TSTP Solution File: SCT171_3 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SCT171_3 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:51:02 EDT 2023
% Result : Theorem 17.63s 5.17s
% Output : Refutation 18.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 1102
% Syntax : Number of formulae : 1682 ( 312 unt; 524 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 : 276 ( 276 >; 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_type,type,
arrow_1335103695le_IIA: fun_fu2098777574l_bool ).
thf(arrow_1361987423le_Lin_type,type,
arrow_1361987423le_Lin: fun_fu638310559l_bool ).
thf(arrow_5070731e_Prof_type,type,
arrow_5070731e_Prof: fun_fu3835832l_bool ).
thf(arrow_216713899_above_type,type,
arrow_216713899_above: fun_fu1287834969t_bool ).
thf(arrow_1525312447_below_type,type,
arrow_1525312447_below: fun_Pr2067565481t_bool > arrow_1893660431le_alt > arrow_1893660431le_alt > fun_Pr2067565481t_bool ).
thf(arrow_1765888670ctator_type,type,
arrow_1765888670ctator: fun_fu2109152051i_bool ).
thf(arrow_1481558583_mkbot_type,type,
arrow_1481558583_mkbot: fun_fu1679793515t_bool ).
thf(arrow_1630265669_mktop_type,type,
arrow_1630265669_mktop: fun_fu1679793515t_bool ).
thf(arrow_320876018nimity_type,type,
arrow_320876018nimity: fun_fu2098777574l_bool ).
thf(cOMBB_1061985500e_indi_type,type,
cOMBB_1061985500e_indi: fun_bo1945492389t_bool > fun_fu1821795357t_bool ).
thf(cOMBB_1869811296e_indi_type,type,
cOMBB_1869811296e_indi: fun_nat_fun_nat_bool > fun_fu1372829539t_bool ).
thf(cOMBB_652885079le_alt_type,type,
cOMBB_652885079le_alt: fun_fu696673523t_bool > fun_fu596987971t_bool ).
thf(cOMBB_1575576719le_alt_type,type,
cOMBB_1575576719le_alt: fun_fu1572237755l_bool > fun_fu263774347l_bool ).
thf(cOMBB_1876517692e_indi_type,type,
cOMBB_1876517692e_indi: fun_fu1287834969t_bool > fun_fu1427663149t_bool ).
thf(cOMBB_80760910e_indi_type,type,
cOMBB_80760910e_indi: fun_fu1679793515t_bool > fun_fu1896276031t_bool ).
thf(cOMBB_1660064607le_alt_type,type,
cOMBB_1660064607le_alt: fun_Pr1085078251l_bool > fun_fu1572237755l_bool ).
thf(cOMBC_395465908l_bool_type,type,
cOMBC_395465908l_bool: fun_fu696673523t_bool ).
thf(cOMBC_557453916t_bool_type,type,
cOMBC_557453916t_bool: fun_fu91004995t_bool ).
thf(cOMBC_1486904681t_bool_type,type,
cOMBC_1486904681t_bool: fun_fu548876995t_bool ).
thf(cOMBC_1417338747t_bool_type,type,
cOMBC_1417338747t_bool: fun_fu2128130023t_bool ).
thf(cOMBC_722552198t_bool_type,type,
cOMBC_722552198t_bool: fun_fu1610971917i_bool ).
thf(cOMBC_156709173t_bool_type,type,
cOMBC_156709173t_bool: fun_fu2030607631t_bool ).
thf(cOMBC_750853729t_bool_type,type,
cOMBC_750853729t_bool: fun_fu205223783t_bool ).
thf(cOMBC_2133093654l_bool_type,type,
cOMBC_2133093654l_bool: fun_fu452089579l_bool ).
thf(cOMBC_593569186l_bool_type,type,
cOMBC_593569186l_bool: fun_fu598681231t_bool ).
thf(cOMBI_nat_type,type,
cOMBI_nat: fun_nat_nat ).
thf(cOMBK_81143760t_bool_type,type,
cOMBK_81143760t_bool: fun_bo377688929l_bool ).
thf(cOMBK_198697344le_alt_type,type,
cOMBK_198697344le_alt: fun_bo1431306493t_bool ).
thf(cOMBK_1987648063le_alt_type,type,
cOMBK_1987648063le_alt: fun_fu857388591i_bool ).
thf(cOMBK_138598520le_alt_type,type,
cOMBK_138598520le_alt: fun_fu459284641l_bool ).
thf(cOMBK_751896174le_alt_type,type,
cOMBK_751896174le_alt: fun_fu32501645t_bool ).
thf(cOMBK_1520063231e_indi_type,type,
cOMBK_1520063231e_indi: fun_fu1868761018l_bool ).
thf(cOMBK_650639032l_bool_type,type,
cOMBK_650639032l_bool: fun_fu151575155l_bool ).
thf(cOMBK_1701906001t_bool_type,type,
cOMBK_1701906001t_bool: fun_fu329401612l_bool ).
thf(cOMBK_1650320063e_indi_type,type,
cOMBK_1650320063e_indi: fun_fu1847201208t_bool ).
thf(cOMBK_5056120l_bool_type,type,
cOMBK_5056120l_bool: fun_fu1414555455t_bool ).
thf(cOMBK_681766254t_unit_type,type,
cOMBK_681766254t_unit: fun_fu1648543689t_bool ).
thf(cOMBS_1925466437t_bool_type,type,
cOMBS_1925466437t_bool: fun_Ar535288606t_bool > fun_fu419698981t_bool ).
thf(cOMBS_1181656689t_bool_type,type,
cOMBS_1181656689t_bool: fun_Ar516759882t_bool > fun_fu1037963345t_bool ).
thf(finite1672073426e_indi_type,type,
finite1672073426e_indi: fun_fu1603738721ol_nat ).
thf(finite92092049e_indi_type,type,
finite92092049e_indi: fun_fu844176604l_bool ).
thf(inj_on1960344199di_nat_type,type,
inj_on1960344199di_nat: fun_Ar671024215di_nat > fun_fu844176604l_bool ).
thf(inj_on_nat_nat_type,type,
inj_on_nat_nat: fun_nat_nat > fun_fu425979586l_bool ).
thf(pi_Arr959578316t_bool_type,type,
pi_Arr959578316t_bool: fun_Ar1809396326i_bool > fun_Ar1474557608l_bool > fun_fu3835832l_bool ).
thf(pi_Arr1460528004le_alt_type,type,
pi_Arr1460528004le_alt: fun_Ar1809396326i_bool > fun_Ar274636406t_bool > fun_fu802339430t_bool ).
thf(pi_boo1111177555t_bool_type,type,
pi_boo1111177555t_bool: fun_bool_bool > fun_bo377688929l_bool > fun_fu1618772927l_bool ).
thf(pi_boo7125949le_alt_type,type,
pi_boo7125949le_alt: fun_bool_bool > fun_bo1431306493t_bool > fun_fu1168191263t_bool ).
thf(pi_Pro1820940723le_alt_type,type,
pi_Pro1820940723le_alt: fun_Pr1643180309t_bool > fun_Pr1887398791t_bool > fun_fu524263445t_bool ).
thf(pi_fun1746584570t_bool_type,type,
pi_fun1746584570t_bool: fun_fu3835832l_bool > fun_fu1863781882l_bool > fun_fu2098777574l_bool ).
thf(pi_Pro837265796e_indi_type,type,
pi_Pro837265796e_indi: fun_Pr2067565481t_bool > fun_Pr895221296i_bool > fun_fu902545894i_bool ).
thf(pi_Pro1238944957t_bool_type,type,
pi_Pro1238944957t_bool: fun_Pr2067565481t_bool > fun_Pr1780397033l_bool > fun_fu638310559l_bool ).
thf(pi_Pro346842291t_unit_type,type,
pi_Pro346842291t_unit: fun_Pr2067565481t_bool > fun_Pr1069395679t_bool > fun_fu1428746645t_bool ).
thf(one_one_nat_type,type,
one_one_nat: nat ).
thf(plus_plus_nat_type,type,
plus_plus_nat: fun_nat_fun_nat_nat ).
thf(times_times_nat_type,type,
times_times_nat: nat > fun_nat_nat ).
thf(zero_zero_nat_type,type,
zero_zero_nat: nat ).
thf(hilber1580028780di_nat_type,type,
hilber1580028780di_nat: fun_Ar1809396326i_bool > fun_Ar671024215di_nat > fun_na699243463e_indi ).
thf(hilber195283148at_nat_type,type,
hilber195283148at_nat: fun_nat_bool > fun_nat_nat > fun_nat_nat ).
thf(if_fun523439385t_bool_type,type,
if_fun523439385t_bool: fun_bo1945492389t_bool ).
thf(suc_type,type,
suc: fun_nat_nat ).
thf(nat_size_type,type,
nat_size: fun_nat_nat ).
thf(size_size_nat_type,type,
size_size_nat: fun_nat_nat ).
thf(ord_less_nat_type,type,
ord_less_nat: fun_nat_fun_nat_bool ).
thf(ord_le19409623t_bool_type,type,
ord_le19409623t_bool: fun_fu625013235l_bool ).
thf(ord_le1478665215t_bool_type,type,
ord_le1478665215t_bool: fun_fu643206625l_bool ).
thf(ord_less_eq_nat_type,type,
ord_less_eq_nat: fun_nat_fun_nat_bool ).
thf(ord_le172225251t_bool_type,type,
ord_le172225251t_bool: fun_fu625013235l_bool ).
thf(ord_le742797417l_bool_type,type,
ord_le742797417l_bool: fun_fu1393819981l_bool ).
thf(ord_le1545885909l_bool_type,type,
ord_le1545885909l_bool: fun_fu1265985907l_bool ).
thf(ord_le1577377523t_bool_type,type,
ord_le1577377523t_bool: fun_fu643206625l_bool ).
thf(top_top_bool_type,type,
top_top_bool: bool ).
thf(top_to951839027t_bool_type,type,
top_to951839027t_bool: fun_Ar331856045t_bool ).
thf(top_to788185952i_bool_type,type,
top_to788185952i_bool: fun_Ar1809396326i_bool ).
thf(top_to1647826457l_bool_type,type,
top_to1647826457l_bool: fun_bool_bool ).
thf(top_top_fun_nat_bool_type,type,
top_top_fun_nat_bool: fun_nat_bool ).
thf(top_to1257323279t_bool_type,type,
top_to1257323279t_bool: fun_Pr1643180309t_bool ).
thf(top_to553140914l_bool_type,type,
top_to553140914l_bool: fun_fu3835832l_bool ).
thf(top_to827110112l_bool_type,type,
top_to827110112l_bool: fun_fu2098777574l_bool ).
thf(top_to1312956197l_bool_type,type,
top_to1312956197l_bool: fun_fu638310559l_bool ).
thf(top_to1138392227t_bool_type,type,
top_to1138392227t_bool: fun_Pr2067565481t_bool ).
thf(produc1590937303le_alt_type,type,
produc1590937303le_alt: fun_Ar2121501495le_alt ).
thf(collec2125531966t_bool_type,type,
collec2125531966t_bool: fun_fu1824295331l_bool ).
thf(collec1988958098le_alt_type,type,
collec1988958098le_alt: fun_fu1550952061t_bool ).
thf(fFalse_type,type,
fFalse: bool ).
thf(fTrue_type,type,
fTrue: bool ).
thf(fequal_nat_type,type,
fequal_nat: fun_nat_fun_nat_bool ).
thf(hAPP_A1748732503t_bool_type,type,
hAPP_A1748732503t_bool: fun_Ar17477381t_bool > arrow_1893660431le_alt > bool ).
thf(hAPP_A2063800319t_bool_type,type,
hAPP_A2063800319t_bool: fun_Ar331856045t_bool > arrow_1893660431le_alt > fun_Ar17477381t_bool ).
thf(hAPP_A1608658241l_bool_type,type,
hAPP_A1608658241l_bool: fun_Ar1995913199l_bool > arrow_1893660431le_alt > fun_Ar339057223l_bool ).
thf(hAPP_A1058422557t_bool_type,type,
hAPP_A1058422557t_bool: fun_Ar797671557t_bool > arrow_1893660431le_alt > fun_Ar1573071255t_bool ).
thf(hAPP_A1146194953le_alt_type,type,
hAPP_A1146194953le_alt: fun_Ar2121501495le_alt > arrow_1893660431le_alt > fun_Ar245737999le_alt ).
thf(hAPP_A1889513822t_bool_type,type,
hAPP_A1889513822t_bool: fun_Ar1753411852t_bool > arrow_1893660431le_alt > fun_Ar64685412t_bool ).
thf(hAPP_A425126512t_bool_type,type,
hAPP_A425126512t_bool: fun_Ar1623257374t_bool > arrow_1893660431le_alt > fun_Ar274636406t_bool ).
thf(hAPP_A442239897l_bool_type,type,
hAPP_A442239897l_bool: fun_Ar339057223l_bool > arrow_1893660431le_alt > fun_fu638310559l_bool ).
thf(hAPP_A656921921t_bool_type,type,
hAPP_A656921921t_bool: fun_Ar636018671t_bool > arrow_1893660431le_alt > fun_fu1534804551t_bool ).
thf(hAPP_A1601437999t_bool_type,type,
hAPP_A1601437999t_bool: fun_Ar1573071255t_bool > arrow_1893660431le_alt > fun_Pr2067565481t_bool ).
thf(hAPP_A1299015393le_alt_type,type,
hAPP_A1299015393le_alt: fun_Ar245737999le_alt > arrow_1893660431le_alt > produc472769767le_alt ).
thf(hAPP_A997847300i_bool_type,type,
hAPP_A997847300i_bool: fun_Ar1809396326i_bool > arrow_856714788e_indi > bool ).
thf(hAPP_A376526755di_nat_type,type,
hAPP_A376526755di_nat: fun_Ar671024215di_nat > arrow_856714788e_indi > nat ).
thf(hAPP_A38124190t_bool_type,type,
hAPP_A38124190t_bool: fun_Ar290235730t_bool > arrow_856714788e_indi > fun_Ar797671557t_bool ).
thf(hAPP_A1309733808t_bool_type,type,
hAPP_A1309733808t_bool: fun_Ar64685412t_bool > arrow_856714788e_indi > fun_Ar1573071255t_bool ).
thf(hAPP_A1686943911t_bool_type,type,
hAPP_A1686943911t_bool: fun_Ar603939593t_bool > arrow_856714788e_indi > fun_nat_bool ).
thf(hAPP_A1597696899l_bool_type,type,
hAPP_A1597696899l_bool: fun_Ar1047186533l_bool > arrow_856714788e_indi > fun_fu844176604l_bool ).
thf(hAPP_A897398598l_bool_type,type,
hAPP_A897398598l_bool: fun_Ar1474557608l_bool > arrow_856714788e_indi > fun_fu638310559l_bool ).
thf(hAPP_A1395684458t_bool_type,type,
hAPP_A1395684458t_bool: fun_Ar535288606t_bool > arrow_856714788e_indi > fun_fu297564241t_bool ).
thf(hAPP_A834130326t_bool_type,type,
hAPP_A834130326t_bool: fun_Ar516759882t_bool > arrow_856714788e_indi > fun_fu1550952061t_bool ).
thf(hAPP_A1646126530t_bool_type,type,
hAPP_A1646126530t_bool: fun_Ar274636406t_bool > arrow_856714788e_indi > fun_Pr2067565481t_bool ).
thf(hAPP_A899858958le_alt_type,type,
hAPP_A899858958le_alt: fun_Ar338949104le_alt > arrow_856714788e_indi > produc472769767le_alt ).
thf(hAPP_bool_bool_type,type,
hAPP_bool_bool: fun_bool_bool > bool > bool ).
thf(hAPP_b1787118453l_bool_type,type,
hAPP_b1787118453l_bool: fun_bo492988759l_bool > bool > fun_fu1255657237l_bool ).
thf(hAPP_b1272691967l_bool_type,type,
hAPP_b1272691967l_bool: fun_bo377688929l_bool > bool > fun_fu638310559l_bool ).
thf(hAPP_b35146737t_bool_type,type,
hAPP_b35146737t_bool: fun_bo1945492389t_bool > bool > fun_fu297564241t_bool ).
thf(hAPP_b128655177t_bool_type,type,
hAPP_b128655177t_bool: fun_bo1431306493t_bool > bool > fun_Pr2067565481t_bool ).
thf(hAPP_b2094455111le_alt_type,type,
hAPP_b2094455111le_alt: fun_bo1682907689le_alt > bool > produc472769767le_alt ).
thf(hAPP_n1937165849e_indi_type,type,
hAPP_n1937165849e_indi: fun_na699243463e_indi > nat > arrow_856714788e_indi ).
thf(hAPP_nat_bool_type,type,
hAPP_nat_bool: fun_nat_bool > nat > bool ).
thf(hAPP_nat_nat_type,type,
hAPP_nat_nat: fun_nat_nat > nat > nat ).
thf(hAPP_n1312530466t_bool_type,type,
hAPP_n1312530466t_bool: fun_na300967376t_bool > nat > fun_Ar331856045t_bool ).
thf(hAPP_n34002993i_bool_type,type,
hAPP_n34002993i_bool: fun_na2037635353i_bool > nat > fun_Ar1809396326i_bool ).
thf(hAPP_n1699378549t_bool_type,type,
hAPP_n1699378549t_bool: fun_nat_fun_nat_bool > nat > fun_nat_bool ).
thf(hAPP_nat_fun_nat_nat_type,type,
hAPP_nat_fun_nat_nat: fun_nat_fun_nat_nat > nat > fun_nat_nat ).
thf(hAPP_n1161265524t_bool_type,type,
hAPP_n1161265524t_bool: fun_na998785244t_bool > nat > fun_Pr2067565481t_bool ).
thf(hAPP_P1676879539t_bool_type,type,
hAPP_P1676879539t_bool: fun_Pr1643180309t_bool > product_unit > bool ).
thf(hAPP_P607165281l_bool_type,type,
hAPP_P607165281l_bool: fun_Pr1863373635l_bool > product_unit > fun_fu309829899l_bool ).
thf(hAPP_P1914371027t_bool_type,type,
hAPP_P1914371027t_bool: fun_Pr1887398791t_bool > product_unit > fun_Pr2067565481t_bool ).
thf(hAPP_P396106045le_alt_type,type,
hAPP_P396106045le_alt: fun_Pr2090226719le_alt > product_unit > produc472769767le_alt ).
thf(hAPP_f1452856589l_bool_type,type,
hAPP_f1452856589l_bool: fun_fu573468015l_bool > fun_Ar331856045t_bool > bool ).
thf(hAPP_f1403773274ol_nat_type,type,
hAPP_f1403773274ol_nat: fun_fu1677555470ol_nat > fun_Ar331856045t_bool > nat ).
thf(hAPP_f1055587775l_bool_type,type,
hAPP_f1055587775l_bool: fun_fu625013235l_bool > fun_Ar331856045t_bool > fun_fu573468015l_bool ).
thf(hAPP_f105674721t_bool_type,type,
hAPP_f105674721t_bool: fun_fu596987971t_bool > fun_Ar1995913199l_bool > fun_Ar636018671t_bool ).
thf(hAPP_f184584489l_bool_type,type,
hAPP_f184584489l_bool: fun_fu263774347l_bool > fun_Ar2121501495le_alt > fun_Ar1995913199l_bool ).
thf(hAPP_f1689397393t_bool_type,type,
hAPP_f1689397393t_bool: fun_fu696673523t_bool > fun_Ar339057223l_bool > fun_fu1534804551t_bool ).
thf(hAPP_f1081591777t_bool_type,type,
hAPP_f1081591777t_bool: fun_fu91004995t_bool > fun_Ar636018671t_bool > fun_fu1118734319t_bool ).
thf(hAPP_f1536341593l_bool_type,type,
hAPP_f1536341593l_bool: fun_fu1572237755l_bool > fun_Ar245737999le_alt > fun_Ar339057223l_bool ).
thf(hAPP_f584385070l_bool_type,type,
hAPP_f584385070l_bool: fun_fu844176604l_bool > fun_Ar1809396326i_bool > bool ).
thf(hAPP_f846027769ol_nat_type,type,
hAPP_f846027769ol_nat: fun_fu1603738721ol_nat > fun_Ar1809396326i_bool > nat ).
thf(hAPP_f668886383t_bool_type,type,
hAPP_f668886383t_bool: fun_fu1821795357t_bool > fun_Ar1809396326i_bool > fun_Ar535288606t_bool ).
thf(hAPP_f359069313i_bool_type,type,
hAPP_f359069313i_bool: fun_fu857388591i_bool > fun_Ar1809396326i_bool > fun_Pr895221296i_bool ).
thf(hAPP_f966656047t_bool_type,type,
hAPP_f966656047t_bool: fun_fu1372829539t_bool > fun_Ar671024215di_nat > fun_Ar603939593t_bool ).
thf(hAPP_f2102110817t_bool_type,type,
hAPP_f2102110817t_bool: fun_fu548876995t_bool > fun_Ar290235730t_bool > fun_Ar1753411852t_bool ).
thf(hAPP_f1631649925t_bool_type,type,
hAPP_f1631649925t_bool: fun_fu2128130023t_bool > fun_Ar64685412t_bool > fun_Ar1623257374t_bool ).
thf(hAPP_f721434149i_bool_type,type,
hAPP_f721434149i_bool: fun_fu1610971917i_bool > fun_Ar603939593t_bool > fun_na2037635353i_bool ).
thf(hAPP_f1908974253t_bool_type,type,
hAPP_f1908974253t_bool: fun_fu2030607631t_bool > fun_Ar535288606t_bool > fun_fu230081932t_bool ).
thf(hAPP_f601594885t_bool_type,type,
hAPP_f601594885t_bool: fun_fu205223783t_bool > fun_Ar516759882t_bool > fun_fu1847201208t_bool ).
thf(hAPP_f995490902l_bool_type,type,
hAPP_f995490902l_bool: fun_fu3835832l_bool > fun_Ar274636406t_bool > bool ).
thf(hAPP_f1751344075t_bool_type,type,
hAPP_f1751344075t_bool: fun_fu1427663149t_bool > fun_Ar274636406t_bool > fun_Ar290235730t_bool ).
thf(hAPP_f831214557t_bool_type,type,
hAPP_f831214557t_bool: fun_fu1896276031t_bool > fun_Ar274636406t_bool > fun_Ar64685412t_bool ).
thf(hAPP_f1001205955t_bool_type,type,
hAPP_f1001205955t_bool: fun_fu419698981t_bool > fun_Ar274636406t_bool > fun_Ar516759882t_bool ).
thf(hAPP_f1302887663t_bool_type,type,
hAPP_f1302887663t_bool: fun_fu1037963345t_bool > fun_Ar274636406t_bool > fun_Ar274636406t_bool ).
thf(hAPP_f1225332775l_bool_type,type,
hAPP_f1225332775l_bool: fun_fu361117961l_bool > fun_Ar274636406t_bool > fun_fu1370139438l_bool ).
thf(hAPP_f1915815064l_bool_type,type,
hAPP_f1915815064l_bool: fun_fu1863781882l_bool > fun_Ar274636406t_bool > fun_fu638310559l_bool ).
thf(hAPP_f2008608496t_bool_type,type,
hAPP_f2008608496t_bool: fun_fu2114379172t_bool > fun_Ar274636406t_bool > fun_Pr2067565481t_bool ).
thf(hAPP_f766019597l_bool_type,type,
hAPP_f766019597l_bool: fun_fu2141985013l_bool > fun_Ar338949104le_alt > fun_fu762833832l_bool ).
thf(hAPP_f387058535l_bool_type,type,
hAPP_f387058535l_bool: fun_fu1255657237l_bool > fun_bool_bool > bool ).
thf(hAPP_f612708895l_bool_type,type,
hAPP_f612708895l_bool: fun_fu1393819981l_bool > fun_bool_bool > fun_fu1255657237l_bool ).
thf(hAPP_f699791347l_bool_type,type,
hAPP_f699791347l_bool: fun_fu459284641l_bool > fun_bool_bool > fun_Pr1780397033l_bool ).
thf(hAPP_f416878261l_bool_type,type,
hAPP_f416878261l_bool: fun_fu827796887l_bool > fun_bo1431306493t_bool > fun_fu422653621l_bool ).
thf(hAPP_f334747853l_bool_type,type,
hAPP_f334747853l_bool: fun_fu662095797l_bool > fun_bo1682907689le_alt > fun_fu1304377569l_bool ).
thf(hAPP_f54304608l_bool_type,type,
hAPP_f54304608l_bool: fun_fu425979586l_bool > fun_nat_bool > bool ).
thf(hAPP_f2028818269l_bool_type,type,
hAPP_f2028818269l_bool: fun_fu309829899l_bool > fun_Pr1643180309t_bool > bool ).
thf(hAPP_f723483871t_bool_type,type,
hAPP_f723483871t_bool: fun_fu32501645t_bool > fun_Pr1643180309t_bool > fun_Pr1069395679t_bool ).
thf(hAPP_f41367117l_bool_type,type,
hAPP_f41367117l_bool: fun_fu323675445l_bool > fun_Pr2090226719le_alt > fun_fu152274135l_bool ).
thf(hAPP_f73423488l_bool_type,type,
hAPP_f73423488l_bool: fun_fu1370139438l_bool > fun_fu3835832l_bool > bool ).
thf(hAPP_f1572141188l_bool_type,type,
hAPP_f1572141188l_bool: fun_fu2098777574l_bool > fun_fu2114379172t_bool > bool ).
thf(hAPP_f399308031i_bool_type,type,
hAPP_f399308031i_bool: fun_fu2109152051i_bool > fun_fu2114379172t_bool > fun_Ar1809396326i_bool ).
thf(hAPP_f1714503811l_bool_type,type,
hAPP_f1714503811l_bool: fun_fu1383920485l_bool > fun_fu2114379172t_bool > fun_fu1992232028l_bool ).
thf(hAPP_f1754488902l_bool_type,type,
hAPP_f1754488902l_bool: fun_fu762833832l_bool > fun_fu802339430t_bool > bool ).
thf(hAPP_f398210311l_bool_type,type,
hAPP_f398210311l_bool: fun_fu422653621l_bool > fun_fu1618772927l_bool > bool ).
thf(hAPP_f1620711039l_bool_type,type,
hAPP_f1620711039l_bool: fun_fu1304377569l_bool > fun_fu1168191263t_bool > bool ).
thf(hAPP_f684683381l_bool_type,type,
hAPP_f684683381l_bool: fun_fu152274135l_bool > fun_fu524263445t_bool > bool ).
thf(hAPP_f975209902l_bool_type,type,
hAPP_f975209902l_bool: fun_fu1992232028l_bool > fun_fu2098777574l_bool > bool ).
thf(hAPP_f2124588998l_bool_type,type,
hAPP_f2124588998l_bool: fun_fu1132933928l_bool > fun_fu902545894i_bool > bool ).
thf(hAPP_f182583295l_bool_type,type,
hAPP_f182583295l_bool: fun_fu2013733473l_bool > fun_fu638310559l_bool > bool ).
thf(hAPP_f1487854056ol_nat_type,type,
hAPP_f1487854056ol_nat: fun_fu955147676ol_nat > fun_fu638310559l_bool > nat ).
thf(hAPP_f1717907078l_bool_type,type,
hAPP_f1717907078l_bool: fun_fu1868761018l_bool > fun_fu638310559l_bool > fun_Ar1474557608l_bool ).
thf(hAPP_f86272063l_bool_type,type,
hAPP_f86272063l_bool: fun_fu151575155l_bool > fun_fu638310559l_bool > fun_bo377688929l_bool ).
thf(hAPP_f1104294872l_bool_type,type,
hAPP_f1104294872l_bool: fun_fu329401612l_bool > fun_fu638310559l_bool > fun_fu1863781882l_bool ).
thf(hAPP_f1722316607l_bool_type,type,
hAPP_f1722316607l_bool: fun_fu1265985907l_bool > fun_fu638310559l_bool > fun_fu2013733473l_bool ).
thf(hAPP_f1060563265l_bool_type,type,
hAPP_f1060563265l_bool: fun_fu1824295331l_bool > fun_fu638310559l_bool > fun_fu638310559l_bool ).
thf(hAPP_f1776355587l_bool_type,type,
hAPP_f1776355587l_bool: fun_fu452089579l_bool > fun_fu864675765l_bool > fun_fu1824295331l_bool ).
thf(hAPP_f1159856629l_bool_type,type,
hAPP_f1159856629l_bool: fun_fu627447383l_bool > fun_fu1428746645t_bool > bool ).
thf(hAPP_f1187850253l_bool_type,type,
hAPP_f1187850253l_bool: fun_fu916781301l_bool > fun_Pr1509342064e_indi > fun_fu1132933928l_bool ).
thf(hAPP_f52567537l_bool_type,type,
hAPP_f52567537l_bool: fun_fu638310559l_bool > fun_Pr2067565481t_bool > bool ).
thf(hAPP_f1842225014ol_nat_type,type,
hAPP_f1842225014ol_nat: fun_fu841105374ol_nat > fun_Pr2067565481t_bool > nat ).
thf(hAPP_f234621849t_bool_type,type,
hAPP_f234621849t_bool: fun_fu1534804551t_bool > fun_Pr2067565481t_bool > fun_Ar17477381t_bool ).
thf(hAPP_f449303873t_bool_type,type,
hAPP_f449303873t_bool: fun_fu1118734319t_bool > fun_Pr2067565481t_bool > fun_Ar331856045t_bool ).
thf(hAPP_f1550387441t_bool_type,type,
hAPP_f1550387441t_bool: fun_fu1287834969t_bool > fun_Pr2067565481t_bool > fun_Ar797671557t_bool ).
thf(hAPP_f1761571331t_bool_type,type,
hAPP_f1761571331t_bool: fun_fu1679793515t_bool > fun_Pr2067565481t_bool > fun_Ar1573071255t_bool ).
thf(hAPP_f1344464862t_bool_type,type,
hAPP_f1344464862t_bool: fun_fu230081932t_bool > fun_Pr2067565481t_bool > fun_Ar516759882t_bool ).
thf(hAPP_f480276746t_bool_type,type,
hAPP_f480276746t_bool: fun_fu1847201208t_bool > fun_Pr2067565481t_bool > fun_Ar274636406t_bool ).
thf(hAPP_f1723896209t_bool_type,type,
hAPP_f1723896209t_bool: fun_fu1414555455t_bool > fun_Pr2067565481t_bool > fun_bo1431306493t_bool ).
thf(hAPP_f15777819t_bool_type,type,
hAPP_f15777819t_bool: fun_fu1648543689t_bool > fun_Pr2067565481t_bool > fun_Pr1887398791t_bool ).
thf(hAPP_f1482930381l_bool_type,type,
hAPP_f1482930381l_bool: fun_fu864675765l_bool > fun_Pr2067565481t_bool > fun_fu2013733473l_bool ).
thf(hAPP_f930900275l_bool_type,type,
hAPP_f930900275l_bool: fun_fu643206625l_bool > fun_Pr2067565481t_bool > fun_fu638310559l_bool ).
thf(hAPP_f1299954409t_bool_type,type,
hAPP_f1299954409t_bool: fun_fu297564241t_bool > fun_Pr2067565481t_bool > fun_fu1550952061t_bool ).
thf(hAPP_f1356305429t_bool_type,type,
hAPP_f1356305429t_bool: fun_fu1550952061t_bool > fun_Pr2067565481t_bool > fun_Pr2067565481t_bool ).
thf(hAPP_f1700632141l_bool_type,type,
hAPP_f1700632141l_bool: fun_fu318801205l_bool > fun_Pr376858015t_unit > fun_fu627447383l_bool ).
thf(hAPP_f1033183015t_bool_type,type,
hAPP_f1033183015t_bool: fun_fu598681231t_bool > fun_Pr1085078251l_bool > fun_fu1550952061t_bool ).
thf(hAPP_P276596750e_indi_type,type,
hAPP_P276596750e_indi: fun_Pr1509342064e_indi > produc472769767le_alt > arrow_856714788e_indi ).
thf(hAPP_P1178790471t_bool_type,type,
hAPP_P1178790471t_bool: fun_Pr2067565481t_bool > produc472769767le_alt > bool ).
thf(hAPP_P1069491261t_unit_type,type,
hAPP_P1069491261t_unit: fun_Pr376858015t_unit > produc472769767le_alt > product_unit ).
thf(hAPP_P1859429372i_bool_type,type,
hAPP_P1859429372i_bool: fun_Pr895221296i_bool > produc472769767le_alt > fun_Ar1809396326i_bool ).
thf(hAPP_P1103642805l_bool_type,type,
hAPP_P1103642805l_bool: fun_Pr1780397033l_bool > produc472769767le_alt > fun_bool_bool ).
thf(hAPP_P2037731755t_bool_type,type,
hAPP_P2037731755t_bool: fun_Pr1069395679t_bool > produc472769767le_alt > fun_Pr1643180309t_bool ).
thf(hAPP_P38525833l_bool_type,type,
hAPP_P38525833l_bool: fun_Pr1085078251l_bool > produc472769767le_alt > fun_fu638310559l_bool ).
thf(hBOOL_type,type,
hBOOL: bool > $o ).
thf(member1479139729e_indi_type,type,
member1479139729e_indi: fun_Ar1047186533l_bool ).
thf(member_bool_type,type,
member_bool: fun_bo492988759l_bool ).
thf(member_Product_unit_type,type,
member_Product_unit: fun_Pr1863373635l_bool ).
thf(member933336803t_bool_type,type,
member933336803t_bool: fun_fu361117961l_bool ).
thf(member387840963le_alt_type,type,
member387840963le_alt: fun_fu2141985013l_bool ).
thf(member1133581546t_bool_type,type,
member1133581546t_bool: fun_fu827796887l_bool ).
thf(member684813948le_alt_type,type,
member684813948le_alt: fun_fu662095797l_bool ).
thf(member869664626le_alt_type,type,
member869664626le_alt: fun_fu323675445l_bool ).
thf(member173038353t_bool_type,type,
member173038353t_bool: fun_fu1383920485l_bool ).
thf(member1558233923e_indi_type,type,
member1558233923e_indi: fun_fu916781301l_bool ).
thf(member1069471740t_bool_type,type,
member1069471740t_bool: fun_fu864675765l_bool ).
thf(member1303779570t_unit_type,type,
member1303779570t_unit: fun_fu318801205l_bool ).
thf(member1333168212le_alt_type,type,
member1333168212le_alt: fun_Pr1085078251l_bool ).
thf(f_type,type,
f: fun_fu2114379172t_bool ).
thf(lab_type,type,
lab: fun_Pr2067565481t_bool ).
thf(lba_type,type,
lba: fun_Pr2067565481t_bool ).
thf(p_type,type,
p: fun_Ar274636406t_bool ).
thf(a_type,type,
a: arrow_1893660431le_alt ).
thf(b_type,type,
b: arrow_1893660431le_alt ).
thf(c_type,type,
c: arrow_1893660431le_alt ).
thf(d_type,type,
d: arrow_1893660431le_alt ).
thf(e_type,type,
e: arrow_1893660431le_alt ).
thf(h_type,type,
h: fun_Ar671024215di_nat ).
thf(n_type,type,
n: nat ).
thf(433,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( B = A )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_xt1_I4_J) ).
thf(2163,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( B = A )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(116,axiom,
! [A: nat,B: nat,C: fun_nat_nat] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ C ) @ top_top_fun_nat_bool ) )
=> ( ( ( hAPP_nat_nat @ C @ A )
= B )
=> ( ( hAPP_nat_nat @ ( hilber195283148at_nat @ top_top_fun_nat_bool @ C ) @ B )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_inv__f__eq) ).
thf(1036,plain,
! [A: nat,B: nat,C: fun_nat_nat] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ C ) @ top_top_fun_nat_bool ) )
=> ( ( ( hAPP_nat_nat @ C @ A )
= B )
=> ( ( hAPP_nat_nat @ ( hilber195283148at_nat @ top_top_fun_nat_bool @ C ) @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(350,axiom,
! [A: nat] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_981_less__not__refl) ).
thf(1879,plain,
! [A: nat] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(396,axiom,
! [A: arrow_856714788e_indi] :
( ( hBOOL @ ( hAPP_A997847300i_bool @ top_to788185952i_bool @ A ) )
<=> ( hBOOL @ top_top_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_top__apply) ).
thf(2031,plain,
! [A: arrow_856714788e_indi] :
( ( ( hBOOL @ ( hAPP_A997847300i_bool @ top_to788185952i_bool @ A ) )
=> ( hBOOL @ top_top_bool ) )
& ( ( hBOOL @ top_top_bool )
=> ( hBOOL @ ( hAPP_A997847300i_bool @ top_to788185952i_bool @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(407,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1045_neq0__conv) ).
thf(2072,plain,
! [A: nat] :
( ( ( A != zero_zero_nat )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( A != zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(267,axiom,
! [A: fun_fu1679793515t_bool,B: fun_Ar274636406t_bool,C: arrow_856714788e_indi] :
( ( hAPP_A1309733808t_bool @ ( hAPP_f831214557t_bool @ ( cOMBB_80760910e_indi @ A ) @ B ) @ C )
= ( hAPP_f1761571331t_bool @ A @ ( hAPP_A1646126530t_bool @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ef) ).
thf(1559,plain,
! [A: fun_fu1679793515t_bool,B: fun_Ar274636406t_bool,C: arrow_856714788e_indi] :
( ( hAPP_A1309733808t_bool @ ( hAPP_f831214557t_bool @ ( cOMBB_80760910e_indi @ A ) @ B ) @ C )
= ( hAPP_f1761571331t_bool @ A @ ( hAPP_A1646126530t_bool @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(314,axiom,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
thf(1729,plain,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(167,axiom,
! [A: nat,B: nat] :
( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_988_nat__add__commute) ).
thf(1237,plain,
! [A: nat,B: nat] :
( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(114,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1002_trans__less__add1) ).
thf(1031,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(378,axiom,
! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool,C: fun_Ar331856045t_bool] :
( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ B ) @ C ) )
=> ( ( B = A )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_xt1_I4_J) ).
thf(1982,plain,
! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool,C: fun_Ar331856045t_bool] :
( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ B ) @ C ) )
=> ( ( B = A )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(372,axiom,
! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool] :
( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ A ) @ B ) )
<=> ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ A ) @ B ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_404_order__le__less) ).
thf(1956,plain,
! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool] :
( ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ A ) @ B ) )
| ( A = B ) ) )
& ( ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ A ) @ B ) )
| ( A = B ) )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(277,axiom,
! [A: fun_fu2114379172t_bool,B: fun_fu1863781882l_bool,C: fun_fu3835832l_bool] :
( ! [D: fun_Ar274636406t_bool] :
( ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ D ) @ C ) )
=> ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ ( hAPP_f2008608496t_bool @ A @ D ) ) @ ( hAPP_f1915815064l_bool @ B @ D ) ) ) )
=> ( hBOOL @ ( hAPP_f975209902l_bool @ ( hAPP_f1714503811l_bool @ member173038353t_bool @ A ) @ ( pi_fun1746584570t_bool @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_649_Pi__I) ).
thf(1586,plain,
! [A: fun_fu2114379172t_bool,B: fun_fu1863781882l_bool,C: fun_fu3835832l_bool] :
( ! [D: fun_Ar274636406t_bool] :
( ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ D ) @ C ) )
=> ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ ( hAPP_f2008608496t_bool @ A @ D ) ) @ ( hAPP_f1915815064l_bool @ B @ D ) ) ) )
=> ( hBOOL @ ( hAPP_f975209902l_bool @ ( hAPP_f1714503811l_bool @ member173038353t_bool @ A ) @ ( pi_fun1746584570t_bool @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(59,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_742_add__less__imp__less__left) ).
thf(809,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(414,axiom,
! [A: fun_Ar274636406t_bool,B: fun_fu2114379172t_bool,C: fun_fu3835832l_bool,D: fun_fu1863781882l_bool] :
( ( hBOOL @ ( hAPP_f975209902l_bool @ ( hAPP_f1714503811l_bool @ member173038353t_bool @ B ) @ ( pi_fun1746584570t_bool @ C @ D ) ) )
=> ( ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ ( hAPP_f2008608496t_bool @ B @ A ) ) @ ( hAPP_f1915815064l_bool @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_576_Pi__mem) ).
thf(2094,plain,
! [A: fun_Ar274636406t_bool,B: fun_fu2114379172t_bool,C: fun_fu3835832l_bool,D: fun_fu1863781882l_bool] :
( ( hBOOL @ ( hAPP_f975209902l_bool @ ( hAPP_f1714503811l_bool @ member173038353t_bool @ B ) @ ( pi_fun1746584570t_bool @ C @ D ) ) )
=> ( ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ ( hAPP_f2008608496t_bool @ B @ A ) ) @ ( hAPP_f1915815064l_bool @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(219,axiom,
! [A: nat,B: fun_nat_bool] :
( ( hBOOL @ ( hAPP_nat_bool @ B @ zero_zero_nat ) )
=> ( ! [C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ B @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ B @ ( hAPP_nat_nat @ suc @ C ) ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1126_nat__induct) ).
