%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SWW474_2 : TPTP v8.2.0. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n008.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 : Tue May 21 06:50:11 EDT 2024

% Result   : Theorem 95.62s 23.55s
% Output   : Refutation 97.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      : 1346
% Syntax   : Number of formulae    : 2162 ( 576 unt; 532 typ;   0 def)
%            Number of atoms       : 4157 (1347 equ;   0 cnn)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives : 28400 ( 501   ~; 115   |; 381   &;25372   @)
%                                         ( 116 <=>;1915  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   25 (   9 avg)
%            Number of types       :  177 ( 176 usr)
%            Number of type conns  :  423 ( 423   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  358 ( 356 usr; 112 con; 0-2 aty)
%            Number of variables   : 4329 (   0   ^4211   !; 118   ?;4329   :)

% Comments : 
%------------------------------------------------------------------------------
thf(com_type,type,
    com: $tType ).

thf(pname_type,type,
    pname: $tType ).

thf(state_type,type,
    state: $tType ).

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

thf(hoare_1875481847_state_type,type,
    hoare_1875481847_state: $tType ).

thf(option_com_type,type,
    option_com: $tType ).

thf(option_pname_type,type,
    option_pname: $tType ).

thf(option1681283416_state_type,type,
    option1681283416_state: $tType ).

thf(fun_com_bool_type,type,
    fun_com_bool: $tType ).

thf(fun_co2032091866_state_type,type,
    fun_co2032091866_state: $tType ).

thf(fun_co1633267573l_bool_type,type,
    fun_co1633267573l_bool: $tType ).

thf(fun_co2038576728m_bool_type,type,
    fun_co2038576728m_bool: $tType ).

thf(fun_co879055186_state_type,type,
    fun_co879055186_state: $tType ).

thf(fun_pname_com_type,type,
    fun_pname_com: $tType ).

thf(fun_pname_pname_type,type,
    fun_pname_pname: $tType ).

thf(fun_pname_bool_type,type,
    fun_pname_bool: $tType ).

thf(fun_pn664418900_state_type,type,
    fun_pn664418900_state: $tType ).

thf(fun_pname_option_com_type,type,
    fun_pname_option_com: $tType ).

thf(fun_pn92346699_state_type,type,
    fun_pn92346699_state: $tType ).

thf(fun_pn1208287926_pname_type,type,
    fun_pn1208287926_pname: $tType ).

thf(fun_pn800050071e_bool_type,type,
    fun_pn800050071e_bool: $tType ).

thf(fun_pn12888928e_bool_type,type,
    fun_pn12888928e_bool: $tType ).

thf(fun_pn250273176l_bool_type,type,
    fun_pn250273176l_bool: $tType ).

thf(fun_pn760644914e_bool_type,type,
    fun_pn760644914e_bool: $tType ).

thf(fun_pn1776597836_state_type,type,
    fun_pn1776597836_state: $tType ).

thf(fun_pn1243268074_state_type,type,
    fun_pn1243268074_state: $tType ).

thf(fun_pn1580610524on_com_type,type,
    fun_pn1580610524on_com: $tType ).

thf(fun_pn1673019570on_com_type,type,
    fun_pn1673019570on_com: $tType ).

thf(fun_pn422929397l_bool_type,type,
    fun_pn422929397l_bool: $tType ).

thf(fun_pn479984722e_bool_type,type,
    fun_pn479984722e_bool: $tType ).

thf(fun_pn1610849624_state_type,type,
    fun_pn1610849624_state: $tType ).

thf(fun_pn249986828l_bool_type,type,
    fun_pn249986828l_bool: $tType ).

thf(fun_state_bool_type,type,
    fun_state_bool: $tType ).

thf(fun_st1506752259e_bool_type,type,
    fun_st1506752259e_bool: $tType ).

thf(fun_st858662806e_bool_type,type,
    fun_st858662806e_bool: $tType ).

thf(fun_st2116860965l_bool_type,type,
    fun_st2116860965l_bool: $tType ).

thf(fun_st2063251938l_bool_type,type,
    fun_st2063251938l_bool: $tType ).

thf(fun_st1483075957e_bool_type,type,
    fun_st1483075957e_bool: $tType ).

thf(fun_st277393160e_bool_type,type,
    fun_st277393160e_bool: $tType ).

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

thf(fun_bo1936561970e_bool_type,type,
    fun_bo1936561970e_bool: $tType ).

thf(fun_bo898473669e_bool_type,type,
    fun_bo898473669e_bool: $tType ).

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

thf(fun_bo840793679_state_type,type,
    fun_bo840793679_state: $tType ).

thf(fun_bo79750167on_com_type,type,
    fun_bo79750167on_com: $tType ).

thf(fun_Ho1653816318_pname_type,type,
    fun_Ho1653816318_pname: $tType ).

thf(fun_Ho1996104121e_bool_type,type,
    fun_Ho1996104121e_bool: $tType ).

thf(fun_Ho1455141843_state_type,type,
    fun_Ho1455141843_state: $tType ).

thf(fun_Ho14659478e_bool_type,type,
    fun_Ho14659478e_bool: $tType ).

thf(fun_Ho1896286681l_bool_type,type,
    fun_Ho1896286681l_bool: $tType ).

thf(fun_Ho1695028467e_bool_type,type,
    fun_Ho1695028467e_bool: $tType ).

thf(fun_Ho784854669_state_type,type,
    fun_Ho784854669_state: $tType ).

thf(fun_Ho760178998l_bool_type,type,
    fun_Ho760178998l_bool: $tType ).

thf(fun_Ho1085560331l_bool_type,type,
    fun_Ho1085560331l_bool: $tType ).

thf(fun_Ho1110608055e_bool_type,type,
    fun_Ho1110608055e_bool: $tType ).

thf(fun_option_com_com_type,type,
    fun_option_com_com: $tType ).

thf(fun_op606842979on_com_type,type,
    fun_op606842979on_com: $tType ).

thf(fun_op564655445on_com_type,type,
    fun_op564655445on_com: $tType ).

thf(fun_fu1362071682l_bool_type,type,
    fun_fu1362071682l_bool: $tType ).

thf(fun_fu241528037m_bool_type,type,
    fun_fu241528037m_bool: $tType ).

thf(fun_fu973320112_state_type,type,
    fun_fu973320112_state: $tType ).

thf(fun_fu642263570_state_type,type,
    fun_fu642263570_state: $tType ).

thf(fun_fu264874349e_bool_type,type,
    fun_fu264874349e_bool: $tType ).

thf(fun_fu1499449723_pname_type,type,
    fun_fu1499449723_pname: $tType ).

thf(fun_fu1430349052l_bool_type,type,
    fun_fu1430349052l_bool: $tType ).

thf(fun_fu1604182422_state_type,type,
    fun_fu1604182422_state: $tType ).

thf(fun_fu410713561e_bool_type,type,
    fun_fu410713561e_bool: $tType ).

thf(fun_fu1286003254e_bool_type,type,
    fun_fu1286003254e_bool: $tType ).

thf(fun_fu152205775l_bool_type,type,
    fun_fu152205775l_bool: $tType ).

thf(fun_fu2016078089_state_type,type,
    fun_fu2016078089_state: $tType ).

thf(fun_fu637830609on_com_type,type,
    fun_fu637830609on_com: $tType ).

thf(fun_fu31783638l_bool_type,type,
    fun_fu31783638l_bool: $tType ).

thf(fun_fu1176632176e_bool_type,type,
    fun_fu1176632176e_bool: $tType ).

thf(fun_fu802393907l_bool_type,type,
    fun_fu802393907l_bool: $tType ).

thf(fun_fu2101097872e_bool_type,type,
    fun_fu2101097872e_bool: $tType ).

thf(fun_fu514526030l_bool_type,type,
    fun_fu514526030l_bool: $tType ).

thf(fun_fu931343505l_bool_type,type,
    fun_fu931343505l_bool: $tType ).

thf(fun_fu1232732404l_bool_type,type,
    fun_fu1232732404l_bool: $tType ).

thf(fun_fu1904437005_state_type,type,
    fun_fu1904437005_state: $tType ).

thf(fun_fu557884239e_bool_type,type,
    fun_fu557884239e_bool: $tType ).

thf(fun_fu1869380457_state_type,type,
    fun_fu1869380457_state: $tType ).

thf(fun_fu1742234008me_com_type,type,
    fun_fu1742234008me_com: $tType ).

thf(fun_fu311741085on_com_type,type,
    fun_fu311741085on_com: $tType ).

thf(fun_fu544728625on_com_type,type,
    fun_fu544728625on_com: $tType ).

thf(fun_fu993978052_state_type,type,
    fun_fu993978052_state: $tType ).

thf(fun_fu25451830e_bool_type,type,
    fun_fu25451830e_bool: $tType ).

thf(fun_fu577621651e_bool_type,type,
    fun_fu577621651e_bool: $tType ).

