mem__def, fact_1104_Suc__le__eq, fact_507_xt1_I8_J, fact_124_xt1_I9_J, fact_1186_weak__decr__stable, fact_743_add__less__imp__less__right, fact_980_pred__subset__eq, fact_766_xt6, fact_358_order__eq__iff, help_COMBB_1_1_COMBB_000tc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs_, fact_487_xt1_I7_J, fact_429_xt1_I12_J, fact_534_top__le, fact_1140_le__square, fact_144_order__less__imp__not__less, fact_184__096_Ic_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Am, fact_1084_add__Suc, fact_37_UNIV__I, fact_1091_not__less__eq__eq, fact_1028_termination__basic__simps_I2_J, fact_73_dictator__def, fact_24_unanimity__def, fact_643_Pi__I, fact_956_set__mp, fact_238_linorder__le__cases, fact_984_less__irrefl__nat, fact_571_Pi__mem, help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000_426, fact_9_pairwise__neutrality, fact_427_xt1_I12_J, fact_1088_le__SucI, fact_992_nat__add__right__cancel, fact_314_xt1_I3_J, fact_521_top__unique, fact_104_order__less__trans, fact_1023_mono__nat__linear__lb, fact_33_UNIV__I, fact_46_iso__tuple__UNIV__I, fact_1058_less__imp__add__positive, fact_1164_mult__Suc__right, fact_1066_Suc__neq__Zero, fact_14_PW, fact_1_u, fact_549_Pi__mem, fact_84__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amk, fact_1002_trans__less__add1, fact_747_add__less__cancel__left, fact_287_xt1_I4_J, fact_1145_nat__mult__eq__1__iff, fact_739_add__right__mono, fact_327_order__antisym__conv, fact_277_order__antisym, fact_996_le__trans, fact_740_add__le__cancel__left, fact_1167_mult__eq__self__implies__10, fact_477_order__less__le__trans, fact_1009_le__eq__less__or__eq, fact_27_top1I, fact_1045_neq0__conv, fact_76__096a_A_126_061_Ab_096, fact_155_linorder__less__linear, fact_1090_le__Suc__eq, fact_157_linorder__neq__iff, help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ef_403, fact_1011_le__neq__implies__less, fact_324_ord__eq__le__trans, fact_738_add__left__mono, fact_1049_plus__nat_Oadd__0, fact_15_split__paired__All, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ef_425, fact_187_inv__f__eq, fact_805_xt4, fact_1178_nat__mult__eq__cancel1, fact_728_add__right__imp__eq, fact_260_xt1_I5_J, fact_679_xt7, fact_981_less__not__refl, fact_1156_mult__0, fact_404_order__le__less, fact_1020_add__le__mono, help_fFalse_1_1_U, fact_987_nat__less__cases, fact_702_xt7, fact_712_less__fun__def, fact_44_iso__tuple__UNIV__I, fact_621_Pi__I, fact_667_xt5, help_COMBB_1_1_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs___428, fact_581_funcset__mem, fact_7__C1_C, fact_19_n_I1_J, fact_1102_less__eq__Suc__le, fact_1096_less__Suc__eq__0__disj, fact_597_funcset__mem, fact_5_in__mktop, fact_598_funcset__mem, fact_986_less__not__refl3, fact_185__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Am, fact_729_add__imp__eq, fact_284_order__antisym, fact_156_not__less__iff__gr__or__eq, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ef, fact_384_order__less__le, help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__prod_Itc__Arrow____Order_, fact_995_eq__imp__le, fact_148_order__less__not__sym, fact_221_complete__Lin, fact_467_xt1_I11_J, fact_294_xt1_I4_J, fact_982_nat__neq__iff, fact_310_xt1_I3_J, fact_1077_less__SucI, fact_226_order__refl, fact_669_xt5, fact_1050_Nat_Oadd__0__right, fact_977_pred__subset__eq, fact_1075_less__trans__Suc, fact_234_order__refl, fact_352_order__eq__refl, fact_1109_One__nat__def, fact_417_order__neq__le__trans, fact_829_order__less__le__subst1, fact_265_xt1_I5_J, fact_436_order__less__imp__le, fact_1080_Suc__less__eq, fact_72__096_Ie_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amk, fact_913_subsetD, fact_1184_nat__size, fact_1022_add__leD1, fact_1120_Suc__le__D, fact_497_order__le__less__trans, fact_652_inj__imp__inv__eq, fact_1095_less__Suc0, fact_580_inj__on__id2, fact_1057_ex__least__nat__le, fact_997_le__antisym, fact_1024_less__mono__imp__le__mono, fact_16__096_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai, fact_17__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto, fact_38_UNIV__I, fact_1029_termination__basic__simps_I1_J, help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ef, fact_1174_nat__mult__commute, fact_778_xt4, fact_1092_Suc__n__not__le__n, fact_654_add__less__le__mono, fact_10__C3_C, fact_90_above__Lin, fact_200_PiE, fact_75__096Lba_A_058_ALin_096, fact_335_order__antisym__conv, fact_768_xt6, fact_34_UNIV__I, help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe, fact_81_PiProf, fact_905_equalityI, fact_509_xt1_I8_J, fact_1065_n__not__Suc__n, fact_861_order__le__less__subst2, fact_1161_mult__less__cancel1, fact_1165_mult__Suc, fact_1054_less__eq__nat_Osimps_I1_J, fact_884_order__le__less__subst2, fact_511_xt1_I8_J, fact_501_order__le__less__trans, fact_713_less__fun__def, fact_1019_add__le__mono1, fact_320_ord__eq__le__trans, fact_280_order__antisym, fact_392_less__le__not__le, fact_918_subsetD, fact_1082_not__less__eq, fact_1163_Suc__mult__less__cancel1, fact_190_PiE, fact_1005_add__less__mono, fact_817_order__le__less__subst1, fact_45_iso__tuple__UNIV__I, fact_53_top__apply, fact_733_ab__semigroup__add__class_Oadd__ac_I1_J, fact_36_UNIV__I, fact_939_psubset__imp__subset, fact_451_order__le__imp__less__or__eq, fact_967_in__mono, 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_80__096_Ib_M_Aa_J_A_126_058_ALab_096, fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto
% 27.36/8.39  % No. of inferences in proof: 1158
% 27.36/8.39  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 7826 ms resp. 6728 ms w/o parsing
% 29.88/9.02  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 30.33/9.03  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------