thf(1411,plain,
! [A: nat,B: fun_nat_bool] :
( ( hBOOL @ ( hAPP_nat_bool @ B @ zero_zero_nat ) )
=> ( ! [C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ B @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ B @ ( hAPP_nat_nat @ suc @ C ) ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(332,axiom,
~ ! [A: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_f846027769ol_nat @ finite1672073426e_indi @ top_to788185952i_bool ) ) )
=> ( ! [B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ b ) @ a ) ) @ ( hAPP_f2008608496t_bool @ f @ ( hAPP_f480276746t_bool @ ( hAPP_f601594885t_bool @ cOMBC_750853729t_bool @ ( hAPP_f1344464862t_bool @ ( hAPP_f1908974253t_bool @ cOMBC_156709173t_bool @ ( hAPP_f668886383t_bool @ ( cOMBB_1061985500e_indi @ if_fun523439385t_bool ) @ ( hAPP_n34002993i_bool @ ( hAPP_f721434149i_bool @ cOMBC_722552198t_bool @ ( hAPP_f966656047t_bool @ ( cOMBB_1869811296e_indi @ ord_less_nat ) @ h ) ) @ B ) ) ) @ lab ) ) @ lba ) ) ) ) )
=> ~ ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ a ) @ b ) ) @ ( hAPP_f2008608496t_bool @ f @ ( hAPP_f480276746t_bool @ ( hAPP_f601594885t_bool @ cOMBC_750853729t_bool @ ( hAPP_f1344464862t_bool @ ( hAPP_f1908974253t_bool @ cOMBC_156709173t_bool @ ( hAPP_f668886383t_bool @ ( cOMBB_1061985500e_indi @ if_fun523439385t_bool ) @ ( hAPP_n34002993i_bool @ ( hAPP_f721434149i_bool @ cOMBC_722552198t_bool @ ( hAPP_f966656047t_bool @ ( cOMBB_1869811296e_indi @ ord_less_nat ) @ h ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ one_one_nat ) ) ) ) @ lab ) ) @ lba ) ) ) ) ) ),
file('/export/starexec/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(1823,plain,
~ ! [A: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_f846027769ol_nat @ finite1672073426e_indi @ top_to788185952i_bool ) ) )
=> ( ! [B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ b ) @ a ) ) @ ( hAPP_f2008608496t_bool @ f @ ( hAPP_f480276746t_bool @ ( hAPP_f601594885t_bool @ cOMBC_750853729t_bool @ ( hAPP_f1344464862t_bool @ ( hAPP_f1908974253t_bool @ cOMBC_156709173t_bool @ ( hAPP_f668886383t_bool @ ( cOMBB_1061985500e_indi @ if_fun523439385t_bool ) @ ( hAPP_n34002993i_bool @ ( hAPP_f721434149i_bool @ cOMBC_722552198t_bool @ ( hAPP_f966656047t_bool @ ( cOMBB_1869811296e_indi @ ord_less_nat ) @ h ) ) @ B ) ) ) @ lab ) ) @ lba ) ) ) ) )
=> ~ ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ a ) @ b ) ) @ ( hAPP_f2008608496t_bool @ f @ ( hAPP_f480276746t_bool @ ( hAPP_f601594885t_bool @ cOMBC_750853729t_bool @ ( hAPP_f1344464862t_bool @ ( hAPP_f1908974253t_bool @ cOMBC_156709173t_bool @ ( hAPP_f668886383t_bool @ ( cOMBB_1061985500e_indi @ if_fun523439385t_bool ) @ ( hAPP_n34002993i_bool @ ( hAPP_f721434149i_bool @ cOMBC_722552198t_bool @ ( hAPP_f966656047t_bool @ ( cOMBB_1869811296e_indi @ ord_less_nat ) @ h ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ one_one_nat ) ) ) ) @ lab ) ) @ lba ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(157,axiom,
! [A: nat,B: nat,C: fun_nat_nat] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ C ) @ top_top_fun_nat_bool ) )
=> ( ( ( hAPP_nat_nat @ C @ A )
= ( hAPP_nat_nat @ C @ B ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_615_injD) ).
thf(1190,plain,
! [A: nat,B: nat,C: fun_nat_nat] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ C ) @ top_top_fun_nat_bool ) )
=> ( ( ( hAPP_nat_nat @ C @ A )
= ( hAPP_nat_nat @ C @ B ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(192,axiom,
! [A: nat] :
( ( hAPP_nat_nat @ size_size_nat @ ( hAPP_nat_nat @ suc @ A ) )
= ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ ( hAPP_nat_nat @ size_size_nat @ A ) ) @ ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1183_nat_Osize_I4_J) ).
thf(1315,plain,
! [A: nat] :
( ( hAPP_nat_nat @ size_size_nat @ ( hAPP_nat_nat @ suc @ A ) )
= ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ ( hAPP_nat_nat @ size_size_nat @ A ) ) @ ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(524,axiom,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ A ) @ B ) )
<=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_712_less__fun__def) ).
thf(2595,plain,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
( ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ B ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(307,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_986_less__not__refl3) ).
thf(1686,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(453,axiom,
! [A: fun_na300967376t_bool,B: fun_Ar331856045t_bool,C: nat,D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ ( hAPP_n1312530466t_bool @ A @ D ) ) @ B ) )
=> ( ! [E: nat,F: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ E ) @ F ) )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ ( hAPP_n1312530466t_bool @ A @ E ) ) @ ( hAPP_n1312530466t_bool @ A @ F ) ) ) )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ ( hAPP_n1312530466t_bool @ A @ C ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_900_order__less__le__subst2) ).
thf(2250,plain,
! [A: fun_na300967376t_bool,B: fun_Ar331856045t_bool,C: nat,D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ ( hAPP_n1312530466t_bool @ A @ D ) ) @ B ) )
=> ( ! [E: nat,F: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ E ) @ F ) )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ ( hAPP_n1312530466t_bool @ A @ E ) ) @ ( hAPP_n1312530466t_bool @ A @ F ) ) ) )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ ( hAPP_n1312530466t_bool @ A @ C ) ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(343,axiom,
! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool] :
( ( A != B )
=> ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ B ) @ A ) )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_427_xt1_I12_J) ).
thf(1855,plain,
! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool] :
( ( A != B )
=> ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ B ) @ A ) )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(280,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_order__antisym__conv) ).
thf(1596,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(24,axiom,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ C )
= ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1149_add__mult__distrib) ).
thf(683,plain,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ C )
= ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(351,axiom,
! [A: nat,B: nat] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_407_leI) ).
thf(1882,plain,
! [A: nat,B: nat] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(532,axiom,
! [A: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ top_to1138392227t_bool ) @ A ) )
=> ( A = top_to1138392227t_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_534_top__le) ).
thf(2622,plain,
! [A: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ top_to1138392227t_bool ) @ A ) )
=> ( A = top_to1138392227t_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(542,axiom,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
( ( B = C )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_ord__eq__le__trans) ).
thf(2644,plain,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
( ( B = C )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(404,axiom,
! [A: product_unit,B: fun_Pr1643180309t_bool] :
( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ A ) @ B ) )
<=> ( hBOOL @ ( hAPP_P1676879539t_bool @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_mem__def) ).
thf(2062,plain,
! [A: product_unit,B: fun_Pr1643180309t_bool] :
( ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_P1676879539t_bool @ B @ A ) ) )
& ( ( hBOOL @ ( hAPP_P1676879539t_bool @ B @ A ) )
=> ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(286,axiom,
! [A: fun_Ar274636406t_bool,B: fun_Ar1474557608l_bool,C: fun_Ar1809396326i_bool] :
( ! [D: arrow_856714788e_indi] :
( ( hBOOL @ ( hAPP_f584385070l_bool @ ( hAPP_A1597696899l_bool @ member1479139729e_indi @ D ) @ C ) )
=> ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ ( hAPP_A1646126530t_bool @ A @ D ) ) @ ( hAPP_A897398598l_bool @ B @ D ) ) ) )
=> ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ A ) @ ( pi_Arr959578316t_bool @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_650_Pi__I) ).
thf(1618,plain,
! [A: fun_Ar274636406t_bool,B: fun_Ar1474557608l_bool,C: fun_Ar1809396326i_bool] :
( ! [D: arrow_856714788e_indi] :
( ( hBOOL @ ( hAPP_f584385070l_bool @ ( hAPP_A1597696899l_bool @ member1479139729e_indi @ D ) @ C ) )
=> ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ ( hAPP_A1646126530t_bool @ A @ D ) ) @ ( hAPP_A897398598l_bool @ B @ D ) ) ) )
=> ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ A ) @ ( pi_Arr959578316t_bool @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(366,axiom,
! [A: fun_Pr2067565481t_bool] : ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ A ) @ top_to1312956197l_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_UNIV__I) ).
thf(1939,plain,
! [A: fun_Pr2067565481t_bool] : ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ A ) @ top_to1312956197l_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(129,axiom,
! [A: fun_bool_bool,B: produc472769767le_alt] :
( ( hAPP_P1103642805l_bool @ ( hAPP_f699791347l_bool @ cOMBK_138598520le_alt @ A ) @ B )
= 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(1073,plain,
! [A: fun_bool_bool,B: produc472769767le_alt] :
( ( hAPP_P1103642805l_bool @ ( hAPP_f699791347l_bool @ cOMBK_138598520le_alt @ A ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(161,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) )
=> ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1074_less__SucE) ).
thf(1205,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) )
=> ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(463,axiom,
! [A: arrow_856714788e_indi] :
( ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_A376526755di_nat @ h @ A ) ) @ n ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ e ) @ d ) ) @ ( hAPP_A1601437999t_bool @ ( hAPP_f1761571331t_bool @ arrow_1630265669_mktop @ ( hAPP_A1646126530t_bool @ p @ A ) ) @ e ) ) ) )
& ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_A376526755di_nat @ h @ A ) ) @ n ) )
=> ( ( ( ( hAPP_A376526755di_nat @ h @ A )
= n )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ e ) @ d ) ) @ ( hAPP_A1601437999t_bool @ ( hAPP_A1058422557t_bool @ ( hAPP_f1550387441t_bool @ arrow_216713899_above @ ( hAPP_A1646126530t_bool @ p @ A ) ) @ c ) @ e ) ) ) )
& ( ( ( hAPP_A376526755di_nat @ h @ A )
!= n )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ e ) @ d ) ) @ ( hAPP_A1601437999t_bool @ ( hAPP_f1761571331t_bool @ arrow_1481558583_mkbot @ ( hAPP_A1646126530t_bool @ p @ A ) ) @ e ) ) ) ) ) ) )
<=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_A376526755di_nat @ h @ A ) ) @ n ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ b ) @ a ) ) @ lab ) ) )
& ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_A376526755di_nat @ h @ A ) ) @ n ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ b ) @ a ) ) @ lba ) ) ) ) ),
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(2282,plain,
! [A: arrow_856714788e_indi] :
( ( ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_A376526755di_nat @ h @ A ) ) @ n ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ e ) @ d ) ) @ ( hAPP_A1601437999t_bool @ ( hAPP_f1761571331t_bool @ arrow_1630265669_mktop @ ( hAPP_A1646126530t_bool @ p @ A ) ) @ e ) ) ) )
& ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_A376526755di_nat @ h @ A ) ) @ n ) )
=> ( ( ( ( hAPP_A376526755di_nat @ h @ A )
= n )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ e ) @ d ) ) @ ( hAPP_A1601437999t_bool @ ( hAPP_A1058422557t_bool @ ( hAPP_f1550387441t_bool @ arrow_216713899_above @ ( hAPP_A1646126530t_bool @ p @ A ) ) @ c ) @ e ) ) ) )
& ( ( ( hAPP_A376526755di_nat @ h @ A )
!= n )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ e ) @ d ) ) @ ( hAPP_A1601437999t_bool @ ( hAPP_f1761571331t_bool @ arrow_1481558583_mkbot @ ( hAPP_A1646126530t_bool @ p @ A ) ) @ e ) ) ) ) ) ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_A376526755di_nat @ h @ A ) ) @ n ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ b ) @ a ) ) @ lab ) ) )
& ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_A376526755di_nat @ h @ A ) ) @ n ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ b ) @ a ) ) @ lba ) ) ) ) )
& ( ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_A376526755di_nat @ h @ A ) ) @ n ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ b ) @ a ) ) @ lab ) ) )
& ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_A376526755di_nat @ h @ A ) ) @ n ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ b ) @ a ) ) @ lba ) ) ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_A376526755di_nat @ h @ A ) ) @ n ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ e ) @ d ) ) @ ( hAPP_A1601437999t_bool @ ( hAPP_f1761571331t_bool @ arrow_1630265669_mktop @ ( hAPP_A1646126530t_bool @ p @ A ) ) @ e ) ) ) )
& ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_A376526755di_nat @ h @ A ) ) @ n ) )
=> ( ( ( ( hAPP_A376526755di_nat @ h @ A )
= n )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ e ) @ d ) ) @ ( hAPP_A1601437999t_bool @ ( hAPP_A1058422557t_bool @ ( hAPP_f1550387441t_bool @ arrow_216713899_above @ ( hAPP_A1646126530t_bool @ p @ A ) ) @ c ) @ e ) ) ) )
& ( ( ( hAPP_A376526755di_nat @ h @ A )
!= n )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ e ) @ d ) ) @ ( hAPP_A1601437999t_bool @ ( hAPP_f1761571331t_bool @ arrow_1481558583_mkbot @ ( hAPP_A1646126530t_bool @ p @ A ) ) @ e ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(551,axiom,
c != d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__096c_A_126_061_Ad_096) ).
thf(2671,plain,
c != d,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(553,axiom,
hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ c ) @ e ) ) @ ( hAPP_f2008608496t_bool @ f @ ( hAPP_f1302887663t_bool @ ( cOMBS_1181656689t_bool @ ( hAPP_f1001205955t_bool @ ( cOMBS_1925466437t_bool @ ( hAPP_f668886383t_bool @ ( cOMBB_1061985500e_indi @ if_fun523439385t_bool ) @ ( hAPP_n34002993i_bool @ ( hAPP_f721434149i_bool @ cOMBC_722552198t_bool @ ( hAPP_f966656047t_bool @ ( cOMBB_1869811296e_indi @ ord_less_nat ) @ h ) ) @ n ) ) ) @ ( hAPP_A425126512t_bool @ ( hAPP_f1631649925t_bool @ cOMBC_1417338747t_bool @ ( hAPP_f831214557t_bool @ ( cOMBB_80760910e_indi @ arrow_1630265669_mktop ) @ p ) ) @ e ) ) ) @ ( hAPP_f1302887663t_bool @ ( cOMBS_1181656689t_bool @ ( hAPP_f1001205955t_bool @ ( cOMBS_1925466437t_bool @ ( hAPP_f668886383t_bool @ ( cOMBB_1061985500e_indi @ if_fun523439385t_bool ) @ ( hAPP_n34002993i_bool @ ( hAPP_f721434149i_bool @ cOMBC_722552198t_bool @ ( hAPP_f966656047t_bool @ ( cOMBB_1869811296e_indi @ fequal_nat ) @ h ) ) @ n ) ) ) @ ( hAPP_A425126512t_bool @ ( hAPP_f1631649925t_bool @ cOMBC_1417338747t_bool @ ( hAPP_A1889513822t_bool @ ( hAPP_f2102110817t_bool @ cOMBC_1486904681t_bool @ ( hAPP_f1751344075t_bool @ ( cOMBB_1876517692e_indi @ arrow_216713899_above ) @ p ) ) @ c ) ) @ e ) ) ) @ ( hAPP_A425126512t_bool @ ( hAPP_f1631649925t_bool @ cOMBC_1417338747t_bool @ ( hAPP_f831214557t_bool @ ( cOMBB_80760910e_indi @ arrow_1481558583_mkbot ) @ p ) ) @ e ) ) ) ) ),
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(2676,plain,
hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ c ) @ e ) ) @ ( hAPP_f2008608496t_bool @ f @ ( hAPP_f1302887663t_bool @ ( cOMBS_1181656689t_bool @ ( hAPP_f1001205955t_bool @ ( cOMBS_1925466437t_bool @ ( hAPP_f668886383t_bool @ ( cOMBB_1061985500e_indi @ if_fun523439385t_bool ) @ ( hAPP_n34002993i_bool @ ( hAPP_f721434149i_bool @ cOMBC_722552198t_bool @ ( hAPP_f966656047t_bool @ ( cOMBB_1869811296e_indi @ ord_less_nat ) @ h ) ) @ n ) ) ) @ ( hAPP_A425126512t_bool @ ( hAPP_f1631649925t_bool @ cOMBC_1417338747t_bool @ ( hAPP_f831214557t_bool @ ( cOMBB_80760910e_indi @ arrow_1630265669_mktop ) @ p ) ) @ e ) ) ) @ ( hAPP_f1302887663t_bool @ ( cOMBS_1181656689t_bool @ ( hAPP_f1001205955t_bool @ ( cOMBS_1925466437t_bool @ ( hAPP_f668886383t_bool @ ( cOMBB_1061985500e_indi @ if_fun523439385t_bool ) @ ( hAPP_n34002993i_bool @ ( hAPP_f721434149i_bool @ cOMBC_722552198t_bool @ ( hAPP_f966656047t_bool @ ( cOMBB_1869811296e_indi @ fequal_nat ) @ h ) ) @ n ) ) ) @ ( hAPP_A425126512t_bool @ ( hAPP_f1631649925t_bool @ cOMBC_1417338747t_bool @ ( hAPP_A1889513822t_bool @ ( hAPP_f2102110817t_bool @ cOMBC_1486904681t_bool @ ( hAPP_f1751344075t_bool @ ( cOMBB_1876517692e_indi @ arrow_216713899_above ) @ p ) ) @ c ) ) @ e ) ) ) @ ( hAPP_A425126512t_bool @ ( hAPP_f1631649925t_bool @ cOMBC_1417338747t_bool @ ( hAPP_f831214557t_bool @ ( cOMBB_80760910e_indi @ arrow_1481558583_mkbot ) @ p ) ) @ e ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(420,axiom,
! [A: nat,B: nat] :
( ( A = B )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_353_order__eq__refl) ).
thf(2114,plain,
! [A: nat,B: nat] :
( ( A = B )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(147,axiom,
! [A: nat,B: nat] :
( ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B )
= zero_zero_nat )
<=> ( ( A = zero_zero_nat )
& ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1051_add__is__0) ).
thf(1142,plain,
! [A: nat,B: nat] :
( ( ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B )
= zero_zero_nat )
=> ( ( A = zero_zero_nat )
& ( B = zero_zero_nat ) ) )
& ( ( ( A = zero_zero_nat )
& ( B = zero_zero_nat ) )
=> ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B )
= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(245,axiom,
! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool] :
( ( A != B )
=> ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_417_order__neq__le__trans) ).
thf(1497,plain,
! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool] :
( ( A != B )
=> ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(131,axiom,
! [A: fun_fu638310559l_bool,B: fun_fu638310559l_bool,C: fun_fu638310559l_bool] :
( ( B = C )
=> ( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_xt1_I3_J) ).
thf(1078,plain,
! [A: fun_fu638310559l_bool,B: fun_fu638310559l_bool,C: fun_fu638310559l_bool] :
( ( B = C )
=> ( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(302,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_985_less__not__refl2) ).
thf(1671,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(297,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_997_le__antisym) ).
thf(1655,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(146,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1104_Suc__le__eq) ).
thf(1137,plain,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(384,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1010_less__imp__le__nat) ).
thf(1999,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(180,axiom,
! [A: fun_fu638310559l_bool,B: fun_fu638310559l_bool] :
( ( A = B )
<=> ( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ A ) @ B ) )
& ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_355_order__eq__iff) ).
thf(1275,plain,
! [A: fun_fu638310559l_bool,B: fun_fu638310559l_bool] :
( ( ( A = B )
=> ( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ A ) @ B ) )
& ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ B ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ A ) @ B ) )
& ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ B ) @ A ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(61,axiom,
! [A: nat,B: nat,C: fun_nat_nat] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ C ) @ top_top_fun_nat_bool ) )
=> ( ( ( hAPP_nat_nat @ C @ A )
= ( hAPP_nat_nat @ C @ B ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_613_inj__eq) ).
thf(814,plain,
! [A: nat,B: nat,C: fun_nat_nat] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ C ) @ top_top_fun_nat_bool ) )
=> ( ( ( ( hAPP_nat_nat @ C @ A )
= ( hAPP_nat_nat @ C @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( hAPP_nat_nat @ C @ A )
= ( hAPP_nat_nat @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(534,axiom,
! [A: fun_Pr2067565481t_bool] : ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_order__refl) ).
thf(2627,plain,
! [A: fun_Pr2067565481t_bool] : ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(294,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_441_linorder__antisym__conv2) ).
thf(1640,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(371,axiom,
! [A: fun_Ar331856045t_bool] : ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ A ) @ top_to951839027t_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_517_top__greatest) ).
thf(1954,plain,
! [A: fun_Ar331856045t_bool] : ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ A ) @ top_to951839027t_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(232,axiom,
hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ a ) @ b ) ) @ ( hAPP_f2008608496t_bool @ f @ ( hAPP_f480276746t_bool @ ( hAPP_f601594885t_bool @ cOMBC_750853729t_bool @ ( hAPP_f1344464862t_bool @ ( hAPP_f1908974253t_bool @ cOMBC_156709173t_bool @ ( hAPP_f668886383t_bool @ ( cOMBB_1061985500e_indi @ if_fun523439385t_bool ) @ ( hAPP_n34002993i_bool @ ( hAPP_f721434149i_bool @ cOMBC_722552198t_bool @ ( hAPP_f966656047t_bool @ ( cOMBB_1869811296e_indi @ ord_less_nat ) @ h ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ n ) @ one_one_nat ) ) ) ) @ lab ) ) @ lba ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_n_I3_J) ).
thf(1458,plain,
hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ a ) @ b ) ) @ ( hAPP_f2008608496t_bool @ f @ ( hAPP_f480276746t_bool @ ( hAPP_f601594885t_bool @ cOMBC_750853729t_bool @ ( hAPP_f1344464862t_bool @ ( hAPP_f1908974253t_bool @ cOMBC_156709173t_bool @ ( hAPP_f668886383t_bool @ ( cOMBB_1061985500e_indi @ if_fun523439385t_bool ) @ ( hAPP_n34002993i_bool @ ( hAPP_f721434149i_bool @ cOMBC_722552198t_bool @ ( hAPP_f966656047t_bool @ ( cOMBB_1869811296e_indi @ ord_less_nat ) @ h ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ n ) @ one_one_nat ) ) ) ) @ lab ) ) @ lba ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(515,axiom,
! [A: fun_Pr2067565481t_bool] : ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ top_to1138392227t_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_516_top__greatest) ).
thf(2575,plain,
! [A: fun_Pr2067565481t_bool] : ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ top_to1138392227t_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(380,axiom,
! [A: fun_na998785244t_bool,B: fun_Pr2067565481t_bool,C: nat,D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ ( hAPP_n1161265524t_bool @ A @ D ) ) @ B ) )
=> ( ! [E: nat,F: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ E ) @ F ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ ( hAPP_n1161265524t_bool @ A @ E ) ) @ ( hAPP_n1161265524t_bool @ A @ F ) ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ ( hAPP_n1161265524t_bool @ A @ C ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_898_order__less__le__subst2) ).
thf(1988,plain,
! [A: fun_na998785244t_bool,B: fun_Pr2067565481t_bool,C: nat,D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ ( hAPP_n1161265524t_bool @ A @ D ) ) @ B ) )
=> ( ! [E: nat,F: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ E ) @ F ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ ( hAPP_n1161265524t_bool @ A @ E ) ) @ ( hAPP_n1161265524t_bool @ A @ F ) ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ ( hAPP_n1161265524t_bool @ A @ C ) ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(484,axiom,
hBOOL @ ( hAPP_f1572141188l_bool @ arrow_320876018nimity @ f ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_u) ).
thf(2459,plain,
hBOOL @ ( hAPP_f1572141188l_bool @ arrow_320876018nimity @ f ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(335,axiom,
! [A: fun_Ar636018671t_bool,B: fun_Pr2067565481t_bool,C: arrow_1893660431le_alt] :
( ( hAPP_A2063800319t_bool @ ( hAPP_f449303873t_bool @ ( hAPP_f1081591777t_bool @ cOMBC_557453916t_bool @ A ) @ B ) @ C )
= ( hAPP_f234621849t_bool @ ( hAPP_A656921921t_bool @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_000t_414) ).
thf(1835,plain,
! [A: fun_Ar636018671t_bool,B: fun_Pr2067565481t_bool,C: arrow_1893660431le_alt] :
( ( hAPP_A2063800319t_bool @ ( hAPP_f449303873t_bool @ ( hAPP_f1081591777t_bool @ cOMBC_557453916t_bool @ A ) @ B ) @ C )
= ( hAPP_f234621849t_bool @ ( hAPP_A656921921t_bool @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(213,axiom,
! [A: nat] :
( A
!= ( hAPP_nat_nat @ suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1065_n__not__Suc__n) ).
thf(1391,plain,
! [A: nat] :
( A
!= ( hAPP_nat_nat @ suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(49,axiom,
! [A: nat] :
( ( hAPP_nat_nat @ suc @ A )
= ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ one_one_nat ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1119_Suc__eq__plus1__left) ).
thf(782,plain,
! [A: nat] :
( ( hAPP_nat_nat @ suc @ A )
= ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ one_one_nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(284,axiom,
! [A: nat,B: fun_fu841105374ol_nat,C: fun_Pr2067565481t_bool,D: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_f1842225014ol_nat @ B @ C ) ) )
=> ( ! [E: fun_Pr2067565481t_bool,F: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ F ) @ E ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f1842225014ol_nat @ B @ F ) ) @ ( hAPP_f1842225014ol_nat @ B @ E ) ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_f1842225014ol_nat @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_702_xt7) ).
thf(1613,plain,
! [A: nat,B: fun_fu841105374ol_nat,C: fun_Pr2067565481t_bool,D: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_f1842225014ol_nat @ B @ C ) ) )
=> ( ! [E: fun_Pr2067565481t_bool,F: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ F ) @ E ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f1842225014ol_nat @ B @ F ) ) @ ( hAPP_f1842225014ol_nat @ B @ E ) ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_f1842225014ol_nat @ B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(435,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_xt1_I10_J) ).
thf(2173,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(495,axiom,
! [A: fun_bo1682907689le_alt,B: fun_bo1431306493t_bool,C: fun_bool_bool] :
( ! [D: bool] :
( ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ D ) @ C ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_b2094455111le_alt @ A @ D ) ) @ ( hAPP_b128655177t_bool @ B @ D ) ) ) )
=> ( hBOOL @ ( hAPP_f1620711039l_bool @ ( hAPP_f334747853l_bool @ member684813948le_alt @ A ) @ ( pi_boo7125949le_alt @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_635_Pi__I) ).
thf(2516,plain,
! [A: fun_bo1682907689le_alt,B: fun_bo1431306493t_bool,C: fun_bool_bool] :
( ! [D: bool] :
( ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ D ) @ C ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_b2094455111le_alt @ A @ D ) ) @ ( hAPP_b128655177t_bool @ B @ D ) ) ) )
=> ( hBOOL @ ( hAPP_f1620711039l_bool @ ( hAPP_f334747853l_bool @ member684813948le_alt @ A ) @ ( pi_boo7125949le_alt @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(353,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_440_order__less__imp__le) ).
thf(1887,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(319,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_430_leD) ).
thf(1746,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(79,axiom,
! [A: fun_fu638310559l_bool,B: fun_fu638310559l_bool] :
( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ B ) @ A ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_905_equalityI) ).
thf(898,plain,
! [A: fun_fu638310559l_bool,B: fun_fu638310559l_bool] :
( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ B ) @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(169,axiom,
! [A: nat] :
( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ zero_zero_nat ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1049_plus__nat_Oadd__0) ).
thf(1243,plain,
! [A: nat] :
( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ zero_zero_nat ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(143,axiom,
! [A: nat] :
( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ zero_zero_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1050_Nat_Oadd__0__right) ).
thf(1127,plain,
! [A: nat] :
( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ zero_zero_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(101,axiom,
! [A: fun_fu638310559l_bool] : ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_order__refl) ).
thf(973,plain,
! [A: fun_fu638310559l_bool] : ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(120,axiom,
! [A: fun_fu638310559l_bool] :
( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ top_to1312956197l_bool ) @ A ) )
=> ( A = top_to1312956197l_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_530_top__le) ).
thf(1046,plain,
! [A: fun_fu638310559l_bool] :
( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ top_to1312956197l_bool ) @ A ) )
=> ( A = top_to1312956197l_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(313,axiom,
! [A: nat,B: nat] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_374_linorder__not__less) ).
thf(1724,plain,
! [A: nat,B: nat] :
( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
=> ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(239,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
<=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_396_less__le__not__le) ).
thf(1475,plain,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(405,axiom,
! [A: arrow_856714788e_indi,B: fun_Ar274636406t_bool,C: fun_Ar1809396326i_bool,D: fun_fu638310559l_bool] :
( ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ B ) @ ( pi_Arr959578316t_bool @ C @ ( hAPP_f1717907078l_bool @ cOMBK_1520063231e_indi @ D ) ) ) )
=> ( ( hBOOL @ ( hAPP_f584385070l_bool @ ( hAPP_A1597696899l_bool @ member1479139729e_indi @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ ( hAPP_A1646126530t_bool @ B @ A ) ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_611_funcset__mem) ).
thf(2067,plain,
! [A: arrow_856714788e_indi,B: fun_Ar274636406t_bool,C: fun_Ar1809396326i_bool,D: fun_fu638310559l_bool] :
( ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ B ) @ ( pi_Arr959578316t_bool @ C @ ( hAPP_f1717907078l_bool @ cOMBK_1520063231e_indi @ D ) ) ) )
=> ( ( hBOOL @ ( hAPP_f584385070l_bool @ ( hAPP_A1597696899l_bool @ member1479139729e_indi @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ ( hAPP_A1646126530t_bool @ B @ A ) ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(256,axiom,
! [A: bool] : ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ A ) @ top_to1647826457l_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_iso__tuple__UNIV__I) ).
thf(1529,plain,
! [A: bool] : ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ A ) @ top_to1647826457l_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(526,axiom,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ B ) @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_xt1_I5_J) ).
thf(2603,plain,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ B ) @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(225,axiom,
! [A: fun_fu638310559l_bool,B: arrow_856714788e_indi] :
( ( hAPP_A897398598l_bool @ ( hAPP_f1717907078l_bool @ cOMBK_1520063231e_indi @ A ) @ B )
= 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(1430,plain,
! [A: fun_fu638310559l_bool,B: arrow_856714788e_indi] :
( ( hAPP_A897398598l_bool @ ( hAPP_f1717907078l_bool @ cOMBK_1520063231e_indi @ A ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(50,axiom,
! [A: nat,B: nat] :
( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1085_add__Suc__right) ).
thf(785,plain,
! [A: nat,B: nat] :
( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) )
= ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(460,axiom,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ A ) @ B ) )
<=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_392_less__le__not__le) ).
thf(2269,plain,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
( ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ B ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(347,axiom,
! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool] :
( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ A ) @ B ) )
=> ( ( B != A )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_469_xt1_I11_J) ).
thf(1871,plain,
! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool] :
( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ A ) @ B ) )
=> ( ( B != A )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(191,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1020_add__le__mono) ).
thf(1313,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ D ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(273,axiom,
! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool] :
( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ B ) @ A ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_order__antisym) ).
thf(1577,plain,
! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool] :
( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ B ) @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(510,axiom,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
( ( A != B )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_415_order__neq__le__trans) ).
thf(2562,plain,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
( ( A != B )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(424,axiom,
! [A: nat,B: nat] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_linorder__antisym__conv3) ).
thf(2126,plain,
! [A: nat,B: nat] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(124,axiom,
! [A: nat] :
( ( hAPP_nat_nat @ suc @ A )
!= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1069_Suc__not__Zero) ).
thf(1055,plain,
! [A: nat] :
( ( hAPP_nat_nat @ suc @ A )
!= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(218,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1003_trans__less__add2) ).
thf(1409,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(345,axiom,
! [A: nat,B: nat] :
( ( A != B )
<=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_982_nat__neq__iff) ).
thf(1860,plain,
! [A: nat,B: nat] :
( ( ( A != B )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(177,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ B ) ) )
<=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
& ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1160_mult__less__cancel2) ).
thf(1264,plain,
! [A: nat,B: nat,C: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
& ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) ) ) )
& ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
& ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(446,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_order__less__imp__not__less) ).
thf(2217,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(250,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_501_order__le__less__trans) ).
thf(1511,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(85,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1016_nat__add__left__cancel__le) ).
thf(917,plain,
! [A: nat,B: nat,C: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(31,axiom,
! [A: nat,B: nat] :
( ( one_one_nat
= ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) )
<=> ( ( A = one_one_nat )
& ( B = one_one_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1147_nat__1__eq__mult__iff) ).
thf(702,plain,
! [A: nat,B: nat] :
( ( ( one_one_nat
= ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) )
=> ( ( A = one_one_nat )
& ( B = one_one_nat ) ) )
& ( ( ( A = one_one_nat )
& ( B = one_one_nat ) )
=> ( one_one_nat
= ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(234,axiom,
! [A: arrow_856714788e_indi,B: fun_Ar274636406t_bool,C: fun_Ar1809396326i_bool,D: fun_Ar1474557608l_bool] :
( ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ B ) @ ( pi_Arr959578316t_bool @ C @ D ) ) )
=> ( ( hBOOL @ ( hAPP_f584385070l_bool @ ( hAPP_A1597696899l_bool @ member1479139729e_indi @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ ( hAPP_A1646126530t_bool @ B @ A ) ) @ ( hAPP_A897398598l_bool @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_577_Pi__mem) ).
thf(1462,plain,
! [A: arrow_856714788e_indi,B: fun_Ar274636406t_bool,C: fun_Ar1809396326i_bool,D: fun_Ar1474557608l_bool] :
( ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ B ) @ ( pi_Arr959578316t_bool @ C @ D ) ) )
=> ( ( hBOOL @ ( hAPP_f584385070l_bool @ ( hAPP_A1597696899l_bool @ member1479139729e_indi @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ ( hAPP_A1646126530t_bool @ B @ A ) ) @ ( hAPP_A897398598l_bool @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(125,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_748_add__less__cancel__right) ).
thf(1059,plain,
! [A: nat,B: nat,C: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(567,axiom,
! [A: fun_fu1572237755l_bool,B: fun_Ar2121501495le_alt,C: arrow_1893660431le_alt] :
( ( hAPP_A1608658241l_bool @ ( hAPP_f184584489l_bool @ ( cOMBB_1575576719le_alt @ A ) @ B ) @ C )
= ( hAPP_f1536341593l_bool @ A @ ( hAPP_A1146194953le_alt @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__) ).
thf(2745,plain,
! [A: fun_fu1572237755l_bool,B: fun_Ar2121501495le_alt,C: arrow_1893660431le_alt] :
( ( hAPP_A1608658241l_bool @ ( hAPP_f184584489l_bool @ ( cOMBB_1575576719le_alt @ A ) @ B ) @ C )
= ( hAPP_f1536341593l_bool @ A @ ( hAPP_A1146194953le_alt @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(475,axiom,
! [A: produc472769767le_alt,B: fun_Pr376858015t_unit,C: fun_Pr2067565481t_bool,D: fun_Pr1643180309t_bool] :
( ( hBOOL @ ( hAPP_f1159856629l_bool @ ( hAPP_f1700632141l_bool @ member1303779570t_unit @ B ) @ ( pi_Pro346842291t_unit @ C @ ( hAPP_f723483871t_bool @ cOMBK_751896174le_alt @ D ) ) ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ ( hAPP_P1069491261t_unit @ B @ A ) ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_583_funcset__mem) ).
thf(2356,plain,
! [A: produc472769767le_alt,B: fun_Pr376858015t_unit,C: fun_Pr2067565481t_bool,D: fun_Pr1643180309t_bool] :
( ( hBOOL @ ( hAPP_f1159856629l_bool @ ( hAPP_f1700632141l_bool @ member1303779570t_unit @ B ) @ ( pi_Pro346842291t_unit @ C @ ( hAPP_f723483871t_bool @ cOMBK_751896174le_alt @ D ) ) ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ ( hAPP_P1069491261t_unit @ B @ A ) ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(263,axiom,
a != b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76__096a_A_126_061_Ab_096) ).
thf(1545,plain,
a != b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(362,axiom,
! [A: nat,B: nat] :
( ( A != B )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Nat__Onat_T) ).
thf(1922,plain,
! [A: nat,B: nat] :
( ( A != B )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(576,axiom,
! [A: produc472769767le_alt,B: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ A ) @ B ) )
<=> ( hBOOL @ ( hAPP_P1178790471t_bool @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_mem__def) ).
thf(2857,plain,
! [A: produc472769767le_alt,B: fun_Pr2067565481t_bool] :
( ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_P1178790471t_bool @ B @ A ) ) )
& ( ( hBOOL @ ( hAPP_P1178790471t_bool @ B @ A ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(140,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1007_add__lessD1) ).
thf(1115,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(270,axiom,
! [A: fun_bo1945492389t_bool,B: fun_Ar1809396326i_bool,C: arrow_856714788e_indi] :
( ( hAPP_A1395684458t_bool @ ( hAPP_f668886383t_bool @ ( cOMBB_1061985500e_indi @ A ) @ B ) @ C )
= ( hAPP_b35146737t_bool @ A @ ( hAPP_A997847300i_bool @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow_) ).
thf(1568,plain,
! [A: fun_bo1945492389t_bool,B: fun_Ar1809396326i_bool,C: arrow_856714788e_indi] :
( ( hAPP_A1395684458t_bool @ ( hAPP_f668886383t_bool @ ( cOMBB_1061985500e_indi @ A ) @ B ) @ C )
= ( hAPP_b35146737t_bool @ A @ ( hAPP_A997847300i_bool @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(394,axiom,
! [A: nat,B: arrow_856714788e_indi,C: fun_Ar671024215di_nat,D: fun_Ar1809396326i_bool] :
( ( hBOOL @ ( hAPP_f584385070l_bool @ ( inj_on1960344199di_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_f584385070l_bool @ ( hAPP_A1597696899l_bool @ member1479139729e_indi @ B ) @ D ) )
=> ( ( ( hAPP_A376526755di_nat @ C @ B )
= A )
=> ( ( hAPP_n1937165849e_indi @ ( hilber1580028780di_nat @ D @ C ) @ A )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_618_inv__into__f__eq) ).
thf(2024,plain,
! [A: nat,B: arrow_856714788e_indi,C: fun_Ar671024215di_nat,D: fun_Ar1809396326i_bool] :
( ( hBOOL @ ( hAPP_f584385070l_bool @ ( inj_on1960344199di_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_f584385070l_bool @ ( hAPP_A1597696899l_bool @ member1479139729e_indi @ B ) @ D ) )
=> ( ( ( hAPP_A376526755di_nat @ C @ B )
= A )
=> ( ( hAPP_n1937165849e_indi @ ( hilber1580028780di_nat @ D @ C ) @ A )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(166,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_740_add__le__cancel__left) ).
thf(1232,plain,
! [A: nat,B: nat,C: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(355,axiom,
! [A: nat,B: nat,C: nat] :
( ( B = C )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_xt1_I3_J) ).
thf(1892,plain,
! [A: nat,B: nat,C: nat] :
( ( B = C )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(208,axiom,
! [A: nat,B: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1014_le__add1) ).
thf(1379,plain,
! [A: nat,B: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(100,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) )
=> ~ ! [C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) )
=> ( B
!= ( hAPP_nat_nat @ suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1122_Suc__lessE) ).
thf(969,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) )
=> ~ ! [C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) )
=> ( B
!= ( hAPP_nat_nat @ suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(8,axiom,
! [A: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ zero_zero_nat ) @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1156_mult__0) ).
thf(606,plain,
! [A: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ zero_zero_nat ) @ A )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(388,axiom,
! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool,C: fun_Ar331856045t_bool] :
( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_489_xt1_I7_J) ).
thf(2007,plain,
! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool,C: fun_Ar331856045t_bool] :
( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(87,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_744_add__strict__mono) ).
thf(924,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ D ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(369,axiom,
! [A: product_unit] : ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ A ) @ top_to1257323279t_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_iso__tuple__UNIV__I) ).
thf(1946,plain,
! [A: product_unit] : ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ A ) @ top_to1257323279t_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(15,axiom,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ B ) @ C ) )
= ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1150_add__mult__distrib2) ).
thf(646,plain,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ B ) @ C ) )
= ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(579,axiom,
~ ! [A: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ a ) @ b ) ) @ A ) )
=> ~ ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ A ) @ arrow_1361987423le_Lin ) ) ),
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(2880,plain,
~ ! [A: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ a ) @ b ) ) @ A ) )
=> ~ ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ A ) @ arrow_1361987423le_Lin ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(333,axiom,
! [A: fun_Pr2067565481t_bool,B: arrow_1893660431le_alt,C: arrow_1893660431le_alt] :
( ( B != C )
=> ( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ A ) @ arrow_1361987423le_Lin ) )
=> ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ ( arrow_1525312447_below @ A @ B @ C ) ) @ arrow_1361987423le_Lin ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_578_below__Lin) ).
thf(1828,plain,
! [A: fun_Pr2067565481t_bool,B: arrow_1893660431le_alt,C: arrow_1893660431le_alt] :
( ( B != C )
=> ( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ A ) @ arrow_1361987423le_Lin ) )
=> ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ ( arrow_1525312447_below @ A @ B @ C ) ) @ arrow_1361987423le_Lin ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(148,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) )
<=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
| ( A
= ( hAPP_nat_nat @ suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1090_le__Suc__eq) ).
thf(1151,plain,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
| ( A
= ( hAPP_nat_nat @ suc @ B ) ) ) )
& ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
| ( A
= ( hAPP_nat_nat @ suc @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(508,axiom,
! [A: arrow_1893660431le_alt,B: arrow_1893660431le_alt,C: arrow_1893660431le_alt,D: arrow_1893660431le_alt] :
( ( ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ A ) @ B )
= ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ C ) @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_Pair__inject) ).
thf(2555,plain,
! [A: arrow_1893660431le_alt,B: arrow_1893660431le_alt,C: arrow_1893660431le_alt,D: arrow_1893660431le_alt] :
( ( ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ A ) @ B )
= ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ C ) @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(469,axiom,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ A ) @ B ) )
<=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ B ) )
& ( A != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_925_psubset__eq) ).
thf(2335,plain,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
( ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ B ) )
& ( A != B ) ) )
& ( ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ B ) )
& ( A != B ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(122,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1028_termination__basic__simps_I2_J) ).
thf(1051,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(82,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1103_less__Suc__eq__le) ).
thf(905,plain,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(437,axiom,
! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool,C: fun_Ar331856045t_bool] :
( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_509_xt1_I8_J) ).
thf(2178,plain,
! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool,C: fun_Ar331856045t_bool] :
( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(448,axiom,
! [A: fun_fu2114379172t_bool] : ( hBOOL @ ( hAPP_f975209902l_bool @ ( hAPP_f1714503811l_bool @ member173038353t_bool @ A ) @ top_to827110112l_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_iso__tuple__UNIV__I) ).
thf(2222,plain,
! [A: fun_fu2114379172t_bool] : ( hBOOL @ ( hAPP_f975209902l_bool @ ( hAPP_f1714503811l_bool @ member173038353t_bool @ A ) @ top_to827110112l_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(186,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1108_Suc__le__lessD) ).
thf(1302,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(300,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_order__trans) ).
thf(1664,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(412,axiom,
( top_to1138392227t_bool
= ( hAPP_f1356305429t_bool @ collec1988958098le_alt @ ( hAPP_b128655177t_bool @ cOMBK_198697344le_alt @ fTrue ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_UNIV__def) ).
thf(2090,plain,
( top_to1138392227t_bool
= ( hAPP_f1356305429t_bool @ collec1988958098le_alt @ ( hAPP_b128655177t_bool @ cOMBK_198697344le_alt @ fTrue ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(5,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1142_mult__le__mono1) ).
thf(591,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(117,axiom,
! [A: fun_fu638310559l_bool,B: fun_fu638310559l_bool,C: fun_fu638310559l_bool] :
( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_xt1_I6_J) ).
thf(1040,plain,
! [A: fun_fu638310559l_bool,B: fun_fu638310559l_bool,C: fun_fu638310559l_bool] :
( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(291,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_996_le__trans) ).