thf(fun_fu1779604751l_bool_type,type,
    fun_fu1779604751l_bool: $tType ).

thf(fun_fu2087509785_state_type,type,
    fun_fu2087509785_state: $tType ).

thf(fun_fu2096203996_state_type,type,
    fun_fu2096203996_state: $tType ).

thf(fun_fu1576495102e_bool_type,type,
    fun_fu1576495102e_bool: $tType ).

thf(fun_fu2056752087l_bool_type,type,
    fun_fu2056752087l_bool: $tType ).

thf(fun_fu1045989665e_bool_type,type,
    fun_fu1045989665e_bool: $tType ).

thf(fun_fu1646366334_state_type,type,
    fun_fu1646366334_state: $tType ).

thf(fun_fu1848601144_state_type,type,
    fun_fu1848601144_state: $tType ).

thf(fun_fu1908735358on_com_type,type,
    fun_fu1908735358on_com: $tType ).

thf(fun_fu1867668424on_com_type,type,
    fun_fu1867668424on_com: $tType ).

thf(fun_fu696558561e_bool_type,type,
    fun_fu696558561e_bool: $tType ).

thf(fun_fu1018334113e_bool_type,type,
    fun_fu1018334113e_bool: $tType ).

thf(fun_fu1956604286_state_type,type,
    fun_fu1956604286_state: $tType ).

thf(fun_fu1543647229e_bool_type,type,
    fun_fu1543647229e_bool: $tType ).

thf(fun_fu93307442l_bool_type,type,
    fun_fu93307442l_bool: $tType ).

thf(fun_fu373216837e_bool_type,type,
    fun_fu373216837e_bool: $tType ).

thf(fun_fu1998731480e_bool_type,type,
    fun_fu1998731480e_bool: $tType ).

thf(fun_fu1658206819l_bool_type,type,
    fun_fu1658206819l_bool: $tType ).

thf(fun_fu827928799_state_type,type,
    fun_fu827928799_state: $tType ).

thf(fun_fu404278912_state_type,type,
    fun_fu404278912_state: $tType ).

thf(fun_fu2104550360e_bool_type,type,
    fun_fu2104550360e_bool: $tType ).

thf(fun_fu402792811e_bool_type,type,
    fun_fu402792811e_bool: $tType ).

thf(fun_fu475229566e_bool_type,type,
    fun_fu475229566e_bool: $tType ).

thf(fun_fu1982748883l_bool_type,type,
    fun_fu1982748883l_bool: $tType ).

thf(fun_fu1867913342e_bool_type,type,
    fun_fu1867913342e_bool: $tType ).

thf(fun_fu1454697805e_bool_type,type,
    fun_fu1454697805e_bool: $tType ).

thf(fun_fu1088452192e_bool_type,type,
    fun_fu1088452192e_bool: $tType ).

thf(fun_fu1219323149e_bool_type,type,
    fun_fu1219323149e_bool: $tType ).

thf(fun_fu1047394976e_bool_type,type,
    fun_fu1047394976e_bool: $tType ).

thf(fun_fu13754701e_bool_type,type,
    fun_fu13754701e_bool: $tType ).

thf(fun_fu1436120077e_bool_type,type,
    fun_fu1436120077e_bool: $tType ).

thf(fun_fu2020320649e_bool_type,type,
    fun_fu2020320649e_bool: $tType ).

thf(fun_fu235184776_pname_type,type,
    fun_fu235184776_pname: $tType ).

thf(fun_fu689207471l_bool_type,type,
    fun_fu689207471l_bool: $tType ).

thf(fun_fu385705929_state_type,type,
    fun_fu385705929_state: $tType ).

thf(fun_fu1040518284e_bool_type,type,
    fun_fu1040518284e_bool: $tType ).

thf(fun_fu854396771l_bool_type,type,
    fun_fu854396771l_bool: $tType ).

thf(fun_fu1296727421e_bool_type,type,
    fun_fu1296727421e_bool: $tType ).

thf(fun_fu811519275l_bool_type,type,
    fun_fu811519275l_bool: $tType ).

thf(fun_fu775812037e_bool_type,type,
    fun_fu775812037e_bool: $tType ).

thf(fun_fu1962076352l_bool_type,type,
    fun_fu1962076352l_bool: $tType ).

thf(fun_fu1173762305l_bool_type,type,
    fun_fu1173762305l_bool: $tType ).

thf(fun_fu947547457e_bool_type,type,
    fun_fu947547457e_bool: $tType ).

thf(fun_fu2083718837l_bool_type,type,
    fun_fu2083718837l_bool: $tType ).

thf(fun_fu2107095047l_bool_type,type,
    fun_fu2107095047l_bool: $tType ).

thf(fun_fu1653236447e_bool_type,type,
    fun_fu1653236447e_bool: $tType ).

thf(fun_fu2091051353e_bool_type,type,
    fun_fu2091051353e_bool: $tType ).

thf(fun_fu1007240549l_bool_type,type,
    fun_fu1007240549l_bool: $tType ).

thf(fun_fu1856979029e_bool_type,type,
    fun_fu1856979029e_bool: $tType ).

thf(fun_fu572183031e_bool_type,type,
    fun_fu572183031e_bool: $tType ).

thf(fun_fu302189515e_bool_type,type,
    fun_fu302189515e_bool: $tType ).

thf(fun_fu601378633l_bool_type,type,
    fun_fu601378633l_bool: $tType ).

thf(fun_fu1403260939e_bool_type,type,
    fun_fu1403260939e_bool: $tType ).

thf(fun_fu1067265135e_bool_type,type,
    fun_fu1067265135e_bool: $tType ).

thf(fun_fu349737825e_bool_type,type,
    fun_fu349737825e_bool: $tType ).

thf(fun_fu265667599e_bool_type,type,
    fun_fu265667599e_bool: $tType ).

thf(fun_fu399576434l_bool_type,type,
    fun_fu399576434l_bool: $tType ).

thf(fun_fu608906319e_bool_type,type,
    fun_fu608906319e_bool: $tType ).

thf(fun_fu1333785210e_bool_type,type,
    fun_fu1333785210e_bool: $tType ).

thf(fun_fu2087345469l_bool_type,type,
    fun_fu2087345469l_bool: $tType ).

thf(fun_fu1747008875l_bool_type,type,
    fun_fu1747008875l_bool: $tType ).

thf(fun_fu1911931399l_bool_type,type,
    fun_fu1911931399l_bool: $tType ).

thf(fun_fu1759027710l_bool_type,type,
    fun_fu1759027710l_bool: $tType ).

thf(fun_fu764251295e_bool_type,type,
    fun_fu764251295e_bool: $tType ).

thf(fun_fu154623769l_bool_type,type,
    fun_fu154623769l_bool: $tType ).

thf(fun_fu502368472l_bool_type,type,
    fun_fu502368472l_bool: $tType ).

thf(fun_fu542338571l_bool_type,type,
    fun_fu542338571l_bool: $tType ).

thf(fun_fu1901728075l_bool_type,type,
    fun_fu1901728075l_bool: $tType ).

thf(fun_fu445680937l_bool_type,type,
    fun_fu445680937l_bool: $tType ).

thf(fun_fu372702637e_bool_type,type,
    fun_fu372702637e_bool: $tType ).

thf(fun_fu237807729l_bool_type,type,
    fun_fu237807729l_bool: $tType ).

thf(fun_fu2122198606e_bool_type,type,
    fun_fu2122198606e_bool: $tType ).

thf(fun_fu1163781179e_bool_type,type,
    fun_fu1163781179e_bool: $tType ).

thf(fun_fu663891139l_bool_type,type,
    fun_fu663891139l_bool: $tType ).

thf(fun_fu2072024677l_bool_type,type,
    fun_fu2072024677l_bool: $tType ).

thf(fun_fu90736755l_bool_type,type,
    fun_fu90736755l_bool: $tType ).

thf(fun_fu1415736773l_bool_type,type,
    fun_fu1415736773l_bool: $tType ).

thf(fun_fu1900462437e_bool_type,type,
    fun_fu1900462437e_bool: $tType ).

thf(fun_fu262057981l_bool_type,type,
    fun_fu262057981l_bool: $tType ).

thf(fun_fu1370073565l_bool_type,type,
    fun_fu1370073565l_bool: $tType ).

thf(fun_fu1703951883l_bool_type,type,
    fun_fu1703951883l_bool: $tType ).

thf(fun_fu1923372391l_bool_type,type,
    fun_fu1923372391l_bool: $tType ).

thf(fun_fu1805752587l_bool_type,type,
    fun_fu1805752587l_bool: $tType ).

thf(fun_fu1438281908l_bool_type,type,
    fun_fu1438281908l_bool: $tType ).

thf(fun_fu1610316873l_bool_type,type,
    fun_fu1610316873l_bool: $tType ).