thf(1632,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(344,axiom,
! [A: arrow_856714788e_indi,B: fun_Ar274636406t_bool,C: fun_Ar1809396326i_bool,D: fun_Ar1474557608l_bool] :
( ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ B ) @ ( pi_Arr959578316t_bool @ C @ D ) ) )
=> ( ~ ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ ( hAPP_A1646126530t_bool @ B @ A ) ) @ ( hAPP_A897398598l_bool @ D @ A ) ) )
=> ~ ( hBOOL @ ( hAPP_f584385070l_bool @ ( hAPP_A1597696899l_bool @ member1479139729e_indi @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_PiE) ).
thf(1858,plain,
! [A: arrow_856714788e_indi,B: fun_Ar274636406t_bool,C: fun_Ar1809396326i_bool,D: fun_Ar1474557608l_bool] :
( ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ B ) @ ( pi_Arr959578316t_bool @ C @ D ) ) )
=> ( ~ ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ ( hAPP_A1646126530t_bool @ B @ A ) ) @ ( hAPP_A897398598l_bool @ D @ A ) ) )
=> ~ ( hBOOL @ ( hAPP_f584385070l_bool @ ( hAPP_A1597696899l_bool @ member1479139729e_indi @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(422,axiom,
hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ n ) @ ( hAPP_f846027769ol_nat @ finite1672073426e_indi @ top_to788185952i_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_n_I1_J) ).
thf(2122,plain,
hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ n ) @ ( hAPP_f846027769ol_nat @ finite1672073426e_indi @ top_to788185952i_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(304,axiom,
! [A: arrow_856714788e_indi,B: fun_Ar671024215di_nat,C: fun_Ar1809396326i_bool] :
( ( hBOOL @ ( hAPP_f584385070l_bool @ ( inj_on1960344199di_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f584385070l_bool @ ( hAPP_A1597696899l_bool @ member1479139729e_indi @ A ) @ C ) )
=> ( ( hAPP_n1937165849e_indi @ ( hilber1580028780di_nat @ C @ B ) @ ( hAPP_A376526755di_nat @ B @ A ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_616_inv__into__f__f) ).
thf(1677,plain,
! [A: arrow_856714788e_indi,B: fun_Ar671024215di_nat,C: fun_Ar1809396326i_bool] :
( ( hBOOL @ ( hAPP_f584385070l_bool @ ( inj_on1960344199di_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f584385070l_bool @ ( hAPP_A1597696899l_bool @ member1479139729e_indi @ A ) @ C ) )
=> ( ( hAPP_n1937165849e_indi @ ( hilber1580028780di_nat @ C @ B ) @ ( hAPP_A376526755di_nat @ B @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(503,axiom,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_939_psubset__imp__subset) ).
thf(2540,plain,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(46,axiom,
! [A: fun_fu638310559l_bool] :
( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ top_to1312956197l_bool ) @ A ) )
<=> ( A = top_to1312956197l_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_521_top__unique) ).
thf(766,plain,
! [A: fun_fu638310559l_bool] :
( ( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ top_to1312956197l_bool ) @ A ) )
=> ( A = top_to1312956197l_bool ) )
& ( ( A = top_to1312956197l_bool )
=> ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ top_to1312956197l_bool ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(339,axiom,
! [A: fun_Ar274636406t_bool,B: fun_fu2114379172t_bool,C: fun_fu3835832l_bool,D: fun_fu638310559l_bool] :
( ( hBOOL @ ( hAPP_f975209902l_bool @ ( hAPP_f1714503811l_bool @ member173038353t_bool @ B ) @ ( pi_fun1746584570t_bool @ C @ ( hAPP_f1104294872l_bool @ cOMBK_1701906001t_bool @ D ) ) ) )
=> ( ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ ( hAPP_f2008608496t_bool @ B @ A ) ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_610_funcset__mem) ).
thf(1843,plain,
! [A: fun_Ar274636406t_bool,B: fun_fu2114379172t_bool,C: fun_fu3835832l_bool,D: fun_fu638310559l_bool] :
( ( hBOOL @ ( hAPP_f975209902l_bool @ ( hAPP_f1714503811l_bool @ member173038353t_bool @ B ) @ ( pi_fun1746584570t_bool @ C @ ( hAPP_f1104294872l_bool @ cOMBK_1701906001t_bool @ D ) ) ) )
=> ( ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ ( hAPP_f2008608496t_bool @ B @ A ) ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(530,axiom,
! [A: arrow_856714788e_indi] : ( hBOOL @ ( hAPP_A997847300i_bool @ top_to788185952i_bool @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_top1I) ).
thf(2618,plain,
! [A: arrow_856714788e_indi] : ( hBOOL @ ( hAPP_A997847300i_bool @ top_to788185952i_bool @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(356,axiom,
! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool,C: fun_Ar331856045t_bool] :
( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_xt1_I6_J) ).
thf(1896,plain,
! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool,C: fun_Ar331856045t_bool] :
( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
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 )
=> ( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ C ) @ arrow_1361987423le_Lin ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ A ) @ B ) ) @ ( arrow_1525312447_below @ C @ D @ E ) ) )
<=> ( ( A != B )
& ( ( B = D )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ A ) @ E ) ) @ C ) ) )
& ( ( B != D )
=> ( ( ( A = D )
=> ( ( B = E )
| ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ E ) @ B ) ) @ C ) ) ) )
& ( ( A != D )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ A ) @ B ) ) @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_in__below) ).
thf(2424,plain,
! [A: arrow_1893660431le_alt,B: arrow_1893660431le_alt,C: fun_Pr2067565481t_bool,D: arrow_1893660431le_alt,E: arrow_1893660431le_alt] :
( ( D != E )
=> ( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ C ) @ arrow_1361987423le_Lin ) )
=> ( ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ A ) @ B ) ) @ ( arrow_1525312447_below @ C @ D @ E ) ) )
=> ( ( A != B )
& ( ( B = D )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ A ) @ E ) ) @ C ) ) )
& ( ( B != D )
=> ( ( ( A = D )
=> ( ( B = E )
| ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ E ) @ B ) ) @ C ) ) ) )
& ( ( A != D )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ A ) @ B ) ) @ C ) ) ) ) ) ) )
& ( ( ( A != B )
& ( ( B = D )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ A ) @ E ) ) @ C ) ) )
& ( ( B != D )
=> ( ( ( A = D )
=> ( ( B = E )
| ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ E ) @ B ) ) @ C ) ) ) )
& ( ( A != D )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ A ) @ B ) ) @ C ) ) ) ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ A ) @ B ) ) @ ( arrow_1525312447_below @ C @ D @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(255,axiom,
! [A: fun_Ar331856045t_bool,B: fun_na300967376t_bool,C: nat,D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ A ) @ ( hAPP_n1312530466t_bool @ B @ C ) ) )
=> ( ! [E: nat,F: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ F ) @ E ) )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ ( hAPP_n1312530466t_bool @ B @ F ) ) @ ( hAPP_n1312530466t_bool @ B @ E ) ) ) )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ A ) @ ( hAPP_n1312530466t_bool @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_669_xt5) ).
thf(1526,plain,
! [A: fun_Ar331856045t_bool,B: fun_na300967376t_bool,C: nat,D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ A ) @ ( hAPP_n1312530466t_bool @ B @ C ) ) )
=> ( ! [E: nat,F: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ F ) @ E ) )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ ( hAPP_n1312530466t_bool @ B @ F ) ) @ ( hAPP_n1312530466t_bool @ B @ E ) ) ) )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ A ) @ ( hAPP_n1312530466t_bool @ B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(199,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ B ) ) )
<=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1172_mult__le__cancel2) ).
thf(1345,plain,
! [A: nat,B: nat,C: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) ) ) )
& ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(226,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ ( hAPP_nat_nat @ suc @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1072_Suc__less__SucD) ).
thf(1433,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ ( hAPP_nat_nat @ suc @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(368,axiom,
! [A: nat,B: fun_na998785244t_bool,C: nat,D: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ ( hAPP_n1161265524t_bool @ B @ C ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) )
=> ( ! [E: nat,F: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ F ) @ E ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ ( hAPP_n1161265524t_bool @ B @ F ) ) @ ( hAPP_n1161265524t_bool @ B @ E ) ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ ( hAPP_n1161265524t_bool @ B @ A ) ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_778_xt4) ).
thf(1943,plain,
! [A: nat,B: fun_na998785244t_bool,C: nat,D: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ ( hAPP_n1161265524t_bool @ B @ C ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) )
=> ( ! [E: nat,F: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ F ) @ E ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ ( hAPP_n1161265524t_bool @ B @ F ) ) @ ( hAPP_n1161265524t_bool @ B @ E ) ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ ( hAPP_n1161265524t_bool @ B @ A ) ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(521,axiom,
! [A: fun_Pr1085078251l_bool,B: fun_Ar245737999le_alt,C: arrow_1893660431le_alt] :
( ( hAPP_A442239897l_bool @ ( hAPP_f1536341593l_bool @ ( cOMBB_1660064607le_alt @ A ) @ B ) @ C )
= ( hAPP_P38525833l_bool @ A @ ( hAPP_A1299015393le_alt @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs_) ).
thf(2586,plain,
! [A: fun_Pr1085078251l_bool,B: fun_Ar245737999le_alt,C: arrow_1893660431le_alt] :
( ( hAPP_A442239897l_bool @ ( hAPP_f1536341593l_bool @ ( cOMBB_1660064607le_alt @ A ) @ B ) @ C )
= ( hAPP_P38525833l_bool @ A @ ( hAPP_A1299015393le_alt @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(230,axiom,
! [A: arrow_1893660431le_alt,B: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ B ) @ arrow_1361987423le_Lin ) )
=> ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ ( hAPP_A1601437999t_bool @ ( hAPP_f1761571331t_bool @ arrow_1630265669_mktop @ B ) @ A ) ) @ arrow_1361987423le_Lin ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_mktop__Lin) ).
thf(1447,plain,
! [A: arrow_1893660431le_alt,B: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ B ) @ arrow_1361987423le_Lin ) )
=> ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ ( hAPP_A1601437999t_bool @ ( hAPP_f1761571331t_bool @ arrow_1630265669_mktop @ B ) @ A ) ) @ arrow_1361987423le_Lin ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(491,axiom,
! [A: fun_Ar274636406t_bool] : ( hBOOL @ ( hAPP_f995490902l_bool @ top_to553140914l_bool @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_top1I) ).
thf(2483,plain,
! [A: fun_Ar274636406t_bool] : ( hBOOL @ ( hAPP_f995490902l_bool @ top_to553140914l_bool @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(498,axiom,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ A ) @ B ) )
<=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ B ) )
& ( A != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_382_order__less__le) ).
thf(2523,plain,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
( ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ B ) )
& ( A != B ) ) )
& ( ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ B ) )
& ( A != B ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(324,axiom,
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ c ) @ e ) ) @ ( hAPP_f2008608496t_bool @ f @ ( hAPP_f1302887663t_bool @ ( cOMBS_1181656689t_bool @ ( hAPP_f1001205955t_bool @ ( cOMBS_1925466437t_bool @ ( hAPP_f668886383t_bool @ ( cOMBB_1061985500e_indi @ if_fun523439385t_bool ) @ ( hAPP_n34002993i_bool @ ( hAPP_f721434149i_bool @ cOMBC_722552198t_bool @ ( hAPP_f966656047t_bool @ ( cOMBB_1869811296e_indi @ ord_less_nat ) @ h ) ) @ n ) ) ) @ ( hAPP_A425126512t_bool @ ( hAPP_f1631649925t_bool @ cOMBC_1417338747t_bool @ ( hAPP_f831214557t_bool @ ( cOMBB_80760910e_indi @ arrow_1630265669_mktop ) @ p ) ) @ e ) ) ) @ ( hAPP_f1302887663t_bool @ ( cOMBS_1181656689t_bool @ ( hAPP_f1001205955t_bool @ ( cOMBS_1925466437t_bool @ ( hAPP_f668886383t_bool @ ( cOMBB_1061985500e_indi @ if_fun523439385t_bool ) @ ( hAPP_n34002993i_bool @ ( hAPP_f721434149i_bool @ cOMBC_722552198t_bool @ ( hAPP_f966656047t_bool @ ( cOMBB_1869811296e_indi @ fequal_nat ) @ h ) ) @ n ) ) ) @ ( hAPP_A425126512t_bool @ ( hAPP_f1631649925t_bool @ cOMBC_1417338747t_bool @ ( hAPP_A1889513822t_bool @ ( hAPP_f2102110817t_bool @ cOMBC_1486904681t_bool @ ( hAPP_f1751344075t_bool @ ( cOMBB_1876517692e_indi @ arrow_216713899_above ) @ p ) ) @ c ) ) @ e ) ) ) @ ( hAPP_A425126512t_bool @ ( hAPP_f1631649925t_bool @ cOMBC_1417338747t_bool @ ( hAPP_f831214557t_bool @ ( cOMBB_80760910e_indi @ arrow_1481558583_mkbot ) @ p ) ) @ e ) ) ) ) ) )
<=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ a ) @ b ) ) @ ( hAPP_f2008608496t_bool @ f @ ( hAPP_f480276746t_bool @ ( hAPP_f601594885t_bool @ cOMBC_750853729t_bool @ ( hAPP_f1344464862t_bool @ ( hAPP_f1908974253t_bool @ cOMBC_156709173t_bool @ ( hAPP_f668886383t_bool @ ( cOMBB_1061985500e_indi @ if_fun523439385t_bool ) @ ( hAPP_n34002993i_bool @ ( hAPP_f721434149i_bool @ cOMBC_722552198t_bool @ ( hAPP_f966656047t_bool @ ( cOMBB_1869811296e_indi @ ord_less_nat ) @ h ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ n ) @ one_one_nat ) ) ) ) @ lab ) ) @ lba ) ) ) ) ),
file('/export/starexec/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(1796,plain,
( ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ c ) @ e ) ) @ ( hAPP_f2008608496t_bool @ f @ ( hAPP_f1302887663t_bool @ ( cOMBS_1181656689t_bool @ ( hAPP_f1001205955t_bool @ ( cOMBS_1925466437t_bool @ ( hAPP_f668886383t_bool @ ( cOMBB_1061985500e_indi @ if_fun523439385t_bool ) @ ( hAPP_n34002993i_bool @ ( hAPP_f721434149i_bool @ cOMBC_722552198t_bool @ ( hAPP_f966656047t_bool @ ( cOMBB_1869811296e_indi @ ord_less_nat ) @ h ) ) @ n ) ) ) @ ( hAPP_A425126512t_bool @ ( hAPP_f1631649925t_bool @ cOMBC_1417338747t_bool @ ( hAPP_f831214557t_bool @ ( cOMBB_80760910e_indi @ arrow_1630265669_mktop ) @ p ) ) @ e ) ) ) @ ( hAPP_f1302887663t_bool @ ( cOMBS_1181656689t_bool @ ( hAPP_f1001205955t_bool @ ( cOMBS_1925466437t_bool @ ( hAPP_f668886383t_bool @ ( cOMBB_1061985500e_indi @ if_fun523439385t_bool ) @ ( hAPP_n34002993i_bool @ ( hAPP_f721434149i_bool @ cOMBC_722552198t_bool @ ( hAPP_f966656047t_bool @ ( cOMBB_1869811296e_indi @ fequal_nat ) @ h ) ) @ n ) ) ) @ ( hAPP_A425126512t_bool @ ( hAPP_f1631649925t_bool @ cOMBC_1417338747t_bool @ ( hAPP_A1889513822t_bool @ ( hAPP_f2102110817t_bool @ cOMBC_1486904681t_bool @ ( hAPP_f1751344075t_bool @ ( cOMBB_1876517692e_indi @ arrow_216713899_above ) @ p ) ) @ c ) ) @ e ) ) ) @ ( hAPP_A425126512t_bool @ ( hAPP_f1631649925t_bool @ cOMBC_1417338747t_bool @ ( hAPP_f831214557t_bool @ ( cOMBB_80760910e_indi @ arrow_1481558583_mkbot ) @ p ) ) @ e ) ) ) ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ a ) @ b ) ) @ ( hAPP_f2008608496t_bool @ f @ ( hAPP_f480276746t_bool @ ( hAPP_f601594885t_bool @ cOMBC_750853729t_bool @ ( hAPP_f1344464862t_bool @ ( hAPP_f1908974253t_bool @ cOMBC_156709173t_bool @ ( hAPP_f668886383t_bool @ ( cOMBB_1061985500e_indi @ if_fun523439385t_bool ) @ ( hAPP_n34002993i_bool @ ( hAPP_f721434149i_bool @ cOMBC_722552198t_bool @ ( hAPP_f966656047t_bool @ ( cOMBB_1869811296e_indi @ ord_less_nat ) @ h ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ n ) @ one_one_nat ) ) ) ) @ lab ) ) @ lba ) ) ) ) )
& ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ a ) @ b ) ) @ ( hAPP_f2008608496t_bool @ f @ ( hAPP_f480276746t_bool @ ( hAPP_f601594885t_bool @ cOMBC_750853729t_bool @ ( hAPP_f1344464862t_bool @ ( hAPP_f1908974253t_bool @ cOMBC_156709173t_bool @ ( hAPP_f668886383t_bool @ ( cOMBB_1061985500e_indi @ if_fun523439385t_bool ) @ ( hAPP_n34002993i_bool @ ( hAPP_f721434149i_bool @ cOMBC_722552198t_bool @ ( hAPP_f966656047t_bool @ ( cOMBB_1869811296e_indi @ ord_less_nat ) @ h ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ n ) @ one_one_nat ) ) ) ) @ lab ) ) @ lba ) ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ c ) @ e ) ) @ ( hAPP_f2008608496t_bool @ f @ ( hAPP_f1302887663t_bool @ ( cOMBS_1181656689t_bool @ ( hAPP_f1001205955t_bool @ ( cOMBS_1925466437t_bool @ ( hAPP_f668886383t_bool @ ( cOMBB_1061985500e_indi @ if_fun523439385t_bool ) @ ( hAPP_n34002993i_bool @ ( hAPP_f721434149i_bool @ cOMBC_722552198t_bool @ ( hAPP_f966656047t_bool @ ( cOMBB_1869811296e_indi @ ord_less_nat ) @ h ) ) @ n ) ) ) @ ( hAPP_A425126512t_bool @ ( hAPP_f1631649925t_bool @ cOMBC_1417338747t_bool @ ( hAPP_f831214557t_bool @ ( cOMBB_80760910e_indi @ arrow_1630265669_mktop ) @ p ) ) @ e ) ) ) @ ( hAPP_f1302887663t_bool @ ( cOMBS_1181656689t_bool @ ( hAPP_f1001205955t_bool @ ( cOMBS_1925466437t_bool @ ( hAPP_f668886383t_bool @ ( cOMBB_1061985500e_indi @ if_fun523439385t_bool ) @ ( hAPP_n34002993i_bool @ ( hAPP_f721434149i_bool @ cOMBC_722552198t_bool @ ( hAPP_f966656047t_bool @ ( cOMBB_1869811296e_indi @ fequal_nat ) @ h ) ) @ n ) ) ) @ ( hAPP_A425126512t_bool @ ( hAPP_f1631649925t_bool @ cOMBC_1417338747t_bool @ ( hAPP_A1889513822t_bool @ ( hAPP_f2102110817t_bool @ cOMBC_1486904681t_bool @ ( hAPP_f1751344075t_bool @ ( cOMBB_1876517692e_indi @ arrow_216713899_above ) @ p ) ) @ c ) ) @ e ) ) ) @ ( hAPP_A425126512t_bool @ ( hAPP_f1631649925t_bool @ cOMBC_1417338747t_bool @ ( hAPP_f831214557t_bool @ ( cOMBB_80760910e_indi @ arrow_1481558583_mkbot ) @ p ) ) @ e ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(564,axiom,
! [A: fun_Pr1085078251l_bool,B: fun_Pr2067565481t_bool,C: produc472769767le_alt] :
( ( hAPP_P1178790471t_bool @ ( hAPP_f1356305429t_bool @ ( hAPP_f1033183015t_bool @ cOMBC_593569186l_bool @ A ) @ B ) @ C )
= ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs_) ).
thf(2718,plain,
! [A: fun_Pr1085078251l_bool,B: fun_Pr2067565481t_bool,C: produc472769767le_alt] :
( ( hAPP_P1178790471t_bool @ ( hAPP_f1356305429t_bool @ ( hAPP_f1033183015t_bool @ cOMBC_593569186l_bool @ A ) @ B ) @ C )
= ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(442,axiom,
! [A: fun_Pr2067565481t_bool,B: bool] :
( ( hAPP_b128655177t_bool @ ( hAPP_f1723896209t_bool @ cOMBK_5056120l_bool @ A ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ef) ).
thf(2205,plain,
! [A: fun_Pr2067565481t_bool,B: bool] :
( ( hAPP_b128655177t_bool @ ( hAPP_f1723896209t_bool @ cOMBK_5056120l_bool @ A ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(282,axiom,
! [A: fun_Ar331856045t_bool] :
( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ top_to951839027t_bool ) @ A ) )
<=> ( A = top_to951839027t_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_526_top__unique) ).
thf(1604,plain,
! [A: fun_Ar331856045t_bool] :
( ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ top_to951839027t_bool ) @ A ) )
=> ( A = top_to951839027t_bool ) )
& ( ( A = top_to951839027t_bool )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ top_to951839027t_bool ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(390,axiom,
! [A: bool,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ B ) )
=> ( hBOOL @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_order__less__imp__triv) ).
thf(2011,plain,
! [A: bool,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ B ) )
=> ( hBOOL @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(188,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) )
=> ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( A
= ( hAPP_nat_nat @ suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1087_le__SucE) ).
thf(1306,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) )
=> ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( A
= ( hAPP_nat_nat @ suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(421,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_order__less__imp__not__eq2) ).
thf(2118,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(190,axiom,
! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1059_lessI) ).
thf(1311,plain,
! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(127,axiom,
! [A: nat] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1092_Suc__n__not__le__n) ).
thf(1067,plain,
! [A: nat] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(55,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1177_nat__mult__less__cancel1) ).
thf(798,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ C ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(237,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_376_linorder__le__less__linear) ).
thf(1470,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(360,axiom,
! [A: fun_fu2114379172t_bool,B: fun_fu2098777574l_bool] :
( ( hBOOL @ ( hAPP_f975209902l_bool @ ( hAPP_f1714503811l_bool @ member173038353t_bool @ A ) @ B ) )
<=> ( hBOOL @ ( hAPP_f1572141188l_bool @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_mem__def) ).
thf(1915,plain,
! [A: fun_fu2114379172t_bool,B: fun_fu2098777574l_bool] :
( ( ( hBOOL @ ( hAPP_f975209902l_bool @ ( hAPP_f1714503811l_bool @ member173038353t_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f1572141188l_bool @ B @ A ) ) )
& ( ( hBOOL @ ( hAPP_f1572141188l_bool @ B @ A ) )
=> ( hBOOL @ ( hAPP_f975209902l_bool @ ( hAPP_f1714503811l_bool @ member173038353t_bool @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(33,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
<=> ? [C: nat] :
( B
= ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1015_le__iff__add) ).
thf(714,plain,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ? [C: nat] :
( B
= ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) )
& ( ? [C: nat] :
( B
= ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(479,axiom,
! [A: arrow_856714788e_indi] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ c ) @ d ) ) @ ( hAPP_A1646126530t_bool @ p @ A ) ) )
<=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_A376526755di_nat @ h @ A ) ) @ n ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ c ) @ d ) ) @ ( hAPP_A1601437999t_bool @ ( hAPP_f1761571331t_bool @ arrow_1630265669_mktop @ ( hAPP_A1646126530t_bool @ p @ A ) ) @ e ) ) ) )
& ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_A376526755di_nat @ h @ A ) ) @ n ) )
=> ( ( ( ( hAPP_A376526755di_nat @ h @ A )
= n )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ c ) @ d ) ) @ ( hAPP_A1601437999t_bool @ ( hAPP_A1058422557t_bool @ ( hAPP_f1550387441t_bool @ arrow_216713899_above @ ( hAPP_A1646126530t_bool @ p @ A ) ) @ c ) @ e ) ) ) )
& ( ( ( hAPP_A376526755di_nat @ h @ A )
!= n )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ c ) @ d ) ) @ ( hAPP_A1601437999t_bool @ ( hAPP_f1761571331t_bool @ arrow_1481558583_mkbot @ ( hAPP_A1646126530t_bool @ p @ A ) ) @ e ) ) ) ) ) ) ) ),
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(2382,plain,
! [A: arrow_856714788e_indi] :
( ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ c ) @ d ) ) @ ( hAPP_A1646126530t_bool @ p @ A ) ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_A376526755di_nat @ h @ A ) ) @ n ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ c ) @ d ) ) @ ( hAPP_A1601437999t_bool @ ( hAPP_f1761571331t_bool @ arrow_1630265669_mktop @ ( hAPP_A1646126530t_bool @ p @ A ) ) @ e ) ) ) )
& ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_A376526755di_nat @ h @ A ) ) @ n ) )
=> ( ( ( ( hAPP_A376526755di_nat @ h @ A )
= n )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ c ) @ d ) ) @ ( hAPP_A1601437999t_bool @ ( hAPP_A1058422557t_bool @ ( hAPP_f1550387441t_bool @ arrow_216713899_above @ ( hAPP_A1646126530t_bool @ p @ A ) ) @ c ) @ e ) ) ) )
& ( ( ( hAPP_A376526755di_nat @ h @ A )
!= n )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ c ) @ d ) ) @ ( hAPP_A1601437999t_bool @ ( hAPP_f1761571331t_bool @ arrow_1481558583_mkbot @ ( hAPP_A1646126530t_bool @ p @ A ) ) @ e ) ) ) ) ) ) ) )
& ( ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_A376526755di_nat @ h @ A ) ) @ n ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ c ) @ d ) ) @ ( hAPP_A1601437999t_bool @ ( hAPP_f1761571331t_bool @ arrow_1630265669_mktop @ ( hAPP_A1646126530t_bool @ p @ A ) ) @ e ) ) ) )
& ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_A376526755di_nat @ h @ A ) ) @ n ) )
=> ( ( ( ( hAPP_A376526755di_nat @ h @ A )
= n )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ c ) @ d ) ) @ ( hAPP_A1601437999t_bool @ ( hAPP_A1058422557t_bool @ ( hAPP_f1550387441t_bool @ arrow_216713899_above @ ( hAPP_A1646126530t_bool @ p @ A ) ) @ c ) @ e ) ) ) )
& ( ( ( hAPP_A376526755di_nat @ h @ A )
!= n )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ c ) @ d ) ) @ ( hAPP_A1601437999t_bool @ ( hAPP_f1761571331t_bool @ arrow_1481558583_mkbot @ ( hAPP_A1646126530t_bool @ p @ A ) ) @ e ) ) ) ) ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ c ) @ d ) ) @ ( hAPP_A1646126530t_bool @ p @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(522,axiom,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ B ) @ A ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_order__antisym) ).
thf(2589,plain,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ B ) @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(560,axiom,
~ ! [A: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ b ) @ a ) ) @ A ) )
=> ~ ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ A ) @ arrow_1361987423le_Lin ) ) ),
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(2705,plain,
~ ! [A: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ b ) @ a ) ) @ A ) )
=> ~ ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ A ) @ arrow_1361987423le_Lin ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(41,axiom,
! [A: fun_fu638310559l_bool,B: fun_fu638310559l_bool] :
( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ B ) @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_xt1_I5_J) ).
thf(746,plain,
! [A: fun_fu638310559l_bool,B: fun_fu638310559l_bool] :
( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ B ) @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(525,axiom,
! [A: arrow_856714788e_indi,B: fun_Ar338949104le_alt,C: fun_Ar1809396326i_bool,D: fun_Ar274636406t_bool] :
( ( hBOOL @ ( hAPP_f1754488902l_bool @ ( hAPP_f766019597l_bool @ member387840963le_alt @ B ) @ ( pi_Arr1460528004le_alt @ C @ D ) ) )
=> ( ~ ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A899858958le_alt @ B @ A ) ) @ ( hAPP_A1646126530t_bool @ D @ A ) ) )
=> ~ ( hBOOL @ ( hAPP_f584385070l_bool @ ( hAPP_A1597696899l_bool @ member1479139729e_indi @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_PiE) ).
thf(2601,plain,
! [A: arrow_856714788e_indi,B: fun_Ar338949104le_alt,C: fun_Ar1809396326i_bool,D: fun_Ar274636406t_bool] :
( ( hBOOL @ ( hAPP_f1754488902l_bool @ ( hAPP_f766019597l_bool @ member387840963le_alt @ B ) @ ( pi_Arr1460528004le_alt @ C @ D ) ) )
=> ( ~ ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A899858958le_alt @ B @ A ) ) @ ( hAPP_A1646126530t_bool @ D @ A ) ) )
=> ~ ( hBOOL @ ( hAPP_f584385070l_bool @ ( hAPP_A1597696899l_bool @ member1479139729e_indi @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(118,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1106_Suc__leI) ).
thf(1042,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(253,axiom,
! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool,C: fun_Ar331856045t_bool] :
( ( B = C )
=> ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_xt1_I3_J) ).
thf(1519,plain,
! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool,C: fun_Ar331856045t_bool] :
( ( B = C )
=> ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(173,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1159_mult__less__mono1) ).
thf(1255,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(72,axiom,
! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1043_le0) ).
thf(862,plain,
! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(428,axiom,
? [A: fun_Pr2067565481t_bool] : ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ A ) @ arrow_1361987423le_Lin ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1030_linear__alt) ).
thf(2147,plain,
? [A: fun_Pr2067565481t_bool] : ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ A ) @ arrow_1361987423le_Lin ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(301,axiom,
! [A: fun_Ar274636406t_bool] :
( ( hBOOL @ ( hAPP_f995490902l_bool @ top_to553140914l_bool @ A ) )
<=> ( hBOOL @ top_top_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_top__apply) ).
thf(1666,plain,
! [A: fun_Ar274636406t_bool] :
( ( ( hBOOL @ ( hAPP_f995490902l_bool @ top_to553140914l_bool @ A ) )
=> ( hBOOL @ top_top_bool ) )
& ( ( hBOOL @ top_top_bool )
=> ( hBOOL @ ( hAPP_f995490902l_bool @ top_to553140914l_bool @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(242,axiom,
! [A: fun_na699243463e_indi,B: fun_Ar671024215di_nat] :
( ( hBOOL @ ( hAPP_f584385070l_bool @ ( inj_on1960344199di_nat @ B ) @ top_to788185952i_bool ) )
=> ( ! [C: nat] :
( ( hAPP_A376526755di_nat @ B @ ( hAPP_n1937165849e_indi @ A @ C ) )
= C )
=> ( ( hilber1580028780di_nat @ top_to788185952i_bool @ B )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_651_inj__imp__inv__eq) ).
thf(1487,plain,
! [A: fun_na699243463e_indi,B: fun_Ar671024215di_nat] :
( ( hBOOL @ ( hAPP_f584385070l_bool @ ( inj_on1960344199di_nat @ B ) @ top_to788185952i_bool ) )
=> ( ! [C: nat] :
( ( hAPP_A376526755di_nat @ B @ ( hAPP_n1937165849e_indi @ A @ C ) )
= C )
=> ( ( hilber1580028780di_nat @ top_to788185952i_bool @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(28,axiom,
! [A: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ one_one_nat ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1148_nat__mult__1) ).
thf(693,plain,
! [A: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ one_one_nat ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(527,axiom,
! [A: fun_Pr2090226719le_alt,B: fun_Pr1887398791t_bool,C: fun_Pr1643180309t_bool] :
( ! [D: product_unit] :
( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ D ) @ C ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_P396106045le_alt @ A @ D ) ) @ ( hAPP_P1914371027t_bool @ B @ D ) ) ) )
=> ( hBOOL @ ( hAPP_f684683381l_bool @ ( hAPP_f41367117l_bool @ member869664626le_alt @ A ) @ ( pi_Pro1820940723le_alt @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_636_Pi__I) ).
thf(2606,plain,
! [A: fun_Pr2090226719le_alt,B: fun_Pr1887398791t_bool,C: fun_Pr1643180309t_bool] :
( ! [D: product_unit] :
( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ D ) @ C ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_P396106045le_alt @ A @ D ) ) @ ( hAPP_P1914371027t_bool @ B @ D ) ) ) )
=> ( hBOOL @ ( hAPP_f684683381l_bool @ ( hAPP_f41367117l_bool @ member869664626le_alt @ A ) @ ( pi_Pro1820940723le_alt @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(425,axiom,
! [A: nat,B: fun_Ar331856045t_bool,C: fun_na300967376t_bool,D: nat] :
( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ B ) @ ( hAPP_n1312530466t_bool @ C @ D ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ D ) @ A ) )
=> ( ! [E: nat,F: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ E ) @ F ) )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ ( hAPP_n1312530466t_bool @ C @ E ) ) @ ( hAPP_n1312530466t_bool @ C @ F ) ) ) )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ B ) @ ( hAPP_n1312530466t_bool @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_817_order__le__less__subst1) ).
thf(2132,plain,
! [A: nat,B: fun_Ar331856045t_bool,C: fun_na300967376t_bool,D: nat] :
( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ B ) @ ( hAPP_n1312530466t_bool @ C @ D ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ D ) @ A ) )
=> ( ! [E: nat,F: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ E ) @ F ) )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ ( hAPP_n1312530466t_bool @ C @ E ) ) @ ( hAPP_n1312530466t_bool @ C @ F ) ) ) )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ B ) @ ( hAPP_n1312530466t_bool @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(211,axiom,
! [A: fun_fu638310559l_bool,B: fun_Pr2067565481t_bool,C: fun_fu638310559l_bool] :
( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_961_set__rev__mp) ).
thf(1387,plain,
! [A: fun_fu638310559l_bool,B: fun_Pr2067565481t_bool,C: fun_fu638310559l_bool] :
( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(83,axiom,
! [A: fun_Pr2067565481t_bool,B: fun_fu638310559l_bool,C: fun_fu638310559l_bool] :
( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_918_subsetD) ).
thf(910,plain,
! [A: fun_Pr2067565481t_bool,B: fun_fu638310559l_bool,C: fun_fu638310559l_bool] :
( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(198,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_746_add__strict__right__mono) ).
thf(1343,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(509,axiom,
! [A: product_unit,B: fun_Pr2090226719le_alt,C: fun_Pr1643180309t_bool,D: fun_Pr1887398791t_bool] :
( ( hBOOL @ ( hAPP_f684683381l_bool @ ( hAPP_f41367117l_bool @ member869664626le_alt @ B ) @ ( pi_Pro1820940723le_alt @ C @ D ) ) )
=> ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_P396106045le_alt @ B @ A ) ) @ ( hAPP_P1914371027t_bool @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_564_Pi__mem) ).
thf(2560,plain,
! [A: product_unit,B: fun_Pr2090226719le_alt,C: fun_Pr1643180309t_bool,D: fun_Pr1887398791t_bool] :
( ( hBOOL @ ( hAPP_f684683381l_bool @ ( hAPP_f41367117l_bool @ member869664626le_alt @ B ) @ ( pi_Pro1820940723le_alt @ C @ D ) ) )
=> ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_P396106045le_alt @ B @ A ) ) @ ( hAPP_P1914371027t_bool @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(201,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_747_add__less__cancel__left) ).
thf(1355,plain,
! [A: nat,B: nat,C: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(274,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_order__less__asym) ).
thf(1580,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(247,axiom,
! [A: fun_Ar331856045t_bool] :
( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ top_to951839027t_bool ) @ A ) )
=> ( A = top_to951839027t_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_535_top__le) ).
thf(1502,plain,
! [A: fun_Ar331856045t_bool] :
( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ top_to951839027t_bool ) @ A ) )
=> ( A = top_to951839027t_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(62,axiom,
! [A: fun_nat_bool,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ A @ B ) )
=> ( ! [C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ A @ ( hAPP_nat_nat @ suc @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ A @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ A @ zero_zero_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1125_zero__induct) ).
thf(820,plain,
! [A: fun_nat_bool,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ A @ B ) )
=> ( ! [C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ A @ ( hAPP_nat_nat @ suc @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ A @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ A @ zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(51,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1158_mult__less__mono2) ).
thf(788,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(205,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1170_one__less__mult) ).
thf(1370,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(281,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_xt1_I9_J) ).
thf(1602,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(550,axiom,
hBOOL @ ( hAPP_f584385070l_bool @ finite92092049e_indi @ top_to788185952i_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1031_finite__indi) ).
thf(2670,plain,
hBOOL @ ( hAPP_f584385070l_bool @ finite92092049e_indi @ top_to788185952i_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(361,axiom,
! [A: bool] : ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ A ) @ top_to1647826457l_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_UNIV__I) ).
thf(1920,plain,
! [A: bool] : ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ A ) @ top_to1647826457l_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(12,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) )
<=> ( ( A = zero_zero_nat )
| ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1179_nat__mult__eq__cancel__disj) ).
thf(625,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) )
=> ( ( A = zero_zero_nat )
| ( B = C ) ) )
& ( ( ( A = zero_zero_nat )
| ( B = C ) )
=> ( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(511,axiom,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
( ( A != B )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ B ) @ A ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_425_xt1_I12_J) ).
thf(2565,plain,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
( ( A != B )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ B ) @ A ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(528,axiom,
! [A: produc472769767le_alt,B: fun_Pr1509342064e_indi,C: fun_Pr2067565481t_bool,D: fun_Pr895221296i_bool] :
( ( hBOOL @ ( hAPP_f2124588998l_bool @ ( hAPP_f1187850253l_bool @ member1558233923e_indi @ B ) @ ( pi_Pro837265796e_indi @ C @ D ) ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_f584385070l_bool @ ( hAPP_A1597696899l_bool @ member1479139729e_indi @ ( hAPP_P276596750e_indi @ B @ A ) ) @ ( hAPP_P1859429372i_bool @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_548_Pi__mem) ).
thf(2609,plain,
! [A: produc472769767le_alt,B: fun_Pr1509342064e_indi,C: fun_Pr2067565481t_bool,D: fun_Pr895221296i_bool] :
( ( hBOOL @ ( hAPP_f2124588998l_bool @ ( hAPP_f1187850253l_bool @ member1558233923e_indi @ B ) @ ( pi_Pro837265796e_indi @ C @ D ) ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_f584385070l_bool @ ( hAPP_A1597696899l_bool @ member1479139729e_indi @ ( hAPP_P276596750e_indi @ B @ A ) ) @ ( hAPP_P1859429372i_bool @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(77,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1025_termination__basic__simps_I3_J) ).
thf(889,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(323,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
<=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_406_order__le__less) ).
thf(1787,plain,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
| ( A = B ) ) )
& ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
| ( A = B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(467,axiom,
! [A: produc472769767le_alt] : ( hBOOL @ ( hAPP_P1178790471t_bool @ top_to1138392227t_bool @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_top1I) ).
thf(2327,plain,
! [A: produc472769767le_alt] : ( hBOOL @ ( hAPP_P1178790471t_bool @ top_to1138392227t_bool @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(470,axiom,
! [A: fun_Pr2067565481t_bool] :
( ! [B: produc472769767le_alt] : ( hBOOL @ ( hAPP_P1178790471t_bool @ A @ B ) )
<=> ! [B: arrow_1893660431le_alt,C: arrow_1893660431le_alt] : ( hBOOL @ ( hAPP_P1178790471t_bool @ A @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_split__paired__All) ).
thf(2344,plain,
! [A: fun_Pr2067565481t_bool] :
( ( ! [B: produc472769767le_alt] : ( hBOOL @ ( hAPP_P1178790471t_bool @ A @ B ) )
=> ! [B: arrow_1893660431le_alt,C: arrow_1893660431le_alt] : ( hBOOL @ ( hAPP_P1178790471t_bool @ A @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ B ) @ C ) ) ) )
& ( ! [B: arrow_1893660431le_alt,C: arrow_1893660431le_alt] : ( hBOOL @ ( hAPP_P1178790471t_bool @ A @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ B ) @ C ) ) )
=> ! [B: produc472769767le_alt] : ( hBOOL @ ( hAPP_P1178790471t_bool @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(292,axiom,
! [A: fun_Ar516759882t_bool,B: fun_Ar274636406t_bool,C: arrow_856714788e_indi] :
( ( hAPP_A1646126530t_bool @ ( hAPP_f1302887663t_bool @ ( cOMBS_1181656689t_bool @ A ) @ B ) @ C )
= ( hAPP_f1356305429t_bool @ ( hAPP_A834130326t_bool @ A @ C ) @ ( hAPP_A1646126530t_bool @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000) ).
thf(1634,plain,
! [A: fun_Ar516759882t_bool,B: fun_Ar274636406t_bool,C: arrow_856714788e_indi] :
( ( hAPP_A1646126530t_bool @ ( hAPP_f1302887663t_bool @ ( cOMBS_1181656689t_bool @ A ) @ B ) @ C )
= ( hAPP_f1356305429t_bool @ ( hAPP_A834130326t_bool @ A @ C ) @ ( hAPP_A1646126530t_bool @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(419,axiom,
! [A: product_unit] : ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ A ) @ top_to1257323279t_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_UNIV__I) ).
thf(2112,plain,
! [A: product_unit] : ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ A ) @ top_to1257323279t_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(317,axiom,
! [A: fun_nat_fun_nat_bool,B: fun_Ar671024215di_nat,C: arrow_856714788e_indi] :
( ( hAPP_A1686943911t_bool @ ( hAPP_f966656047t_bool @ ( cOMBB_1869811296e_indi @ A ) @ B ) @ C )
= ( hAPP_n1699378549t_bool @ A @ ( hAPP_A376526755di_nat @ B @ C ) ) ),
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(1740,plain,
! [A: fun_nat_fun_nat_bool,B: fun_Ar671024215di_nat,C: arrow_856714788e_indi] :
( ( hAPP_A1686943911t_bool @ ( hAPP_f966656047t_bool @ ( cOMBB_1869811296e_indi @ A ) @ B ) @ C )
= ( hAPP_n1699378549t_bool @ A @ ( hAPP_A376526755di_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(272,axiom,
! [A: nat,B: nat,C: nat] :
( ( B = C )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_ord__eq__less__trans) ).
thf(1573,plain,
! [A: nat,B: nat,C: nat] :
( ( B = C )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(545,axiom,
! [A: product_unit] : ( hBOOL @ ( hAPP_P1676879539t_bool @ top_to1257323279t_bool @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_top1I) ).
thf(2653,plain,
! [A: product_unit] : ( hBOOL @ ( hAPP_P1676879539t_bool @ top_to1257323279t_bool @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(70,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) )
<=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) @ A ) )
& ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1171_one__le__mult__iff) ).