thf(fun_fu1787620979l_bool_type,type,
    fun_fu1787620979l_bool: $tType ).

thf(fun_fu1086366823l_bool_type,type,
    fun_fu1086366823l_bool: $tType ).

thf(fun_fu2056529149l_bool_type,type,
    fun_fu2056529149l_bool: $tType ).

thf(fun_fu544723403l_bool_type,type,
    fun_fu544723403l_bool: $tType ).

thf(cOMBB_1364904209_pname_type,type,
    cOMBB_1364904209_pname: fun_co2032091866_state > fun_fu973320112_state ).

thf(cOMBB_542850580_pname_type,type,
    cOMBB_542850580_pname: fun_pn800050071e_bool > fun_fu264874349e_bool ).

thf(cOMBB_315976743_state_type,type,
    cOMBB_315976743_state: fun_pn800050071e_bool > fun_fu2020320649e_bool ).

thf(cOMBB_598082538e_bool_type,type,
    cOMBB_598082538e_bool: fun_pn800050071e_bool > fun_fu265667599e_bool ).

thf(cOMBB_184405641e_bool_type,type,
    cOMBB_184405641e_bool: fun_pn800050071e_bool > fun_fu372702637e_bool ).

thf(cOMBB_647938656_pname_type,type,
    cOMBB_647938656_pname: fun_bool_bool > fun_fu410713561e_bool ).

thf(cOMBB_160679318_state_type,type,
    cOMBB_160679318_state: fun_bool_bool > fun_fu373216837e_bool ).

thf(cOMBB_1424001755_state_type,type,
    cOMBB_1424001755_state: fun_bool_bool > fun_fu1296727421e_bool ).

thf(cOMBB_307249310e_bool_type,type,
    cOMBB_307249310e_bool: fun_bool_bool > fun_fu2087345469l_bool ).

thf(cOMBB_469839573e_bool_type,type,
    cOMBB_469839573e_bool: fun_bool_bool > fun_fu663891139l_bool ).

thf(cOMBB_675860798_pname_type,type,
    cOMBB_675860798_pname: fun_bo1549164019l_bool > fun_fu152205775l_bool ).

thf(cOMBB_188601460_state_type,type,
    cOMBB_188601460_state: fun_bo1549164019l_bool > fun_fu1658206819l_bool ).

thf(cOMBB_242064253_state_type,type,
    cOMBB_242064253_state: fun_bo1549164019l_bool > fun_fu811519275l_bool ).

thf(cOMBB_2095475776e_bool_type,type,
    cOMBB_2095475776e_bool: fun_bo1549164019l_bool > fun_fu1747008875l_bool ).

thf(cOMBB_532710323e_bool_type,type,
    cOMBB_532710323e_bool: fun_bo1549164019l_bool > fun_fu2072024677l_bool ).

thf(cOMBB_1989814576_pname_type,type,
    cOMBB_1989814576_pname: fun_bo840793679_state > fun_fu2016078089_state ).

thf(cOMBB_1394247784_pname_type,type,
    cOMBB_1394247784_pname: fun_bo79750167on_com > fun_fu637830609on_com ).

thf(cOMBB_2037342654_pname_type,type,
    cOMBB_2037342654_pname: fun_Ho1695028467e_bool > fun_fu557884239e_bool ).

thf(cOMBB_1903241981_state_type,type,
    cOMBB_1903241981_state: fun_Ho1695028467e_bool > fun_fu1653236447e_bool ).

thf(cOMBB_93797312e_bool_type,type,
    cOMBB_93797312e_bool: fun_Ho1695028467e_bool > fun_fu764251295e_bool ).

thf(cOMBB_1094554675e_bool_type,type,
    cOMBB_1094554675e_bool: fun_Ho1695028467e_bool > fun_fu1900462437e_bool ).

thf(cOMBB_923936821_pname_type,type,
    cOMBB_923936821_pname: fun_option_com_com > fun_fu1742234008me_com ).

thf(cOMBB_530759491_pname_type,type,
    cOMBB_530759491_pname: fun_fu1430349052l_bool > fun_fu25451830e_bool ).

thf(cOMBB_408569982_pname_type,type,
    cOMBB_408569982_pname: fun_fu802393907l_bool > fun_fu1779604751l_bool ).

thf(cOMBB_582022205_state_type,type,
    cOMBB_582022205_state: fun_fu802393907l_bool > fun_fu1007240549l_bool ).

thf(cOMBB_1911358915_state_type,type,
    cOMBB_1911358915_state: fun_fu93307442l_bool > fun_fu2104550360e_bool ).

thf(cOMBB_1476898461_state_type,type,
    cOMBB_1476898461_state: fun_fu1998731480e_bool > fun_fu475229566e_bool ).

thf(cOMBB_1759179140_state_type,type,
    cOMBB_1759179140_state: fun_fu1658206819l_bool > fun_fu1982748883l_bool ).

thf(cOMBB_718493681_pname_type,type,
    cOMBB_718493681_pname: fun_fu404278912_state > fun_fu2096203996_state ).

thf(cOMBB_1036740637_state_type,type,
    cOMBB_1036740637_state: fun_fu2104550360e_bool > fun_fu1867913342e_bool ).

thf(cOMBB_1757942702_state_type,type,
    cOMBB_1757942702_state: fun_fu1219323149e_bool > fun_fu1454697805e_bool ).

thf(cOMBB_20296667_state_type,type,
    cOMBB_20296667_state: fun_fu1047394976e_bool > fun_fu1088452192e_bool ).

thf(cOMBB_1380679615_state_type,type,
    cOMBB_1380679615_state: fun_fu689207471l_bool > fun_fu572183031e_bool ).

thf(cOMBB_2094848682_pname_type,type,
    cOMBB_2094848682_pname: fun_fu1173762305l_bool > fun_fu2056752087l_bool ).

thf(cOMBB_2063006993_state_type,type,
    cOMBB_2063006993_state: fun_fu1173762305l_bool > fun_fu601378633l_bool ).

thf(cOMBC_1149511130e_bool_type,type,
    cOMBC_1149511130e_bool: fun_fu577621651e_bool ).

thf(cOMBC_951029257e_bool_type,type,
    cOMBC_951029257e_bool: fun_fu1045989665e_bool ).

thf(cOMBC_1058051404l_bool_type,type,
    cOMBC_1058051404l_bool: fun_fu696558561e_bool ).

thf(cOMBC_1123258281e_bool_type,type,
    cOMBC_1123258281e_bool: fun_fu1018334113e_bool ).

thf(cOMBC_1788166607l_bool_type,type,
    cOMBC_1788166607l_bool: fun_fu1543647229e_bool ).

thf(cOMBC_2027030106e_bool_type,type,
    cOMBC_2027030106e_bool: fun_fu402792811e_bool ).

thf(cOMBC_231445413l_bool_type,type,
    cOMBC_231445413l_bool: fun_fu1219323149e_bool ).

thf(cOMBC_471052088e_bool_type,type,
    cOMBC_471052088e_bool: fun_fu13754701e_bool ).

thf(cOMBC_952831051e_bool_type,type,
    cOMBC_952831051e_bool: fun_fu1436120077e_bool ).

thf(cOMBC_1259060397e_bool_type,type,
    cOMBC_1259060397e_bool: fun_fu2091051353e_bool ).

thf(cOMBC_1972244470e_bool_type,type,
    cOMBC_1972244470e_bool: fun_fu302189515e_bool ).

thf(cOMBC_2049654457l_bool_type,type,
    cOMBC_2049654457l_bool: fun_fu1403260939e_bool ).

thf(cOMBC_1099403170l_bool_type,type,
    cOMBC_1099403170l_bool: fun_fu1067265135e_bool ).

thf(cOMBC_483615668e_bool_type,type,
    cOMBC_483615668e_bool: fun_fu349737825e_bool ).

thf(cOMBC_1004116266e_bool_type,type,
    cOMBC_1004116266e_bool: fun_fu154623769l_bool ).

thf(cOMBC_620146361e_bool_type,type,
    cOMBC_620146361e_bool: fun_fu542338571l_bool ).

thf(cOMBC_1284144636l_bool_type,type,
    cOMBC_1284144636l_bool: fun_fu1901728075l_bool ).

thf(cOMBC_1988546018l_bool_type,type,
    cOMBC_1988546018l_bool: fun_fu445680937l_bool ).

thf(cOMBC_217340069e_bool_type,type,
    cOMBC_217340069e_bool: fun_fu262057981l_bool ).

thf(cOMBC_685773310e_bool_type,type,
    cOMBC_685773310e_bool: fun_fu1703951883l_bool ).

thf(cOMBC_195806106l_bool_type,type,
    cOMBC_195806106l_bool: fun_fu1923372391l_bool ).

thf(cOMBC_1909905718l_bool_type,type,
    cOMBC_1909905718l_bool: fun_fu1805752587l_bool ).

thf(cOMBC_7971162l_bool_type,type,
    cOMBC_7971162l_bool: fun_fu1787620979l_bool ).

thf(cOMBC_686159718l_bool_type,type,
    cOMBC_686159718l_bool: fun_fu544723403l_bool ).

thf(cOMBK_1595564845_state_type,type,
    cOMBK_1595564845_state: pname > fun_Ho1653816318_pname ).

thf(cOMBK_bool_pname_type,type,
    cOMBK_bool_pname: bool > fun_pname_bool ).

thf(cOMBK_2086958736_state_type,type,
    cOMBK_2086958736_state: bool > fun_Ho1996104121e_bool ).

thf(cOMBK_1857069011e_bool_type,type,
    cOMBK_1857069011e_bool: bool > fun_fu1430349052l_bool ).

thf(cOMBK_1224513760e_bool_type,type,
    cOMBK_1224513760e_bool: bool > fun_fu689207471l_bool ).

thf(cOMBK_1032401873_pname_type,type,
    cOMBK_1032401873_pname: hoare_1875481847_state > fun_pn664418900_state ).

thf(cOMBK_631994958_state_type,type,
    cOMBK_631994958_state: fun_state_bool > fun_st1506752259e_bool ).

thf(cOMBS_1674056844_state_type,type,
    cOMBS_1674056844_state: fun_fu993978052_state ).

thf(cOMBS_568398431l_bool_type,type,
    cOMBS_568398431l_bool: fun_fu1576495102e_bool ).

thf(cOMBS_629630867_state_type,type,
    cOMBS_629630867_state: fun_fu1646366334_state ).

thf(cOMBS_602905655_state_type,type,
    cOMBS_602905655_state: fun_fu1848601144_state ).

thf(cOMBS_904531235on_com_type,type,
    cOMBS_904531235on_com: fun_fu1908735358on_com ).

thf(cOMBS_1529518335on_com_type,type,
    cOMBS_1529518335on_com: fun_fu1867668424on_com ).

thf(cOMBS_475568287_state_type,type,
    cOMBS_475568287_state: fun_fu1956604286_state ).

thf(cOMBS_1378840469l_bool_type,type,
    cOMBS_1378840469l_bool: fun_fu1047394976e_bool ).

thf(cOMBS_896408300l_bool_type,type,
    cOMBS_896408300l_bool: fun_fu1856979029e_bool ).

thf(cOMBS_350070575l_bool_type,type,
    cOMBS_350070575l_bool: fun_fu502368472l_bool ).

thf(cOMBS_1451994324l_bool_type,type,
    cOMBS_1451994324l_bool: fun_fu1370073565l_bool ).

thf(wt_type,type,
    wt: fun_com_bool ).

thf(wT_bodies_type,type,
    wT_bodies: bool ).

thf(body_type,type,
    body: fun_pname_option_com ).

thf(body_1_type,type,
    body_1: fun_pname_com ).

thf(skip_type,type,
    skip: com ).

thf(semi_type,type,
    semi: com > com > com ).

thf(while_type,type,
    while: fun_state_bool > com > com ).

thf(finite_finite_pname_type,type,
    finite_finite_pname: fun_fu1430349052l_bool ).

thf(finite1792194148_state_type,type,
    finite1792194148_state: fun_fu689207471l_bool ).

thf(finite595471783e_bool_type,type,
    finite595471783e_bool: fun_fu399576434l_bool ).

thf(finite1559130124e_bool_type,type,
    finite1559130124e_bool: fun_fu237807729l_bool ).

thf(finite786885583l_bool_type,type,
    finite786885583l_bool: fun_fu1438281908l_bool ).

thf(finite1234242204l_bool_type,type,
    finite1234242204l_bool: fun_fu1086366823l_bool ).

thf(finite1282449217_pname_type,type,
    finite1282449217_pname: fun_pn1208287926_pname > fun_fu1499449723_pname > bool ).

thf(finite1782051386_state_type,type,
    finite1782051386_state: fun_Ho784854669_state > fun_fu385705929_state > bool ).

thf(finite1626890877e_bool_type,type,
    finite1626890877e_bool: fun_fu2101097872e_bool > fun_fu608906319e_bool > bool ).

thf(finite792754358e_bool_type,type,
    finite792754358e_bool: fun_fu947547457e_bool > fun_fu1163781179e_bool > bool ).

thf(finite89670078_pname_type,type,
    finite89670078_pname: fun_pn1208287926_pname > fun_fu1499449723_pname > bool ).

thf(finite1514162941_state_type,type,
    finite1514162941_state: fun_Ho784854669_state > fun_fu385705929_state > bool ).

thf(finite1268145088e_bool_type,type,
    finite1268145088e_bool: fun_fu2101097872e_bool > fun_fu608906319e_bool > bool ).

thf(finite1619424307e_bool_type,type,
    finite1619424307e_bool: fun_fu947547457e_bool > fun_fu1163781179e_bool > bool ).

thf(minus_1015773161e_bool_type,type,
    minus_1015773161e_bool: fun_fu2101097872e_bool ).

thf(minus_589155914e_bool_type,type,
    minus_589155914e_bool: fun_fu947547457e_bool ).

thf(minus_1290075917l_bool_type,type,
    minus_1290075917l_bool: fun_fu1759027710l_bool ).

thf(minus_1959767774l_bool_type,type,
    minus_1959767774l_bool: fun_fu1415736773l_bool ).

thf(the_pname_type,type,
    the_pname: fun_fu1499449723_pname ).

thf(the_Ho1017792262_state_type,type,
    the_Ho1017792262_state: fun_fu385705929_state ).

thf(hoare_Mirabelle_MGT_type,type,
    hoare_Mirabelle_MGT: fun_co2032091866_state ).

thf(hoare_2131502867_state_type,type,
    hoare_2131502867_state: fun_Ho1996104121e_bool > fun_fu689207471l_bool ).

thf(hoare_390430481_state_type,type,
    hoare_390430481_state: fun_Ho1996104121e_bool > fun_fu689207471l_bool ).

thf(hoare_1239590103gleton_type,type,
    hoare_1239590103gleton: bool ).

thf(hoare_13225861_state_type,type,
    hoare_13225861_state: fun_fu404278912_state ).

thf(if_Hoa1541320583_state_type,type,
    if_Hoa1541320583_state: fun_bo840793679_state ).

thf(if_option_com_type,type,
    if_option_com: fun_bo79750167on_com ).

thf(semila1635148844e_bool_type,type,
    semila1635148844e_bool: fun_fu2101097872e_bool ).

thf(semila657954503e_bool_type,type,
    semila657954503e_bool: fun_fu947547457e_bool ).

thf(semila1130628874l_bool_type,type,
    semila1130628874l_bool: fun_fu1759027710l_bool ).

thf(semila1058800161l_bool_type,type,
    semila1058800161l_bool: fun_fu1415736773l_bool ).

thf(semila1168014441p_bool_type,type,
    semila1168014441p_bool: fun_bo1549164019l_bool ).

thf(semila278973382e_bool_type,type,
    semila278973382e_bool: fun_fu2101097872e_bool ).

thf(semila1107643821e_bool_type,type,
    semila1107643821e_bool: fun_fu947547457e_bool ).

thf(semila1782091504l_bool_type,type,
    semila1782091504l_bool: fun_fu1759027710l_bool ).

thf(semila1703230395l_bool_type,type,
    semila1703230395l_bool: fun_fu1415736773l_bool ).

thf(dom_pname_com_type,type,
    dom_pname_com: fun_pname_option_com > fun_pname_bool ).

thf(evalc_type,type,
    evalc: com > fun_st1506752259e_bool ).

thf(some_com_type,type,
    some_com: com > option_com ).

thf(some_pname_type,type,
    some_pname: pname > option_pname ).

thf(some_H2141159592_state_type,type,
    some_H2141159592_state: hoare_1875481847_state > option1681283416_state ).

thf(set_com_type,type,
    set_com: option_com > fun_com_bool ).

thf(set_pname_type,type,
    set_pname: option_pname > fun_pname_bool ).

thf(set_Ho691846255_state_type,type,
    set_Ho691846255_state: option1681283416_state > fun_Ho1996104121e_bool ).

thf(the_com_type,type,
    the_com: fun_option_com_com ).

thf(bot_bot_bool_type,type,
    bot_bot_bool: bool ).

thf(bot_bot_fun_com_bool_type,type,
    bot_bot_fun_com_bool: fun_com_bool ).

thf(bot_bo844097828e_bool_type,type,
    bot_bo844097828e_bool: fun_pname_bool ).

thf(bot_bo1715400655e_bool_type,type,
    bot_bo1715400655e_bool: fun_Ho1996104121e_bool ).

thf(bot_bo1649642514l_bool_type,type,
    bot_bo1649642514l_bool: fun_fu1430349052l_bool ).