thf(852,plain,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) @ A ) )
& ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) @ B ) ) ) )
& ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) @ A ) )
& ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(574,axiom,
! [A: arrow_1893660431le_alt,B: arrow_1893660431le_alt,C: fun_Pr2067565481t_bool,D: arrow_1893660431le_alt] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ A ) @ B ) ) @ ( hAPP_A1601437999t_bool @ ( hAPP_f1761571331t_bool @ arrow_1481558583_mkbot @ C ) @ D ) ) )
<=> ( ( B != D )
& ( ( A = D )
=> ( A != B ) )
& ( ( A != D )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ A ) @ B ) ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_in__mkbot) ).
thf(2826,plain,
! [A: arrow_1893660431le_alt,B: arrow_1893660431le_alt,C: fun_Pr2067565481t_bool,D: arrow_1893660431le_alt] :
( ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ A ) @ B ) ) @ ( hAPP_A1601437999t_bool @ ( hAPP_f1761571331t_bool @ arrow_1481558583_mkbot @ C ) @ D ) ) )
=> ( ( B != D )
& ( ( A = D )
=> ( A != B ) )
& ( ( A != D )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ A ) @ B ) ) @ C ) ) ) ) )
& ( ( ( B != D )
& ( ( A = D )
=> ( A != B ) )
& ( ( A != D )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ A ) @ B ) ) @ C ) ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ A ) @ B ) ) @ ( hAPP_A1601437999t_bool @ ( hAPP_f1761571331t_bool @ arrow_1481558583_mkbot @ C ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(159,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ B ) )
<=> ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_992_nat__add__right__cancel) ).
thf(1195,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ B ) )
=> ( A = C ) )
& ( ( A = C )
=> ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(217,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1021_add__leD2) ).
thf(1407,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(202,axiom,
! [A: fun_fu955147676ol_nat,B: nat,C: fun_fu638310559l_bool,D: fun_fu638310559l_bool] :
( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_f1487854056ol_nat @ A @ D ) ) @ B ) )
=> ( ! [E: fun_fu638310559l_bool,F: fun_fu638310559l_bool] :
( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ E ) @ F ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f1487854056ol_nat @ A @ E ) ) @ ( hAPP_f1487854056ol_nat @ A @ F ) ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_f1487854056ol_nat @ A @ C ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_881_order__le__less__subst2) ).
thf(1360,plain,
! [A: fun_fu955147676ol_nat,B: nat,C: fun_fu638310559l_bool,D: fun_fu638310559l_bool] :
( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_f1487854056ol_nat @ A @ D ) ) @ B ) )
=> ( ! [E: fun_fu638310559l_bool,F: fun_fu638310559l_bool] :
( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ E ) @ F ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f1487854056ol_nat @ A @ E ) ) @ ( hAPP_f1487854056ol_nat @ A @ F ) ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_f1487854056ol_nat @ A @ C ) ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(94,axiom,
! [A: fun_Pr2067565481t_bool,B: fun_fu638310559l_bool,C: fun_fu638310559l_bool] :
( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_956_set__mp) ).
thf(948,plain,
! [A: fun_Pr2067565481t_bool,B: fun_fu638310559l_bool,C: fun_fu638310559l_bool] :
( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(258,axiom,
! [A: fun_Pr2067565481t_bool] : ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ A ) @ top_to1312956197l_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_iso__tuple__UNIV__I) ).
thf(1534,plain,
! [A: fun_Pr2067565481t_bool] : ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ A ) @ top_to1312956197l_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(493,axiom,
~ ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ a ) @ b ) ) @ lba ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79__096_Ia_M_Ab_J_A_126_058_ALba_096) ).
thf(2509,plain,
~ ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ a ) @ b ) ) @ lba ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(536,axiom,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ B ) @ A ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_908_equalityI) ).
thf(2631,plain,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ B ) @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(501,axiom,
~ ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ b ) @ a ) ) @ lab ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80__096_Ib_M_Aa_J_A_126_058_ALab_096) ).
thf(2537,plain,
~ ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ b ) @ a ) ) @ lab ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(6,axiom,
! [A: nat,B: nat] :
( ( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B )
= zero_zero_nat )
<=> ( ( A = zero_zero_nat )
| ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1154_mult__is__0) ).
thf(593,plain,
! [A: nat,B: nat] :
( ( ( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B )
= zero_zero_nat )
=> ( ( A = zero_zero_nat )
| ( B = zero_zero_nat ) ) )
& ( ( ( A = zero_zero_nat )
| ( B = zero_zero_nat ) )
=> ( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B )
= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(539,axiom,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_436_order__less__imp__le) ).
thf(2638,plain,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(215,axiom,
! [A: fun_Ar535288606t_bool,B: fun_Ar274636406t_bool,C: arrow_856714788e_indi] :
( ( hAPP_A834130326t_bool @ ( hAPP_f1001205955t_bool @ ( cOMBS_1925466437t_bool @ A ) @ B ) @ C )
= ( hAPP_f1299954409t_bool @ ( hAPP_A1395684458t_bool @ A @ C ) @ ( hAPP_A1646126530t_bool @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000_427) ).
thf(1397,plain,
! [A: fun_Ar535288606t_bool,B: fun_Ar274636406t_bool,C: arrow_856714788e_indi] :
( ( hAPP_A834130326t_bool @ ( hAPP_f1001205955t_bool @ ( cOMBS_1925466437t_bool @ A ) @ B ) @ C )
= ( hAPP_f1299954409t_bool @ ( hAPP_A1395684458t_bool @ A @ C ) @ ( hAPP_A1646126530t_bool @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(178,axiom,
! [A: nat] :
( ( hAPP_n1699378549t_bool @ ord_less_nat @ A )
= ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1110_less__eq__Suc__le__raw) ).
thf(1270,plain,
! [A: nat] :
( ( hAPP_n1699378549t_bool @ ord_less_nat @ A )
= ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(175,axiom,
! [A: fun_Pr2067565481t_bool] :
( ( pi_Pro1238944957t_bool @ A @ ( hAPP_f699791347l_bool @ cOMBK_138598520le_alt @ top_to1647826457l_bool ) )
= top_to1312956197l_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_Pi__UNIV) ).
thf(1259,plain,
! [A: fun_Pr2067565481t_bool] :
( ( pi_Pro1238944957t_bool @ A @ ( hAPP_f699791347l_bool @ cOMBK_138598520le_alt @ top_to1647826457l_bool ) )
= top_to1312956197l_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(142,axiom,
! [A: nat,B: nat] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1079_not__less__less__Suc__eq) ).
thf(1121,plain,
! [A: nat,B: nat] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(477,axiom,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ B ) )
<=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ A ) @ B ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_932_subset__iff__psubset__eq) ).
thf(2359,plain,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
( ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ A ) @ B ) )
| ( A = B ) ) )
& ( ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ A ) @ B ) )
| ( A = B ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(207,axiom,
! [A: fun_fu638310559l_bool,B: fun_fu638310559l_bool,C: fun_fu638310559l_bool] :
( ( B = C )
=> ( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_ord__eq__le__trans) ).
thf(1375,plain,
! [A: fun_fu638310559l_bool,B: fun_fu638310559l_bool,C: fun_fu638310559l_bool] :
( ( B = C )
=> ( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(516,axiom,
! [A: fun_Pr2067565481t_bool,B: produc472769767le_alt,C: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_964_set__rev__mp) ).
thf(2577,plain,
! [A: fun_Pr2067565481t_bool,B: produc472769767le_alt,C: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(126,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_729_add__imp__eq) ).
thf(1064,plain,
! [A: nat,B: nat,C: nat] :
( ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(561,axiom,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_946_psubset__subset__trans) ).
thf(2709,plain,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(374,axiom,
! [A: fun_nat_bool] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ suc ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1093_inj__Suc) ).
thf(1970,plain,
! [A: fun_nat_bool] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ suc ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(104,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) )
<=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1173_mult__le__cancel1) ).
thf(980,plain,
! [A: nat,B: nat,C: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) ) )
& ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(557,axiom,
! [A: produc472769767le_alt] : ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ A ) @ top_to1138392227t_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_iso__tuple__UNIV__I) ).
thf(2692,plain,
! [A: produc472769767le_alt] : ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ A ) @ top_to1138392227t_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
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 )
=> ( ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ B ) @ arrow_5070731e_Prof ) )
=> ( ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ A ) @ arrow_5070731e_Prof ) )
=> ( ! [G: arrow_856714788e_indi] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ E ) @ F ) ) @ ( hAPP_A1646126530t_bool @ B @ G ) ) )
<=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ C ) @ D ) ) @ ( hAPP_A1646126530t_bool @ A @ G ) ) ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ E ) @ F ) ) @ ( hAPP_f2008608496t_bool @ f @ B ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ C ) @ D ) ) @ ( hAPP_f2008608496t_bool @ f @ A ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7__C1_C) ).
thf(2694,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 )
=> ( ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ B ) @ arrow_5070731e_Prof ) )
=> ( ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ A ) @ arrow_5070731e_Prof ) )
=> ( ! [G: arrow_856714788e_indi] :
( ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ E ) @ F ) ) @ ( hAPP_A1646126530t_bool @ B @ G ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ C ) @ D ) ) @ ( hAPP_A1646126530t_bool @ A @ G ) ) ) )
& ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ C ) @ D ) ) @ ( hAPP_A1646126530t_bool @ A @ G ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ E ) @ F ) ) @ ( hAPP_A1646126530t_bool @ B @ G ) ) ) ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ E ) @ F ) ) @ ( hAPP_f2008608496t_bool @ f @ B ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ C ) @ D ) ) @ ( hAPP_f2008608496t_bool @ f @ A ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(223,axiom,
! [A: nat,B: fun_fu955147676ol_nat,C: fun_fu638310559l_bool,D: fun_fu638310559l_bool] :
( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_f1487854056ol_nat @ B @ C ) ) )
=> ( ! [E: fun_fu638310559l_bool,F: fun_fu638310559l_bool] :
( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ F ) @ E ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f1487854056ol_nat @ B @ F ) ) @ ( hAPP_f1487854056ol_nat @ B @ E ) ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_f1487854056ol_nat @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_699_xt7) ).
thf(1425,plain,
! [A: nat,B: fun_fu955147676ol_nat,C: fun_fu638310559l_bool,D: fun_fu638310559l_bool] :
( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_f1487854056ol_nat @ B @ C ) ) )
=> ( ! [E: fun_fu638310559l_bool,F: fun_fu638310559l_bool] :
( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ F ) @ E ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f1487854056ol_nat @ B @ F ) ) @ ( hAPP_f1487854056ol_nat @ B @ E ) ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_f1487854056ol_nat @ B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(261,axiom,
! [A: fun_Ar274636406t_bool,B: fun_fu2114379172t_bool,C: fun_fu3835832l_bool,D: fun_fu1863781882l_bool] :
( ( hBOOL @ ( hAPP_f975209902l_bool @ ( hAPP_f1714503811l_bool @ member173038353t_bool @ B ) @ ( pi_fun1746584570t_bool @ C @ D ) ) )
=> ( ~ ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ ( hAPP_f2008608496t_bool @ B @ A ) ) @ ( hAPP_f1915815064l_bool @ D @ A ) ) )
=> ~ ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_PiE) ).
thf(1540,plain,
! [A: fun_Ar274636406t_bool,B: fun_fu2114379172t_bool,C: fun_fu3835832l_bool,D: fun_fu1863781882l_bool] :
( ( hBOOL @ ( hAPP_f975209902l_bool @ ( hAPP_f1714503811l_bool @ member173038353t_bool @ B ) @ ( pi_fun1746584570t_bool @ C @ D ) ) )
=> ( ~ ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ ( hAPP_f2008608496t_bool @ B @ A ) ) @ ( hAPP_f1915815064l_bool @ D @ A ) ) )
=> ~ ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(108,axiom,
! [A: fun_Ar516759882t_bool,B: fun_Pr2067565481t_bool,C: arrow_856714788e_indi] :
( ( hAPP_A1646126530t_bool @ ( hAPP_f480276746t_bool @ ( hAPP_f601594885t_bool @ cOMBC_750853729t_bool @ A ) @ B ) @ C )
= ( hAPP_f1356305429t_bool @ ( hAPP_A834130326t_bool @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000_418) ).
thf(1006,plain,
! [A: fun_Ar516759882t_bool,B: fun_Pr2067565481t_bool,C: arrow_856714788e_indi] :
( ( hAPP_A1646126530t_bool @ ( hAPP_f480276746t_bool @ ( hAPP_f601594885t_bool @ cOMBC_750853729t_bool @ A ) @ B ) @ C )
= ( hAPP_f1356305429t_bool @ ( hAPP_A834130326t_bool @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(149,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1073_Suc__lessD) ).
thf(1160,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(466,axiom,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ B ) @ C ) )
=> ( ( B = A )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_xt1_I4_J) ).
thf(2323,plain,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ B ) @ C ) )
=> ( ( B = A )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(154,axiom,
! [A: fun_Ar1809396326i_bool] :
( ( pi_Arr959578316t_bool @ A @ ( hAPP_f1717907078l_bool @ cOMBK_1520063231e_indi @ top_to1312956197l_bool ) )
= top_to553140914l_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_Pi__UNIV) ).
thf(1182,plain,
! [A: fun_Ar1809396326i_bool] :
( ( pi_Arr959578316t_bool @ A @ ( hAPP_f1717907078l_bool @ cOMBK_1520063231e_indi @ top_to1312956197l_bool ) )
= top_to553140914l_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(464,axiom,
! [A: produc472769767le_alt,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_970_in__mono) ).
thf(2312,plain,
! [A: produc472769767le_alt,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(471,axiom,
! [A: product_unit,B: fun_Pr2090226719le_alt,C: fun_Pr1643180309t_bool,D: fun_Pr1887398791t_bool] :
( ( hBOOL @ ( hAPP_f684683381l_bool @ ( hAPP_f41367117l_bool @ member869664626le_alt @ B ) @ ( pi_Pro1820940723le_alt @ C @ D ) ) )
=> ( ~ ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_P396106045le_alt @ B @ A ) ) @ ( hAPP_P1914371027t_bool @ D @ A ) ) )
=> ~ ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_PiE) ).
thf(2349,plain,
! [A: product_unit,B: fun_Pr2090226719le_alt,C: fun_Pr1643180309t_bool,D: fun_Pr1887398791t_bool] :
( ( hBOOL @ ( hAPP_f684683381l_bool @ ( hAPP_f41367117l_bool @ member869664626le_alt @ B ) @ ( pi_Pro1820940723le_alt @ C @ D ) ) )
=> ( ~ ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_P396106045le_alt @ B @ A ) ) @ ( hAPP_P1914371027t_bool @ D @ A ) ) )
=> ~ ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(398,axiom,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
( ( hAPP_f1356305429t_bool @ ( hAPP_f1299954409t_bool @ ( hAPP_b35146737t_bool @ if_fun523439385t_bool @ fTrue ) @ A ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiq) ).
thf(2038,plain,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
( ( hAPP_f1356305429t_bool @ ( hAPP_f1299954409t_bool @ ( hAPP_b35146737t_bool @ if_fun523439385t_bool @ fTrue ) @ A ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(410,axiom,
! [A: arrow_856714788e_indi] : ( hBOOL @ ( hAPP_f584385070l_bool @ ( hAPP_A1597696899l_bool @ member1479139729e_indi @ A ) @ top_to788185952i_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_UNIV__I) ).
thf(2085,plain,
! [A: arrow_856714788e_indi] : ( hBOOL @ ( hAPP_f584385070l_bool @ ( hAPP_A1597696899l_bool @ member1479139729e_indi @ A ) @ top_to788185952i_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(354,axiom,
! [A: nat] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1046_less__nat__zero__code) ).
thf(1889,plain,
! [A: nat] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(489,axiom,
! [A: arrow_856714788e_indi,B: fun_fu2114379172t_bool] :
( ( hBOOL @ ( hAPP_f975209902l_bool @ ( hAPP_f1714503811l_bool @ member173038353t_bool @ B ) @ ( pi_fun1746584570t_bool @ arrow_5070731e_Prof @ ( hAPP_f1104294872l_bool @ cOMBK_1701906001t_bool @ arrow_1361987423le_Lin ) ) ) )
=> ( ! [C: fun_Ar274636406t_bool] :
( ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ C ) @ arrow_5070731e_Prof ) )
=> ! [D: arrow_1893660431le_alt,E: arrow_1893660431le_alt] :
( ( D != E )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ D ) @ E ) ) @ ( hAPP_A1646126530t_bool @ C @ A ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ D ) @ E ) ) @ ( hAPP_f2008608496t_bool @ B @ C ) ) ) ) ) )
=> ( hBOOL @ ( hAPP_A997847300i_bool @ ( hAPP_f399308031i_bool @ arrow_1765888670ctator @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_dictatorI) ).
thf(2472,plain,
! [A: arrow_856714788e_indi,B: fun_fu2114379172t_bool] :
( ( hBOOL @ ( hAPP_f975209902l_bool @ ( hAPP_f1714503811l_bool @ member173038353t_bool @ B ) @ ( pi_fun1746584570t_bool @ arrow_5070731e_Prof @ ( hAPP_f1104294872l_bool @ cOMBK_1701906001t_bool @ arrow_1361987423le_Lin ) ) ) )
=> ( ! [C: fun_Ar274636406t_bool] :
( ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ C ) @ arrow_5070731e_Prof ) )
=> ! [D: arrow_1893660431le_alt,E: arrow_1893660431le_alt] :
( ( D != E )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ D ) @ E ) ) @ ( hAPP_A1646126530t_bool @ C @ A ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ D ) @ E ) ) @ ( hAPP_f2008608496t_bool @ B @ C ) ) ) ) ) )
=> ( hBOOL @ ( hAPP_A997847300i_bool @ ( hAPP_f399308031i_bool @ arrow_1765888670ctator @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(222,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) )
<=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
& ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1162_nat__0__less__mult__iff) ).
thf(1419,plain,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
& ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) ) ) )
& ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
& ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(485,axiom,
! [A: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ top_to1312956197l_bool @ A ) )
<=> ( hBOOL @ top_top_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_top__apply) ).
thf(2460,plain,
! [A: fun_Pr2067565481t_bool] :
( ( ( hBOOL @ ( hAPP_f52567537l_bool @ top_to1312956197l_bool @ A ) )
=> ( hBOOL @ top_top_bool ) )
& ( ( hBOOL @ top_top_bool )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ top_to1312956197l_bool @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(572,axiom,
! [A: fun_Ar274636406t_bool,B: fun_Ar274636406t_bool,C: arrow_1893660431le_alt,D: arrow_1893660431le_alt] :
( ( C != D )
=> ( ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ B ) @ arrow_5070731e_Prof ) )
=> ( ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ A ) @ arrow_5070731e_Prof ) )
=> ( ! [E: arrow_856714788e_indi] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ C ) @ D ) ) @ ( hAPP_A1646126530t_bool @ B @ E ) ) )
<=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ D ) @ C ) ) @ ( hAPP_A1646126530t_bool @ A @ E ) ) ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ C ) @ D ) ) @ ( hAPP_f2008608496t_bool @ f @ B ) ) )
<=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ D ) @ C ) ) @ ( hAPP_f2008608496t_bool @ f @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10__C3_C) ).
thf(2798,plain,
! [A: fun_Ar274636406t_bool,B: fun_Ar274636406t_bool,C: arrow_1893660431le_alt,D: arrow_1893660431le_alt] :
( ( C != D )
=> ( ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ B ) @ arrow_5070731e_Prof ) )
=> ( ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ A ) @ arrow_5070731e_Prof ) )
=> ( ! [E: arrow_856714788e_indi] :
( ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ C ) @ D ) ) @ ( hAPP_A1646126530t_bool @ B @ E ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ D ) @ C ) ) @ ( hAPP_A1646126530t_bool @ A @ E ) ) ) )
& ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ D ) @ C ) ) @ ( hAPP_A1646126530t_bool @ A @ E ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ C ) @ D ) ) @ ( hAPP_A1646126530t_bool @ B @ E ) ) ) ) )
=> ( ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ C ) @ D ) ) @ ( hAPP_f2008608496t_bool @ f @ B ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ D ) @ C ) ) @ ( hAPP_f2008608496t_bool @ f @ A ) ) ) )
& ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ D ) @ C ) ) @ ( hAPP_f2008608496t_bool @ f @ A ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ C ) @ D ) ) @ ( hAPP_f2008608496t_bool @ f @ B ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(113,axiom,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ B ) @ C ) )
= ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ B ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_989_nat__add__left__commute) ).
thf(1028,plain,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ B ) @ C ) )
= ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ B ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(132,axiom,
! [A: nat,B: fun_nat_bool] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ B @ zero_zero_nat ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ B @ A ) )
=> ? [C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ A ) )
& ! [D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ D ) @ C ) )
=> ~ ( hBOOL @ ( hAPP_nat_bool @ B @ D ) ) )
& ( hBOOL @ ( hAPP_nat_bool @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1057_ex__least__nat__le) ).
thf(1082,plain,
! [A: nat,B: fun_nat_bool] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ B @ zero_zero_nat ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ B @ A ) )
=> ? [C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ A ) )
& ! [D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ D ) @ C ) )
=> ~ ( hBOOL @ ( hAPP_nat_bool @ B @ D ) ) )
& ( hBOOL @ ( hAPP_nat_bool @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(183,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1018_trans__le__add2) ).
thf(1292,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(89,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_735_add__le__imp__le__left) ).
thf(933,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(80,axiom,
( one_one_nat
= ( hAPP_nat_nat @ suc @ zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1109_One__nat__def) ).
thf(901,plain,
( one_one_nat
= ( hAPP_nat_nat @ suc @ zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(25,axiom,
( ( hAPP_nat_nat @ size_size_nat @ zero_zero_nat )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1185_nat_Osize_I3_J) ).
thf(686,plain,
( ( hAPP_nat_nat @ size_size_nat @ zero_zero_nat )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(220,axiom,
! [A: nat,B: nat] :
( ( ( hAPP_nat_nat @ suc @ A )
= ( hAPP_nat_nat @ suc @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1062_Suc__inject) ).
thf(1414,plain,
! [A: nat,B: nat] :
( ( ( hAPP_nat_nat @ suc @ A )
= ( hAPP_nat_nat @ suc @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(401,axiom,
! [A: fun_Ar603939593t_bool,B: nat,C: arrow_856714788e_indi] :
( ( hAPP_A997847300i_bool @ ( hAPP_n34002993i_bool @ ( hAPP_f721434149i_bool @ cOMBC_722552198t_bool @ A ) @ B ) @ C )
= ( hAPP_nat_bool @ ( hAPP_A1686943911t_bool @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000) ).
thf(2053,plain,
! [A: fun_Ar603939593t_bool,B: nat,C: arrow_856714788e_indi] :
( ( hAPP_A997847300i_bool @ ( hAPP_n34002993i_bool @ ( hAPP_f721434149i_bool @ cOMBC_722552198t_bool @ A ) @ B ) @ C )
= ( hAPP_nat_bool @ ( hAPP_A1686943911t_bool @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(441,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
<=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
& ( A != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1008_nat__less__le) ).
thf(2196,plain,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
& ( A != B ) ) )
& ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
& ( A != B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(338,axiom,
hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ lba ) @ arrow_1361987423le_Lin ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75__096Lba_A_058_ALin_096) ).
thf(1842,plain,
hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ lba ) @ arrow_1361987423le_Lin ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(14,axiom,
! [A: nat,B: nat] :
( ( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B )
= one_one_nat )
<=> ( ( A = one_one_nat )
& ( B = one_one_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1145_nat__mult__eq__1__iff) ).
thf(637,plain,
! [A: nat,B: nat] :
( ( ( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B )
= one_one_nat )
=> ( ( A = one_one_nat )
& ( B = one_one_nat ) ) )
& ( ( ( A = one_one_nat )
& ( B = one_one_nat ) )
=> ( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B )
= one_one_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(276,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_order__less__asym_H) ).
thf(1584,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(11,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ B ) ) @ D ) )
= ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) @ B ) ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1180_left__add__mult__distrib) ).
thf(622,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ B ) ) @ D ) )
= ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) @ B ) ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(195,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) )
<=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1081_less__Suc__eq) ).
thf(1324,plain,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
| ( A = B ) ) )
& ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
| ( A = B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(135,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1075_less__trans__Suc) ).
thf(1099,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(18,axiom,
( ( hAPP_nat_nat @ nat_size @ zero_zero_nat )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1182_nat_Osize_I1_J) ).
thf(654,plain,
( ( hAPP_nat_nat @ nat_size @ zero_zero_nat )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(376,axiom,
! [A: fun_fu696673523t_bool,B: fun_Ar1995913199l_bool,C: arrow_1893660431le_alt] :
( ( hAPP_A656921921t_bool @ ( hAPP_f105674721t_bool @ ( cOMBB_652885079le_alt @ A ) @ B ) @ C )
= ( hAPP_f1689397393t_bool @ A @ ( hAPP_A1608658241l_bool @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs___428) ).
thf(1974,plain,
! [A: fun_fu696673523t_bool,B: fun_Ar1995913199l_bool,C: arrow_1893660431le_alt] :
( ( hAPP_A656921921t_bool @ ( hAPP_f105674721t_bool @ ( cOMBB_652885079le_alt @ A ) @ B ) @ C )
= ( hAPP_f1689397393t_bool @ A @ ( hAPP_A1608658241l_bool @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(474,axiom,
hBOOL @ fTrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fTrue_1_1_U) ).
thf(2355,plain,
hBOOL @ fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(486,axiom,
! [A: bool,B: fun_bo1682907689le_alt,C: fun_bool_bool,D: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f1620711039l_bool @ ( hAPP_f334747853l_bool @ member684813948le_alt @ B ) @ ( pi_boo7125949le_alt @ C @ ( hAPP_f1723896209t_bool @ cOMBK_5056120l_bool @ D ) ) ) )
=> ( ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_b2094455111le_alt @ B @ A ) ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_597_funcset__mem) ).
thf(2465,plain,
! [A: bool,B: fun_bo1682907689le_alt,C: fun_bool_bool,D: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f1620711039l_bool @ ( hAPP_f334747853l_bool @ member684813948le_alt @ B ) @ ( pi_boo7125949le_alt @ C @ ( hAPP_f1723896209t_bool @ cOMBK_5056120l_bool @ D ) ) ) )
=> ( ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_b2094455111le_alt @ B @ A ) ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(34,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) )
<=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_991_nat__add__left__cancel) ).
thf(721,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) )
=> ( B = C ) )
& ( ( B = C )
=> ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(325,axiom,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_983_linorder__neqE__nat) ).
thf(1799,plain,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(348,axiom,
! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_993_le__refl) ).
thf(1874,plain,
! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(577,axiom,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_477_order__less__le__trans) ).
thf(2862,plain,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(170,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( ( ( hAPP_nat_nat @ suc @ A )
!= B )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1076_Suc__lessI) ).
thf(1246,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( ( ( hAPP_nat_nat @ suc @ A )
!= B )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(312,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
<=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1009_le__eq__less__or__eq) ).
thf(1715,plain,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
| ( A = B ) ) )
& ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
| ( A = B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(48,axiom,
! [A: fun_na300967376t_bool,B: fun_Ar331856045t_bool,C: nat,D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ ( hAPP_n1312530466t_bool @ A @ D ) ) @ B ) )
=> ( ! [E: nat,F: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ E ) @ F ) )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ ( hAPP_n1312530466t_bool @ A @ E ) ) @ ( hAPP_n1312530466t_bool @ A @ F ) ) ) )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ ( hAPP_n1312530466t_bool @ A @ C ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_863_order__le__less__subst2) ).
thf(779,plain,
! [A: fun_na300967376t_bool,B: fun_Ar331856045t_bool,C: nat,D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ ( hAPP_n1312530466t_bool @ A @ D ) ) @ B ) )
=> ( ! [E: nat,F: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ E ) @ F ) )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ ( hAPP_n1312530466t_bool @ A @ E ) ) @ ( hAPP_n1312530466t_bool @ A @ F ) ) ) )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ ( hAPP_n1312530466t_bool @ A @ C ) ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(289,axiom,
! [A: fun_Ar331856045t_bool,B: nat,C: fun_fu1677555470ol_nat,D: fun_Ar331856045t_bool] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_f1403773274ol_nat @ C @ D ) ) )
=> ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ D ) @ A ) )
=> ( ! [E: fun_Ar331856045t_bool,F: fun_Ar331856045t_bool] :
( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ E ) @ F ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f1403773274ol_nat @ C @ E ) ) @ ( hAPP_f1403773274ol_nat @ C @ F ) ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_f1403773274ol_nat @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_854_order__less__le__subst1) ).
thf(1627,plain,
! [A: fun_Ar331856045t_bool,B: nat,C: fun_fu1677555470ol_nat,D: fun_Ar331856045t_bool] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_f1403773274ol_nat @ C @ D ) ) )
=> ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ D ) @ A ) )
=> ( ! [E: fun_Ar331856045t_bool,F: fun_Ar331856045t_bool] :
( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ E ) @ F ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f1403773274ol_nat @ C @ E ) ) @ ( hAPP_f1403773274ol_nat @ C @ F ) ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_f1403773274ol_nat @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(171,axiom,
! [A: nat] :
( zero_zero_nat
!= ( hAPP_nat_nat @ suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1071_Zero__not__Suc) ).
thf(1249,plain,
! [A: nat] :
( zero_zero_nat
!= ( hAPP_nat_nat @ suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(496,axiom,
! [A: bool,B: fun_bo1682907689le_alt,C: fun_bool_bool,D: fun_bo1431306493t_bool] :
( ( hBOOL @ ( hAPP_f1620711039l_bool @ ( hAPP_f334747853l_bool @ member684813948le_alt @ B ) @ ( pi_boo7125949le_alt @ C @ D ) ) )
=> ( ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_b2094455111le_alt @ B @ A ) ) @ ( hAPP_b128655177t_bool @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_563_Pi__mem) ).
thf(2519,plain,
! [A: bool,B: fun_bo1682907689le_alt,C: fun_bool_bool,D: fun_bo1431306493t_bool] :
( ( hBOOL @ ( hAPP_f1620711039l_bool @ ( hAPP_f334747853l_bool @ member684813948le_alt @ B ) @ ( pi_boo7125949le_alt @ C @ D ) ) )
=> ( ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_b2094455111le_alt @ B @ A ) ) @ ( hAPP_b128655177t_bool @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(430,axiom,
! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool] :
( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ A ) @ B ) )
=> ( ( A != B )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_459_order__le__neq__trans) ).
thf(2153,plain,
! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool] :
( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ A ) @ B ) )
=> ( ( A != B )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(334,axiom,
! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool,C: fun_Ar331856045t_bool] :
( ( B = C )
=> ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_ord__eq__le__trans) ).
thf(1831,plain,
! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool,C: fun_Ar331856045t_bool] :
( ( B = C )
=> ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(265,axiom,
! [A: arrow_856714788e_indi,B: fun_Ar1809396326i_bool] :
( ( hBOOL @ ( hAPP_f584385070l_bool @ ( hAPP_A1597696899l_bool @ member1479139729e_indi @ A ) @ B ) )
<=> ( hBOOL @ ( hAPP_A997847300i_bool @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_mem__def) ).
thf(1552,plain,
! [A: arrow_856714788e_indi,B: fun_Ar1809396326i_bool] :
( ( ( hBOOL @ ( hAPP_f584385070l_bool @ ( hAPP_A1597696899l_bool @ member1479139729e_indi @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_A997847300i_bool @ B @ A ) ) )
& ( ( hBOOL @ ( hAPP_A997847300i_bool @ B @ A ) )
=> ( hBOOL @ ( hAPP_f584385070l_bool @ ( hAPP_A1597696899l_bool @ member1479139729e_indi @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(451,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( A != B )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_461_order__le__neq__trans) ).
thf(2243,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( A != B )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(107,axiom,
! [A: nat] :
( ( hAPP_nat_nat @ suc @ A )
!= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1066_Suc__neq__Zero) ).
thf(1002,plain,
! [A: nat] :
( ( hAPP_nat_nat @ suc @ A )
!= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(342,axiom,
! [A: nat,B: nat] :
( ( A != B )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_429_xt1_I12_J) ).
thf(1852,plain,
! [A: nat,B: nat] :
( ( A != B )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(196,axiom,
! [A: nat] :
( ( hAPP_nat_nat @ cOMBI_nat @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBI_1_1_COMBI_000tc__Nat__Onat_U) ).
thf(1333,plain,
! [A: nat] :
( ( hAPP_nat_nat @ cOMBI_nat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(537,axiom,
~ ( hBOOL @ fFalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
thf(2634,plain,
~ ( hBOOL @ fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(133,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) )
<=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
& ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1161_mult__less__cancel1) ).
thf(1086,plain,
! [A: nat,B: nat,C: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
& ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) ) ) )
& ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
& ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(443,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( ( C = A )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_ord__less__eq__trans) ).
thf(2208,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( ( C = A )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(156,axiom,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ C )
= ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_733_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(1187,plain,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ C )
= ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(285,axiom,
! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool,C: fun_Ar331856045t_bool] :
( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_order__trans) ).
thf(1616,plain,
! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool,C: fun_Ar331856045t_bool] :
( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(21,axiom,
! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1141_le__cube) ).
thf(662,plain,
! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(315,axiom,
! [A: fun_fu638310559l_bool,B: fun_fu638310559l_bool] :
( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ ( hAPP_f1060563265l_bool @ ( hAPP_f1776355587l_bool @ cOMBC_2133093654l_bool @ member1069471740t_bool ) @ A ) ) @ ( hAPP_f1060563265l_bool @ ( hAPP_f1776355587l_bool @ cOMBC_2133093654l_bool @ member1069471740t_bool ) @ B ) ) )
<=> ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_977_pred__subset__eq) ).
thf(1732,plain,
! [A: fun_fu638310559l_bool,B: fun_fu638310559l_bool] :
( ( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ ( hAPP_f1060563265l_bool @ ( hAPP_f1776355587l_bool @ cOMBC_2133093654l_bool @ member1069471740t_bool ) @ A ) ) @ ( hAPP_f1060563265l_bool @ ( hAPP_f1776355587l_bool @ cOMBC_2133093654l_bool @ member1069471740t_bool ) @ B ) ) )
=> ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ ( hAPP_f1060563265l_bool @ ( hAPP_f1776355587l_bool @ cOMBC_2133093654l_bool @ member1069471740t_bool ) @ A ) ) @ ( hAPP_f1060563265l_bool @ ( hAPP_f1776355587l_bool @ cOMBC_2133093654l_bool @ member1069471740t_bool ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(88,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) )
<=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1055_add__gr__0) ).
thf(926,plain,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) ) ) )
& ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(381,axiom,
! [A: fun_fu2114379172t_bool] : ( hBOOL @ ( hAPP_f975209902l_bool @ ( hAPP_f1714503811l_bool @ member173038353t_bool @ A ) @ top_to827110112l_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_UNIV__I) ).
thf(1991,plain,
! [A: fun_fu2114379172t_bool] : ( hBOOL @ ( hAPP_f975209902l_bool @ ( hAPP_f1714503811l_bool @ member173038353t_bool @ A ) @ top_to827110112l_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(193,axiom,
! [A: fun_nat_nat,B: fun_nat_nat] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ B ) @ top_top_fun_nat_bool ) )
=> ( ! [C: nat] :
( ( hAPP_nat_nat @ B @ ( hAPP_nat_nat @ A @ C ) )
= C )
=> ( ( hilber195283148at_nat @ top_top_fun_nat_bool @ B )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_652_inj__imp__inv__eq) ).
thf(1318,plain,
! [A: fun_nat_nat,B: fun_nat_nat] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ B ) @ top_top_fun_nat_bool ) )
=> ( ! [C: nat] :
( ( hAPP_nat_nat @ B @ ( hAPP_nat_nat @ A @ C ) )
= C )
=> ( ( hilber195283148at_nat @ top_top_fun_nat_bool @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(160,axiom,
! [A: nat,B: fun_Ar331856045t_bool,C: fun_na300967376t_bool,D: nat] :
( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ B ) @ ( hAPP_n1312530466t_bool @ C @ D ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ D ) @ A ) )
=> ( ! [E: nat,F: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ E ) @ F ) )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ ( hAPP_n1312530466t_bool @ C @ E ) ) @ ( hAPP_n1312530466t_bool @ C @ F ) ) ) )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ B ) @ ( hAPP_n1312530466t_bool @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_829_order__less__le__subst1) ).
thf(1202,plain,
! [A: nat,B: fun_Ar331856045t_bool,C: fun_na300967376t_bool,D: nat] :
( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ B ) @ ( hAPP_n1312530466t_bool @ C @ D ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ D ) @ A ) )
=> ( ! [E: nat,F: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ E ) @ F ) )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ ( hAPP_n1312530466t_bool @ C @ E ) ) @ ( hAPP_n1312530466t_bool @ C @ F ) ) ) )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ B ) @ ( hAPP_n1312530466t_bool @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(53,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ D ) )
=> ( ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ D )
= ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1006_less__add__eq__less) ).
thf(792,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ D ) )
=> ( ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ D )
= ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(568,axiom,
! [A: fun_fu2114379172t_bool] :
( ( hBOOL @ ( hAPP_f1572141188l_bool @ arrow_320876018nimity @ A ) )
<=> ! [B: fun_Ar274636406t_bool] :
( ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ B ) @ arrow_5070731e_Prof ) )
=> ! [C: arrow_1893660431le_alt,D: arrow_1893660431le_alt] :
( ! [E: arrow_856714788e_indi] : ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ C ) @ D ) ) @ ( hAPP_A1646126530t_bool @ B @ E ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ C ) @ D ) ) @ ( hAPP_f2008608496t_bool @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_unanimity__def) ).
thf(2748,plain,
! [A: fun_fu2114379172t_bool] :
( ( ( hBOOL @ ( hAPP_f1572141188l_bool @ arrow_320876018nimity @ A ) )
=> ! [B: fun_Ar274636406t_bool] :
( ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ B ) @ arrow_5070731e_Prof ) )
=> ! [C: arrow_1893660431le_alt,D: arrow_1893660431le_alt] :
( ! [E: arrow_856714788e_indi] : ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ C ) @ D ) ) @ ( hAPP_A1646126530t_bool @ B @ E ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ C ) @ D ) ) @ ( hAPP_f2008608496t_bool @ A @ B ) ) ) ) ) )
& ( ! [B: fun_Ar274636406t_bool] :
( ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ B ) @ arrow_5070731e_Prof ) )
=> ! [C: arrow_1893660431le_alt,D: arrow_1893660431le_alt] :
( ! [E: arrow_856714788e_indi] : ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ C ) @ D ) ) @ ( hAPP_A1646126530t_bool @ B @ E ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ C ) @ D ) ) @ ( hAPP_f2008608496t_bool @ A @ B ) ) ) ) )
=> ( hBOOL @ ( hAPP_f1572141188l_bool @ arrow_320876018nimity @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(152,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ C ) )
=> ( ( ( hAPP_nat_nat @ ( times_times_nat @ C ) @ A )
= ( hAPP_nat_nat @ ( times_times_nat @ C ) @ B ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1178_nat__mult__eq__cancel1) ).
thf(1170,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ C ) )
=> ( ( ( ( hAPP_nat_nat @ ( times_times_nat @ C ) @ A )
= ( hAPP_nat_nat @ ( times_times_nat @ C ) @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( hAPP_nat_nat @ ( times_times_nat @ C ) @ A )
= ( hAPP_nat_nat @ ( times_times_nat @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(181,axiom,
! [A: nat,B: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1099_less__add__Suc1) ).
thf(1286,plain,
! [A: nat,B: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
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 )
=> ( ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ B ) @ arrow_5070731e_Prof ) )
=> ( ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ A ) @ arrow_5070731e_Prof ) )
=> ( ! [G: arrow_856714788e_indi] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ E ) @ F ) ) @ ( hAPP_A1646126530t_bool @ B @ G ) ) )
<=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ C ) @ D ) ) @ ( hAPP_A1646126530t_bool @ A @ G ) ) ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ E ) @ F ) ) @ ( hAPP_f2008608496t_bool @ f @ B ) ) )
<=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ C ) @ D ) ) @ ( hAPP_f2008608496t_bool @ f @ A ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_pairwise__neutrality) ).
thf(2368,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 )
=> ( ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ B ) @ arrow_5070731e_Prof ) )
=> ( ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ A ) @ arrow_5070731e_Prof ) )
=> ( ! [G: arrow_856714788e_indi] :
( ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ E ) @ F ) ) @ ( hAPP_A1646126530t_bool @ B @ G ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ C ) @ D ) ) @ ( hAPP_A1646126530t_bool @ A @ G ) ) ) )
& ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ C ) @ D ) ) @ ( hAPP_A1646126530t_bool @ A @ G ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ E ) @ F ) ) @ ( hAPP_A1646126530t_bool @ B @ G ) ) ) ) )
=> ( ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ E ) @ F ) ) @ ( hAPP_f2008608496t_bool @ f @ B ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ C ) @ D ) ) @ ( hAPP_f2008608496t_bool @ f @ A ) ) ) )
& ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ C ) @ D ) ) @ ( hAPP_f2008608496t_bool @ f @ A ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ E ) @ F ) ) @ ( hAPP_f2008608496t_bool @ f @ B ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(112,axiom,
! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1054_less__eq__nat_Osimps_I1_J) ).
thf(1026,plain,
! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(151,axiom,
! [A: fun_Ar331856045t_bool,B: fun_na300967376t_bool,C: nat,D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ A ) @ ( hAPP_n1312530466t_bool @ B @ C ) ) )
=> ( ! [E: nat,F: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ F ) @ E ) )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ ( hAPP_n1312530466t_bool @ B @ F ) ) @ ( hAPP_n1312530466t_bool @ B @ E ) ) ) )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ A ) @ ( hAPP_n1312530466t_bool @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_681_xt7) ).
thf(1167,plain,
! [A: fun_Ar331856045t_bool,B: fun_na300967376t_bool,C: nat,D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ A ) @ ( hAPP_n1312530466t_bool @ B @ C ) ) )
=> ( ! [E: nat,F: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ F ) @ E ) )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ ( hAPP_n1312530466t_bool @ B @ F ) ) @ ( hAPP_n1312530466t_bool @ B @ E ) ) ) )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ A ) @ ( hAPP_n1312530466t_bool @ B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(96,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( ( B
!= ( hAPP_nat_nat @ suc @ A ) )
=> ~ ! [C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) )
=> ( B
!= ( hAPP_nat_nat @ suc @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1121_lessE) ).
thf(953,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( ( B
!= ( hAPP_nat_nat @ suc @ A ) )
=> ~ ! [C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) )
=> ( B
!= ( hAPP_nat_nat @ suc @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(155,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1004_add__less__mono1) ).
thf(1185,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(47,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ suc @ A ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1107_le__less__Suc__eq) ).
thf(773,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ suc @ A ) ) )
=> ( B = A ) )
& ( ( B = A )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ suc @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(383,axiom,
! [A: fun_bo1431306493t_bool,B: fun_bo377688929l_bool,C: fun_bool_bool] :
( ! [D: bool] :
( ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ D ) @ C ) )
=> ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ ( hAPP_b128655177t_bool @ A @ D ) ) @ ( hAPP_b1272691967l_bool @ B @ D ) ) ) )
=> ( hBOOL @ ( hAPP_f398210311l_bool @ ( hAPP_f416878261l_bool @ member1133581546t_bool @ A ) @ ( pi_boo1111177555t_bool @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_643_Pi__I) ).
thf(1996,plain,
! [A: fun_bo1431306493t_bool,B: fun_bo377688929l_bool,C: fun_bool_bool] :
( ! [D: bool] :
( ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ D ) @ C ) )
=> ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ ( hAPP_b128655177t_bool @ A @ D ) ) @ ( hAPP_b1272691967l_bool @ B @ D ) ) ) )
=> ( hBOOL @ ( hAPP_f398210311l_bool @ ( hAPP_f416878261l_bool @ member1133581546t_bool @ A ) @ ( pi_boo1111177555t_bool @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(145,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1169_n__less__n__mult__m) ).
thf(1135,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(385,axiom,
! [A: fun_Pr2067565481t_bool,B: arrow_1893660431le_alt,C: arrow_1893660431le_alt] :
( ( B != C )
=> ( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ A ) @ arrow_1361987423le_Lin ) )
=> ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ ( hAPP_A1601437999t_bool @ ( hAPP_A1058422557t_bool @ ( hAPP_f1550387441t_bool @ arrow_216713899_above @ A ) @ B ) @ C ) ) @ arrow_1361987423le_Lin ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_above__Lin) ).
thf(2001,plain,
! [A: fun_Pr2067565481t_bool,B: arrow_1893660431le_alt,C: arrow_1893660431le_alt] :
( ( B != C )
=> ( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ A ) @ arrow_1361987423le_Lin ) )
=> ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ ( hAPP_A1601437999t_bool @ ( hAPP_A1058422557t_bool @ ( hAPP_f1550387441t_bool @ arrow_216713899_above @ A ) @ B ) @ C ) ) @ arrow_1361987423le_Lin ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(98,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_738_add__left__mono) ).
thf(965,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
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 )
=> ( ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ B ) @ arrow_5070731e_Prof ) )
=> ( ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ A ) @ arrow_5070731e_Prof ) )
=> ( ! [G: arrow_856714788e_indi] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ E ) @ F ) ) @ ( hAPP_A1646126530t_bool @ B @ G ) ) )
<=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ C ) @ D ) ) @ ( hAPP_A1646126530t_bool @ A @ G ) ) ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ E ) @ F ) ) @ ( hAPP_f2008608496t_bool @ f @ B ) ) )
<=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ C ) @ D ) ) @ ( hAPP_f2008608496t_bool @ f @ A ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6__C2_C) ).
thf(2677,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 )
=> ( ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ B ) @ arrow_5070731e_Prof ) )
=> ( ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ A ) @ arrow_5070731e_Prof ) )
=> ( ! [G: arrow_856714788e_indi] :
( ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ E ) @ F ) ) @ ( hAPP_A1646126530t_bool @ B @ G ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ C ) @ D ) ) @ ( hAPP_A1646126530t_bool @ A @ G ) ) ) )
& ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ C ) @ D ) ) @ ( hAPP_A1646126530t_bool @ A @ G ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ E ) @ F ) ) @ ( hAPP_A1646126530t_bool @ B @ G ) ) ) ) )
=> ( ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ E ) @ F ) ) @ ( hAPP_f2008608496t_bool @ f @ B ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ C ) @ D ) ) @ ( hAPP_f2008608496t_bool @ f @ A ) ) ) )
& ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ C ) @ D ) ) @ ( hAPP_f2008608496t_bool @ f @ A ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ E ) @ F ) ) @ ( hAPP_f2008608496t_bool @ f @ B ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(321,axiom,
! [A: arrow_856714788e_indi] :
( ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_A376526755di_nat @ h @ A ) ) @ n ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ c ) @ e ) ) @ ( hAPP_A1601437999t_bool @ ( hAPP_f1761571331t_bool @ arrow_1630265669_mktop @ ( hAPP_A1646126530t_bool @ p @ A ) ) @ e ) ) ) )
& ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_A376526755di_nat @ h @ A ) ) @ n ) )
=> ( ( ( ( hAPP_A376526755di_nat @ h @ A )
= n )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ c ) @ e ) ) @ ( hAPP_A1601437999t_bool @ ( hAPP_A1058422557t_bool @ ( hAPP_f1550387441t_bool @ arrow_216713899_above @ ( hAPP_A1646126530t_bool @ p @ A ) ) @ c ) @ e ) ) ) )
& ( ( ( hAPP_A376526755di_nat @ h @ A )
!= n )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ c ) @ e ) ) @ ( hAPP_A1601437999t_bool @ ( hAPP_f1761571331t_bool @ arrow_1481558583_mkbot @ ( hAPP_A1646126530t_bool @ p @ A ) ) @ e ) ) ) ) ) ) )
<=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_A376526755di_nat @ h @ A ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ n ) @ one_one_nat ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ a ) @ b ) ) @ lab ) ) )
& ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_A376526755di_nat @ h @ A ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ n ) @ one_one_nat ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ a ) @ b ) ) @ lba ) ) ) ) ),
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(1754,plain,
! [A: arrow_856714788e_indi] :
( ( ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_A376526755di_nat @ h @ A ) ) @ n ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ c ) @ e ) ) @ ( hAPP_A1601437999t_bool @ ( hAPP_f1761571331t_bool @ arrow_1630265669_mktop @ ( hAPP_A1646126530t_bool @ p @ A ) ) @ e ) ) ) )
& ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_A376526755di_nat @ h @ A ) ) @ n ) )
=> ( ( ( ( hAPP_A376526755di_nat @ h @ A )
= n )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ c ) @ e ) ) @ ( hAPP_A1601437999t_bool @ ( hAPP_A1058422557t_bool @ ( hAPP_f1550387441t_bool @ arrow_216713899_above @ ( hAPP_A1646126530t_bool @ p @ A ) ) @ c ) @ e ) ) ) )
& ( ( ( hAPP_A376526755di_nat @ h @ A )
!= n )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ c ) @ e ) ) @ ( hAPP_A1601437999t_bool @ ( hAPP_f1761571331t_bool @ arrow_1481558583_mkbot @ ( hAPP_A1646126530t_bool @ p @ A ) ) @ e ) ) ) ) ) ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_A376526755di_nat @ h @ A ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ n ) @ one_one_nat ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ a ) @ b ) ) @ lab ) ) )
& ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_A376526755di_nat @ h @ A ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ n ) @ one_one_nat ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ a ) @ b ) ) @ lba ) ) ) ) )
& ( ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_A376526755di_nat @ h @ A ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ n ) @ one_one_nat ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ a ) @ b ) ) @ lab ) ) )
& ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_A376526755di_nat @ h @ A ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ n ) @ one_one_nat ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ a ) @ b ) ) @ lba ) ) ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_A376526755di_nat @ h @ A ) ) @ n ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ c ) @ e ) ) @ ( hAPP_A1601437999t_bool @ ( hAPP_f1761571331t_bool @ arrow_1630265669_mktop @ ( hAPP_A1646126530t_bool @ p @ A ) ) @ e ) ) ) )
& ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_A376526755di_nat @ h @ A ) ) @ n ) )
=> ( ( ( ( hAPP_A376526755di_nat @ h @ A )
= n )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ c ) @ e ) ) @ ( hAPP_A1601437999t_bool @ ( hAPP_A1058422557t_bool @ ( hAPP_f1550387441t_bool @ arrow_216713899_above @ ( hAPP_A1646126530t_bool @ p @ A ) ) @ c ) @ e ) ) ) )
& ( ( ( hAPP_A376526755di_nat @ h @ A )
!= n )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ c ) @ e ) ) @ ( hAPP_A1601437999t_bool @ ( hAPP_f1761571331t_bool @ arrow_1481558583_mkbot @ ( hAPP_A1646126530t_bool @ p @ A ) ) @ e ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(305,axiom,
! [A: product_unit] :
( ( hBOOL @ ( hAPP_P1676879539t_bool @ top_to1257323279t_bool @ A ) )
<=> ( hBOOL @ top_top_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_top__apply) ).
thf(1680,plain,
! [A: product_unit] :
( ( ( hBOOL @ ( hAPP_P1676879539t_bool @ top_to1257323279t_bool @ A ) )
=> ( hBOOL @ top_top_bool ) )
& ( ( hBOOL @ top_top_bool )
=> ( hBOOL @ ( hAPP_P1676879539t_bool @ top_to1257323279t_bool @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(137,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_741_add__le__cancel__right) ).
thf(1103,plain,
! [A: nat,B: nat,C: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(520,axiom,
hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ a ) @ b ) ) @ lab ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096) ).
thf(2585,plain,
hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ a ) @ b ) ) @ lab ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(63,axiom,
( arrow_5070731e_Prof
= ( pi_Arr959578316t_bool @ top_to788185952i_bool @ ( hAPP_f1717907078l_bool @ cOMBK_1520063231e_indi @ arrow_1361987423le_Lin ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_579_Prof__def) ).
thf(824,plain,
( arrow_5070731e_Prof
= ( pi_Arr959578316t_bool @ top_to788185952i_bool @ ( hAPP_f1717907078l_bool @ cOMBK_1520063231e_indi @ arrow_1361987423le_Lin ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(179,axiom,
! [A: fun_Pr2067565481t_bool,B: fun_fu638310559l_bool,C: fun_fu638310559l_bool] :
( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_967_in__mono) ).
thf(1273,plain,
! [A: fun_Pr2067565481t_bool,B: fun_fu638310559l_bool,C: fun_fu638310559l_bool] :
( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(513,axiom,
! [A: arrow_1893660431le_alt,B: arrow_1893660431le_alt,C: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ C ) @ arrow_1361987423le_Lin ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ A ) @ B ) ) @ C ) )
=> ~ ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ B ) @ A ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_Lin__irrefl) ).
thf(2570,plain,
! [A: arrow_1893660431le_alt,B: arrow_1893660431le_alt,C: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ C ) @ arrow_1361987423le_Lin ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ A ) @ B ) ) @ C ) )
=> ~ ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ B ) @ A ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(264,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( B != zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1047_gr__implies__not0) ).
thf(1548,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( B != zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(395,axiom,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_linorder__neqE) ).
thf(2028,plain,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(454,axiom,
! [A: bool,B: fun_bo1431306493t_bool,C: fun_bool_bool,D: fun_bo377688929l_bool] :
( ( hBOOL @ ( hAPP_f398210311l_bool @ ( hAPP_f416878261l_bool @ member1133581546t_bool @ B ) @ ( pi_boo1111177555t_bool @ C @ D ) ) )
=> ( ~ ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ ( hAPP_b128655177t_bool @ B @ A ) ) @ ( hAPP_b1272691967l_bool @ D @ A ) ) )
=> ~ ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_PiE) ).
thf(2253,plain,
! [A: bool,B: fun_bo1431306493t_bool,C: fun_bool_bool,D: fun_bo377688929l_bool] :
( ( hBOOL @ ( hAPP_f398210311l_bool @ ( hAPP_f416878261l_bool @ member1133581546t_bool @ B ) @ ( pi_boo1111177555t_bool @ C @ D ) ) )
=> ( ~ ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ ( hAPP_b128655177t_bool @ B @ A ) ) @ ( hAPP_b1272691967l_bool @ D @ A ) ) )
=> ~ ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(461,axiom,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ A ) @ B ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_447_order__le__imp__less__or__eq) ).
thf(2275,plain,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ A ) @ B ) )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(429,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_less__imp__neq) ).
thf(2149,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(102,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ? [B: nat] :
( A
= ( hAPP_nat_nat @ suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1123_not0__implies__Suc) ).
thf(975,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ? [B: nat] :
( A
= ( hAPP_nat_nat @ suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(352,axiom,
! [A: bool,B: produc472769767le_alt] :
( ( hAPP_P1178790471t_bool @ ( hAPP_b128655177t_bool @ cOMBK_198697344le_alt @ A ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__prod_Itc__Arrow____Order____Mirabe) ).
thf(1884,plain,
! [A: bool,B: produc472769767le_alt] :
( ( hAPP_P1178790471t_bool @ ( hAPP_b128655177t_bool @ cOMBK_198697344le_alt @ A ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(547,axiom,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
( ( B = C )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_xt1_I3_J) ).
thf(2657,plain,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
( ( B = C )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(296,axiom,
! [A: fun_na998785244t_bool,B: fun_Pr2067565481t_bool,C: nat,D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ ( hAPP_n1161265524t_bool @ A @ D ) ) @ B ) )
=> ( ! [E: nat,F: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ E ) @ F ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ ( hAPP_n1161265524t_bool @ A @ E ) ) @ ( hAPP_n1161265524t_bool @ A @ F ) ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ ( hAPP_n1161265524t_bool @ A @ C ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_861_order__le__less__subst2) ).
thf(1652,plain,
! [A: fun_na998785244t_bool,B: fun_Pr2067565481t_bool,C: nat,D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ ( hAPP_n1161265524t_bool @ A @ D ) ) @ B ) )
=> ( ! [E: nat,F: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ E ) @ F ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ ( hAPP_n1161265524t_bool @ A @ E ) ) @ ( hAPP_n1161265524t_bool @ A @ F ) ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ ( hAPP_n1161265524t_bool @ A @ C ) ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(40,axiom,
! [A: fun_nat_nat] :
( ! [B: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ A @ ( hAPP_nat_nat @ suc @ B ) ) ) @ ( hAPP_nat_nat @ A @ B ) ) )
=> ? [B: nat] :
! [C: nat] :
( ( hAPP_nat_nat @ A @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ B ) @ C ) )
= ( hAPP_nat_nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1186_weak__decr__stable) ).
thf(743,plain,
! [A: fun_nat_nat] :
( ! [B: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ A @ ( hAPP_nat_nat @ suc @ B ) ) ) @ ( hAPP_nat_nat @ A @ B ) ) )
=> ? [B: nat] :
! [C: nat] :
( ( hAPP_nat_nat @ A @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ B ) @ C ) )
= ( hAPP_nat_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(97,axiom,
! [A: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) )
<=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1095_less__Suc0) ).
thf(958,plain,
! [A: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) )
=> ( A = zero_zero_nat ) )
& ( ( A = zero_zero_nat )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(310,axiom,
! [A: nat,B: nat] :
( ( A != B )
<=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_linorder__neq__iff) ).
thf(1701,plain,
! [A: nat,B: nat] :
( ( ( A != B )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(373,axiom,
! [A: bool,B: fun_bool_bool] :
( ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ A ) @ B ) )
<=> ( hBOOL @ ( hAPP_bool_bool @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_mem__def) ).
thf(1965,plain,
! [A: bool,B: fun_bool_bool] :
( ( ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_bool_bool @ B @ A ) ) )
& ( ( hBOOL @ ( hAPP_bool_bool @ B @ A ) )
=> ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(164,axiom,
! [A: nat] :
( ( hAPP_nat_nat @ suc @ A )
= ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ one_one_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1118_Suc__eq__plus1) ).
thf(1226,plain,
! [A: nat] :
( ( hAPP_nat_nat @ suc @ A )
= ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ one_one_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(322,axiom,
! [A: fun_Ar64685412t_bool,B: arrow_1893660431le_alt,C: arrow_856714788e_indi] :
( ( hAPP_A1646126530t_bool @ ( hAPP_A425126512t_bool @ ( hAPP_f1631649925t_bool @ cOMBC_1417338747t_bool @ A ) @ B ) @ C )
= ( hAPP_A1601437999t_bool @ ( hAPP_A1309733808t_bool @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000_411) ).
thf(1784,plain,
! [A: fun_Ar64685412t_bool,B: arrow_1893660431le_alt,C: arrow_856714788e_indi] :
( ( hAPP_A1646126530t_bool @ ( hAPP_A425126512t_bool @ ( hAPP_f1631649925t_bool @ cOMBC_1417338747t_bool @ A ) @ B ) @ C )
= ( hAPP_A1601437999t_bool @ ( hAPP_A1309733808t_bool @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(212,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_655_add__le__less__mono) ).
thf(1389,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ D ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(552,axiom,
! [A: fun_Pr2067565481t_bool] : ( hBOOL @ ( hAPP_f52567537l_bool @ top_to1312956197l_bool @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_top1I) ).
thf(2674,plain,
! [A: fun_Pr2067565481t_bool] : ( hBOOL @ ( hAPP_f52567537l_bool @ top_to1312956197l_bool @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(392,axiom,
! [A: nat,B: nat] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_375_linorder__not__le) ).
thf(2016,plain,
! [A: nat,B: nat] :
( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) )
=> ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(512,axiom,
! [A: arrow_856714788e_indi,B: fun_Ar338949104le_alt,C: fun_Ar1809396326i_bool,D: fun_Ar274636406t_bool] :
( ( hBOOL @ ( hAPP_f1754488902l_bool @ ( hAPP_f766019597l_bool @ member387840963le_alt @ B ) @ ( pi_Arr1460528004le_alt @ C @ D ) ) )
=> ( ( hBOOL @ ( hAPP_f584385070l_bool @ ( hAPP_A1597696899l_bool @ member1479139729e_indi @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A899858958le_alt @ B @ A ) ) @ ( hAPP_A1646126530t_bool @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_562_Pi__mem) ).
thf(2568,plain,
! [A: arrow_856714788e_indi,B: fun_Ar338949104le_alt,C: fun_Ar1809396326i_bool,D: fun_Ar274636406t_bool] :
( ( hBOOL @ ( hAPP_f1754488902l_bool @ ( hAPP_f766019597l_bool @ member387840963le_alt @ B ) @ ( pi_Arr1460528004le_alt @ C @ D ) ) )
=> ( ( hBOOL @ ( hAPP_f584385070l_bool @ ( hAPP_A1597696899l_bool @ member1479139729e_indi @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A899858958le_alt @ B @ A ) ) @ ( hAPP_A1646126530t_bool @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(64,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ C ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1163_Suc__mult__less__cancel1) ).
thf(826,plain,
! [A: nat,B: nat,C: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(32,axiom,
! [A: nat,B: nat] :
( ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B )
= A )
=> ( B = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1052_add__eq__self__zero) ).
thf(711,plain,
! [A: nat,B: nat] :
( ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B )
= A )
=> ( B = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(224,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1022_add__leD1) ).
thf(1428,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(134,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ B ) )
<=> ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_731_add__right__cancel) ).
thf(1092,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ B ) )
=> ( A = C ) )
& ( ( A = C )
=> ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(57,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ? [C: nat] :
( B
= ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1116_less__imp__Suc__add) ).
thf(804,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ? [C: nat] :
( B
= ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(235,axiom,
! [A: nat] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1042_less__zeroE) ).
thf(1464,plain,
! [A: nat] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(163,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1017_trans__le__add1) ).
thf(1224,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(476,axiom,
hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ c ) @ d ) ) @ ( hAPP_f2008608496t_bool @ f @ ( hAPP_f1302887663t_bool @ ( cOMBS_1181656689t_bool @ ( hAPP_f1001205955t_bool @ ( cOMBS_1925466437t_bool @ ( hAPP_f668886383t_bool @ ( cOMBB_1061985500e_indi @ if_fun523439385t_bool ) @ ( hAPP_n34002993i_bool @ ( hAPP_f721434149i_bool @ cOMBC_722552198t_bool @ ( hAPP_f966656047t_bool @ ( cOMBB_1869811296e_indi @ ord_less_nat ) @ h ) ) @ n ) ) ) @ ( hAPP_A425126512t_bool @ ( hAPP_f1631649925t_bool @ cOMBC_1417338747t_bool @ ( hAPP_f831214557t_bool @ ( cOMBB_80760910e_indi @ arrow_1630265669_mktop ) @ p ) ) @ e ) ) ) @ ( hAPP_f1302887663t_bool @ ( cOMBS_1181656689t_bool @ ( hAPP_f1001205955t_bool @ ( cOMBS_1925466437t_bool @ ( hAPP_f668886383t_bool @ ( cOMBB_1061985500e_indi @ if_fun523439385t_bool ) @ ( hAPP_n34002993i_bool @ ( hAPP_f721434149i_bool @ cOMBC_722552198t_bool @ ( hAPP_f966656047t_bool @ ( cOMBB_1869811296e_indi @ fequal_nat ) @ h ) ) @ n ) ) ) @ ( hAPP_A425126512t_bool @ ( hAPP_f1631649925t_bool @ cOMBC_1417338747t_bool @ ( hAPP_A1889513822t_bool @ ( hAPP_f2102110817t_bool @ cOMBC_1486904681t_bool @ ( hAPP_f1751344075t_bool @ ( cOMBB_1876517692e_indi @ arrow_216713899_above ) @ p ) ) @ c ) ) @ e ) ) ) @ ( hAPP_A425126512t_bool @ ( hAPP_f1631649925t_bool @ cOMBC_1417338747t_bool @ ( hAPP_f831214557t_bool @ ( cOMBB_80760910e_indi @ arrow_1481558583_mkbot ) @ p ) ) @ e ) ) ) ) ),
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(2358,plain,
hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ c ) @ d ) ) @ ( hAPP_f2008608496t_bool @ f @ ( hAPP_f1302887663t_bool @ ( cOMBS_1181656689t_bool @ ( hAPP_f1001205955t_bool @ ( cOMBS_1925466437t_bool @ ( hAPP_f668886383t_bool @ ( cOMBB_1061985500e_indi @ if_fun523439385t_bool ) @ ( hAPP_n34002993i_bool @ ( hAPP_f721434149i_bool @ cOMBC_722552198t_bool @ ( hAPP_f966656047t_bool @ ( cOMBB_1869811296e_indi @ ord_less_nat ) @ h ) ) @ n ) ) ) @ ( hAPP_A425126512t_bool @ ( hAPP_f1631649925t_bool @ cOMBC_1417338747t_bool @ ( hAPP_f831214557t_bool @ ( cOMBB_80760910e_indi @ arrow_1630265669_mktop ) @ p ) ) @ e ) ) ) @ ( hAPP_f1302887663t_bool @ ( cOMBS_1181656689t_bool @ ( hAPP_f1001205955t_bool @ ( cOMBS_1925466437t_bool @ ( hAPP_f668886383t_bool @ ( cOMBB_1061985500e_indi @ if_fun523439385t_bool ) @ ( hAPP_n34002993i_bool @ ( hAPP_f721434149i_bool @ cOMBC_722552198t_bool @ ( hAPP_f966656047t_bool @ ( cOMBB_1869811296e_indi @ fequal_nat ) @ h ) ) @ n ) ) ) @ ( hAPP_A425126512t_bool @ ( hAPP_f1631649925t_bool @ cOMBC_1417338747t_bool @ ( hAPP_A1889513822t_bool @ ( hAPP_f2102110817t_bool @ cOMBC_1486904681t_bool @ ( hAPP_f1751344075t_bool @ ( cOMBB_1876517692e_indi @ arrow_216713899_above ) @ p ) ) @ c ) ) @ e ) ) ) @ ( hAPP_A425126512t_bool @ ( hAPP_f1631649925t_bool @ cOMBC_1417338747t_bool @ ( hAPP_f831214557t_bool @ ( cOMBB_80760910e_indi @ arrow_1481558583_mkbot ) @ p ) ) @ e ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(303,axiom,
! [A: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ n ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ b ) @ a ) ) @ ( hAPP_f2008608496t_bool @ f @ ( hAPP_f480276746t_bool @ ( hAPP_f601594885t_bool @ cOMBC_750853729t_bool @ ( hAPP_f1344464862t_bool @ ( hAPP_f1908974253t_bool @ cOMBC_156709173t_bool @ ( hAPP_f668886383t_bool @ ( cOMBB_1061985500e_indi @ if_fun523439385t_bool ) @ ( hAPP_n34002993i_bool @ ( hAPP_f721434149i_bool @ cOMBC_722552198t_bool @ ( hAPP_f966656047t_bool @ ( cOMBB_1869811296e_indi @ ord_less_nat ) @ h ) ) @ A ) ) ) @ lab ) ) @ lba ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_n_I2_J) ).
thf(1675,plain,
! [A: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ n ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ b ) @ a ) ) @ ( hAPP_f2008608496t_bool @ f @ ( hAPP_f480276746t_bool @ ( hAPP_f601594885t_bool @ cOMBC_750853729t_bool @ ( hAPP_f1344464862t_bool @ ( hAPP_f1908974253t_bool @ cOMBC_156709173t_bool @ ( hAPP_f668886383t_bool @ ( cOMBB_1061985500e_indi @ if_fun523439385t_bool ) @ ( hAPP_n34002993i_bool @ ( hAPP_f721434149i_bool @ cOMBC_722552198t_bool @ ( hAPP_f966656047t_bool @ ( cOMBB_1869811296e_indi @ ord_less_nat ) @ h ) ) @ A ) ) ) @ lab ) ) @ lba ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(45,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ ( hAPP_nat_nat @ suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1060_Suc__mono) ).
thf(764,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ ( hAPP_nat_nat @ suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(408,axiom,
! [A: produc472769767le_alt,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool,D: fun_bool_bool] :
( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ B ) @ ( pi_Pro1238944957t_bool @ C @ ( hAPP_f699791347l_bool @ cOMBK_138598520le_alt @ D ) ) ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ ( hAPP_P1178790471t_bool @ B @ A ) ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_581_funcset__mem) ).
thf(2079,plain,
! [A: produc472769767le_alt,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool,D: fun_bool_bool] :
( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ B ) @ ( pi_Pro1238944957t_bool @ C @ ( hAPP_f699791347l_bool @ cOMBK_138598520le_alt @ D ) ) ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ ( hAPP_P1178790471t_bool @ B @ A ) ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(497,axiom,
! [A: produc472769767le_alt,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_959_set__mp) ).
thf(2521,plain,
! [A: produc472769767le_alt,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(565,axiom,
! [A: arrow_1893660431le_alt,B: arrow_1893660431le_alt,C: fun_Pr2067565481t_bool,D: arrow_1893660431le_alt] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ A ) @ B ) ) @ ( hAPP_A1601437999t_bool @ ( hAPP_f1761571331t_bool @ arrow_1630265669_mktop @ C ) @ D ) ) )
<=> ( ( A != D )
& ( ( B = D )
=> ( A != B ) )
& ( ( B != D )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ A ) @ B ) ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_in__mktop) ).
thf(2721,plain,
! [A: arrow_1893660431le_alt,B: arrow_1893660431le_alt,C: fun_Pr2067565481t_bool,D: arrow_1893660431le_alt] :
( ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ A ) @ B ) ) @ ( hAPP_A1601437999t_bool @ ( hAPP_f1761571331t_bool @ arrow_1630265669_mktop @ C ) @ D ) ) )
=> ( ( A != D )
& ( ( B = D )
=> ( A != B ) )
& ( ( B != D )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ A ) @ B ) ) @ C ) ) ) ) )
& ( ( ( A != D )
& ( ( B = D )
=> ( A != B ) )
& ( ( B != D )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ A ) @ B ) ) @ C ) ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ A ) @ B ) ) @ ( hAPP_A1601437999t_bool @ ( hAPP_f1761571331t_bool @ arrow_1630265669_mktop @ C ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(65,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ? [C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ C ) )
& ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1058_less__imp__add__positive) ).
thf(831,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ? [C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ C ) )
& ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(490,axiom,
! [A: arrow_1893660431le_alt,B: arrow_1893660431le_alt,C: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ C ) @ arrow_1361987423le_Lin ) )
=> ( ( A != B )
=> ( ~ ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ A ) @ B ) ) @ C ) )
<=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ B ) @ A ) ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_notin__Lin__iff) ).
thf(2478,plain,
! [A: arrow_1893660431le_alt,B: arrow_1893660431le_alt,C: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ C ) @ arrow_1361987423le_Lin ) )
=> ( ( A != B )
=> ( ( ~ ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ A ) @ B ) ) @ C ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ B ) @ A ) ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ B ) @ A ) ) @ C ) )
=> ~ ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ A ) @ B ) ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(110,axiom,
! [A: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ zero_zero_nat ) )
<=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1053_le__0__eq) ).
thf(1011,plain,
! [A: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ zero_zero_nat ) )
=> ( A = zero_zero_nat ) )
& ( ( A = zero_zero_nat )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(262,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( B != A )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_471_xt1_I11_J) ).
thf(1542,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( B != A )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(38,axiom,
! [A: nat,B: nat] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1078_less__antisym) ).
thf(737,plain,
! [A: nat,B: nat] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(16,axiom,
! [A: nat,B: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) )
= ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1164_mult__Suc__right) ).
thf(649,plain,
! [A: nat,B: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) )
= ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(308,axiom,
! [A: nat,B: nat] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
<=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_not__less__iff__gr__or__eq) ).
thf(1690,plain,
! [A: nat,B: nat] :
( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) )
| ( A = B ) ) )
& ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) )
| ( A = B ) )
=> ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(541,axiom,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_order__trans) ).
thf(2642,plain,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(450,axiom,
! [A: fun_Ar671024215di_nat,B: fun_Ar1809396326i_bool] :
( ( hBOOL @ ( hAPP_f584385070l_bool @ ( inj_on1960344199di_nat @ A ) @ B ) )
<=> ! [C: arrow_856714788e_indi] :
( ( hBOOL @ ( hAPP_f584385070l_bool @ ( hAPP_A1597696899l_bool @ member1479139729e_indi @ C ) @ B ) )
=> ! [D: arrow_856714788e_indi] :
( ( hBOOL @ ( hAPP_f584385070l_bool @ ( hAPP_A1597696899l_bool @ member1479139729e_indi @ D ) @ B ) )
=> ( ( ( hAPP_A376526755di_nat @ A @ C )
= ( hAPP_A376526755di_nat @ A @ D ) )
=> ( C = D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_539_inj__on__def) ).
thf(2229,plain,
! [A: fun_Ar671024215di_nat,B: fun_Ar1809396326i_bool] :
( ( ( hBOOL @ ( hAPP_f584385070l_bool @ ( inj_on1960344199di_nat @ A ) @ B ) )
=> ! [C: arrow_856714788e_indi] :
( ( hBOOL @ ( hAPP_f584385070l_bool @ ( hAPP_A1597696899l_bool @ member1479139729e_indi @ C ) @ B ) )
=> ! [D: arrow_856714788e_indi] :
( ( hBOOL @ ( hAPP_f584385070l_bool @ ( hAPP_A1597696899l_bool @ member1479139729e_indi @ D ) @ B ) )
=> ( ( ( hAPP_A376526755di_nat @ A @ C )
= ( hAPP_A376526755di_nat @ A @ D ) )
=> ( C = D ) ) ) ) )
& ( ! [C: arrow_856714788e_indi] :
( ( hBOOL @ ( hAPP_f584385070l_bool @ ( hAPP_A1597696899l_bool @ member1479139729e_indi @ C ) @ B ) )
=> ! [D: arrow_856714788e_indi] :
( ( hBOOL @ ( hAPP_f584385070l_bool @ ( hAPP_A1597696899l_bool @ member1479139729e_indi @ D ) @ B ) )
=> ( ( ( hAPP_A376526755di_nat @ A @ C )
= ( hAPP_A376526755di_nat @ A @ D ) )
=> ( C = D ) ) ) )
=> ( hBOOL @ ( hAPP_f584385070l_bool @ ( inj_on1960344199di_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(482,axiom,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_xt1_I6_J) ).
thf(2422,plain,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(141,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ~ ! [B: nat] :
( A
!= ( hAPP_nat_nat @ suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1124_nat_Oexhaust) ).
thf(1117,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ~ ! [B: nat] :
( A
!= ( hAPP_nat_nat @ suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(106,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) )
<=> ( ( A = zero_zero_nat )
| ? [C: nat] :
( ( A
= ( hAPP_nat_nat @ suc @ C ) )
& ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1096_less__Suc__eq__0__disj) ).
thf(990,plain,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) )
=> ( ( A = zero_zero_nat )
| ? [C: nat] :
( ( A
= ( hAPP_nat_nat @ suc @ C ) )
& ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ B ) ) ) ) )
& ( ( ( A = zero_zero_nat )
| ? [C: nat] :
( ( A
= ( hAPP_nat_nat @ suc @ C ) )
& ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ B ) ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(365,axiom,
! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool] :
( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ A ) @ B ) )
<=> ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_713_less__fun__def) ).
thf(1933,plain,
! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool] :
( ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ B ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(456,axiom,
! [A: produc472769767le_alt] :
( ( hBOOL @ ( hAPP_P1178790471t_bool @ top_to1138392227t_bool @ A ) )
<=> ( hBOOL @ top_top_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_top__apply) ).
thf(2257,plain,
! [A: produc472769767le_alt] :
( ( ( hBOOL @ ( hAPP_P1178790471t_bool @ top_to1138392227t_bool @ A ) )
=> ( hBOOL @ top_top_bool ) )
& ( ( hBOOL @ top_top_bool )
=> ( hBOOL @ ( hAPP_P1178790471t_bool @ top_to1138392227t_bool @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(278,axiom,
hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ p ) @ arrow_5070731e_Prof ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3__096P_A_058_AProf_096) ).
thf(1589,plain,
hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ p ) @ arrow_5070731e_Prof ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(452,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( ( B = A )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_xt1_I2_J) ).
thf(2246,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( ( B = A )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(244,axiom,
! [A: fun_Ar671024215di_nat] :
( ! [B: arrow_856714788e_indi,C: arrow_856714788e_indi] :
( ( ( hAPP_A376526755di_nat @ A @ B )
= ( hAPP_A376526755di_nat @ A @ C ) )
=> ( B = C ) )
=> ( hBOOL @ ( hAPP_f584385070l_bool @ ( inj_on1960344199di_nat @ A ) @ top_to788185952i_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_656_injI) ).
thf(1492,plain,
! [A: fun_Ar671024215di_nat] :
( ! [B: arrow_856714788e_indi,C: arrow_856714788e_indi] :
( ( ( hAPP_A376526755di_nat @ A @ B )
= ( hAPP_A376526755di_nat @ A @ C ) )
=> ( B = C ) )
=> ( hBOOL @ ( hAPP_f584385070l_bool @ ( inj_on1960344199di_nat @ A ) @ top_to788185952i_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(271,axiom,
! [A: produc472769767le_alt,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool,D: fun_Pr1780397033l_bool] :
( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ B ) @ ( pi_Pro1238944957t_bool @ C @ D ) ) )
=> ( ~ ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ ( hAPP_P1178790471t_bool @ B @ A ) ) @ ( hAPP_P1103642805l_bool @ D @ A ) ) )
=> ~ ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_PiE) ).
thf(1571,plain,
! [A: produc472769767le_alt,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool,D: fun_Pr1780397033l_bool] :
( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ B ) @ ( pi_Pro1238944957t_bool @ C @ D ) ) )
=> ( ~ ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ ( hAPP_P1178790471t_bool @ B @ A ) ) @ ( hAPP_P1103642805l_bool @ D @ A ) ) )
=> ~ ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(228,axiom,
! [A: fun_Pr2067565481t_bool,B: arrow_856714788e_indi] :
( ( hAPP_A1646126530t_bool @ ( hAPP_f480276746t_bool @ cOMBK_1650320063e_indi @ A ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ef_405) ).
thf(1439,plain,
! [A: fun_Pr2067565481t_bool,B: arrow_856714788e_indi] :
( ( hAPP_A1646126530t_bool @ ( hAPP_f480276746t_bool @ cOMBK_1650320063e_indi @ A ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(438,axiom,
! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool] :
( ( A = B )
<=> ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ A ) @ B ) )
& ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_362_order__eq__iff) ).
thf(2180,plain,
! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool] :
( ( ( A = B )
=> ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ A ) @ B ) )
& ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ B ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ A ) @ B ) )
& ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ B ) @ A ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(60,axiom,
! [A: fun_fu638310559l_bool,B: nat,C: fun_fu955147676ol_nat,D: fun_fu638310559l_bool] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_f1487854056ol_nat @ C @ D ) ) )
=> ( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ D ) @ A ) )
=> ( ! [E: fun_fu638310559l_bool,F: fun_fu638310559l_bool] :
( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ E ) @ F ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f1487854056ol_nat @ C @ E ) ) @ ( hAPP_f1487854056ol_nat @ C @ F ) ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_f1487854056ol_nat @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_847_order__less__le__subst1) ).
thf(811,plain,
! [A: fun_fu638310559l_bool,B: nat,C: fun_fu955147676ol_nat,D: fun_fu638310559l_bool] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_f1487854056ol_nat @ C @ D ) ) )
=> ( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ D ) @ A ) )
=> ( ! [E: fun_fu638310559l_bool,F: fun_fu638310559l_bool] :
( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ E ) @ F ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f1487854056ol_nat @ C @ E ) ) @ ( hAPP_f1487854056ol_nat @ C @ F ) ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_f1487854056ol_nat @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
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 )
=> ( ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ B ) @ arrow_5070731e_Prof ) )
=> ( ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ A ) @ arrow_5070731e_Prof ) )
=> ( ! [F: arrow_856714788e_indi] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ D ) @ E ) ) @ ( hAPP_A1646126530t_bool @ B @ F ) ) )
<=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ E ) @ C ) ) @ ( hAPP_A1646126530t_bool @ A @ F ) ) ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ D ) @ E ) ) @ ( hAPP_f2008608496t_bool @ f @ B ) ) )
<=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ E ) @ C ) ) @ ( hAPP_f2008608496t_bool @ f @ A ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8__C4_C) ).
thf(2812,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 )
=> ( ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ B ) @ arrow_5070731e_Prof ) )
=> ( ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ A ) @ arrow_5070731e_Prof ) )
=> ( ! [F: arrow_856714788e_indi] :
( ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ D ) @ E ) ) @ ( hAPP_A1646126530t_bool @ B @ F ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ E ) @ C ) ) @ ( hAPP_A1646126530t_bool @ A @ F ) ) ) )
& ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ E ) @ C ) ) @ ( hAPP_A1646126530t_bool @ A @ F ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ D ) @ E ) ) @ ( hAPP_A1646126530t_bool @ B @ F ) ) ) ) )
=> ( ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ D ) @ E ) ) @ ( hAPP_f2008608496t_bool @ f @ B ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ E ) @ C ) ) @ ( hAPP_f2008608496t_bool @ f @ A ) ) ) )
& ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ E ) @ C ) ) @ ( hAPP_f2008608496t_bool @ f @ A ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ D ) @ E ) ) @ ( hAPP_f2008608496t_bool @ f @ B ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(9,axiom,
! [A: nat,B: nat] :
( ( A
= ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) )
=> ( ( B = one_one_nat )
| ( A = zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1167_mult__eq__self__implies__10) ).
thf(609,plain,
! [A: nat,B: nat] :
( ( A
= ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) )
=> ( ( B = one_one_nat )
| ( A = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(459,axiom,
! [A: produc472769767le_alt,B: fun_Pr1509342064e_indi,C: fun_Pr2067565481t_bool,D: fun_Ar1809396326i_bool] :
( ( hBOOL @ ( hAPP_f2124588998l_bool @ ( hAPP_f1187850253l_bool @ member1558233923e_indi @ B ) @ ( pi_Pro837265796e_indi @ C @ ( hAPP_f359069313i_bool @ cOMBK_1987648063le_alt @ D ) ) ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_f584385070l_bool @ ( hAPP_A1597696899l_bool @ member1479139729e_indi @ ( hAPP_P276596750e_indi @ B @ A ) ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_582_funcset__mem) ).
thf(2267,plain,
! [A: produc472769767le_alt,B: fun_Pr1509342064e_indi,C: fun_Pr2067565481t_bool,D: fun_Ar1809396326i_bool] :
( ( hBOOL @ ( hAPP_f2124588998l_bool @ ( hAPP_f1187850253l_bool @ member1558233923e_indi @ B ) @ ( pi_Pro837265796e_indi @ C @ ( hAPP_f359069313i_bool @ cOMBK_1987648063le_alt @ D ) ) ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_f584385070l_bool @ ( hAPP_A1597696899l_bool @ member1479139729e_indi @ ( hAPP_P276596750e_indi @ B @ A ) ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
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 )
=> ( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ C ) @ arrow_1361987423le_Lin ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ A ) @ B ) ) @ ( hAPP_A1601437999t_bool @ ( hAPP_A1058422557t_bool @ ( hAPP_f1550387441t_bool @ arrow_216713899_above @ C ) @ D ) @ E ) ) )
<=> ( ( A != B )
& ( ( A = E )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ D ) @ B ) ) @ C ) ) )
& ( ( A != E )
=> ( ( ( B = E )
=> ( ( A = D )
| ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ A ) @ D ) ) @ C ) ) ) )
& ( ( B != E )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ A ) @ B ) ) @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_in__above) ).
thf(2757,plain,
! [A: arrow_1893660431le_alt,B: arrow_1893660431le_alt,C: fun_Pr2067565481t_bool,D: arrow_1893660431le_alt,E: arrow_1893660431le_alt] :
( ( D != E )
=> ( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ C ) @ arrow_1361987423le_Lin ) )
=> ( ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ A ) @ B ) ) @ ( hAPP_A1601437999t_bool @ ( hAPP_A1058422557t_bool @ ( hAPP_f1550387441t_bool @ arrow_216713899_above @ C ) @ D ) @ E ) ) )
=> ( ( A != B )
& ( ( A = E )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ D ) @ B ) ) @ C ) ) )
& ( ( A != E )
=> ( ( ( B = E )
=> ( ( A = D )
| ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ A ) @ D ) ) @ C ) ) ) )
& ( ( B != E )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ A ) @ B ) ) @ C ) ) ) ) ) ) )
& ( ( ( A != B )
& ( ( A = E )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ D ) @ B ) ) @ C ) ) )
& ( ( A != E )
=> ( ( ( B = E )
=> ( ( A = D )
| ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ A ) @ D ) ) @ C ) ) ) )
& ( ( B != E )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ A ) @ B ) ) @ C ) ) ) ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ A ) @ B ) ) @ ( hAPP_A1601437999t_bool @ ( hAPP_A1058422557t_bool @ ( hAPP_f1550387441t_bool @ arrow_216713899_above @ C ) @ D ) @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(69,axiom,
! [A: nat] :
( zero_zero_nat
!= ( hAPP_nat_nat @ suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1067_Zero__neq__Suc) ).
thf(848,plain,
! [A: nat] :
( zero_zero_nat
!= ( hAPP_nat_nat @ suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(336,axiom,
hBOOL @ ( hAPP_f975209902l_bool @ ( hAPP_f1714503811l_bool @ member173038353t_bool @ f ) @ ( pi_fun1746584570t_bool @ arrow_5070731e_Prof @ ( hAPP_f1104294872l_bool @ cOMBK_1701906001t_bool @ arrow_1361987423le_Lin ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_assms_I1_J) ).