thf(bot_bo973479705l_bool_type,type,
    bot_bo973479705l_bool: fun_fu689207471l_bool ).

thf(ord_less_eq_bool_type,type,
    ord_less_eq_bool: fun_bo1549164019l_bool ).

thf(ord_le313189616e_bool_type,type,
    ord_le313189616e_bool: fun_fu802393907l_bool ).

thf(ord_le233469699e_bool_type,type,
    ord_le233469699e_bool: fun_fu1173762305l_bool ).

thf(ord_le675606854l_bool_type,type,
    ord_le675606854l_bool: fun_fu1911931399l_bool ).

thf(ord_le724727525l_bool_type,type,
    ord_le724727525l_bool: fun_fu90736755l_bool ).

thf(collect_pname_type,type,
    collect_pname: fun_fu410713561e_bool ).

thf(collec1735317154_state_type,type,
    collec1735317154_state: fun_fu1296727421e_bool ).

thf(collec1974731493e_bool_type,type,
    collec1974731493e_bool: fun_fu2087345469l_bool ).

thf(collec771609166e_bool_type,type,
    collec771609166e_bool: fun_fu663891139l_bool ).

thf(collec1613912337l_bool_type,type,
    collec1613912337l_bool: fun_fu1610316873l_bool ).

thf(collec925828570l_bool_type,type,
    collec925828570l_bool: fun_fu2056529149l_bool ).

thf(image_pname_pname_type,type,
    image_pname_pname: fun_pname_pname > fun_fu410713561e_bool ).

thf(image_1283223414_state_type,type,
    image_1283223414_state: fun_pn664418900_state > fun_fu1176632176e_bool ).

thf(image_47868345e_bool_type,type,
    image_47868345e_bool: fun_pn800050071e_bool > fun_fu802393907l_bool ).

thf(image_1165561978e_bool_type,type,
    image_1165561978e_bool: fun_pn760644914e_bool > fun_fu514526030l_bool ).

thf(image_720060442_pname_type,type,
    image_720060442_pname: fun_Ho1653816318_pname > fun_fu1040518284e_bool ).

thf(image_436941729_state_type,type,
    image_436941729_state: fun_Ho1455141843_state > fun_fu1296727421e_bool ).

thf(image_412748388e_bool_type,type,
    image_412748388e_bool: fun_Ho14659478e_bool > fun_fu1962076352l_bool ).

thf(image_896278159e_bool_type,type,
    image_896278159e_bool: fun_Ho1695028467e_bool > fun_fu1173762305l_bool ).

thf(image_1283814551_pname_type,type,
    image_1283814551_pname: fun_fu1499449723_pname > fun_fu608906319e_bool ).

thf(image_1943894628_state_type,type,
    image_1943894628_state: fun_fu1604182422_state > fun_fu1333785210e_bool ).

thf(image_2063528359e_bool_type,type,
    image_2063528359e_bool: fun_fu410713561e_bool > fun_fu2087345469l_bool ).

thf(image_1169820240_pname_type,type,
    image_1169820240_pname: fun_fu235184776_pname > fun_fu2122198606e_bool ).

thf(image_1669234411_state_type,type,
    image_1669234411_state: fun_fu385705929_state > fun_fu1163781179e_bool ).

thf(image_1852024517e_bool_type,type,
    image_1852024517e_bool: fun_fu1296727421e_bool > fun_fu663891139l_bool ).

thf(insert_com_type,type,
    insert_com: fun_co2038576728m_bool ).

thf(insert_pname_type,type,
    insert_pname: fun_pn479984722e_bool ).

thf(insert694999549_state_type,type,
    insert694999549_state: fun_Ho1110608055e_bool ).

thf(insert1325755072e_bool_type,type,
    insert1325755072e_bool: fun_fu1232732404l_bool ).

thf(insert504309043e_bool_type,type,
    insert504309043e_bool: fun_fu2107095047l_bool ).

thf(the_elem_pname_type,type,
    the_elem_pname: fun_fu1499449723_pname ).

thf(the_el1031305112_state_type,type,
    the_el1031305112_state: fun_fu385705929_state ).

thf(fAll_state_type,type,
    fAll_state: fun_fu93307442l_bool ).

thf(fFalse_type,type,
    fFalse: bool ).

thf(fNot_type,type,
    fNot: fun_bool_bool ).

thf(fTrue_type,type,
    fTrue: bool ).

thf(fconj_type,type,
    fconj: fun_bo1549164019l_bool ).

thf(fdisj_type,type,
    fdisj: fun_bo1549164019l_bool ).

thf(fequal_pname_type,type,
    fequal_pname: fun_pn800050071e_bool ).

thf(fequal_state_type,type,
    fequal_state: fun_st1506752259e_bool ).

thf(fequal391417144_state_type,type,
    fequal391417144_state: fun_Ho1695028467e_bool ).

thf(fequal533582459e_bool_type,type,
    fequal533582459e_bool: fun_fu802393907l_bool ).

thf(fequal259518520e_bool_type,type,
    fequal259518520e_bool: fun_fu1173762305l_bool ).

thf(fimplies_type,type,
    fimplies: fun_bo1549164019l_bool ).

thf(hAPP_com_bool_type,type,
    hAPP_com_bool: fun_com_bool > com > bool ).

thf(hAPP_c406083500_state_type,type,
    hAPP_c406083500_state: fun_co2032091866_state > com > hoare_1875481847_state ).

thf(hAPP_c667411853l_bool_type,type,
    hAPP_c667411853l_bool: fun_co1633267573l_bool > com > fun_fu1362071682l_bool ).

thf(hAPP_c566651504m_bool_type,type,
    hAPP_c566651504m_bool: fun_co2038576728m_bool > com > fun_fu241528037m_bool ).

thf(hAPP_c681126378_state_type,type,
    hAPP_c681126378_state: fun_co879055186_state > com > fun_fu827928799_state ).

thf(hAPP_pname_com_type,type,
    hAPP_pname_com: fun_pname_com > pname > com ).

thf(hAPP_pname_pname_type,type,
    hAPP_pname_pname: fun_pname_pname > pname > pname ).

thf(hAPP_pname_bool_type,type,
    hAPP_pname_bool: fun_pname_bool > pname > bool ).

thf(hAPP_p702226982_state_type,type,
    hAPP_p702226982_state: fun_pn664418900_state > pname > hoare_1875481847_state ).

thf(hAPP_p799580910on_com_type,type,
    hAPP_p799580910on_com: fun_pname_option_com > pname > option_com ).

thf(hAPP_p2012996835_state_type,type,
    hAPP_p2012996835_state: fun_pn92346699_state > pname > fun_co879055186_state ).

thf(hAPP_p1170154830_pname_type,type,
    hAPP_p1170154830_pname: fun_pn1208287926_pname > pname > fun_pname_pname ).

thf(hAPP_p61793385e_bool_type,type,
    hAPP_p61793385e_bool: fun_pn800050071e_bool > pname > fun_pname_bool ).

thf(hAPP_p1637813682e_bool_type,type,
    hAPP_p1637813682e_bool: fun_pn12888928e_bool > pname > fun_st1506752259e_bool ).

thf(hAPP_p393069232l_bool_type,type,
    hAPP_p393069232l_bool: fun_pn250273176l_bool > pname > fun_bool_bool ).

thf(hAPP_p1537966538e_bool_type,type,
    hAPP_p1537966538e_bool: fun_pn760644914e_bool > pname > fun_Ho1996104121e_bool ).

thf(hAPP_p1279250276_state_type,type,
    hAPP_p1279250276_state: fun_pn1776597836_state > pname > fun_Ho1455141843_state ).

thf(hAPP_p1513527868_state_type,type,
    hAPP_p1513527868_state: fun_pn1243268074_state > pname > fun_Ho784854669_state ).

thf(hAPP_p1086945780on_com_type,type,
    hAPP_p1086945780on_com: fun_pn1580610524on_com > pname > fun_op606842979on_com ).

thf(hAPP_p1164893188on_com_type,type,
    hAPP_p1164893188on_com: fun_pn1673019570on_com > pname > fun_op564655445on_com ).

thf(hAPP_p338031245l_bool_type,type,
    hAPP_p338031245l_bool: fun_pn422929397l_bool > pname > fun_fu1430349052l_bool ).

thf(hAPP_p905327722e_bool_type,type,
    hAPP_p905327722e_bool: fun_pn479984722e_bool > pname > fun_fu410713561e_bool ).

thf(hAPP_p1985340144_state_type,type,
    hAPP_p1985340144_state: fun_pn1610849624_state > pname > fun_fu827928799_state ).

thf(hAPP_p1265998686l_bool_type,type,
    hAPP_p1265998686l_bool: fun_pn249986828l_bool > pname > fun_fu689207471l_bool ).

thf(hAPP_state_bool_type,type,
    hAPP_state_bool: fun_state_bool > state > bool ).

thf(hAPP_s1806633685e_bool_type,type,
    hAPP_s1806633685e_bool: fun_st1506752259e_bool > state > fun_state_bool ).

thf(hAPP_s336103912e_bool_type,type,
    hAPP_s336103912e_bool: fun_st858662806e_bool > state > fun_st1506752259e_bool ).

thf(hAPP_s2001034685l_bool_type,type,
    hAPP_s2001034685l_bool: fun_st2116860965l_bool > state > fun_st2063251938l_bool ).

thf(hAPP_s58564346l_bool_type,type,
    hAPP_s58564346l_bool: fun_st2063251938l_bool > state > fun_bool_bool ).

thf(hAPP_s1874344717e_bool_type,type,
    hAPP_s1874344717e_bool: fun_st1483075957e_bool > state > fun_bo1936561970e_bool ).

thf(hAPP_s1226857760e_bool_type,type,
    hAPP_s1226857760e_bool: fun_st277393160e_bool > state > fun_fu373216837e_bool ).