thf(1838,plain,
hBOOL @ ( hAPP_f975209902l_bool @ ( hAPP_f1714503811l_bool @ member173038353t_bool @ f ) @ ( pi_fun1746584570t_bool @ arrow_5070731e_Prof @ ( hAPP_f1104294872l_bool @ cOMBK_1701906001t_bool @ arrow_1361987423le_Lin ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(504,axiom,
! [A: fun_Pr376858015t_unit,B: fun_Pr1069395679t_bool,C: fun_Pr2067565481t_bool] :
( ! [D: produc472769767le_alt] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ D ) @ C ) )
=> ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ ( hAPP_P1069491261t_unit @ A @ D ) ) @ ( hAPP_P2037731755t_bool @ B @ D ) ) ) )
=> ( hBOOL @ ( hAPP_f1159856629l_bool @ ( hAPP_f1700632141l_bool @ member1303779570t_unit @ A ) @ ( pi_Pro346842291t_unit @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_621_Pi__I) ).
thf(2542,plain,
! [A: fun_Pr376858015t_unit,B: fun_Pr1069395679t_bool,C: fun_Pr2067565481t_bool] :
( ! [D: produc472769767le_alt] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ D ) @ C ) )
=> ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ ( hAPP_P1069491261t_unit @ A @ D ) ) @ ( hAPP_P2037731755t_bool @ B @ D ) ) ) )
=> ( hBOOL @ ( hAPP_f1159856629l_bool @ ( hAPP_f1700632141l_bool @ member1303779570t_unit @ A ) @ ( pi_Pro346842291t_unit @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(209,axiom,
! [A: fun_nat_bool,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ A @ C ) )
=> ( ! [D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ A @ ( hAPP_nat_nat @ suc @ D ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ A @ D ) ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1115_inc__induct) ).
thf(1381,plain,
! [A: fun_nat_bool,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ A @ C ) )
=> ( ! [D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ A @ ( hAPP_nat_nat @ suc @ D ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ A @ D ) ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(468,axiom,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ B ) @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_order__antisym__conv) ).
thf(2329,plain,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ B ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(331,axiom,
! [A: fun_Pr2067565481t_bool,B: fun_fu841105374ol_nat,C: fun_Pr2067565481t_bool,D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_f1842225014ol_nat @ B @ C ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ C ) )
=> ( ! [E: fun_Pr2067565481t_bool,F: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ F ) @ E ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f1842225014ol_nat @ B @ F ) ) @ ( hAPP_f1842225014ol_nat @ B @ E ) ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_f1842225014ol_nat @ B @ A ) ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_801_xt4) ).
thf(1820,plain,
! [A: fun_Pr2067565481t_bool,B: fun_fu841105374ol_nat,C: fun_Pr2067565481t_bool,D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_f1842225014ol_nat @ B @ C ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ C ) )
=> ( ! [E: fun_Pr2067565481t_bool,F: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ F ) @ E ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f1842225014ol_nat @ B @ F ) ) @ ( hAPP_f1842225014ol_nat @ B @ E ) ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_f1842225014ol_nat @ B @ A ) ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(139,axiom,
! [A: nat,B: nat] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1000_not__add__less2) ).
thf(1112,plain,
! [A: nat,B: nat] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(71,axiom,
! [A: nat,B: fun_nat_bool] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ B @ zero_zero_nat ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ B @ A ) )
=> ? [C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ A ) )
& ! [D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ D ) @ C ) )
=> ~ ( hBOOL @ ( hAPP_nat_bool @ B @ D ) ) )
& ( hBOOL @ ( hAPP_nat_bool @ B @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ one_one_nat ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1056_ex__least__nat__less) ).
thf(858,plain,
! [A: nat,B: fun_nat_bool] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ B @ zero_zero_nat ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ B @ A ) )
=> ? [C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ A ) )
& ! [D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ D ) @ C ) )
=> ~ ( hBOOL @ ( hAPP_nat_bool @ B @ D ) ) )
& ( hBOOL @ ( hAPP_nat_bool @ B @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ one_one_nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(266,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_511_xt1_I8_J) ).
thf(1557,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(465,axiom,
! [A: arrow_1893660431le_alt,B: arrow_1893660431le_alt,C: arrow_1893660431le_alt,D: arrow_1893660431le_alt] :
( ( ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ A ) @ B )
= ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ C ) @ D ) )
<=> ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_Pair__eq) ).
thf(2314,plain,
! [A: arrow_1893660431le_alt,B: arrow_1893660431le_alt,C: arrow_1893660431le_alt,D: arrow_1893660431le_alt] :
( ( ( ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ A ) @ B )
= ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ C ) @ D ) )
=> ( ( A = C )
& ( B = D ) ) )
& ( ( ( A = C )
& ( B = D ) )
=> ( ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ A ) @ B )
= ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(533,axiom,
! [A: fun_Pr2067565481t_bool] : ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ top_to1138392227t_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_722_subset__UNIV) ).
thf(2625,plain,
! [A: fun_Pr2067565481t_bool] : ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ top_to1138392227t_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(290,axiom,
! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool,C: fun_Ar331856045t_bool] :
( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_479_order__less__le__trans) ).
thf(1630,plain,
! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool,C: fun_Ar331856045t_bool] :
( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(382,axiom,
! [A: nat,B: fun_Pr2067565481t_bool,C: fun_na998785244t_bool,D: nat] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ B ) @ ( hAPP_n1161265524t_bool @ C @ D ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ D ) @ A ) )
=> ( ! [E: nat,F: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ E ) @ F ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ ( hAPP_n1161265524t_bool @ C @ E ) ) @ ( hAPP_n1161265524t_bool @ C @ F ) ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ B ) @ ( hAPP_n1161265524t_bool @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_815_order__le__less__subst1) ).
thf(1993,plain,
! [A: nat,B: fun_Pr2067565481t_bool,C: fun_na998785244t_bool,D: nat] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ B ) @ ( hAPP_n1161265524t_bool @ C @ D ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ D ) @ A ) )
=> ( ! [E: nat,F: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ E ) @ F ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ ( hAPP_n1161265524t_bool @ C @ E ) ) @ ( hAPP_n1161265524t_bool @ C @ F ) ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ B ) @ ( hAPP_n1161265524t_bool @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(358,axiom,
! [A: fun_Pr2067565481t_bool,B: nat,C: fun_fu841105374ol_nat,D: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_f1842225014ol_nat @ C @ D ) ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ D ) @ A ) )
=> ( ! [E: fun_Pr2067565481t_bool,F: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ E ) @ F ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f1842225014ol_nat @ C @ E ) ) @ ( hAPP_f1842225014ol_nat @ C @ F ) ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_f1842225014ol_nat @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_850_order__less__le__subst1) ).
thf(1909,plain,
! [A: fun_Pr2067565481t_bool,B: nat,C: fun_fu841105374ol_nat,D: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_f1842225014ol_nat @ C @ D ) ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ D ) @ A ) )
=> ( ! [E: fun_Pr2067565481t_bool,F: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ E ) @ F ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f1842225014ol_nat @ C @ E ) ) @ ( hAPP_f1842225014ol_nat @ C @ F ) ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_f1842225014ol_nat @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(150,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ ( hAPP_nat_nat @ suc @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1089_Suc__le__mono) ).
thf(1162,plain,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ ( hAPP_nat_nat @ suc @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ ( hAPP_nat_nat @ suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(462,axiom,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
( ( A = B )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_order__eq__refl) ).
thf(2278,plain,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
( ( A = B )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(507,axiom,
! [A: fun_nat_bool] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ cOMBI_nat ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_580_inj__on__id2) ).
thf(2553,plain,
! [A: fun_nat_bool] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ cOMBI_nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(84,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1102_less__eq__Suc__le) ).
thf(912,plain,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(363,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( C = A )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_ord__le__eq__trans) ).
thf(1926,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( C = A )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(309,axiom,
! [A: fun_Ar274636406t_bool] : ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ A ) @ top_to553140914l_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_UNIV__I) ).
thf(1699,plain,
! [A: fun_Ar274636406t_bool] : ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ A ) @ top_to553140914l_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(444,axiom,
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ e ) @ d ) ) @ ( hAPP_f2008608496t_bool @ f @ ( hAPP_f1302887663t_bool @ ( cOMBS_1181656689t_bool @ ( hAPP_f1001205955t_bool @ ( cOMBS_1925466437t_bool @ ( hAPP_f668886383t_bool @ ( cOMBB_1061985500e_indi @ if_fun523439385t_bool ) @ ( hAPP_n34002993i_bool @ ( hAPP_f721434149i_bool @ cOMBC_722552198t_bool @ ( hAPP_f966656047t_bool @ ( cOMBB_1869811296e_indi @ ord_less_nat ) @ h ) ) @ n ) ) ) @ ( hAPP_A425126512t_bool @ ( hAPP_f1631649925t_bool @ cOMBC_1417338747t_bool @ ( hAPP_f831214557t_bool @ ( cOMBB_80760910e_indi @ arrow_1630265669_mktop ) @ p ) ) @ e ) ) ) @ ( hAPP_f1302887663t_bool @ ( cOMBS_1181656689t_bool @ ( hAPP_f1001205955t_bool @ ( cOMBS_1925466437t_bool @ ( hAPP_f668886383t_bool @ ( cOMBB_1061985500e_indi @ if_fun523439385t_bool ) @ ( hAPP_n34002993i_bool @ ( hAPP_f721434149i_bool @ cOMBC_722552198t_bool @ ( hAPP_f966656047t_bool @ ( cOMBB_1869811296e_indi @ fequal_nat ) @ h ) ) @ n ) ) ) @ ( hAPP_A425126512t_bool @ ( hAPP_f1631649925t_bool @ cOMBC_1417338747t_bool @ ( hAPP_A1889513822t_bool @ ( hAPP_f2102110817t_bool @ cOMBC_1486904681t_bool @ ( hAPP_f1751344075t_bool @ ( cOMBB_1876517692e_indi @ arrow_216713899_above ) @ p ) ) @ c ) ) @ e ) ) ) @ ( hAPP_A425126512t_bool @ ( hAPP_f1631649925t_bool @ cOMBC_1417338747t_bool @ ( hAPP_f831214557t_bool @ ( cOMBB_80760910e_indi @ arrow_1481558583_mkbot ) @ p ) ) @ e ) ) ) ) ) )
<=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ b ) @ a ) ) @ ( hAPP_f2008608496t_bool @ f @ ( hAPP_f480276746t_bool @ ( hAPP_f601594885t_bool @ cOMBC_750853729t_bool @ ( hAPP_f1344464862t_bool @ ( hAPP_f1908974253t_bool @ cOMBC_156709173t_bool @ ( hAPP_f668886383t_bool @ ( cOMBB_1061985500e_indi @ if_fun523439385t_bool ) @ ( hAPP_n34002993i_bool @ ( hAPP_f721434149i_bool @ cOMBC_722552198t_bool @ ( hAPP_f966656047t_bool @ ( cOMBB_1869811296e_indi @ ord_less_nat ) @ h ) ) @ n ) ) ) @ lab ) ) @ lba ) ) ) ) ),
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(2212,plain,
( ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ e ) @ d ) ) @ ( hAPP_f2008608496t_bool @ f @ ( hAPP_f1302887663t_bool @ ( cOMBS_1181656689t_bool @ ( hAPP_f1001205955t_bool @ ( cOMBS_1925466437t_bool @ ( hAPP_f668886383t_bool @ ( cOMBB_1061985500e_indi @ if_fun523439385t_bool ) @ ( hAPP_n34002993i_bool @ ( hAPP_f721434149i_bool @ cOMBC_722552198t_bool @ ( hAPP_f966656047t_bool @ ( cOMBB_1869811296e_indi @ ord_less_nat ) @ h ) ) @ n ) ) ) @ ( hAPP_A425126512t_bool @ ( hAPP_f1631649925t_bool @ cOMBC_1417338747t_bool @ ( hAPP_f831214557t_bool @ ( cOMBB_80760910e_indi @ arrow_1630265669_mktop ) @ p ) ) @ e ) ) ) @ ( hAPP_f1302887663t_bool @ ( cOMBS_1181656689t_bool @ ( hAPP_f1001205955t_bool @ ( cOMBS_1925466437t_bool @ ( hAPP_f668886383t_bool @ ( cOMBB_1061985500e_indi @ if_fun523439385t_bool ) @ ( hAPP_n34002993i_bool @ ( hAPP_f721434149i_bool @ cOMBC_722552198t_bool @ ( hAPP_f966656047t_bool @ ( cOMBB_1869811296e_indi @ fequal_nat ) @ h ) ) @ n ) ) ) @ ( hAPP_A425126512t_bool @ ( hAPP_f1631649925t_bool @ cOMBC_1417338747t_bool @ ( hAPP_A1889513822t_bool @ ( hAPP_f2102110817t_bool @ cOMBC_1486904681t_bool @ ( hAPP_f1751344075t_bool @ ( cOMBB_1876517692e_indi @ arrow_216713899_above ) @ p ) ) @ c ) ) @ e ) ) ) @ ( hAPP_A425126512t_bool @ ( hAPP_f1631649925t_bool @ cOMBC_1417338747t_bool @ ( hAPP_f831214557t_bool @ ( cOMBB_80760910e_indi @ arrow_1481558583_mkbot ) @ p ) ) @ e ) ) ) ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ b ) @ a ) ) @ ( hAPP_f2008608496t_bool @ f @ ( hAPP_f480276746t_bool @ ( hAPP_f601594885t_bool @ cOMBC_750853729t_bool @ ( hAPP_f1344464862t_bool @ ( hAPP_f1908974253t_bool @ cOMBC_156709173t_bool @ ( hAPP_f668886383t_bool @ ( cOMBB_1061985500e_indi @ if_fun523439385t_bool ) @ ( hAPP_n34002993i_bool @ ( hAPP_f721434149i_bool @ cOMBC_722552198t_bool @ ( hAPP_f966656047t_bool @ ( cOMBB_1869811296e_indi @ ord_less_nat ) @ h ) ) @ n ) ) ) @ lab ) ) @ lba ) ) ) ) )
& ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ b ) @ a ) ) @ ( hAPP_f2008608496t_bool @ f @ ( hAPP_f480276746t_bool @ ( hAPP_f601594885t_bool @ cOMBC_750853729t_bool @ ( hAPP_f1344464862t_bool @ ( hAPP_f1908974253t_bool @ cOMBC_156709173t_bool @ ( hAPP_f668886383t_bool @ ( cOMBB_1061985500e_indi @ if_fun523439385t_bool ) @ ( hAPP_n34002993i_bool @ ( hAPP_f721434149i_bool @ cOMBC_722552198t_bool @ ( hAPP_f966656047t_bool @ ( cOMBB_1869811296e_indi @ ord_less_nat ) @ h ) ) @ n ) ) ) @ lab ) ) @ lba ) ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ e ) @ d ) ) @ ( hAPP_f2008608496t_bool @ f @ ( hAPP_f1302887663t_bool @ ( cOMBS_1181656689t_bool @ ( hAPP_f1001205955t_bool @ ( cOMBS_1925466437t_bool @ ( hAPP_f668886383t_bool @ ( cOMBB_1061985500e_indi @ if_fun523439385t_bool ) @ ( hAPP_n34002993i_bool @ ( hAPP_f721434149i_bool @ cOMBC_722552198t_bool @ ( hAPP_f966656047t_bool @ ( cOMBB_1869811296e_indi @ ord_less_nat ) @ h ) ) @ n ) ) ) @ ( hAPP_A425126512t_bool @ ( hAPP_f1631649925t_bool @ cOMBC_1417338747t_bool @ ( hAPP_f831214557t_bool @ ( cOMBB_80760910e_indi @ arrow_1630265669_mktop ) @ p ) ) @ e ) ) ) @ ( hAPP_f1302887663t_bool @ ( cOMBS_1181656689t_bool @ ( hAPP_f1001205955t_bool @ ( cOMBS_1925466437t_bool @ ( hAPP_f668886383t_bool @ ( cOMBB_1061985500e_indi @ if_fun523439385t_bool ) @ ( hAPP_n34002993i_bool @ ( hAPP_f721434149i_bool @ cOMBC_722552198t_bool @ ( hAPP_f966656047t_bool @ ( cOMBB_1869811296e_indi @ fequal_nat ) @ h ) ) @ n ) ) ) @ ( hAPP_A425126512t_bool @ ( hAPP_f1631649925t_bool @ cOMBC_1417338747t_bool @ ( hAPP_A1889513822t_bool @ ( hAPP_f2102110817t_bool @ cOMBC_1486904681t_bool @ ( hAPP_f1751344075t_bool @ ( cOMBB_1876517692e_indi @ arrow_216713899_above ) @ p ) ) @ c ) ) @ e ) ) ) @ ( hAPP_A425126512t_bool @ ( hAPP_f1631649925t_bool @ cOMBC_1417338747t_bool @ ( hAPP_f831214557t_bool @ ( cOMBB_80760910e_indi @ arrow_1481558583_mkbot ) @ p ) ) @ e ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(531,axiom,
! [A: produc472769767le_alt,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_915_subsetD) ).
thf(2620,plain,
! [A: produc472769767le_alt,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(75,axiom,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ C )
= ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_990_nat__add__assoc) ).
thf(883,plain,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ C )
= ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(153,axiom,
! [A: fun_fu638310559l_bool,B: fun_fu638310559l_bool] :
( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ B ) @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_order__antisym__conv) ).
thf(1176,plain,
! [A: fun_fu638310559l_bool,B: fun_fu638310559l_bool] :
( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ A ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ B ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(571,axiom,
hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ b ) @ a ) ) @ lba ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096) ).
thf(2797,plain,
hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ b ) @ a ) ) @ lba ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(417,axiom,
! [A: fun_fu2114379172t_bool,B: arrow_856714788e_indi] :
( ( hBOOL @ ( hAPP_A997847300i_bool @ ( hAPP_f399308031i_bool @ arrow_1765888670ctator @ A ) @ B ) )
<=> ! [C: fun_Ar274636406t_bool] :
( ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ C ) @ arrow_5070731e_Prof ) )
=> ( ( hAPP_f2008608496t_bool @ A @ C )
= ( hAPP_A1646126530t_bool @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_dictator__def) ).
thf(2101,plain,
! [A: fun_fu2114379172t_bool,B: arrow_856714788e_indi] :
( ( ( hBOOL @ ( hAPP_A997847300i_bool @ ( hAPP_f399308031i_bool @ arrow_1765888670ctator @ A ) @ B ) )
=> ! [C: fun_Ar274636406t_bool] :
( ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ C ) @ arrow_5070731e_Prof ) )
=> ( ( hAPP_f2008608496t_bool @ A @ C )
= ( hAPP_A1646126530t_bool @ C @ B ) ) ) )
& ( ! [C: fun_Ar274636406t_bool] :
( ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ C ) @ arrow_5070731e_Prof ) )
=> ( ( hAPP_f2008608496t_bool @ A @ C )
= ( hAPP_A1646126530t_bool @ C @ B ) ) )
=> ( hBOOL @ ( hAPP_A997847300i_bool @ ( hAPP_f399308031i_bool @ arrow_1765888670ctator @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(431,axiom,
? [A: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_f846027769ol_nat @ finite1672073426e_indi @ top_to788185952i_bool ) ) )
& ! [B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ b ) @ a ) ) @ ( hAPP_f2008608496t_bool @ f @ ( hAPP_f480276746t_bool @ ( hAPP_f601594885t_bool @ cOMBC_750853729t_bool @ ( hAPP_f1344464862t_bool @ ( hAPP_f1908974253t_bool @ cOMBC_156709173t_bool @ ( hAPP_f668886383t_bool @ ( cOMBB_1061985500e_indi @ if_fun523439385t_bool ) @ ( hAPP_n34002993i_bool @ ( hAPP_f721434149i_bool @ cOMBC_722552198t_bool @ ( hAPP_f966656047t_bool @ ( cOMBB_1869811296e_indi @ ord_less_nat ) @ h ) ) @ B ) ) ) @ lab ) ) @ lba ) ) ) ) )
& ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ a ) @ b ) ) @ ( hAPP_f2008608496t_bool @ f @ ( hAPP_f480276746t_bool @ ( hAPP_f601594885t_bool @ cOMBC_750853729t_bool @ ( hAPP_f1344464862t_bool @ ( hAPP_f1908974253t_bool @ cOMBC_156709173t_bool @ ( hAPP_f668886383t_bool @ ( cOMBB_1061985500e_indi @ if_fun523439385t_bool ) @ ( hAPP_n34002993i_bool @ ( hAPP_f721434149i_bool @ cOMBC_722552198t_bool @ ( hAPP_f966656047t_bool @ ( cOMBB_1869811296e_indi @ ord_less_nat ) @ h ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ one_one_nat ) ) ) ) @ lab ) ) @ lba ) ) ) ) ),
file('/export/starexec/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(2156,plain,
? [A: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_f846027769ol_nat @ finite1672073426e_indi @ top_to788185952i_bool ) ) )
& ! [B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ b ) @ a ) ) @ ( hAPP_f2008608496t_bool @ f @ ( hAPP_f480276746t_bool @ ( hAPP_f601594885t_bool @ cOMBC_750853729t_bool @ ( hAPP_f1344464862t_bool @ ( hAPP_f1908974253t_bool @ cOMBC_156709173t_bool @ ( hAPP_f668886383t_bool @ ( cOMBB_1061985500e_indi @ if_fun523439385t_bool ) @ ( hAPP_n34002993i_bool @ ( hAPP_f721434149i_bool @ cOMBC_722552198t_bool @ ( hAPP_f966656047t_bool @ ( cOMBB_1869811296e_indi @ ord_less_nat ) @ h ) ) @ B ) ) ) @ lab ) ) @ lba ) ) ) ) )
& ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ a ) @ b ) ) @ ( hAPP_f2008608496t_bool @ f @ ( hAPP_f480276746t_bool @ ( hAPP_f601594885t_bool @ cOMBC_750853729t_bool @ ( hAPP_f1344464862t_bool @ ( hAPP_f1908974253t_bool @ cOMBC_156709173t_bool @ ( hAPP_f668886383t_bool @ ( cOMBB_1061985500e_indi @ if_fun523439385t_bool ) @ ( hAPP_n34002993i_bool @ ( hAPP_f721434149i_bool @ cOMBC_722552198t_bool @ ( hAPP_f966656047t_bool @ ( cOMBB_1869811296e_indi @ ord_less_nat ) @ h ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ one_one_nat ) ) ) ) @ lab ) ) @ lba ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(86,axiom,
! [A: fun_Pr1780397033l_bool,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ ( pi_Pro1238944957t_bool @ C @ A ) ) @ ( pi_Pro1238944957t_bool @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_715_Pi__anti__mono) ).
thf(922,plain,
! [A: fun_Pr1780397033l_bool,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ ( pi_Pro1238944957t_bool @ C @ A ) ) @ ( pi_Pro1238944957t_bool @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(406,axiom,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiq) ).
thf(2069,plain,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(268,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_xt1_I5_J) ).
thf(1562,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(119,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_743_add__less__imp__less__right) ).
thf(1044,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(506,axiom,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ B ) )
=> ( ( B != A )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_467_xt1_I11_J) ).
thf(2550,plain,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ B ) )
=> ( ( B != A )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(523,axiom,
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ c ) @ d ) ) @ ( hAPP_f2008608496t_bool @ f @ p ) ) )
<=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ c ) @ d ) ) @ ( hAPP_f2008608496t_bool @ f @ ( hAPP_f1302887663t_bool @ ( cOMBS_1181656689t_bool @ ( hAPP_f1001205955t_bool @ ( cOMBS_1925466437t_bool @ ( hAPP_f668886383t_bool @ ( cOMBB_1061985500e_indi @ if_fun523439385t_bool ) @ ( hAPP_n34002993i_bool @ ( hAPP_f721434149i_bool @ cOMBC_722552198t_bool @ ( hAPP_f966656047t_bool @ ( cOMBB_1869811296e_indi @ ord_less_nat ) @ h ) ) @ n ) ) ) @ ( hAPP_A425126512t_bool @ ( hAPP_f1631649925t_bool @ cOMBC_1417338747t_bool @ ( hAPP_f831214557t_bool @ ( cOMBB_80760910e_indi @ arrow_1630265669_mktop ) @ p ) ) @ e ) ) ) @ ( hAPP_f1302887663t_bool @ ( cOMBS_1181656689t_bool @ ( hAPP_f1001205955t_bool @ ( cOMBS_1925466437t_bool @ ( hAPP_f668886383t_bool @ ( cOMBB_1061985500e_indi @ if_fun523439385t_bool ) @ ( hAPP_n34002993i_bool @ ( hAPP_f721434149i_bool @ cOMBC_722552198t_bool @ ( hAPP_f966656047t_bool @ ( cOMBB_1869811296e_indi @ fequal_nat ) @ h ) ) @ n ) ) ) @ ( hAPP_A425126512t_bool @ ( hAPP_f1631649925t_bool @ cOMBC_1417338747t_bool @ ( hAPP_A1889513822t_bool @ ( hAPP_f2102110817t_bool @ cOMBC_1486904681t_bool @ ( hAPP_f1751344075t_bool @ ( cOMBB_1876517692e_indi @ arrow_216713899_above ) @ p ) ) @ c ) ) @ e ) ) ) @ ( hAPP_A425126512t_bool @ ( hAPP_f1631649925t_bool @ cOMBC_1417338747t_bool @ ( hAPP_f831214557t_bool @ ( cOMBB_80760910e_indi @ arrow_1481558583_mkbot ) @ p ) ) @ e ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_PW) ).
thf(2592,plain,
( ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ c ) @ d ) ) @ ( hAPP_f2008608496t_bool @ f @ p ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ c ) @ d ) ) @ ( hAPP_f2008608496t_bool @ f @ ( hAPP_f1302887663t_bool @ ( cOMBS_1181656689t_bool @ ( hAPP_f1001205955t_bool @ ( cOMBS_1925466437t_bool @ ( hAPP_f668886383t_bool @ ( cOMBB_1061985500e_indi @ if_fun523439385t_bool ) @ ( hAPP_n34002993i_bool @ ( hAPP_f721434149i_bool @ cOMBC_722552198t_bool @ ( hAPP_f966656047t_bool @ ( cOMBB_1869811296e_indi @ ord_less_nat ) @ h ) ) @ n ) ) ) @ ( hAPP_A425126512t_bool @ ( hAPP_f1631649925t_bool @ cOMBC_1417338747t_bool @ ( hAPP_f831214557t_bool @ ( cOMBB_80760910e_indi @ arrow_1630265669_mktop ) @ p ) ) @ e ) ) ) @ ( hAPP_f1302887663t_bool @ ( cOMBS_1181656689t_bool @ ( hAPP_f1001205955t_bool @ ( cOMBS_1925466437t_bool @ ( hAPP_f668886383t_bool @ ( cOMBB_1061985500e_indi @ if_fun523439385t_bool ) @ ( hAPP_n34002993i_bool @ ( hAPP_f721434149i_bool @ cOMBC_722552198t_bool @ ( hAPP_f966656047t_bool @ ( cOMBB_1869811296e_indi @ fequal_nat ) @ h ) ) @ n ) ) ) @ ( hAPP_A425126512t_bool @ ( hAPP_f1631649925t_bool @ cOMBC_1417338747t_bool @ ( hAPP_A1889513822t_bool @ ( hAPP_f2102110817t_bool @ cOMBC_1486904681t_bool @ ( hAPP_f1751344075t_bool @ ( cOMBB_1876517692e_indi @ arrow_216713899_above ) @ p ) ) @ c ) ) @ e ) ) ) @ ( hAPP_A425126512t_bool @ ( hAPP_f1631649925t_bool @ cOMBC_1417338747t_bool @ ( hAPP_f831214557t_bool @ ( cOMBB_80760910e_indi @ arrow_1481558583_mkbot ) @ p ) ) @ e ) ) ) ) ) ) )
& ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ c ) @ d ) ) @ ( hAPP_f2008608496t_bool @ f @ ( hAPP_f1302887663t_bool @ ( cOMBS_1181656689t_bool @ ( hAPP_f1001205955t_bool @ ( cOMBS_1925466437t_bool @ ( hAPP_f668886383t_bool @ ( cOMBB_1061985500e_indi @ if_fun523439385t_bool ) @ ( hAPP_n34002993i_bool @ ( hAPP_f721434149i_bool @ cOMBC_722552198t_bool @ ( hAPP_f966656047t_bool @ ( cOMBB_1869811296e_indi @ ord_less_nat ) @ h ) ) @ n ) ) ) @ ( hAPP_A425126512t_bool @ ( hAPP_f1631649925t_bool @ cOMBC_1417338747t_bool @ ( hAPP_f831214557t_bool @ ( cOMBB_80760910e_indi @ arrow_1630265669_mktop ) @ p ) ) @ e ) ) ) @ ( hAPP_f1302887663t_bool @ ( cOMBS_1181656689t_bool @ ( hAPP_f1001205955t_bool @ ( cOMBS_1925466437t_bool @ ( hAPP_f668886383t_bool @ ( cOMBB_1061985500e_indi @ if_fun523439385t_bool ) @ ( hAPP_n34002993i_bool @ ( hAPP_f721434149i_bool @ cOMBC_722552198t_bool @ ( hAPP_f966656047t_bool @ ( cOMBB_1869811296e_indi @ fequal_nat ) @ h ) ) @ n ) ) ) @ ( hAPP_A425126512t_bool @ ( hAPP_f1631649925t_bool @ cOMBC_1417338747t_bool @ ( hAPP_A1889513822t_bool @ ( hAPP_f2102110817t_bool @ cOMBC_1486904681t_bool @ ( hAPP_f1751344075t_bool @ ( cOMBB_1876517692e_indi @ arrow_216713899_above ) @ p ) ) @ c ) ) @ e ) ) ) @ ( hAPP_A425126512t_bool @ ( hAPP_f1631649925t_bool @ cOMBC_1417338747t_bool @ ( hAPP_f831214557t_bool @ ( cOMBB_80760910e_indi @ arrow_1481558583_mkbot ) @ p ) ) @ e ) ) ) ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ c ) @ d ) ) @ ( hAPP_f2008608496t_bool @ f @ p ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(227,axiom,
! [A: nat,B: nat,C: nat] :
( ( B = C )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_xt1_I1_J) ).
thf(1435,plain,
! [A: nat,B: nat,C: nat] :
( ( B = C )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(370,axiom,
! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool] :
( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ B ) @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_order__antisym__conv) ).
thf(1948,plain,
! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool] :
( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ A ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ B ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(328,axiom,
! [A: fun_Pr1643180309t_bool,B: produc472769767le_alt] :
( ( hAPP_P2037731755t_bool @ ( hAPP_f723483871t_bool @ cOMBK_751896174le_alt @ A ) @ B )
= 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(1809,plain,
! [A: fun_Pr1643180309t_bool,B: produc472769767le_alt] :
( ( hAPP_P2037731755t_bool @ ( hAPP_f723483871t_bool @ cOMBK_751896174le_alt @ A ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(415,axiom,
! [A: fun_Ar331856045t_bool] : ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_order__refl) ).
thf(2096,plain,
! [A: fun_Ar331856045t_bool] : ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(187,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_739_add__right__mono) ).
thf(1304,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(162,axiom,
! [A: nat,B: nat] :
( ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B )
= ( hAPP_nat_nat @ suc @ zero_zero_nat ) )
<=> ( ( ( A
= ( hAPP_nat_nat @ suc @ zero_zero_nat ) )
& ( B = zero_zero_nat ) )
| ( ( A = zero_zero_nat )
& ( B
= ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1097_add__is__1) ).
thf(1208,plain,
! [A: nat,B: nat] :
( ( ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B )
= ( hAPP_nat_nat @ suc @ zero_zero_nat ) )
=> ( ( ( A
= ( hAPP_nat_nat @ suc @ zero_zero_nat ) )
& ( B = zero_zero_nat ) )
| ( ( A = zero_zero_nat )
& ( B
= ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) ) ) )
& ( ( ( ( A
= ( hAPP_nat_nat @ suc @ zero_zero_nat ) )
& ( B = zero_zero_nat ) )
| ( ( A = zero_zero_nat )
& ( B
= ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) ) )
=> ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B )
= ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(92,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1088_le__SucI) ).
thf(944,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(236,axiom,
! [A: fun_Pr2067565481t_bool,B: fun_na998785244t_bool,C: nat,D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ A ) @ ( hAPP_n1161265524t_bool @ B @ C ) ) )
=> ( ! [E: nat,F: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ F ) @ E ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ ( hAPP_n1161265524t_bool @ B @ F ) ) @ ( hAPP_n1161265524t_bool @ B @ E ) ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ A ) @ ( hAPP_n1161265524t_bool @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_679_xt7) ).
thf(1467,plain,
! [A: fun_Pr2067565481t_bool,B: fun_na998785244t_bool,C: nat,D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ A ) @ ( hAPP_n1161265524t_bool @ B @ C ) ) )
=> ( ! [E: nat,F: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ F ) @ E ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ ( hAPP_n1161265524t_bool @ B @ F ) ) @ ( hAPP_n1161265524t_bool @ B @ E ) ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ A ) @ ( hAPP_n1161265524t_bool @ B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(54,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) )
=> ? [C: nat] :
( B
= ( hAPP_nat_nat @ suc @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1120_Suc__le__D) ).
thf(795,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) )
=> ? [C: nat] :
( B
= ( hAPP_nat_nat @ suc @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(238,axiom,
! [A: nat,B: nat] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( ( A != B )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_linorder__cases) ).
thf(1472,plain,
! [A: nat,B: nat] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( ( A != B )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
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(1018,plain,
! [A: nat] :
( ( ( one_one_nat = A )
=> ( A = one_one_nat ) )
& ( ( A = one_one_nat )
=> ( one_one_nat = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(518,axiom,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_507_xt1_I8_J) ).
thf(2582,plain,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(121,axiom,
! [A: fun_fu638310559l_bool,B: fun_fu638310559l_bool,C: fun_fu638310559l_bool] :
( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_order__trans) ).
thf(1049,plain,
! [A: fun_fu638310559l_bool,B: fun_fu638310559l_bool,C: fun_fu638310559l_bool] :
( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(387,axiom,
! [A: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ A ) @ arrow_1361987423le_Lin ) )
=> ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ ( hAPP_f480276746t_bool @ cOMBK_1650320063e_indi @ A ) ) @ arrow_5070731e_Prof ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_const__Lin__Prof) ).
thf(2005,plain,
! [A: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ A ) @ arrow_1361987423le_Lin ) )
=> ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ ( hAPP_f480276746t_bool @ cOMBK_1650320063e_indi @ A ) ) @ arrow_5070731e_Prof ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(130,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1168_n__less__m__mult__n) ).
thf(1076,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(42,axiom,
! [A: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ? [B: nat] :
( A
= ( hAPP_nat_nat @ suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1117_gr0__implies__Suc) ).
thf(749,plain,
! [A: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ? [B: nat] :
( A
= ( hAPP_nat_nat @ suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(535,axiom,
! [A: produc472769767le_alt,B: fun_Pr376858015t_unit,C: fun_Pr2067565481t_bool,D: fun_Pr1069395679t_bool] :
( ( hBOOL @ ( hAPP_f1159856629l_bool @ ( hAPP_f1700632141l_bool @ member1303779570t_unit @ B ) @ ( pi_Pro346842291t_unit @ C @ D ) ) )
=> ( ~ ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ ( hAPP_P1069491261t_unit @ B @ A ) ) @ ( hAPP_P2037731755t_bool @ D @ A ) ) )
=> ~ ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_PiE) ).
thf(2629,plain,
! [A: produc472769767le_alt,B: fun_Pr376858015t_unit,C: fun_Pr2067565481t_bool,D: fun_Pr1069395679t_bool] :
( ( hBOOL @ ( hAPP_f1159856629l_bool @ ( hAPP_f1700632141l_bool @ member1303779570t_unit @ B ) @ ( pi_Pro346842291t_unit @ C @ D ) ) )
=> ( ~ ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ ( hAPP_P1069491261t_unit @ B @ A ) ) @ ( hAPP_P2037731755t_bool @ D @ A ) ) )
=> ~ ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(340,axiom,
! [A: nat,B: fun_Pr2067565481t_bool,C: fun_na998785244t_bool,D: nat] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ B ) @ ( hAPP_n1161265524t_bool @ C @ D ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ D ) @ A ) )
=> ( ! [E: nat,F: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ E ) @ F ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ ( hAPP_n1161265524t_bool @ C @ E ) ) @ ( hAPP_n1161265524t_bool @ C @ F ) ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ B ) @ ( hAPP_n1161265524t_bool @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_827_order__less__le__subst1) ).
thf(1845,plain,
! [A: nat,B: fun_Pr2067565481t_bool,C: fun_na998785244t_bool,D: nat] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ B ) @ ( hAPP_n1161265524t_bool @ C @ D ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ D ) @ A ) )
=> ( ! [E: nat,F: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ E ) @ F ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ ( hAPP_n1161265524t_bool @ C @ E ) ) @ ( hAPP_n1161265524t_bool @ C @ F ) ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ B ) @ ( hAPP_n1161265524t_bool @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(320,axiom,
! [A: arrow_856714788e_indi,B: arrow_856714788e_indi,C: fun_Ar671024215di_nat] :
( ( hBOOL @ ( hAPP_f584385070l_bool @ ( inj_on1960344199di_nat @ C ) @ top_to788185952i_bool ) )
=> ( ( ( hAPP_A376526755di_nat @ C @ A )
= ( hAPP_A376526755di_nat @ C @ B ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_612_inj__eq) ).
thf(1748,plain,
! [A: arrow_856714788e_indi,B: arrow_856714788e_indi,C: fun_Ar671024215di_nat] :
( ( hBOOL @ ( hAPP_f584385070l_bool @ ( inj_on1960344199di_nat @ C ) @ top_to788185952i_bool ) )
=> ( ( ( ( hAPP_A376526755di_nat @ C @ A )
= ( hAPP_A376526755di_nat @ C @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( hAPP_A376526755di_nat @ C @ A )
= ( hAPP_A376526755di_nat @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(128,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_730_add__left__imp__eq) ).
thf(1070,plain,
! [A: nat,B: nat,C: nat] :
( ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(548,axiom,
! [A: fun_Pr2067565481t_bool] :
( ( A != top_to1138392227t_bool )
<=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ A ) @ top_to1138392227t_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_less__top) ).
thf(2661,plain,
! [A: fun_Pr2067565481t_bool] :
( ( ( A != top_to1138392227t_bool )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ A ) @ top_to1138392227t_bool ) ) )
& ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ A ) @ top_to1138392227t_bool ) )
=> ( A != top_to1138392227t_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(283,axiom,
! [A: nat] : ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ ( hAPP_f480276746t_bool @ ( hAPP_f601594885t_bool @ cOMBC_750853729t_bool @ ( hAPP_f1344464862t_bool @ ( hAPP_f1908974253t_bool @ cOMBC_156709173t_bool @ ( hAPP_f668886383t_bool @ ( cOMBB_1061985500e_indi @ if_fun523439385t_bool ) @ ( hAPP_n34002993i_bool @ ( hAPP_f721434149i_bool @ cOMBC_722552198t_bool @ ( hAPP_f966656047t_bool @ ( cOMBB_1869811296e_indi @ ord_less_nat ) @ h ) ) @ A ) ) ) @ lab ) ) @ lba ) ) @ arrow_5070731e_Prof ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_PiProf) ).
thf(1611,plain,
! [A: nat] : ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ ( hAPP_f480276746t_bool @ ( hAPP_f601594885t_bool @ cOMBC_750853729t_bool @ ( hAPP_f1344464862t_bool @ ( hAPP_f1908974253t_bool @ cOMBC_156709173t_bool @ ( hAPP_f668886383t_bool @ ( cOMBB_1061985500e_indi @ if_fun523439385t_bool ) @ ( hAPP_n34002993i_bool @ ( hAPP_f721434149i_bool @ cOMBC_722552198t_bool @ ( hAPP_f966656047t_bool @ ( cOMBB_1869811296e_indi @ ord_less_nat ) @ h ) ) @ A ) ) ) @ lab ) ) @ lba ) ) @ arrow_5070731e_Prof ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(367,axiom,
! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool] :
( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_438_order__less__imp__le) ).
thf(1941,plain,
! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool] :
( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(257,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( A != B )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1011_le__neq__implies__less) ).
thf(1531,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( A != B )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(556,axiom,
! [A: fun_Pr2067565481t_bool] :
~ ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ top_to1138392227t_bool ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_not__top__less) ).
thf(2689,plain,
! [A: fun_Pr2067565481t_bool] :
~ ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ top_to1138392227t_bool ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(1,conjecture,
hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ c ) @ d ) ) @ ( hAPP_f2008608496t_bool @ f @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ c ) @ d ) ) @ ( hAPP_f2008608496t_bool @ f @ p ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(580,plain,
~ ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ c ) @ d ) ) @ ( hAPP_f2008608496t_bool @ f @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(563,axiom,
! [A: fun_fu864675765l_bool,B: fun_fu638310559l_bool,C: fun_Pr2067565481t_bool] :
( ( hAPP_f52567537l_bool @ ( hAPP_f1060563265l_bool @ ( hAPP_f1776355587l_bool @ cOMBC_2133093654l_bool @ A ) @ B ) @ C )
= ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ef) ).
thf(2715,plain,
! [A: fun_fu864675765l_bool,B: fun_fu638310559l_bool,C: fun_Pr2067565481t_bool] :
( ( hAPP_f52567537l_bool @ ( hAPP_f1060563265l_bool @ ( hAPP_f1776355587l_bool @ cOMBC_2133093654l_bool @ A ) @ B ) @ C )
= ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(27,axiom,
! [A: fun_fu638310559l_bool,B: bool] :
( ( hAPP_b1272691967l_bool @ ( hAPP_f86272063l_bool @ cOMBK_650639032l_bool @ A ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe) ).
thf(690,plain,
! [A: fun_fu638310559l_bool,B: bool] :
( ( hAPP_b1272691967l_bool @ ( hAPP_f86272063l_bool @ cOMBK_650639032l_bool @ A ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(252,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_order__antisym) ).
thf(1516,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(318,axiom,
! [A: arrow_856714788e_indi,B: arrow_856714788e_indi,C: fun_Ar671024215di_nat,D: fun_Ar1809396326i_bool] :
( ( hBOOL @ ( hAPP_f584385070l_bool @ ( inj_on1960344199di_nat @ C ) @ D ) )
=> ( ( A != B )
=> ( ( hBOOL @ ( hAPP_f584385070l_bool @ ( hAPP_A1597696899l_bool @ member1479139729e_indi @ A ) @ D ) )
=> ( ( hBOOL @ ( hAPP_f584385070l_bool @ ( hAPP_A1597696899l_bool @ member1479139729e_indi @ B ) @ D ) )
=> ( ( hAPP_A376526755di_nat @ C @ A )
!= ( hAPP_A376526755di_nat @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_541_inj__on__contraD) ).