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

thf(hAPP_b2019457360e_bool_type,type,
    hAPP_b2019457360e_bool: fun_bo1936561970e_bool > bool > fun_state_bool ).

thf(hAPP_b1095269219e_bool_type,type,
    hAPP_b1095269219e_bool: fun_bo898473669e_bool > bool > fun_st1506752259e_bool ).

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

thf(hAPP_b1347637997_state_type,type,
    hAPP_b1347637997_state: fun_bo840793679_state > bool > fun_Ho784854669_state ).

thf(hAPP_b1679505845on_com_type,type,
    hAPP_b1679505845on_com: fun_bo79750167on_com > bool > fun_op564655445on_com ).

thf(hAPP_H139064010_pname_type,type,
    hAPP_H139064010_pname: fun_Ho1653816318_pname > hoare_1875481847_state > pname ).

thf(hAPP_H1173941847e_bool_type,type,
    hAPP_H1173941847e_bool: fun_Ho1996104121e_bool > hoare_1875481847_state > bool ).

thf(hAPP_H350317809_state_type,type,
    hAPP_H350317809_state: fun_Ho1455141843_state > hoare_1875481847_state > hoare_1875481847_state ).

thf(hAPP_H785152948e_bool_type,type,
    hAPP_H785152948e_bool: fun_Ho14659478e_bool > hoare_1875481847_state > fun_pname_bool ).

thf(hAPP_H377399461l_bool_type,type,
    hAPP_H377399461l_bool: fun_Ho1896286681l_bool > hoare_1875481847_state > fun_bool_bool ).

thf(hAPP_H117293375e_bool_type,type,
    hAPP_H117293375e_bool: fun_Ho1695028467e_bool > hoare_1875481847_state > fun_Ho1996104121e_bool ).

thf(hAPP_H743221337_state_type,type,
    hAPP_H743221337_state: fun_Ho784854669_state > hoare_1875481847_state > fun_Ho1455141843_state ).

thf(hAPP_H434980226l_bool_type,type,
    hAPP_H434980226l_bool: fun_Ho760178998l_bool > hoare_1875481847_state > fun_fu1430349052l_bool ).

thf(hAPP_H810811817l_bool_type,type,
    hAPP_H810811817l_bool: fun_Ho1085560331l_bool > hoare_1875481847_state > fun_fu689207471l_bool ).

thf(hAPP_H1625489667e_bool_type,type,
    hAPP_H1625489667e_bool: fun_Ho1110608055e_bool > hoare_1875481847_state > fun_fu1296727421e_bool ).

thf(hAPP_option_com_com_type,type,
    hAPP_option_com_com: fun_option_com_com > option_com > com ).

thf(hAPP_o356497025on_com_type,type,
    hAPP_o356497025on_com: fun_op606842979on_com > option_com > option_com ).

thf(hAPP_o334540577on_com_type,type,
    hAPP_o334540577on_com: fun_op564655445on_com > option_com > fun_op606842979on_com ).

thf(hAPP_f990396704l_bool_type,type,
    hAPP_f990396704l_bool: fun_fu1362071682l_bool > fun_com_bool > bool ).

thf(hAPP_f1682609283m_bool_type,type,
    hAPP_f1682609283m_bool: fun_fu241528037m_bool > fun_com_bool > fun_com_bool ).

thf(hAPP_f2031411714_state_type,type,
    hAPP_f2031411714_state: fun_fu973320112_state > fun_pname_com > fun_pn664418900_state ).

thf(hAPP_f2116202538_state_type,type,
    hAPP_f2116202538_state: fun_fu642263570_state > fun_pname_com > fun_pn1610849624_state ).

thf(hAPP_f1336811455e_bool_type,type,
    hAPP_f1336811455e_bool: fun_fu264874349e_bool > fun_pname_pname > fun_pn800050071e_bool ).

thf(hAPP_f1297739591_pname_type,type,
    hAPP_f1297739591_pname: fun_fu1499449723_pname > fun_pname_bool > pname ).

thf(hAPP_f1664156314l_bool_type,type,
    hAPP_f1664156314l_bool: fun_fu1430349052l_bool > fun_pname_bool > bool ).

thf(hAPP_f168815540_state_type,type,
    hAPP_f168815540_state: fun_fu1604182422_state > fun_pname_bool > hoare_1875481847_state ).

thf(hAPP_f759274231e_bool_type,type,
    hAPP_f759274231e_bool: fun_fu410713561e_bool > fun_pname_bool > fun_pname_bool ).

thf(hAPP_f180827860e_bool_type,type,
    hAPP_f180827860e_bool: fun_fu1286003254e_bool > fun_pname_bool > fun_pn800050071e_bool ).

thf(hAPP_f1402196763l_bool_type,type,
    hAPP_f1402196763l_bool: fun_fu152205775l_bool > fun_pname_bool > fun_pn250273176l_bool ).

thf(hAPP_f980169511_state_type,type,
    hAPP_f980169511_state: fun_fu2016078089_state > fun_pname_bool > fun_pn1243268074_state ).

thf(hAPP_f755519727on_com_type,type,
    hAPP_f755519727on_com: fun_fu637830609on_com > fun_pname_bool > fun_pn1673019570on_com ).

thf(hAPP_f1476298914l_bool_type,type,
    hAPP_f1476298914l_bool: fun_fu31783638l_bool > fun_pname_bool > fun_bool_bool ).

thf(hAPP_f1291720380e_bool_type,type,
    hAPP_f1291720380e_bool: fun_fu1176632176e_bool > fun_pname_bool > fun_Ho1996104121e_bool ).

thf(hAPP_f434788991l_bool_type,type,
    hAPP_f434788991l_bool: fun_fu802393907l_bool > fun_pname_bool > fun_fu1430349052l_bool ).

thf(hAPP_f1388330588e_bool_type,type,
    hAPP_f1388330588e_bool: fun_fu2101097872e_bool > fun_pname_bool > fun_fu410713561e_bool ).

thf(hAPP_f1522632684l_bool_type,type,
    hAPP_f1522632684l_bool: fun_fu514526030l_bool > fun_pname_bool > fun_fu689207471l_bool ).

thf(hAPP_f556039215l_bool_type,type,
    hAPP_f556039215l_bool: fun_fu931343505l_bool > fun_pname_bool > fun_fu399576434l_bool ).

thf(hAPP_f1320879424l_bool_type,type,
    hAPP_f1320879424l_bool: fun_fu1232732404l_bool > fun_pname_bool > fun_fu2087345469l_bool ).

thf(hAPP_f1981552043_state_type,type,
    hAPP_f1981552043_state: fun_fu1904437005_state > fun_pn664418900_state > fun_pn664418900_state ).

thf(hAPP_f1601283355e_bool_type,type,
    hAPP_f1601283355e_bool: fun_fu557884239e_bool > fun_pn664418900_state > fun_pn760644914e_bool ).

thf(hAPP_f1087244981_state_type,type,
    hAPP_f1087244981_state: fun_fu1869380457_state > fun_pn664418900_state > fun_pn1776597836_state ).

thf(hAPP_f96342628me_com_type,type,
    hAPP_f96342628me_com: fun_fu1742234008me_com > fun_pname_option_com > fun_pname_com ).

thf(hAPP_f2123220539on_com_type,type,
    hAPP_f2123220539on_com: fun_fu311741085on_com > fun_pname_option_com > fun_pname_option_com ).

thf(hAPP_f648377725on_com_type,type,
    hAPP_f648377725on_com: fun_fu544728625on_com > fun_pname_option_com > fun_pn1580610524on_com ).

thf(hAPP_f1339343196_state_type,type,
    hAPP_f1339343196_state: fun_fu993978052_state > fun_pn92346699_state > fun_fu642263570_state ).

thf(hAPP_f42430548e_bool_type,type,
    hAPP_f42430548e_bool: fun_fu25451830e_bool > fun_pn800050071e_bool > fun_pname_bool ).

thf(hAPP_f22061361e_bool_type,type,
    hAPP_f22061361e_bool: fun_fu577621651e_bool > fun_pn800050071e_bool > fun_pn800050071e_bool ).

thf(hAPP_f567934427l_bool_type,type,
    hAPP_f567934427l_bool: fun_fu1779604751l_bool > fun_pn800050071e_bool > fun_pn422929397l_bool ).

thf(hAPP_f1568887991_state_type,type,
    hAPP_f1568887991_state: fun_fu2087509785_state > fun_pn12888928e_bool > fun_pn664418900_state ).

thf(hAPP_f275933352_state_type,type,
    hAPP_f275933352_state: fun_fu2096203996_state > fun_pn12888928e_bool > fun_pn92346699_state ).

thf(hAPP_f649174806e_bool_type,type,
    hAPP_f649174806e_bool: fun_fu1576495102e_bool > fun_pn250273176l_bool > fun_fu410713561e_bool ).

thf(hAPP_f98146217l_bool_type,type,
    hAPP_f98146217l_bool: fun_fu2056752087l_bool > fun_pn760644914e_bool > fun_pn249986828l_bool ).

thf(hAPP_f1564627769e_bool_type,type,
    hAPP_f1564627769e_bool: fun_fu1045989665e_bool > fun_pn760644914e_bool > fun_Ho14659478e_bool ).

thf(hAPP_f1875279510_state_type,type,
    hAPP_f1875279510_state: fun_fu1646366334_state > fun_pn1776597836_state > fun_fu1904437005_state ).

thf(hAPP_f294490838_state_type,type,
    hAPP_f294490838_state: fun_fu1848601144_state > fun_pn1243268074_state > fun_fu1869380457_state ).

thf(hAPP_f1673966486on_com_type,type,
    hAPP_f1673966486on_com: fun_fu1908735358on_com > fun_pn1580610524on_com > fun_fu311741085on_com ).

thf(hAPP_f2093196134on_com_type,type,
    hAPP_f2093196134on_com: fun_fu1867668424on_com > fun_pn1673019570on_com > fun_fu544728625on_com ).

thf(hAPP_f661147897e_bool_type,type,
    hAPP_f661147897e_bool: fun_fu696558561e_bool > fun_pn422929397l_bool > fun_fu410713561e_bool ).

thf(hAPP_f698292281e_bool_type,type,
    hAPP_f698292281e_bool: fun_fu1018334113e_bool > fun_pn479984722e_bool > fun_fu1286003254e_bool ).

thf(hAPP_f891245078_state_type,type,
    hAPP_f891245078_state: fun_fu1956604286_state > fun_pn1610849624_state > fun_fu2087509785_state ).

thf(hAPP_f1967984667e_bool_type,type,
    hAPP_f1967984667e_bool: fun_fu1543647229e_bool > fun_pn249986828l_bool > fun_fu1040518284e_bool ).

thf(hAPP_f327114704l_bool_type,type,
    hAPP_f327114704l_bool: fun_fu93307442l_bool > fun_state_bool > bool ).

thf(hAPP_f1759915619e_bool_type,type,
    hAPP_f1759915619e_bool: fun_fu373216837e_bool > fun_state_bool > fun_state_bool ).

thf(hAPP_f1863945078e_bool_type,type,
    hAPP_f1863945078e_bool: fun_fu1998731480e_bool > fun_state_bool > fun_st1506752259e_bool ).

thf(hAPP_f1259673775l_bool_type,type,
    hAPP_f1259673775l_bool: fun_fu1658206819l_bool > fun_state_bool > fun_st2063251938l_bool ).

thf(hAPP_f1595846909_state_type,type,
    hAPP_f1595846909_state: fun_fu827928799_state > fun_st1506752259e_bool > hoare_1875481847_state ).

thf(hAPP_f1930074316_state_type,type,
    hAPP_f1930074316_state: fun_fu404278912_state > fun_st1506752259e_bool > fun_co879055186_state ).

thf(hAPP_f1012183542e_bool_type,type,
    hAPP_f1012183542e_bool: fun_fu2104550360e_bool > fun_st1506752259e_bool > fun_state_bool ).

thf(hAPP_f817621513e_bool_type,type,
    hAPP_f817621513e_bool: fun_fu402792811e_bool > fun_st1506752259e_bool > fun_st1506752259e_bool ).

thf(hAPP_f249262236e_bool_type,type,
    hAPP_f249262236e_bool: fun_fu475229566e_bool > fun_st1506752259e_bool > fun_st858662806e_bool ).

thf(hAPP_f1283379615l_bool_type,type,
    hAPP_f1283379615l_bool: fun_fu1982748883l_bool > fun_st1506752259e_bool > fun_st2116860965l_bool ).

thf(hAPP_f1935169308e_bool_type,type,
    hAPP_f1935169308e_bool: fun_fu1867913342e_bool > fun_st858662806e_bool > fun_st1506752259e_bool ).

thf(hAPP_f873506917e_bool_type,type,
    hAPP_f873506917e_bool: fun_fu1454697805e_bool > fun_st2116860965l_bool > fun_st1483075957e_bool ).

thf(hAPP_f1138284024e_bool_type,type,
    hAPP_f1138284024e_bool: fun_fu1088452192e_bool > fun_st2116860965l_bool > fun_st277393160e_bool ).

thf(hAPP_f167292325e_bool_type,type,
    hAPP_f167292325e_bool: fun_fu1219323149e_bool > fun_st2063251938l_bool > fun_bo1936561970e_bool ).

thf(hAPP_f644196280e_bool_type,type,
    hAPP_f644196280e_bool: fun_fu1047394976e_bool > fun_st2063251938l_bool > fun_fu373216837e_bool ).

thf(hAPP_f701449317e_bool_type,type,
    hAPP_f701449317e_bool: fun_fu13754701e_bool > fun_st1483075957e_bool > fun_bo898473669e_bool ).

thf(hAPP_f915354021e_bool_type,type,
    hAPP_f915354021e_bool: fun_fu1436120077e_bool > fun_st277393160e_bool > fun_fu1998731480e_bool ).

thf(hAPP_f190028117e_bool_type,type,
    hAPP_f190028117e_bool: fun_fu2020320649e_bool > fun_Ho1653816318_pname > fun_Ho14659478e_bool ).

thf(hAPP_f1542224800_pname_type,type,
    hAPP_f1542224800_pname: fun_fu235184776_pname > fun_Ho1996104121e_bool > pname ).

thf(hAPP_f1408815105l_bool_type,type,
    hAPP_f1408815105l_bool: fun_fu689207471l_bool > fun_Ho1996104121e_bool > bool ).

thf(hAPP_f890249627_state_type,type,
    hAPP_f890249627_state: fun_fu385705929_state > fun_Ho1996104121e_bool > hoare_1875481847_state ).

thf(hAPP_f1148778334e_bool_type,type,
    hAPP_f1148778334e_bool: fun_fu1040518284e_bool > fun_Ho1996104121e_bool > fun_pname_bool ).

thf(hAPP_f78029435l_bool_type,type,
    hAPP_f78029435l_bool: fun_fu854396771l_bool > fun_Ho1996104121e_bool > fun_bool_bool ).

thf(hAPP_f121055253e_bool_type,type,
    hAPP_f121055253e_bool: fun_fu1296727421e_bool > fun_Ho1996104121e_bool > fun_Ho1996104121e_bool ).

thf(hAPP_f932622461l_bool_type,type,
    hAPP_f932622461l_bool: fun_fu811519275l_bool > fun_Ho1996104121e_bool > fun_Ho1896286681l_bool ).

thf(hAPP_f56162711e_bool_type,type,
    hAPP_f56162711e_bool: fun_fu775812037e_bool > fun_Ho1996104121e_bool > fun_Ho1695028467e_bool ).

thf(hAPP_f1628972376l_bool_type,type,
    hAPP_f1628972376l_bool: fun_fu1962076352l_bool > fun_Ho1996104121e_bool > fun_fu1430349052l_bool ).

thf(hAPP_f1873026899l_bool_type,type,
    hAPP_f1873026899l_bool: fun_fu1173762305l_bool > fun_Ho1996104121e_bool > fun_fu689207471l_bool ).

thf(hAPP_f1204759513e_bool_type,type,
    hAPP_f1204759513e_bool: fun_fu947547457e_bool > fun_Ho1996104121e_bool > fun_fu1296727421e_bool ).

thf(hAPP_f640685261l_bool_type,type,
    hAPP_f640685261l_bool: fun_fu2083718837l_bool > fun_Ho1996104121e_bool > fun_fu237807729l_bool ).

thf(hAPP_f872497439l_bool_type,type,
    hAPP_f872497439l_bool: fun_fu2107095047l_bool > fun_Ho1996104121e_bool > fun_fu663891139l_bool ).