thf(1743,plain,
! [A: arrow_856714788e_indi,B: arrow_856714788e_indi,C: fun_Ar671024215di_nat,D: fun_Ar1809396326i_bool] :
( ( hBOOL @ ( hAPP_f584385070l_bool @ ( inj_on1960344199di_nat @ C ) @ D ) )
=> ( ( A != B )
=> ( ( hBOOL @ ( hAPP_f584385070l_bool @ ( hAPP_A1597696899l_bool @ member1479139729e_indi @ A ) @ D ) )
=> ( ( hBOOL @ ( hAPP_f584385070l_bool @ ( hAPP_A1597696899l_bool @ member1479139729e_indi @ B ) @ D ) )
=> ( ( hAPP_A376526755di_nat @ C @ A )
!= ( hAPP_A376526755di_nat @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(216,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
<=> ? [C: nat] :
( B
= ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1101_less__iff__Suc__add) ).
thf(1400,plain,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ? [C: nat] :
( B
= ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) ) )
& ( ? [C: nat] :
( B
= ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(204,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1029_termination__basic__simps_I1_J) ).
thf(1368,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(436,axiom,
! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool] :
( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ A ) @ B ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_449_order__le__imp__less__or__eq) ).
thf(2175,plain,
! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool] :
( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ A ) @ B ) )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(241,axiom,
! [A: nat] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1044_not__less0) ).
thf(1484,plain,
! [A: nat] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(432,axiom,
! [A: fun_Ar1809396326i_bool,B: produc472769767le_alt] :
( ( hAPP_P1859429372i_bool @ ( hAPP_f359069313i_bool @ cOMBK_1987648063le_alt @ A ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs___404) ).
thf(2160,plain,
! [A: fun_Ar1809396326i_bool,B: produc472769767le_alt] :
( ( hAPP_P1859429372i_bool @ ( hAPP_f359069313i_bool @ cOMBK_1987648063le_alt @ A ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(449,axiom,
! [A: fun_Ar274636406t_bool,B: fun_fu3835832l_bool] :
( ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ A ) @ B ) )
<=> ( hBOOL @ ( hAPP_f995490902l_bool @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_mem__def) ).
thf(2224,plain,
! [A: fun_Ar274636406t_bool,B: fun_fu3835832l_bool] :
( ( ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f995490902l_bool @ B @ A ) ) )
& ( ( hBOOL @ ( hAPP_f995490902l_bool @ B @ A ) )
=> ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(293,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
| ( A = B )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_linorder__less__linear) ).
thf(1637,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
| ( A = B )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(176,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_745_add__strict__left__mono) ).
thf(1262,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(447,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_451_order__le__imp__less__or__eq) ).
thf(2219,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(298,axiom,
! [A: fun_fu3835832l_bool] :
( ( pi_fun1746584570t_bool @ A @ ( hAPP_f1104294872l_bool @ cOMBK_1701906001t_bool @ top_to1312956197l_bool ) )
= top_to827110112l_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_Pi__UNIV) ).
thf(1658,plain,
! [A: fun_fu3835832l_bool] :
( ( pi_fun1746584570t_bool @ A @ ( hAPP_f1104294872l_bool @ cOMBK_1701906001t_bool @ top_to1312956197l_bool ) )
= top_to827110112l_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(144,axiom,
! [A: nat,B: nat] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1082_not__less__eq) ).
thf(1130,plain,
! [A: nat,B: nat] :
( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ suc @ A ) ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ suc @ A ) ) )
=> ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(197,axiom,
! [A: nat,B: nat] :
( ( ( hAPP_nat_nat @ suc @ A )
= ( hAPP_nat_nat @ suc @ B ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1063_nat_Oinject) ).
thf(1336,plain,
! [A: nat,B: nat] :
( ( ( ( hAPP_nat_nat @ suc @ A )
= ( hAPP_nat_nat @ suc @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( hAPP_nat_nat @ suc @ A )
= ( hAPP_nat_nat @ suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(311,axiom,
! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool] :
( ( A = B )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_352_order__eq__refl) ).
thf(1711,plain,
! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool] :
( ( A = B )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(123,axiom,
! [A: fun_fu638310559l_bool] : ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ A ) @ top_to1312956197l_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_719_subset__UNIV) ).
thf(1053,plain,
! [A: fun_fu638310559l_bool] : ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ A ) @ top_to1312956197l_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(23,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( times_times_nat @ C ) @ B ) )
<=> ( ( A = C )
| ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1152_mult__cancel2) ).
thf(673,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( times_times_nat @ C ) @ B ) )
=> ( ( A = C )
| ( B = zero_zero_nat ) ) )
& ( ( ( A = C )
| ( B = zero_zero_nat ) )
=> ( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( times_times_nat @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(413,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1027_termination__basic__simps_I5_J) ).
thf(2092,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(260,axiom,
! [A: nat,B: nat] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_linorder__le__cases) ).
thf(1538,plain,
! [A: nat,B: nat] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(505,axiom,
! [A: arrow_1893660431le_alt,B: arrow_1893660431le_alt] :
( ( A != B )
=> ? [C: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ C ) @ arrow_1361987423le_Lin ) )
& ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ A ) @ B ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_complete__Lin) ).
thf(2545,plain,
! [A: arrow_1893660431le_alt,B: arrow_1893660431le_alt] :
( ( A != B )
=> ? [C: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ C ) @ arrow_1361987423le_Lin ) )
& ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ A ) @ B ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(402,axiom,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
( ( hAPP_f1356305429t_bool @ ( hAPP_f1299954409t_bool @ ( hAPP_b35146737t_bool @ if_fun523439385t_bool @ fFalse ) @ A ) @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiq) ).
thf(2056,plain,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
( ( hAPP_f1356305429t_bool @ ( hAPP_f1299954409t_bool @ ( hAPP_b35146737t_bool @ if_fun523439385t_bool @ fFalse ) @ A ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(259,axiom,
! [A: bool,B: fun_bo1431306493t_bool,C: fun_bool_bool,D: fun_bo377688929l_bool] :
( ( hBOOL @ ( hAPP_f398210311l_bool @ ( hAPP_f416878261l_bool @ member1133581546t_bool @ B ) @ ( pi_boo1111177555t_bool @ C @ D ) ) )
=> ( ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ ( hAPP_b128655177t_bool @ B @ A ) ) @ ( hAPP_b1272691967l_bool @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_571_Pi__mem) ).
thf(1536,plain,
! [A: bool,B: fun_bo1431306493t_bool,C: fun_bool_bool,D: fun_bo377688929l_bool] :
( ( hBOOL @ ( hAPP_f398210311l_bool @ ( hAPP_f416878261l_bool @ member1133581546t_bool @ B ) @ ( pi_boo1111177555t_bool @ C @ D ) ) )
=> ( ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ ( hAPP_b128655177t_bool @ B @ A ) ) @ ( hAPP_b1272691967l_bool @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(427,axiom,
! [A: arrow_1893660431le_alt,B: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ B ) @ arrow_1361987423le_Lin ) )
=> ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ ( hAPP_A1601437999t_bool @ ( hAPP_f1761571331t_bool @ arrow_1481558583_mkbot @ B ) @ A ) ) @ arrow_1361987423le_Lin ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_mkbot__Lin) ).
thf(2145,plain,
! [A: arrow_1893660431le_alt,B: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ B ) @ arrow_1361987423le_Lin ) )
=> ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ ( hAPP_A1601437999t_bool @ ( hAPP_f1761571331t_bool @ arrow_1481558583_mkbot @ B ) @ A ) ) @ arrow_1361987423le_Lin ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(206,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ B ) )
=> ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_728_add__right__imp__eq) ).
thf(1372,plain,
! [A: nat,B: nat,C: nat] :
( ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ B ) )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(10,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) )
<=> ( ( B = C )
| ( A = zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1153_mult__cancel1) ).
thf(612,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) )
=> ( ( B = C )
| ( A = zero_zero_nat ) ) )
& ( ( ( B = C )
| ( A = zero_zero_nat ) )
=> ( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(575,axiom,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ B ) )
<=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ A ) @ B ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_402_order__le__less) ).
thf(2848,plain,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
( ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ A ) @ B ) )
| ( A = B ) ) )
& ( ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ A ) @ B ) )
| ( A = B ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(519,axiom,
hBOOL @ ( hAPP_f1572141188l_bool @ arrow_1335103695le_IIA @ f ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_assms_I3_J) ).
thf(2584,plain,
hBOOL @ ( hAPP_f1572141188l_bool @ arrow_1335103695le_IIA @ f ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(168,axiom,
! [A: nat] :
( ( hAPP_nat_nat @ nat_size @ ( hAPP_nat_nat @ suc @ A ) )
= ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ ( hAPP_nat_nat @ nat_size @ A ) ) @ ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1181_nat_Osize_I2_J) ).
thf(1240,plain,
! [A: nat] :
( ( hAPP_nat_nat @ nat_size @ ( hAPP_nat_nat @ suc @ A ) )
= ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ ( hAPP_nat_nat @ nat_size @ A ) ) @ ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(357,axiom,
! [A: nat,B: nat] :
( ( A = B )
<=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
& ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_363_order__eq__iff) ).
thf(1898,plain,
! [A: nat,B: nat] :
( ( ( A = B )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
& ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
& ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(174,axiom,
! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ one_one_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_653_less__add__one) ).
thf(1257,plain,
! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ one_one_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(19,axiom,
! [A: nat,B: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B )
= ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ B ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1165_mult__Suc) ).
thf(656,plain,
! [A: nat,B: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B )
= ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ B ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(326,axiom,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
| ( A = B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1012_less__or__eq__imp__le) ).
thf(1802,plain,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
| ( A = B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(375,axiom,
! [A: arrow_856714788e_indi] : ( hBOOL @ ( hAPP_f584385070l_bool @ ( hAPP_A1597696899l_bool @ member1479139729e_indi @ A ) @ top_to788185952i_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_iso__tuple__UNIV__I) ).
thf(1972,plain,
! [A: arrow_856714788e_indi] : ( hBOOL @ ( hAPP_f584385070l_bool @ ( hAPP_A1597696899l_bool @ member1479139729e_indi @ A ) @ top_to788185952i_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(562,axiom,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ B ) @ C ) )
=> ( ( C = A )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_ord__le__eq__trans) ).
thf(2711,plain,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ B ) @ C ) )
=> ( ( C = A )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(517,axiom,
! [A: fun_Pr1509342064e_indi,B: fun_Pr895221296i_bool,C: fun_Pr2067565481t_bool] :
( ! [D: produc472769767le_alt] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ D ) @ C ) )
=> ( hBOOL @ ( hAPP_f584385070l_bool @ ( hAPP_A1597696899l_bool @ member1479139729e_indi @ ( hAPP_P276596750e_indi @ A @ D ) ) @ ( hAPP_P1859429372i_bool @ B @ D ) ) ) )
=> ( hBOOL @ ( hAPP_f2124588998l_bool @ ( hAPP_f1187850253l_bool @ member1558233923e_indi @ A ) @ ( pi_Pro837265796e_indi @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_620_Pi__I) ).
thf(2579,plain,
! [A: fun_Pr1509342064e_indi,B: fun_Pr895221296i_bool,C: fun_Pr2067565481t_bool] :
( ! [D: produc472769767le_alt] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ D ) @ C ) )
=> ( hBOOL @ ( hAPP_f584385070l_bool @ ( hAPP_A1597696899l_bool @ member1479139729e_indi @ ( hAPP_P276596750e_indi @ A @ D ) ) @ ( hAPP_P1859429372i_bool @ B @ D ) ) ) )
=> ( hBOOL @ ( hAPP_f2124588998l_bool @ ( hAPP_f1187850253l_bool @ member1558233923e_indi @ A ) @ ( pi_Pro837265796e_indi @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(73,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ C ) )
=> ~ ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) )
=> ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_904_add__leE) ).
thf(864,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ C ) )
=> ~ ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) )
=> ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(103,axiom,
! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ top_top_fun_nat_bool @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_top1I) ).
thf(978,plain,
! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ top_top_fun_nat_bool @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(494,axiom,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ ( hAPP_f1356305429t_bool @ ( hAPP_f1033183015t_bool @ cOMBC_593569186l_bool @ member1333168212le_alt ) @ A ) ) @ ( hAPP_f1356305429t_bool @ ( hAPP_f1033183015t_bool @ cOMBC_593569186l_bool @ member1333168212le_alt ) @ B ) ) )
<=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_980_pred__subset__eq) ).
thf(2511,plain,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
( ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ ( hAPP_f1356305429t_bool @ ( hAPP_f1033183015t_bool @ cOMBC_593569186l_bool @ member1333168212le_alt ) @ A ) ) @ ( hAPP_f1356305429t_bool @ ( hAPP_f1033183015t_bool @ cOMBC_593569186l_bool @ member1333168212le_alt ) @ B ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ ( hAPP_f1356305429t_bool @ ( hAPP_f1033183015t_bool @ cOMBC_593569186l_bool @ member1333168212le_alt ) @ A ) ) @ ( hAPP_f1356305429t_bool @ ( hAPP_f1033183015t_bool @ cOMBC_593569186l_bool @ member1333168212le_alt ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(391,axiom,
! [A: fun_fu1287834969t_bool,B: fun_Ar274636406t_bool,C: arrow_856714788e_indi] :
( ( hAPP_A38124190t_bool @ ( hAPP_f1751344075t_bool @ ( cOMBB_1876517692e_indi @ A ) @ B ) @ C )
= ( hAPP_f1550387441t_bool @ A @ ( hAPP_A1646126530t_bool @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ef_425) ).
thf(2013,plain,
! [A: fun_fu1287834969t_bool,B: fun_Ar274636406t_bool,C: arrow_856714788e_indi] :
( ( hAPP_A38124190t_bool @ ( hAPP_f1751344075t_bool @ ( cOMBB_1876517692e_indi @ A ) @ B ) @ C )
= ( hAPP_f1550387441t_bool @ A @ ( hAPP_A1646126530t_bool @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(337,axiom,
! [A: nat] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_order__less__irrefl) ).
thf(1839,plain,
! [A: nat] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(233,axiom,
! [A: nat,B: fun_fu1677555470ol_nat,C: fun_Ar331856045t_bool,D: fun_Ar331856045t_bool] :
( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_f1403773274ol_nat @ B @ C ) ) )
=> ( ! [E: fun_Ar331856045t_bool,F: fun_Ar331856045t_bool] :
( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ F ) @ E ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f1403773274ol_nat @ B @ F ) ) @ ( hAPP_f1403773274ol_nat @ B @ E ) ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_f1403773274ol_nat @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_706_xt7) ).
thf(1459,plain,
! [A: nat,B: fun_fu1677555470ol_nat,C: fun_Ar331856045t_bool,D: fun_Ar331856045t_bool] :
( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_f1403773274ol_nat @ B @ C ) ) )
=> ( ! [E: fun_Ar331856045t_bool,F: fun_Ar331856045t_bool] :
( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ F ) @ E ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f1403773274ol_nat @ B @ F ) ) @ ( hAPP_f1403773274ol_nat @ B @ E ) ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_f1403773274ol_nat @ B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(306,axiom,
hBOOL @ ( hAPP_f584385070l_bool @ ( inj_on1960344199di_nat @ h ) @ top_to788185952i_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_injh) ).
thf(1685,plain,
hBOOL @ ( hAPP_f584385070l_bool @ ( inj_on1960344199di_nat @ h ) @ top_to788185952i_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(194,axiom,
! [A: nat,B: nat,C: fun_nat_nat] :
( ! [D: nat,E: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ D ) @ E ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ C @ D ) ) @ ( hAPP_nat_nat @ C @ E ) ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ C @ A ) ) @ ( hAPP_nat_nat @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1024_less__mono__imp__le__mono) ).
thf(1321,plain,
! [A: nat,B: nat,C: fun_nat_nat] :
( ! [D: nat,E: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ D ) @ E ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ C @ D ) ) @ ( hAPP_nat_nat @ C @ E ) ) ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ C @ A ) ) @ ( hAPP_nat_nat @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(445,axiom,
! [A: nat,B: nat] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_408_not__leE) ).
thf(2215,plain,
! [A: nat,B: nat] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(78,axiom,
! [A: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
<=> ? [B: nat] :
( A
= ( hAPP_nat_nat @ suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1094_gr0__conv__Suc) ).
thf(891,plain,
! [A: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) )
=> ? [B: nat] :
( A
= ( hAPP_nat_nat @ suc @ B ) ) )
& ( ? [B: nat] :
( A
= ( hAPP_nat_nat @ suc @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(566,axiom,
! [A: product_unit,B: fun_Pr2090226719le_alt,C: fun_Pr1643180309t_bool,D: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f684683381l_bool @ ( hAPP_f41367117l_bool @ member869664626le_alt @ B ) @ ( pi_Pro1820940723le_alt @ C @ ( hAPP_f15777819t_bool @ cOMBK_681766254t_unit @ D ) ) ) )
=> ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_P396106045le_alt @ B @ A ) ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_598_funcset__mem) ).
thf(2743,plain,
! [A: product_unit,B: fun_Pr2090226719le_alt,C: fun_Pr1643180309t_bool,D: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f684683381l_bool @ ( hAPP_f41367117l_bool @ member869664626le_alt @ B ) @ ( pi_Pro1820940723le_alt @ C @ ( hAPP_f15777819t_bool @ cOMBK_681766254t_unit @ D ) ) ) )
=> ( ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_P396106045le_alt @ B @ A ) ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(418,axiom,
! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_order__refl) ).
thf(2110,plain,
! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(68,axiom,
! [A: fun_fu638310559l_bool,B: fun_fu638310559l_bool] :
( ( A = B )
=> ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_order__eq__refl) ).
thf(844,plain,
! [A: fun_fu638310559l_bool,B: fun_fu638310559l_bool] :
( ( A = B )
=> ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(138,axiom,
! [A: fun_fu638310559l_bool,B: fun_fu638310559l_bool,C: fun_fu638310559l_bool] :
( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ B ) @ C ) )
=> ( ( B = A )
=> ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_xt1_I4_J) ).
thf(1108,plain,
! [A: fun_fu638310559l_bool,B: fun_fu638310559l_bool,C: fun_fu638310559l_bool] :
( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ B ) @ C ) )
=> ( ( B = A )
=> ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(26,axiom,
! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1140_le__square) ).
thf(688,plain,
! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(81,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1086_Suc__leD) ).
thf(903,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(440,axiom,
( top_to1312956197l_bool
= ( hAPP_f1060563265l_bool @ collec2125531966t_bool @ ( hAPP_b1272691967l_bool @ cOMBK_81143760t_bool @ fTrue ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_UNIV__def) ).
thf(2194,plain,
( top_to1312956197l_bool
= ( hAPP_f1060563265l_bool @ collec2125531966t_bool @ ( hAPP_b1272691967l_bool @ cOMBK_81143760t_bool @ fTrue ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(3,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B )
= ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ C ) )
<=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1151_Suc__mult__cancel1) ).
thf(581,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B )
= ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ C ) )
=> ( B = C ) )
& ( ( B = C )
=> ( ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B )
= ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(529,axiom,
! [A: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ top_to1138392227t_bool ) @ A ) )
<=> ( A = top_to1138392227t_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_525_top__unique) ).
thf(2611,plain,
! [A: fun_Pr2067565481t_bool] :
( ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ top_to1138392227t_bool ) @ A ) )
=> ( A = top_to1138392227t_bool ) )
& ( ( A = top_to1138392227t_bool )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ top_to1138392227t_bool ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(44,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ C ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1166_Suc__mult__le__cancel1) ).
thf(759,plain,
! [A: nat,B: nat,C: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(570,axiom,
! [A: fun_Pr2067565481t_bool,B: fun_fu638310559l_bool] :
( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ A ) @ B ) )
<=> ( hBOOL @ ( hAPP_f52567537l_bool @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_mem__def) ).
thf(2792,plain,
! [A: fun_Pr2067565481t_bool,B: fun_fu638310559l_bool] :
( ( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ B @ A ) ) )
& ( ( hBOOL @ ( hAPP_f52567537l_bool @ B @ A ) )
=> ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(327,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_491_xt1_I7_J) ).
thf(1807,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(279,axiom,
! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool] :
( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ A ) @ B ) )
<=> ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_394_less__le__not__le) ).
thf(1590,plain,
! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool] :
( ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ B ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ A ) @ B ) )
& ~ ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(295,axiom,
! [A: nat,B: nat] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_409_linorder__antisym__conv1) ).
thf(1646,plain,
! [A: nat,B: nat] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(210,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1105_le__imp__less__Suc) ).
thf(1385,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(434,axiom,
! [A: arrow_856714788e_indi,B: arrow_856714788e_indi,C: fun_Ar671024215di_nat,D: fun_Ar1809396326i_bool] :
( ( hBOOL @ ( hAPP_f584385070l_bool @ ( inj_on1960344199di_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_f584385070l_bool @ ( hAPP_A1597696899l_bool @ member1479139729e_indi @ B ) @ D ) )
=> ( ( hBOOL @ ( hAPP_f584385070l_bool @ ( hAPP_A1597696899l_bool @ member1479139729e_indi @ A ) @ D ) )
=> ( ( ( hAPP_A376526755di_nat @ C @ B )
= ( hAPP_A376526755di_nat @ C @ A ) )
<=> ( B = A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_543_inj__on__iff) ).
thf(2167,plain,
! [A: arrow_856714788e_indi,B: arrow_856714788e_indi,C: fun_Ar671024215di_nat,D: fun_Ar1809396326i_bool] :
( ( hBOOL @ ( hAPP_f584385070l_bool @ ( inj_on1960344199di_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_f584385070l_bool @ ( hAPP_A1597696899l_bool @ member1479139729e_indi @ B ) @ D ) )
=> ( ( hBOOL @ ( hAPP_f584385070l_bool @ ( hAPP_A1597696899l_bool @ member1479139729e_indi @ A ) @ D ) )
=> ( ( ( ( hAPP_A376526755di_nat @ C @ B )
= ( hAPP_A376526755di_nat @ C @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP_A376526755di_nat @ C @ B )
= ( hAPP_A376526755di_nat @ C @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(416,axiom,
! [A: fun_fu638310559l_bool,B: fun_Ar274636406t_bool] :
( ( hAPP_f1915815064l_bool @ ( hAPP_f1104294872l_bool @ cOMBK_1701906001t_bool @ A ) @ B )
= 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(2098,plain,
! [A: fun_fu638310559l_bool,B: fun_Ar274636406t_bool] :
( ( hAPP_f1915815064l_bool @ ( hAPP_f1104294872l_bool @ cOMBK_1701906001t_bool @ A ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(240,axiom,
! [A: fun_Pr2067565481t_bool,B: fun_Pr1780397033l_bool,C: fun_Pr2067565481t_bool] :
( ! [D: produc472769767le_alt] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ D ) @ C ) )
=> ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ ( hAPP_P1178790471t_bool @ A @ D ) ) @ ( hAPP_P1103642805l_bool @ B @ D ) ) ) )
=> ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ A ) @ ( pi_Pro1238944957t_bool @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_648_Pi__I) ).
thf(1481,plain,
! [A: fun_Pr2067565481t_bool,B: fun_Pr1780397033l_bool,C: fun_Pr2067565481t_bool] :
( ! [D: produc472769767le_alt] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ D ) @ C ) )
=> ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ ( hAPP_P1178790471t_bool @ A @ D ) ) @ ( hAPP_P1103642805l_bool @ B @ D ) ) ) )
=> ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ A ) @ ( pi_Pro1238944957t_bool @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(17,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1144_mult__le__mono) ).
thf(652,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ D ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(386,axiom,
hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ lab ) @ arrow_1361987423le_Lin ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74__096Lab_A_058_ALin_096) ).
thf(2004,plain,
hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ lab ) @ arrow_1361987423le_Lin ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(254,axiom,
! [A: fun_fu1677555470ol_nat,B: nat,C: fun_Ar331856045t_bool,D: fun_Ar331856045t_bool] :
( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_f1403773274ol_nat @ A @ D ) ) @ B ) )
=> ( ! [E: fun_Ar331856045t_bool,F: fun_Ar331856045t_bool] :
( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ E ) @ F ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f1403773274ol_nat @ A @ E ) ) @ ( hAPP_f1403773274ol_nat @ A @ F ) ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_f1403773274ol_nat @ A @ C ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_888_order__le__less__subst2) ).
thf(1523,plain,
! [A: fun_fu1677555470ol_nat,B: nat,C: fun_Ar331856045t_bool,D: fun_Ar331856045t_bool] :
( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_f1403773274ol_nat @ A @ D ) ) @ B ) )
=> ( ! [E: fun_Ar331856045t_bool,F: fun_Ar331856045t_bool] :
( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ E ) @ F ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f1403773274ol_nat @ A @ E ) ) @ ( hAPP_f1403773274ol_nat @ A @ F ) ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_f1403773274ol_nat @ A @ C ) ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(36,axiom,
! [A: nat] :
( ( hAPP_nat_nat @ suc @ A )
!= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1068_nat_Osimps_I3_J) ).
thf(731,plain,
! [A: nat] :
( ( hAPP_nat_nat @ suc @ A )
!= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(457,axiom,
! [A: fun_Pr2067565481t_bool,B: fun_na998785244t_bool,C: nat,D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ ( hAPP_n1161265524t_bool @ B @ C ) ) )
=> ( ! [E: nat,F: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ F ) @ E ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ ( hAPP_n1161265524t_bool @ B @ F ) ) @ ( hAPP_n1161265524t_bool @ B @ E ) ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ A ) @ ( hAPP_n1161265524t_bool @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_667_xt5) ).
thf(2262,plain,
! [A: fun_Pr2067565481t_bool,B: fun_na998785244t_bool,C: nat,D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ ( hAPP_n1161265524t_bool @ B @ C ) ) )
=> ( ! [E: nat,F: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ F ) @ E ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ ( hAPP_n1161265524t_bool @ B @ F ) ) @ ( hAPP_n1161265524t_bool @ B @ E ) ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ A ) @ ( hAPP_n1161265524t_bool @ B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(4,axiom,
! [A: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ zero_zero_nat )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1155_mult__0__right) ).
thf(588,plain,
! [A: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ zero_zero_nat )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(172,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1019_add__le__mono1) ).
thf(1253,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(30,axiom,
! [A: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ one_one_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1146_nat__mult__1__right) ).
thf(699,plain,
! [A: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(426,axiom,
! [A: fun_nat_fun_nat_bool,B: nat,C: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ A @ C ) @ B ) ) )
=> ( ( ( B = C )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ A @ C ) @ B ) ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ A @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ A @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_987_nat__less__cases) ).
thf(2135,plain,
! [A: fun_nat_fun_nat_bool,B: nat,C: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ A @ C ) @ B ) ) )
=> ( ( ( B = C )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ A @ C ) @ B ) ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ A @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ A @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(480,axiom,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
( ( A = B )
<=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ B ) )
& ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_358_order__eq__iff) ).
thf(2406,plain,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
( ( ( A = B )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ B ) )
& ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ B ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ B ) )
& ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ B ) @ A ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(499,axiom,
! [A: bool,B: fun_bool_bool,C: fun_bool_bool] :
( ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_f612708895l_bool @ ord_le742797417l_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_913_subsetD) ).
thf(2532,plain,
! [A: bool,B: fun_bool_bool,C: fun_bool_bool] :
( ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_f612708895l_bool @ ord_le742797417l_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(249,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1048_gr0I) ).
thf(1508,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(93,axiom,
! [A: bool,B: fun_bo1431306493t_bool,C: fun_bool_bool,D: fun_fu638310559l_bool] :
( ( hBOOL @ ( hAPP_f398210311l_bool @ ( hAPP_f416878261l_bool @ member1133581546t_bool @ B ) @ ( pi_boo1111177555t_bool @ C @ ( hAPP_f86272063l_bool @ cOMBK_650639032l_bool @ D ) ) ) )
=> ( ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ ( hAPP_b128655177t_bool @ B @ A ) ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_605_funcset__mem) ).
thf(946,plain,
! [A: bool,B: fun_bo1431306493t_bool,C: fun_bool_bool,D: fun_fu638310559l_bool] :
( ( hBOOL @ ( hAPP_f398210311l_bool @ ( hAPP_f416878261l_bool @ member1133581546t_bool @ B ) @ ( pi_boo1111177555t_bool @ C @ ( hAPP_f86272063l_bool @ cOMBK_650639032l_bool @ D ) ) ) )
=> ( ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ ( hAPP_b128655177t_bool @ B @ A ) ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(136,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1077_less__SucI) ).
thf(1101,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(389,axiom,
! [A: fun_Ar274636406t_bool] : ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ A ) @ top_to553140914l_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_iso__tuple__UNIV__I) ).
thf(2009,plain,
! [A: fun_Ar274636406t_bool] : ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ A ) @ top_to553140914l_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(409,axiom,
! [A: nat,B: nat] :
( ( A = B )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_995_eq__imp__le) ).
thf(2081,plain,
! [A: nat,B: nat] :
( ( A = B )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(399,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
<=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
& ( A != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_386_order__less__le) ).
thf(2041,plain,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
& ( A != B ) ) )
& ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
& ( A != B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(543,axiom,
! [A: fun_Ar338949104le_alt,B: fun_Ar274636406t_bool,C: fun_Ar1809396326i_bool] :
( ! [D: arrow_856714788e_indi] :
( ( hBOOL @ ( hAPP_f584385070l_bool @ ( hAPP_A1597696899l_bool @ member1479139729e_indi @ D ) @ C ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A899858958le_alt @ A @ D ) ) @ ( hAPP_A1646126530t_bool @ B @ D ) ) ) )
=> ( hBOOL @ ( hAPP_f1754488902l_bool @ ( hAPP_f766019597l_bool @ member387840963le_alt @ A ) @ ( pi_Arr1460528004le_alt @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_634_Pi__I) ).
thf(2648,plain,
! [A: fun_Ar338949104le_alt,B: fun_Ar274636406t_bool,C: fun_Ar1809396326i_bool] :
( ! [D: arrow_856714788e_indi] :
( ( hBOOL @ ( hAPP_f584385070l_bool @ ( hAPP_A1597696899l_bool @ member1479139729e_indi @ D ) @ C ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A899858958le_alt @ A @ D ) ) @ ( hAPP_A1646126530t_bool @ B @ D ) ) ) )
=> ( hBOOL @ ( hAPP_f1754488902l_bool @ ( hAPP_f766019597l_bool @ member387840963le_alt @ A ) @ ( pi_Arr1460528004le_alt @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(184,axiom,
! [A: fun_nat_nat] :
( ! [B: nat,C: nat] :
( ( ( hAPP_nat_nat @ A @ B )
= ( hAPP_nat_nat @ A @ C ) )
=> ( B = C ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ A ) @ top_top_fun_nat_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_657_injI) ).
thf(1294,plain,
! [A: fun_nat_nat] :
( ! [B: nat,C: nat] :
( ( ( hAPP_nat_nat @ A @ B )
= ( hAPP_nat_nat @ A @ C ) )
=> ( B = C ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ A ) @ top_top_fun_nat_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(158,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_736_add__le__imp__le__right) ).
thf(1193,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(251,axiom,
! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool] :
( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ B ) @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_xt1_I5_J) ).
thf(1513,plain,
! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool] :
( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ B ) @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(299,axiom,
! [A: fun_Ar290235730t_bool,B: arrow_1893660431le_alt,C: arrow_856714788e_indi] :
( ( hAPP_A1309733808t_bool @ ( hAPP_A1889513822t_bool @ ( hAPP_f2102110817t_bool @ cOMBC_1486904681t_bool @ A ) @ B ) @ C )
= ( hAPP_A1058422557t_bool @ ( hAPP_A38124190t_bool @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000_417) ).
thf(1661,plain,
! [A: fun_Ar290235730t_bool,B: arrow_1893660431le_alt,C: arrow_856714788e_indi] :
( ( hAPP_A1309733808t_bool @ ( hAPP_A1889513822t_bool @ ( hAPP_f2102110817t_bool @ cOMBC_1486904681t_bool @ A ) @ B ) @ C )
= ( hAPP_A1058422557t_bool @ ( hAPP_A38124190t_bool @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(229,axiom,
! [A: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ top_top_fun_nat_bool @ A ) )
<=> ( hBOOL @ top_top_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_top__apply) ).
thf(1442,plain,
! [A: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ top_top_fun_nat_bool @ A ) )
=> ( hBOOL @ top_top_bool ) )
& ( ( hBOOL @ top_top_bool )
=> ( hBOOL @ ( hAPP_nat_bool @ top_top_fun_nat_bool @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(397,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_994_nat__le__linear) ).
thf(2036,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(189,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1026_termination__basic__simps_I4_J) ).
thf(1309,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(423,axiom,
! [A: fun_fu841105374ol_nat,B: nat,C: fun_Pr2067565481t_bool,D: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_f1842225014ol_nat @ A @ D ) ) @ B ) )
=> ( ! [E: fun_Pr2067565481t_bool,F: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ E ) @ F ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f1842225014ol_nat @ A @ E ) ) @ ( hAPP_f1842225014ol_nat @ A @ F ) ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_f1842225014ol_nat @ A @ C ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_884_order__le__less__subst2) ).
thf(2123,plain,
! [A: fun_fu841105374ol_nat,B: nat,C: fun_Pr2067565481t_bool,D: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_f1842225014ol_nat @ A @ D ) ) @ B ) )
=> ( ! [E: fun_Pr2067565481t_bool,F: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ E ) @ F ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f1842225014ol_nat @ A @ E ) ) @ ( hAPP_f1842225014ol_nat @ A @ F ) ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_f1842225014ol_nat @ A @ C ) ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(43,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) )
<=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_732_add__left__cancel) ).
thf(752,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) )
=> ( B = C ) )
& ( ( B = C )
=> ( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(99,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_654_add__less__le__mono) ).
thf(967,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ D ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(165,axiom,
! [A: nat,B: nat] :
( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B )
= ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1083_add__Suc__shift) ).
thf(1229,plain,
! [A: nat,B: nat] :
( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B )
= ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(349,axiom,
! [A: arrow_856714788e_indi,B: arrow_856714788e_indi,C: fun_Ar671024215di_nat,D: fun_Ar1809396326i_bool] :
( ( hBOOL @ ( hAPP_f584385070l_bool @ ( inj_on1960344199di_nat @ C ) @ D ) )
=> ( ( ( hAPP_A376526755di_nat @ C @ A )
= ( hAPP_A376526755di_nat @ C @ B ) )
=> ( ( hBOOL @ ( hAPP_f584385070l_bool @ ( hAPP_A1597696899l_bool @ member1479139729e_indi @ A ) @ D ) )
=> ( ( hBOOL @ ( hAPP_f584385070l_bool @ ( hAPP_A1597696899l_bool @ member1479139729e_indi @ B ) @ D ) )
=> ( A = B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_545_inj__onD) ).
thf(1876,plain,
! [A: arrow_856714788e_indi,B: arrow_856714788e_indi,C: fun_Ar671024215di_nat,D: fun_Ar1809396326i_bool] :
( ( hBOOL @ ( hAPP_f584385070l_bool @ ( inj_on1960344199di_nat @ C ) @ D ) )
=> ( ( ( hAPP_A376526755di_nat @ C @ A )
= ( hAPP_A376526755di_nat @ C @ B ) )
=> ( ( hBOOL @ ( hAPP_f584385070l_bool @ ( hAPP_A1597696899l_bool @ member1479139729e_indi @ A ) @ D ) )
=> ( ( hBOOL @ ( hAPP_f584385070l_bool @ ( hAPP_A1597696899l_bool @ member1479139729e_indi @ B ) @ D ) )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(379,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_order__less__trans) ).
thf(1986,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(74,axiom,
! [A: nat,B: nat] :
( ( ( hAPP_nat_nat @ suc @ zero_zero_nat )
= ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) )
<=> ( ( ( A
= ( hAPP_nat_nat @ suc @ zero_zero_nat ) )
& ( B = zero_zero_nat ) )
| ( ( A = zero_zero_nat )
& ( B
= ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1098_one__is__add) ).
thf(867,plain,
! [A: nat,B: nat] :
( ( ( ( hAPP_nat_nat @ suc @ zero_zero_nat )
= ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) )
=> ( ( ( A
= ( hAPP_nat_nat @ suc @ zero_zero_nat ) )
& ( B = zero_zero_nat ) )
| ( ( A = zero_zero_nat )
& ( B
= ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) ) ) )
& ( ( ( ( A
= ( hAPP_nat_nat @ suc @ zero_zero_nat ) )
& ( B = zero_zero_nat ) )
| ( ( A = zero_zero_nat )
& ( B
= ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) ) )
=> ( ( hAPP_nat_nat @ suc @ zero_zero_nat )
= ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(7,axiom,
! [A: nat] :
( ( hAPP_nat_nat @ size_size_nat @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1184_nat__size) ).
thf(603,plain,
! [A: nat] :
( ( hAPP_nat_nat @ size_size_nat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(37,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1005_add__less__mono) ).
thf(735,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ D ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(500,axiom,
! [A: bool,B: fun_Pr2067565481t_bool] :
( ( hAPP_f52567537l_bool @ ( hAPP_b1272691967l_bool @ cOMBK_81143760t_bool @ A ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__prod_Itc__Arrow____Order_) ).
thf(2534,plain,
! [A: bool,B: fun_Pr2067565481t_bool] :
( ( hAPP_f52567537l_bool @ ( hAPP_b1272691967l_bool @ cOMBK_81143760t_bool @ A ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(455,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_481_order__less__le__trans) ).
thf(2255,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(95,axiom,
! [A: nat,B: fun_na300967376t_bool,C: nat,D: fun_Ar331856045t_bool] :
( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ ( hAPP_n1312530466t_bool @ B @ C ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) )
=> ( ! [E: nat,F: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ F ) @ E ) )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ ( hAPP_n1312530466t_bool @ B @ F ) ) @ ( hAPP_n1312530466t_bool @ B @ E ) ) ) )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ ( hAPP_n1312530466t_bool @ B @ A ) ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_780_xt4) ).
thf(950,plain,
! [A: nat,B: fun_na300967376t_bool,C: nat,D: fun_Ar331856045t_bool] :
( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ ( hAPP_n1312530466t_bool @ B @ C ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) )
=> ( ! [E: nat,F: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ F ) @ E ) )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ ( hAPP_n1312530466t_bool @ B @ F ) ) @ ( hAPP_n1312530466t_bool @ B @ E ) ) ) )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ ( hAPP_n1312530466t_bool @ B @ A ) ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(66,axiom,
! [A: nat] :
( zero_zero_nat
!= ( hAPP_nat_nat @ suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1070_nat_Osimps_I2_J) ).
thf(835,plain,
! [A: nat] :
( zero_zero_nat
!= ( hAPP_nat_nat @ suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(214,axiom,
! [A: fun_fu638310559l_bool] : ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ A ) @ top_to1312956197l_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_512_top__greatest) ).
thf(1395,plain,
! [A: fun_fu638310559l_bool] : ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ A ) @ top_to1312956197l_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(288,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_order__less__not__sym) ).
thf(1625,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(52,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_737_add__mono) ).
thf(790,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ D ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(400,axiom,
! [A: arrow_856714788e_indi,B: fun_Ar671024215di_nat] :
( ( hBOOL @ ( hAPP_f584385070l_bool @ ( inj_on1960344199di_nat @ B ) @ top_to788185952i_bool ) )
=> ( ( hAPP_n1937165849e_indi @ ( hilber1580028780di_nat @ top_to788185952i_bool @ B ) @ ( hAPP_A376526755di_nat @ B @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_inv__f__f) ).
thf(2050,plain,
! [A: arrow_856714788e_indi,B: fun_Ar671024215di_nat] :
( ( hBOOL @ ( hAPP_f584385070l_bool @ ( inj_on1960344199di_nat @ B ) @ top_to788185952i_bool ) )
=> ( ( hAPP_n1937165849e_indi @ ( hilber1580028780di_nat @ top_to788185952i_bool @ B ) @ ( hAPP_A376526755di_nat @ B @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(538,axiom,
! [A: bool,B: fun_bo1682907689le_alt,C: fun_bool_bool,D: fun_bo1431306493t_bool] :
( ( hBOOL @ ( hAPP_f1620711039l_bool @ ( hAPP_f334747853l_bool @ member684813948le_alt @ B ) @ ( pi_boo7125949le_alt @ C @ D ) ) )
=> ( ~ ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_b2094455111le_alt @ B @ A ) ) @ ( hAPP_b128655177t_bool @ D @ A ) ) )
=> ~ ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_PiE) ).
thf(2636,plain,
! [A: bool,B: fun_bo1682907689le_alt,C: fun_bool_bool,D: fun_bo1431306493t_bool] :
( ( hBOOL @ ( hAPP_f1620711039l_bool @ ( hAPP_f334747853l_bool @ member684813948le_alt @ B ) @ ( pi_boo7125949le_alt @ C @ D ) ) )
=> ( ~ ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_b2094455111le_alt @ B @ A ) ) @ ( hAPP_b128655177t_bool @ D @ A ) ) )
=> ~ ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(56,axiom,
! [A: nat,B: nat] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_999_not__add__less1) ).
thf(801,plain,
! [A: nat,B: nat] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(203,axiom,
! [A: nat,B: nat] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1091_not__less__eq__eq) ).
thf(1363,plain,
! [A: nat,B: nat] :
( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ B ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ B ) ) @ A ) )
=> ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(330,axiom,
! [A: arrow_856714788e_indi,B: nat,C: fun_Ar671024215di_nat] :
( ( hBOOL @ ( hAPP_f584385070l_bool @ ( inj_on1960344199di_nat @ C ) @ top_to788185952i_bool ) )
=> ( ( ( hAPP_A376526755di_nat @ C @ A )
= B )
=> ( ( hAPP_n1937165849e_indi @ ( hilber1580028780di_nat @ top_to788185952i_bool @ C ) @ B )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_inv__f__eq) ).
thf(1816,plain,
! [A: arrow_856714788e_indi,B: nat,C: fun_Ar671024215di_nat] :
( ( hBOOL @ ( hAPP_f584385070l_bool @ ( inj_on1960344199di_nat @ C ) @ top_to788185952i_bool ) )
=> ( ( ( hAPP_A376526755di_nat @ C @ A )
= B )
=> ( ( hAPP_n1937165849e_indi @ ( hilber1580028780di_nat @ top_to788185952i_bool @ C ) @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(58,axiom,
! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1061_zero__less__Suc) ).
thf(807,plain,
! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(514,axiom,
! [A: fun_Ar339057223l_bool,B: fun_Pr2067565481t_bool,C: arrow_1893660431le_alt] :
( ( hAPP_A1748732503t_bool @ ( hAPP_f234621849t_bool @ ( hAPP_f1689397393t_bool @ cOMBC_395465908l_bool @ A ) @ B ) @ C )
= ( hAPP_f52567537l_bool @ ( hAPP_A442239897l_bool @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_000t) ).
thf(2572,plain,
! [A: fun_Ar339057223l_bool,B: fun_Pr2067565481t_bool,C: arrow_1893660431le_alt] :
( ( hAPP_A1748732503t_bool @ ( hAPP_f234621849t_bool @ ( hAPP_f1689397393t_bool @ cOMBC_395465908l_bool @ A ) @ B ) @ C )
= ( hAPP_f52567537l_bool @ ( hAPP_A442239897l_bool @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(559,axiom,
hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ c ) @ d ) ) @ ( hAPP_A1646126530t_bool @ p @ ( hAPP_n1937165849e_indi @ ( hilber1580028780di_nat @ top_to788185952i_bool @ h ) @ n ) ) ),
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(2704,plain,
hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ c ) @ d ) ) @ ( hAPP_A1646126530t_bool @ p @ ( hAPP_n1937165849e_indi @ ( hilber1580028780di_nat @ top_to788185952i_bool @ h ) @ n ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(481,axiom,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ ( hAPP_f449303873t_bool @ ( hAPP_f1081591777t_bool @ cOMBC_557453916t_bool @ ( hAPP_f105674721t_bool @ ( cOMBB_652885079le_alt @ cOMBC_395465908l_bool ) @ ( hAPP_f184584489l_bool @ ( cOMBB_1575576719le_alt @ ( cOMBB_1660064607le_alt @ member1333168212le_alt ) ) @ produc1590937303le_alt ) ) ) @ A ) ) @ ( hAPP_f449303873t_bool @ ( hAPP_f1081591777t_bool @ cOMBC_557453916t_bool @ ( hAPP_f105674721t_bool @ ( cOMBB_652885079le_alt @ cOMBC_395465908l_bool ) @ ( hAPP_f184584489l_bool @ ( cOMBB_1575576719le_alt @ ( cOMBB_1660064607le_alt @ member1333168212le_alt ) ) @ produc1590937303le_alt ) ) ) @ B ) ) )
<=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_718_pred__subset__eq2) ).
thf(2417,plain,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
( ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ ( hAPP_f449303873t_bool @ ( hAPP_f1081591777t_bool @ cOMBC_557453916t_bool @ ( hAPP_f105674721t_bool @ ( cOMBB_652885079le_alt @ cOMBC_395465908l_bool ) @ ( hAPP_f184584489l_bool @ ( cOMBB_1575576719le_alt @ ( cOMBB_1660064607le_alt @ member1333168212le_alt ) ) @ produc1590937303le_alt ) ) ) @ A ) ) @ ( hAPP_f449303873t_bool @ ( hAPP_f1081591777t_bool @ cOMBC_557453916t_bool @ ( hAPP_f105674721t_bool @ ( cOMBB_652885079le_alt @ cOMBC_395465908l_bool ) @ ( hAPP_f184584489l_bool @ ( cOMBB_1575576719le_alt @ ( cOMBB_1660064607le_alt @ member1333168212le_alt ) ) @ produc1590937303le_alt ) ) ) @ B ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ ( hAPP_f449303873t_bool @ ( hAPP_f1081591777t_bool @ cOMBC_557453916t_bool @ ( hAPP_f105674721t_bool @ ( cOMBB_652885079le_alt @ cOMBC_395465908l_bool ) @ ( hAPP_f184584489l_bool @ ( cOMBB_1575576719le_alt @ ( cOMBB_1660064607le_alt @ member1333168212le_alt ) ) @ produc1590937303le_alt ) ) ) @ A ) ) @ ( hAPP_f449303873t_bool @ ( hAPP_f1081591777t_bool @ cOMBC_557453916t_bool @ ( hAPP_f105674721t_bool @ ( cOMBB_652885079le_alt @ cOMBC_395465908l_bool ) @ ( hAPP_f184584489l_bool @ ( cOMBB_1575576719le_alt @ ( cOMBB_1660064607le_alt @ member1333168212le_alt ) ) @ produc1590937303le_alt ) ) ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(22,axiom,
! [A: nat,B: nat] :
( ( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B )
= ( hAPP_nat_nat @ suc @ zero_zero_nat ) )
<=> ( ( A
= ( hAPP_nat_nat @ suc @ zero_zero_nat ) )
& ( B
= ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1157_mult__eq__1__iff) ).
thf(664,plain,
! [A: nat,B: nat] :
( ( ( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B )
= ( hAPP_nat_nat @ suc @ zero_zero_nat ) )
=> ( ( A
= ( hAPP_nat_nat @ suc @ zero_zero_nat ) )
& ( B
= ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) ) )
& ( ( ( A
= ( hAPP_nat_nat @ suc @ zero_zero_nat ) )
& ( B
= ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) )
=> ( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B )
= ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(13,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1143_mult__le__mono2) ).
thf(635,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(29,axiom,
! [A: nat,B: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( times_times_nat @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1174_nat__mult__commute) ).
thf(696,plain,
! [A: nat,B: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B )
= ( hAPP_nat_nat @ ( times_times_nat @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(549,axiom,
! [A: produc472769767le_alt,B: fun_Pr1509342064e_indi,C: fun_Pr2067565481t_bool,D: fun_Pr895221296i_bool] :
( ( hBOOL @ ( hAPP_f2124588998l_bool @ ( hAPP_f1187850253l_bool @ member1558233923e_indi @ B ) @ ( pi_Pro837265796e_indi @ C @ D ) ) )
=> ( ~ ( hBOOL @ ( hAPP_f584385070l_bool @ ( hAPP_A1597696899l_bool @ member1479139729e_indi @ ( hAPP_P276596750e_indi @ B @ A ) ) @ ( hAPP_P1859429372i_bool @ D @ A ) ) )
=> ~ ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_PiE) ).
thf(2668,plain,
! [A: produc472769767le_alt,B: fun_Pr1509342064e_indi,C: fun_Pr2067565481t_bool,D: fun_Pr895221296i_bool] :
( ( hBOOL @ ( hAPP_f2124588998l_bool @ ( hAPP_f1187850253l_bool @ member1558233923e_indi @ B ) @ ( pi_Pro837265796e_indi @ C @ D ) ) )
=> ( ~ ( hBOOL @ ( hAPP_f584385070l_bool @ ( hAPP_A1597696899l_bool @ member1479139729e_indi @ ( hAPP_P276596750e_indi @ B @ A ) ) @ ( hAPP_P1859429372i_bool @ D @ A ) ) )
=> ~ ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(393,axiom,
! [A: arrow_856714788e_indi,B: arrow_856714788e_indi,C: fun_Ar671024215di_nat] :
( ( hBOOL @ ( hAPP_f584385070l_bool @ ( inj_on1960344199di_nat @ C ) @ top_to788185952i_bool ) )
=> ( ( ( hAPP_A376526755di_nat @ C @ A )
= ( hAPP_A376526755di_nat @ C @ B ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_614_injD) ).
thf(2021,plain,
! [A: arrow_856714788e_indi,B: arrow_856714788e_indi,C: fun_Ar671024215di_nat] :
( ( hBOOL @ ( hAPP_f584385070l_bool @ ( inj_on1960344199di_nat @ C ) @ top_to788185952i_bool ) )
=> ( ( ( hAPP_A376526755di_nat @ C @ A )
= ( hAPP_A376526755di_nat @ C @ B ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(544,axiom,
! [A: produc472769767le_alt] : ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ A ) @ top_to1138392227t_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_UNIV__I) ).
thf(2651,plain,
! [A: produc472769767le_alt] : ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ A ) @ top_to1138392227t_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(76,axiom,
! [A: fun_fu638310559l_bool,B: fun_fu955147676ol_nat,C: fun_fu638310559l_bool,D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_f1487854056ol_nat @ B @ C ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ A ) @ C ) )
=> ( ! [E: fun_fu638310559l_bool,F: fun_fu638310559l_bool] :
( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ F ) @ E ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f1487854056ol_nat @ B @ F ) ) @ ( hAPP_f1487854056ol_nat @ B @ E ) ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_f1487854056ol_nat @ B @ A ) ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_798_xt4) ).
thf(886,plain,
! [A: fun_fu638310559l_bool,B: fun_fu955147676ol_nat,C: fun_fu638310559l_bool,D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_f1487854056ol_nat @ B @ C ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ A ) @ C ) )
=> ( ! [E: fun_fu638310559l_bool,F: fun_fu638310559l_bool] :
( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ F ) @ E ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f1487854056ol_nat @ B @ F ) ) @ ( hAPP_f1487854056ol_nat @ B @ E ) ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_f1487854056ol_nat @ B @ A ) ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(115,axiom,
! [A: nat,B: fun_nat_nat] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ B ) @ top_top_fun_nat_bool ) )
=> ( ( hAPP_nat_nat @ ( hilber195283148at_nat @ top_top_fun_nat_bool @ B ) @ ( hAPP_nat_nat @ B @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_inv__f__f) ).
thf(1033,plain,
! [A: nat,B: fun_nat_nat] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( inj_on_nat_nat @ B ) @ top_top_fun_nat_bool ) )
=> ( ( hAPP_nat_nat @ ( hilber195283148at_nat @ top_top_fun_nat_bool @ B ) @ ( hAPP_nat_nat @ B @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(182,axiom,
! [A: nat] :
( ( hAPP_nat_nat @ suc @ A )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1064_Suc__n__not__n) ).
thf(1288,plain,
! [A: nat] :
( ( hAPP_nat_nat @ suc @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(105,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1176_nat__mult__le__cancel1) ).
thf(987,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ C ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( times_times_nat @ C ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(200,axiom,
! [A: fun_fu638310559l_bool,B: fun_fu638310559l_bool] :
( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ B ) @ A ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_order__antisym) ).
thf(1352,plain,
! [A: fun_fu638310559l_bool,B: fun_fu638310559l_bool] :
( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ B ) @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(377,axiom,
! [A: fun_fu2114379172t_bool] :
( ( hBOOL @ ( hAPP_f1572141188l_bool @ top_to827110112l_bool @ A ) )
<=> ( hBOOL @ top_top_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_top__apply) ).
thf(1977,plain,
! [A: fun_fu2114379172t_bool] :
( ( ( hBOOL @ ( hAPP_f1572141188l_bool @ top_to827110112l_bool @ A ) )
=> ( hBOOL @ top_top_bool ) )
& ( ( hBOOL @ top_top_bool )
=> ( hBOOL @ ( hAPP_f1572141188l_bool @ top_to827110112l_bool @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(492,axiom,
! [A: fun_fu2114379172t_bool] :
( ( hBOOL @ ( hAPP_f1572141188l_bool @ arrow_1335103695le_IIA @ A ) )
<=> ! [B: fun_Ar274636406t_bool] :
( ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ B ) @ arrow_5070731e_Prof ) )
=> ! [C: fun_Ar274636406t_bool] :
( ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ C ) @ arrow_5070731e_Prof ) )
=> ! [D: arrow_1893660431le_alt,E: arrow_1893660431le_alt] :
( ! [F: arrow_856714788e_indi] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ D ) @ E ) ) @ ( hAPP_A1646126530t_bool @ B @ F ) ) )
<=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ D ) @ E ) ) @ ( hAPP_A1646126530t_bool @ C @ F ) ) ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ D ) @ E ) ) @ ( hAPP_f2008608496t_bool @ A @ B ) ) )
<=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ D ) @ E ) ) @ ( hAPP_f2008608496t_bool @ A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_IIA__def) ).
thf(2485,plain,
! [A: fun_fu2114379172t_bool] :
( ( ( hBOOL @ ( hAPP_f1572141188l_bool @ arrow_1335103695le_IIA @ A ) )
=> ! [B: fun_Ar274636406t_bool] :
( ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ B ) @ arrow_5070731e_Prof ) )
=> ! [C: fun_Ar274636406t_bool] :
( ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ C ) @ arrow_5070731e_Prof ) )
=> ! [D: arrow_1893660431le_alt,E: arrow_1893660431le_alt] :
( ! [F: arrow_856714788e_indi] :
( ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ D ) @ E ) ) @ ( hAPP_A1646126530t_bool @ B @ F ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ D ) @ E ) ) @ ( hAPP_A1646126530t_bool @ C @ F ) ) ) )
& ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ D ) @ E ) ) @ ( hAPP_A1646126530t_bool @ C @ F ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ D ) @ E ) ) @ ( hAPP_A1646126530t_bool @ B @ F ) ) ) ) )
=> ( ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ D ) @ E ) ) @ ( hAPP_f2008608496t_bool @ A @ B ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ D ) @ E ) ) @ ( hAPP_f2008608496t_bool @ A @ C ) ) ) )
& ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ D ) @ E ) ) @ ( hAPP_f2008608496t_bool @ A @ C ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ D ) @ E ) ) @ ( hAPP_f2008608496t_bool @ A @ B ) ) ) ) ) ) ) ) )
& ( ! [B: fun_Ar274636406t_bool] :
( ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ B ) @ arrow_5070731e_Prof ) )
=> ! [C: fun_Ar274636406t_bool] :
( ( hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ C ) @ arrow_5070731e_Prof ) )
=> ! [D: arrow_1893660431le_alt,E: arrow_1893660431le_alt] :
( ! [F: arrow_856714788e_indi] :
( ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ D ) @ E ) ) @ ( hAPP_A1646126530t_bool @ B @ F ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ D ) @ E ) ) @ ( hAPP_A1646126530t_bool @ C @ F ) ) ) )
& ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ D ) @ E ) ) @ ( hAPP_A1646126530t_bool @ C @ F ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ D ) @ E ) ) @ ( hAPP_A1646126530t_bool @ B @ F ) ) ) ) )
=> ( ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ D ) @ E ) ) @ ( hAPP_f2008608496t_bool @ A @ B ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ D ) @ E ) ) @ ( hAPP_f2008608496t_bool @ A @ C ) ) ) )
& ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ D ) @ E ) ) @ ( hAPP_f2008608496t_bool @ A @ C ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ D ) @ E ) ) @ ( hAPP_f2008608496t_bool @ A @ B ) ) ) ) ) ) ) )
=> ( hBOOL @ ( hAPP_f1572141188l_bool @ arrow_1335103695le_IIA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(487,axiom,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ B ) )
=> ( ( A != B )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_457_order__le__neq__trans) ).
thf(2467,plain,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ B ) )
=> ( ( A != B )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(246,axiom,
! [A: produc472769767le_alt,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool,D: fun_Pr1780397033l_bool] :
( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ B ) @ ( pi_Pro1238944957t_bool @ C @ D ) ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ ( hAPP_P1178790471t_bool @ B @ A ) ) @ ( hAPP_P1103642805l_bool @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_547_Pi__mem) ).
thf(1500,plain,
! [A: produc472769767le_alt,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool,D: fun_Pr1780397033l_bool] :
( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1482930381l_bool @ member1069471740t_bool @ B ) @ ( pi_Pro1238944957t_bool @ C @ D ) ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_f387058535l_bool @ ( hAPP_b1787118453l_bool @ member_bool @ ( hAPP_P1178790471t_bool @ B @ A ) ) @ ( hAPP_P1103642805l_bool @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(502,axiom,
hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ e ) @ d ) ) @ ( hAPP_f2008608496t_bool @ f @ ( hAPP_f1302887663t_bool @ ( cOMBS_1181656689t_bool @ ( hAPP_f1001205955t_bool @ ( cOMBS_1925466437t_bool @ ( hAPP_f668886383t_bool @ ( cOMBB_1061985500e_indi @ if_fun523439385t_bool ) @ ( hAPP_n34002993i_bool @ ( hAPP_f721434149i_bool @ cOMBC_722552198t_bool @ ( hAPP_f966656047t_bool @ ( cOMBB_1869811296e_indi @ ord_less_nat ) @ h ) ) @ n ) ) ) @ ( hAPP_A425126512t_bool @ ( hAPP_f1631649925t_bool @ cOMBC_1417338747t_bool @ ( hAPP_f831214557t_bool @ ( cOMBB_80760910e_indi @ arrow_1630265669_mktop ) @ p ) ) @ e ) ) ) @ ( hAPP_f1302887663t_bool @ ( cOMBS_1181656689t_bool @ ( hAPP_f1001205955t_bool @ ( cOMBS_1925466437t_bool @ ( hAPP_f668886383t_bool @ ( cOMBB_1061985500e_indi @ if_fun523439385t_bool ) @ ( hAPP_n34002993i_bool @ ( hAPP_f721434149i_bool @ cOMBC_722552198t_bool @ ( hAPP_f966656047t_bool @ ( cOMBB_1869811296e_indi @ fequal_nat ) @ h ) ) @ n ) ) ) @ ( hAPP_A425126512t_bool @ ( hAPP_f1631649925t_bool @ cOMBC_1417338747t_bool @ ( hAPP_A1889513822t_bool @ ( hAPP_f2102110817t_bool @ cOMBC_1486904681t_bool @ ( hAPP_f1751344075t_bool @ ( cOMBB_1876517692e_indi @ arrow_216713899_above ) @ p ) ) @ c ) ) @ e ) ) ) @ ( hAPP_A425126512t_bool @ ( hAPP_f1631649925t_bool @ cOMBC_1417338747t_bool @ ( hAPP_f831214557t_bool @ ( cOMBB_80760910e_indi @ arrow_1481558583_mkbot ) @ p ) ) @ e ) ) ) ) ),
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(2539,plain,
hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ e ) @ d ) ) @ ( hAPP_f2008608496t_bool @ f @ ( hAPP_f1302887663t_bool @ ( cOMBS_1181656689t_bool @ ( hAPP_f1001205955t_bool @ ( cOMBS_1925466437t_bool @ ( hAPP_f668886383t_bool @ ( cOMBB_1061985500e_indi @ if_fun523439385t_bool ) @ ( hAPP_n34002993i_bool @ ( hAPP_f721434149i_bool @ cOMBC_722552198t_bool @ ( hAPP_f966656047t_bool @ ( cOMBB_1869811296e_indi @ ord_less_nat ) @ h ) ) @ n ) ) ) @ ( hAPP_A425126512t_bool @ ( hAPP_f1631649925t_bool @ cOMBC_1417338747t_bool @ ( hAPP_f831214557t_bool @ ( cOMBB_80760910e_indi @ arrow_1630265669_mktop ) @ p ) ) @ e ) ) ) @ ( hAPP_f1302887663t_bool @ ( cOMBS_1181656689t_bool @ ( hAPP_f1001205955t_bool @ ( cOMBS_1925466437t_bool @ ( hAPP_f668886383t_bool @ ( cOMBB_1061985500e_indi @ if_fun523439385t_bool ) @ ( hAPP_n34002993i_bool @ ( hAPP_f721434149i_bool @ cOMBC_722552198t_bool @ ( hAPP_f966656047t_bool @ ( cOMBB_1869811296e_indi @ fequal_nat ) @ h ) ) @ n ) ) ) @ ( hAPP_A425126512t_bool @ ( hAPP_f1631649925t_bool @ cOMBC_1417338747t_bool @ ( hAPP_A1889513822t_bool @ ( hAPP_f2102110817t_bool @ cOMBC_1486904681t_bool @ ( hAPP_f1751344075t_bool @ ( cOMBB_1876517692e_indi @ arrow_216713899_above ) @ p ) ) @ c ) ) @ e ) ) ) @ ( hAPP_A425126512t_bool @ ( hAPP_f1631649925t_bool @ cOMBC_1417338747t_bool @ ( hAPP_f831214557t_bool @ ( cOMBB_80760910e_indi @ arrow_1481558583_mkbot ) @ p ) ) @ e ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(185,axiom,
! [A: nat,B: nat,C: fun_nat_nat] :
( ! [D: nat,E: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ D ) @ E ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ C @ D ) ) @ ( hAPP_nat_nat @ C @ E ) ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ ( hAPP_nat_nat @ C @ A ) ) @ B ) ) @ ( hAPP_nat_nat @ C @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1023_mono__nat__linear__lb) ).
thf(1299,plain,
! [A: nat,B: nat,C: fun_nat_nat] :
( ! [D: nat,E: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ D ) @ E ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ C @ D ) ) @ ( hAPP_nat_nat @ C @ E ) ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ ( hAPP_nat_nat @ C @ A ) ) @ B ) ) @ ( hAPP_nat_nat @ C @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(364,axiom,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fTrue_1_1_T) ).
thf(1930,plain,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(473,axiom,
! [A: produc472769767le_alt,B: fun_Pr376858015t_unit,C: fun_Pr2067565481t_bool,D: fun_Pr1069395679t_bool] :
( ( hBOOL @ ( hAPP_f1159856629l_bool @ ( hAPP_f1700632141l_bool @ member1303779570t_unit @ B ) @ ( pi_Pro346842291t_unit @ C @ D ) ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ ( hAPP_P1069491261t_unit @ B @ A ) ) @ ( hAPP_P2037731755t_bool @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_549_Pi__mem) ).
thf(2353,plain,
! [A: produc472769767le_alt,B: fun_Pr376858015t_unit,C: fun_Pr2067565481t_bool,D: fun_Pr1069395679t_bool] :
( ( hBOOL @ ( hAPP_f1159856629l_bool @ ( hAPP_f1700632141l_bool @ member1303779570t_unit @ B ) @ ( pi_Pro346842291t_unit @ C @ D ) ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_f2028818269l_bool @ ( hAPP_P607165281l_bool @ member_Product_unit @ ( hAPP_P1069491261t_unit @ B @ A ) ) @ ( hAPP_P2037731755t_bool @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(67,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1001_nat__add__left__cancel__less) ).
thf(839,plain,
! [A: nat,B: nat,C: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(35,axiom,
! [A: nat,B: nat] :
( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B )
= ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1084_add__Suc) ).
thf(728,plain,
! [A: nat,B: nat] :
( ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B )
= ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(39,axiom,
! [A: fun_Ar535288606t_bool,B: fun_Pr2067565481t_bool,C: arrow_856714788e_indi] :
( ( hAPP_A834130326t_bool @ ( hAPP_f1344464862t_bool @ ( hAPP_f1908974253t_bool @ cOMBC_156709173t_bool @ A ) @ B ) @ C )
= ( hAPP_f1299954409t_bool @ ( hAPP_A1395684458t_bool @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000_426) ).
thf(740,plain,
! [A: fun_Ar535288606t_bool,B: fun_Pr2067565481t_bool,C: arrow_856714788e_indi] :
( ( hAPP_A834130326t_bool @ ( hAPP_f1344464862t_bool @ ( hAPP_f1908974253t_bool @ cOMBC_156709173t_bool @ A ) @ B ) @ C )
= ( hAPP_f1299954409t_bool @ ( hAPP_A1395684458t_bool @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(275,axiom,
! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool,C: fun_Ar331856045t_bool] :
( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_499_order__le__less__trans) ).
thf(1582,plain,
! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool,C: fun_Ar331856045t_bool] :
( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(458,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_365_linorder__linear) ).
thf(2265,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(555,axiom,
! [A: arrow_856714788e_indi,B: fun_Ar338949104le_alt,C: fun_Ar1809396326i_bool,D: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f1754488902l_bool @ ( hAPP_f766019597l_bool @ member387840963le_alt @ B ) @ ( pi_Arr1460528004le_alt @ C @ ( hAPP_f480276746t_bool @ cOMBK_1650320063e_indi @ D ) ) ) )
=> ( ( hBOOL @ ( hAPP_f584385070l_bool @ ( hAPP_A1597696899l_bool @ member1479139729e_indi @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A899858958le_alt @ B @ A ) ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_596_funcset__mem) ).
thf(2687,plain,
! [A: arrow_856714788e_indi,B: fun_Ar338949104le_alt,C: fun_Ar1809396326i_bool,D: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f1754488902l_bool @ ( hAPP_f766019597l_bool @ member387840963le_alt @ B ) @ ( pi_Arr1460528004le_alt @ C @ ( hAPP_f480276746t_bool @ cOMBK_1650320063e_indi @ D ) ) ) )
=> ( ( hBOOL @ ( hAPP_f584385070l_bool @ ( hAPP_A1597696899l_bool @ member1479139729e_indi @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A899858958le_alt @ B @ A ) ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(578,axiom,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
( ! [C: arrow_1893660431le_alt,D: arrow_1893660431le_alt] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ C ) @ D ) ) @ B ) )
<=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ C ) @ D ) ) @ A ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_pred__equals__eq2) ).
thf(2864,plain,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
( ( ! [C: arrow_1893660431le_alt,D: arrow_1893660431le_alt] :
( ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ C ) @ D ) ) @ B ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ C ) @ D ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ C ) @ D ) ) @ A ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ C ) @ D ) ) @ B ) ) ) )
=> ( B = A ) )
& ( ( B = A )
=> ! [C: arrow_1893660431le_alt,D: arrow_1893660431le_alt] :
( ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ C ) @ D ) ) @ B ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ C ) @ D ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ C ) @ D ) ) @ A ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_P38525833l_bool @ member1333168212le_alt @ ( hAPP_A1299015393le_alt @ ( hAPP_A1146194953le_alt @ produc1590937303le_alt @ C ) @ D ) ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(248,axiom,
! [A: nat] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_984_less__irrefl__nat) ).
thf(1505,plain,
! [A: nat] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(287,axiom,
! [A: nat,B: nat,C: nat] :
( ( B = C )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_ord__eq__le__trans) ).
thf(1621,plain,
! [A: nat,B: nat,C: nat] :
( ( B = C )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(540,axiom,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_497_order__le__less__trans) ).
thf(2640,plain,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(91,axiom,
! [A: fun_fu638310559l_bool,B: fun_fu638310559l_bool,C: fun_fu638310559l_bool] :
( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ B ) @ C ) )
=> ( ( C = A )
=> ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_ord__le__eq__trans) ).
thf(940,plain,
! [A: fun_fu638310559l_bool,B: fun_fu638310559l_bool,C: fun_fu638310559l_bool] :
( ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ B ) @ C ) )
=> ( ( C = A )
=> ( hBOOL @ ( hAPP_f182583295l_bool @ ( hAPP_f1722316607l_bool @ ord_le1545885909l_bool @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(316,axiom,
! [A: nat,B: fun_na300967376t_bool,C: nat,D: fun_Ar331856045t_bool] :
( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ ( hAPP_n1312530466t_bool @ B @ C ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) )
=> ( ! [E: nat,F: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ F ) @ E ) )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ ( hAPP_n1312530466t_bool @ B @ F ) ) @ ( hAPP_n1312530466t_bool @ B @ E ) ) ) )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ ( hAPP_n1312530466t_bool @ B @ A ) ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_768_xt6) ).
thf(1737,plain,
! [A: nat,B: fun_na300967376t_bool,C: nat,D: fun_Ar331856045t_bool] :
( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ ( hAPP_n1312530466t_bool @ B @ C ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) )
=> ( ! [E: nat,F: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ F ) @ E ) )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ ( hAPP_n1312530466t_bool @ B @ F ) ) @ ( hAPP_n1312530466t_bool @ B @ E ) ) ) )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ ( hAPP_n1312530466t_bool @ B @ A ) ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(243,axiom,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_xt1_I6_J) ).
thf(1490,plain,
! [A: nat,B: nat,C: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(472,axiom,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_951_subset__psubset__trans) ).
thf(2351,plain,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ C ) @ A ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(411,axiom,
! [A: nat,B: fun_na998785244t_bool,C: nat,D: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ ( hAPP_n1161265524t_bool @ B @ C ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) )
=> ( ! [E: nat,F: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ F ) @ E ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ ( hAPP_n1161265524t_bool @ B @ F ) ) @ ( hAPP_n1161265524t_bool @ B @ E ) ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ ( hAPP_n1161265524t_bool @ B @ A ) ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_766_xt6) ).
thf(2087,plain,
! [A: nat,B: fun_na998785244t_bool,C: nat,D: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ ( hAPP_n1161265524t_bool @ B @ C ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) )
=> ( ! [E: nat,F: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ F ) @ E ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ ( hAPP_n1161265524t_bool @ B @ F ) ) @ ( hAPP_n1161265524t_bool @ B @ E ) ) ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ ( hAPP_n1161265524t_bool @ B @ A ) ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(488,axiom,
! [A: fun_fu2114379172t_bool] : ( hBOOL @ ( hAPP_f1572141188l_bool @ top_to827110112l_bool @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_top1I) ).
thf(2470,plain,
! [A: fun_fu2114379172t_bool] : ( hBOOL @ ( hAPP_f1572141188l_bool @ top_to827110112l_bool @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(359,axiom,
! [A: nat,B: nat] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ A ) @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Nat__Onat_T) ).
thf(1912,plain,
! [A: nat,B: nat] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ A ) @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(546,axiom,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_487_xt1_I7_J) ).
thf(2655,plain,
! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool,C: fun_Pr2067565481t_bool] :
( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1577377523t_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f52567537l_bool @ ( hAPP_f930900275l_bool @ ord_le1478665215t_bool @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(90,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ ( hAPP_nat_nat @ suc @ B ) ) )
<=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1080_Suc__less__eq) ).
thf(935,plain,
! [A: nat,B: nat] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ ( hAPP_nat_nat @ suc @ B ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ ( hAPP_nat_nat @ suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(109,axiom,
! [A: nat,B: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1100_less__add__Suc2) ).
thf(1009,plain,
! [A: nat,B: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(20,axiom,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ C )
= ( hAPP_nat_nat @ ( times_times_nat @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1175_nat__mult__assoc) ).
thf(659,plain,
! [A: nat,B: nat,C: nat] :
( ( hAPP_nat_nat @ ( times_times_nat @ ( hAPP_nat_nat @ ( times_times_nat @ A ) @ B ) ) @ C )
= ( hAPP_nat_nat @ ( times_times_nat @ A ) @ ( hAPP_nat_nat @ ( times_times_nat @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(269,axiom,
! [A: fun_Ar331856045t_bool,B: fun_fu1677555470ol_nat,C: fun_Ar331856045t_bool,D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_f1403773274ol_nat @ B @ C ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ A ) @ C ) )
=> ( ! [E: fun_Ar331856045t_bool,F: fun_Ar331856045t_bool] :
( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ F ) @ E ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f1403773274ol_nat @ B @ F ) ) @ ( hAPP_f1403773274ol_nat @ B @ E ) ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_f1403773274ol_nat @ B @ A ) ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_805_xt4) ).
thf(1565,plain,
! [A: fun_Ar331856045t_bool,B: fun_fu1677555470ol_nat,C: fun_Ar331856045t_bool,D: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_f1403773274ol_nat @ B @ C ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ A ) @ C ) )
=> ( ! [E: fun_Ar331856045t_bool,F: fun_Ar331856045t_bool] :
( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ F ) @ E ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f1403773274ol_nat @ B @ F ) ) @ ( hAPP_f1403773274ol_nat @ B @ E ) ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_f1403773274ol_nat @ B @ A ) ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(341,axiom,
! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool,C: fun_Ar331856045t_bool] :
( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ B ) @ C ) )
=> ( ( C = A )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_ord__le__eq__trans) ).
thf(1848,plain,
! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool,C: fun_Ar331856045t_bool] :
( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ B ) @ C ) )
=> ( ( C = A )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(403,axiom,
! [A: fun_Pr2067565481t_bool,B: product_unit] :
( ( hAPP_P1914371027t_bool @ ( hAPP_f15777819t_bool @ cOMBK_681766254t_unit @ A ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ef_403) ).
thf(2059,plain,
! [A: fun_Pr2067565481t_bool,B: product_unit] :
( ( hAPP_P1914371027t_bool @ ( hAPP_f15777819t_bool @ cOMBK_681766254t_unit @ A ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(439,axiom,
! [A: nat,B: nat] :
( ( A != B )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_419_order__neq__le__trans) ).
thf(2191,plain,
! [A: nat,B: nat] :
( ( A != B )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(231,axiom,
! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool] :
( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ A ) @ B ) )
<=> ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ A ) @ B ) )
& ( A != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_384_order__less__le) ).
thf(1449,plain,
! [A: fun_Ar331856045t_bool,B: fun_Ar331856045t_bool] :
( ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ A ) @ B ) )
& ( A != B ) ) )
& ( ( ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le172225251t_bool @ A ) @ B ) )
& ( A != B ) )
=> ( hBOOL @ ( hAPP_f1452856589l_bool @ ( hAPP_f1055587775l_bool @ ord_le19409623t_bool @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(329,axiom,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_order__less__imp__not__eq) ).
thf(1812,plain,
! [A: nat,B: nat] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(221,axiom,
! [A: nat,B: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1013_le__add2) ).
thf(1417,plain,
! [A: nat,B: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ ( hAPP_nat_fun_nat_nat @ plus_plus_nat @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(346,axiom,
hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ ( hAPP_f1302887663t_bool @ ( cOMBS_1181656689t_bool @ ( hAPP_f1001205955t_bool @ ( cOMBS_1925466437t_bool @ ( hAPP_f668886383t_bool @ ( cOMBB_1061985500e_indi @ if_fun523439385t_bool ) @ ( hAPP_n34002993i_bool @ ( hAPP_f721434149i_bool @ cOMBC_722552198t_bool @ ( hAPP_f966656047t_bool @ ( cOMBB_1869811296e_indi @ ord_less_nat ) @ h ) ) @ n ) ) ) @ ( hAPP_A425126512t_bool @ ( hAPP_f1631649925t_bool @ cOMBC_1417338747t_bool @ ( hAPP_f831214557t_bool @ ( cOMBB_80760910e_indi @ arrow_1630265669_mktop ) @ p ) ) @ e ) ) ) @ ( hAPP_f1302887663t_bool @ ( cOMBS_1181656689t_bool @ ( hAPP_f1001205955t_bool @ ( cOMBS_1925466437t_bool @ ( hAPP_f668886383t_bool @ ( cOMBB_1061985500e_indi @ if_fun523439385t_bool ) @ ( hAPP_n34002993i_bool @ ( hAPP_f721434149i_bool @ cOMBC_722552198t_bool @ ( hAPP_f966656047t_bool @ ( cOMBB_1869811296e_indi @ fequal_nat ) @ h ) ) @ n ) ) ) @ ( hAPP_A425126512t_bool @ ( hAPP_f1631649925t_bool @ cOMBC_1417338747t_bool @ ( hAPP_A1889513822t_bool @ ( hAPP_f2102110817t_bool @ cOMBC_1486904681t_bool @ ( hAPP_f1751344075t_bool @ ( cOMBB_1876517692e_indi @ arrow_216713899_above ) @ p ) ) @ c ) ) @ e ) ) ) @ ( hAPP_A425126512t_bool @ ( hAPP_f1631649925t_bool @ cOMBC_1417338747t_bool @ ( hAPP_f831214557t_bool @ ( cOMBB_80760910e_indi @ arrow_1481558583_mkbot ) @ p ) ) @ e ) ) ) ) @ arrow_5070731e_Prof ),
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(1870,plain,
hBOOL @ ( hAPP_f73423488l_bool @ ( hAPP_f1225332775l_bool @ member933336803t_bool @ ( hAPP_f1302887663t_bool @ ( cOMBS_1181656689t_bool @ ( hAPP_f1001205955t_bool @ ( cOMBS_1925466437t_bool @ ( hAPP_f668886383t_bool @ ( cOMBB_1061985500e_indi @ if_fun523439385t_bool ) @ ( hAPP_n34002993i_bool @ ( hAPP_f721434149i_bool @ cOMBC_722552198t_bool @ ( hAPP_f966656047t_bool @ ( cOMBB_1869811296e_indi @ ord_less_nat ) @ h ) ) @ n ) ) ) @ ( hAPP_A425126512t_bool @ ( hAPP_f1631649925t_bool @ cOMBC_1417338747t_bool @ ( hAPP_f831214557t_bool @ ( cOMBB_80760910e_indi @ arrow_1630265669_mktop ) @ p ) ) @ e ) ) ) @ ( hAPP_f1302887663t_bool @ ( cOMBS_1181656689t_bool @ ( hAPP_f1001205955t_bool @ ( cOMBS_1925466437t_bool @ ( hAPP_f668886383t_bool @ ( cOMBB_1061985500e_indi @ if_fun523439385t_bool ) @ ( hAPP_n34002993i_bool @ ( hAPP_f721434149i_bool @ cOMBC_722552198t_bool @ ( hAPP_f966656047t_bool @ ( cOMBB_1869811296e_indi @ fequal_nat ) @ h ) ) @ n ) ) ) @ ( hAPP_A425126512t_bool @ ( hAPP_f1631649925t_bool @ cOMBC_1417338747t_bool @ ( hAPP_A1889513822t_bool @ ( hAPP_f2102110817t_bool @ cOMBC_1486904681t_bool @ ( hAPP_f1751344075t_bool @ ( cOMBB_1876517692e_indi @ arrow_216713899_above ) @ p ) ) @ c ) ) @ e ) ) ) @ ( hAPP_A425126512t_bool @ ( hAPP_f1631649925t_bool @ cOMBC_1417338747t_bool @ ( hAPP_f831214557t_bool @ ( cOMBB_80760910e_indi @ arrow_1481558583_mkbot ) @ p ) ) @ e ) ) ) ) @ arrow_5070731e_Prof ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(2884,plain,
$false,
inference(e,[status(thm)],[2163,1036,1879,2031,2072,1559,1729,1237,1031,1982,1956,1586,809,2094,1411,1823,1190,1315,2595,1686,2250,1855,1596,683,1882,2622,2644,2062,1618,1939,1073,1205,2282,2671,2676,2114,1142,1497,1078,1671,1655,1137,1999,1275,814,2627,1640,1954,1458,2575,1988,2459,1835,1391,782,1613,2173,2516,1887,1746,898,1243,1127,973,1046,1724,1475,2067,1529,2603,1430,785,2269,1871,1313,1577,2562,2126,1055,1409,1860,1264,2217,1511,917,702,1462,1059,2745,2356,1545,1922,2857,1115,1568,2024,1232,1892,1379,969,606,2007,924,1946,646,2880,1828,1151,2555,2335,1051,905,2178,2222,1302,1664,2090,591,1040,1632,1858,2122,1677,2540,766,1843,2618,1896,2424,1526,1345,1433,1943,2586,1447,2483,2523,1796,2718,2205,1604,2011,1306,2118,1311,1067,798,1470,1915,714,2382,2589,2705,746,2601,1042,1519,1255,862,2147,1666,1487,693,2606,2132,1387,910,1343,2560,1355,1580,1502,820,788,1370,1602,2670,1920,625,2565,2609,889,1787,2327,2344,1634,2112,1740,1573,2653,852,2826,1195,1407,1360,948,1534,2509,2631,2537,593,2638,1397,1270,1259,1121,2359,1375,2577,1064,2709,1970,980,2692,2694,1425,1540,1006,1160,2323,1182,2312,2349,2038,2085,1889,2472,1419,2460,2798,1028,1082,1292,933,901,686,1414,2053,2196,1842,637,1584,622,1324,1099,654,1974,2355,2465,721,1799,1874,2862,1246,1715,779,1627,1249,2519,2153,1831,1552,2243,1002,1852,1333,2634,1086,2208,1187,1616,662,1732,926,1991,1318,1202,792,2748,1170,1286,2368,1026,1167,953,1185,773,1996,1135,2001,965,2677,1754,1680,1103,2585,824,1273,2570,1548,2028,2253,2275,2149,975,1884,2657,1652,743,958,1701,1965,1226,1784,1389,2674,2016,2568,826,711,1428,1092,804,1464,1224,2358,1675,764,2079,2521,2721,831,2478,1011,1542,737,649,1690,2642,2229,2422,1117,990,1933,2257,1589,2246,1492,1571,1439,2180,811,2812,609,2267,2757,848,1838,2542,1381,2329,1820,1112,858,1557,2314,2625,1630,1993,1909,1162,2278,2553,912,1926,1699,2212,2620,883,1176,2797,2101,2156,922,2069,1562,1044,2550,2592,1435,1948,1809,2096,1304,1208,944,1467,795,1472,1018,2582,1049,2005,1076,749,2629,1845,1748,1070,2661,1611,1941,1531,2689,580,2715,690,1516,1743,1400,1368,2175,1484,2160,2224,1637,1262,2219,1658,1130,1336,1711,1053,673,2092,1538,2545,2056,1536,2145,1372,612,2848,2584,1240,1898,1257,656,1802,1972,2711,2579,864,978,2511,2013,1839,1459,1685,1321,2215,891,2743,2110,844,1108,688,903,2194,581,2611,759,2792,1807,1590,1646,1385,2167,2098,1481,652,2004,1523,731,2262,588,1253,699,2135,2406,2532,1508,946,1101,2009,2081,2041,2648,1294,1193,1513,1661,1442,2036,1309,2123,752,967,1229,1876,1986,867,603,735,2534,2255,950,835,1395,1625,790,2050,2636,801,1363,1816,807,2572,2704,2417,664,635,696,2668,2021,2651,886,1033,1288,987,1352,1977,2485,2467,1500,2539,1299,1930,2353,839,728,740,1582,2265,2687,2864,1505,1621,2640,940,1737,1490,2351,2087,2470,1912,2655,935,1009,659,1565,1848,2059,2191,1449,1812,1417,1870]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SCT171_3 : TPTP v8.1.2. Released v5.3.0.
% 0.13/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n011.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Thu May 18 15:30:49 EDT 2023
% 0.16/0.36 % CPUTime :
% 0.83/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.29/1.19 % [INFO] Parsing done (356ms).
% 2.44/1.20 % [INFO] Running in sequential loop mode.
% 2.82/1.40 % [INFO] eprover registered as external prover.
% 2.82/1.40 % [INFO] cvc4 registered as external prover.
% 2.82/1.41 % [INFO] Scanning for conjecture ...
% 3.63/1.64 % [INFO] Found a conjecture and 1278 axioms. Running axiom selection ...
% 4.58/1.95 % [INFO] Axiom selection finished. Selected 577 axioms (removed 701 axioms).
% 5.63/2.24 % [INFO] Problem is typed first-order (TPTP TFF).
% 5.63/2.25 % [INFO] Type checking passed.
% 5.63/2.25 % [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 ...
% 10.68/3.53 % [INFO] [Domain constraints] Detected constraint on bool
% 10.68/3.53 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 11.18/3.65 % [INFO] [Domain constraints] Detected constraint on bool
% 11.18/3.65 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 11.34/3.71 % [INFO] [Domain constraints] Detected constraint on bool
% 11.34/3.71 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 17.63/5.16 % External prover 'e' found a proof!
% 17.63/5.16 % [INFO] Killing All external provers ...
% 17.63/5.16 % Time passed: 4647ms (effective reasoning time: 3956ms)
% 17.63/5.16 % 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)>
% 17.63/5.17 % 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
% 17.63/5.17 % No. of inferences in proof: 1158
% 17.63/5.17 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4647 ms resp. 3956 ms w/o parsing
% 18.86/5.46 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 18.86/5.47 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------