thf(hAPP_f474907569e_bool_type,type,
    hAPP_f474907569e_bool: fun_fu1653236447e_bool > fun_Ho1455141843_state > fun_Ho1695028467e_bool ).

thf(hAPP_f1188413809e_bool_type,type,
    hAPP_f1188413809e_bool: fun_fu2091051353e_bool > fun_Ho14659478e_bool > fun_pn760644914e_bool ).

thf(hAPP_f745653815l_bool_type,type,
    hAPP_f745653815l_bool: fun_fu1007240549l_bool > fun_Ho14659478e_bool > fun_Ho760178998l_bool ).

thf(hAPP_f1300953505e_bool_type,type,
    hAPP_f1300953505e_bool: fun_fu1856979029e_bool > fun_Ho1896286681l_bool > fun_fu1296727421e_bool ).

thf(hAPP_f169892419e_bool_type,type,
    hAPP_f169892419e_bool: fun_fu572183031e_bool > fun_Ho1695028467e_bool > fun_Ho1996104121e_bool ).

thf(hAPP_f2101312745e_bool_type,type,
    hAPP_f2101312745e_bool: fun_fu302189515e_bool > fun_Ho1695028467e_bool > fun_Ho1695028467e_bool ).

thf(hAPP_f2059405973l_bool_type,type,
    hAPP_f2059405973l_bool: fun_fu601378633l_bool > fun_Ho1695028467e_bool > fun_Ho1085560331l_bool ).

thf(hAPP_f406856233e_bool_type,type,
    hAPP_f406856233e_bool: fun_fu1403260939e_bool > fun_Ho760178998l_bool > fun_fu1176632176e_bool ).

thf(hAPP_f1795624711e_bool_type,type,
    hAPP_f1795624711e_bool: fun_fu1067265135e_bool > fun_Ho1085560331l_bool > fun_fu1296727421e_bool ).

thf(hAPP_f392546175e_bool_type,type,
    hAPP_f392546175e_bool: fun_fu349737825e_bool > fun_Ho1110608055e_bool > fun_fu775812037e_bool ).

thf(hAPP_f1385420507e_bool_type,type,
    hAPP_f1385420507e_bool: fun_fu265667599e_bool > fun_fu1499449723_pname > fun_fu410713561e_bool ).

thf(hAPP_f1935102916l_bool_type,type,
    hAPP_f1935102916l_bool: fun_fu399576434l_bool > fun_fu1430349052l_bool > bool ).

thf(hAPP_f674760225e_bool_type,type,
    hAPP_f674760225e_bool: fun_fu608906319e_bool > fun_fu1430349052l_bool > fun_pname_bool ).

thf(hAPP_f1440968210e_bool_type,type,
    hAPP_f1440968210e_bool: fun_fu1333785210e_bool > fun_fu1430349052l_bool > fun_Ho1996104121e_bool ).

thf(hAPP_f559147733l_bool_type,type,
    hAPP_f559147733l_bool: fun_fu2087345469l_bool > fun_fu1430349052l_bool > fun_fu1430349052l_bool ).

thf(hAPP_f143162813l_bool_type,type,
    hAPP_f143162813l_bool: fun_fu1747008875l_bool > fun_fu1430349052l_bool > fun_fu31783638l_bool ).

thf(hAPP_f510955609l_bool_type,type,
    hAPP_f510955609l_bool: fun_fu1911931399l_bool > fun_fu1430349052l_bool > fun_fu399576434l_bool ).

thf(hAPP_f230953622l_bool_type,type,
    hAPP_f230953622l_bool: fun_fu1759027710l_bool > fun_fu1430349052l_bool > fun_fu2087345469l_bool ).

thf(hAPP_f1703905905e_bool_type,type,
    hAPP_f1703905905e_bool: fun_fu764251295e_bool > fun_fu1604182422_state > fun_fu1176632176e_bool ).

thf(hAPP_f2082757169l_bool_type,type,
    hAPP_f2082757169l_bool: fun_fu154623769l_bool > fun_fu410713561e_bool > fun_pn422929397l_bool ).

thf(hAPP_f624840228l_bool_type,type,
    hAPP_f624840228l_bool: fun_fu502368472l_bool > fun_fu31783638l_bool > fun_fu2087345469l_bool ).

thf(hAPP_f492176169l_bool_type,type,
    hAPP_f492176169l_bool: fun_fu542338571l_bool > fun_fu1176632176e_bool > fun_Ho760178998l_bool ).

thf(hAPP_f1297925993l_bool_type,type,
    hAPP_f1297925993l_bool: fun_fu1901728075l_bool > fun_fu802393907l_bool > fun_fu802393907l_bool ).

thf(hAPP_f1145991873l_bool_type,type,
    hAPP_f1145991873l_bool: fun_fu445680937l_bool > fun_fu931343505l_bool > fun_fu2087345469l_bool ).

thf(hAPP_f585615743e_bool_type,type,
    hAPP_f585615743e_bool: fun_fu372702637e_bool > fun_fu235184776_pname > fun_fu1040518284e_bool ).

thf(hAPP_f1699935247l_bool_type,type,
    hAPP_f1699935247l_bool: fun_fu237807729l_bool > fun_fu689207471l_bool > bool ).

thf(hAPP_f75069804e_bool_type,type,
    hAPP_f75069804e_bool: fun_fu2122198606e_bool > fun_fu689207471l_bool > fun_pname_bool ).

thf(hAPP_f962122119e_bool_type,type,
    hAPP_f962122119e_bool: fun_fu1163781179e_bool > fun_fu689207471l_bool > fun_Ho1996104121e_bool ).

thf(hAPP_f900945761l_bool_type,type,
    hAPP_f900945761l_bool: fun_fu663891139l_bool > fun_fu689207471l_bool > fun_fu689207471l_bool ).

thf(hAPP_f440042033l_bool_type,type,
    hAPP_f440042033l_bool: fun_fu2072024677l_bool > fun_fu689207471l_bool > fun_fu854396771l_bool ).

thf(hAPP_f1970936639l_bool_type,type,
    hAPP_f1970936639l_bool: fun_fu90736755l_bool > fun_fu689207471l_bool > fun_fu237807729l_bool ).

thf(hAPP_f19215249l_bool_type,type,
    hAPP_f19215249l_bool: fun_fu1415736773l_bool > fun_fu689207471l_bool > fun_fu663891139l_bool ).

thf(hAPP_f1185879473e_bool_type,type,
    hAPP_f1185879473e_bool: fun_fu1900462437e_bool > fun_fu385705929_state > fun_fu1296727421e_bool ).

thf(hAPP_f662360091l_bool_type,type,
    hAPP_f662360091l_bool: fun_fu262057981l_bool > fun_fu1040518284e_bool > fun_pn249986828l_bool ).

thf(hAPP_f2051813877l_bool_type,type,
    hAPP_f2051813877l_bool: fun_fu1370073565l_bool > fun_fu854396771l_bool > fun_fu663891139l_bool ).

thf(hAPP_f309954467l_bool_type,type,
    hAPP_f309954467l_bool: fun_fu1703951883l_bool > fun_fu1296727421e_bool > fun_Ho1085560331l_bool ).

thf(hAPP_f2051277573l_bool_type,type,
    hAPP_f2051277573l_bool: fun_fu1923372391l_bool > fun_fu1173762305l_bool > fun_fu1173762305l_bool ).

thf(hAPP_f1846363427l_bool_type,type,
    hAPP_f1846363427l_bool: fun_fu1805752587l_bool > fun_fu2083718837l_bool > fun_fu663891139l_bool ).

thf(hAPP_f389811538l_bool_type,type,
    hAPP_f389811538l_bool: fun_fu1438281908l_bool > fun_fu399576434l_bool > bool ).

thf(hAPP_f783502055l_bool_type,type,
    hAPP_f783502055l_bool: fun_fu1610316873l_bool > fun_fu399576434l_bool > fun_fu399576434l_bool ).

thf(hAPP_f1879335953l_bool_type,type,
    hAPP_f1879335953l_bool: fun_fu1787620979l_bool > fun_fu1911931399l_bool > fun_fu1911931399l_bool ).

thf(hAPP_f755416249l_bool_type,type,
    hAPP_f755416249l_bool: fun_fu1086366823l_bool > fun_fu237807729l_bool > bool ).

thf(hAPP_f57684501l_bool_type,type,
    hAPP_f57684501l_bool: fun_fu2056529149l_bool > fun_fu237807729l_bool > fun_fu237807729l_bool ).

thf(hAPP_f1475014121l_bool_type,type,
    hAPP_f1475014121l_bool: fun_fu544723403l_bool > fun_fu90736755l_bool > fun_fu90736755l_bool ).

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

thf(member_com_type,type,
    member_com: fun_co1633267573l_bool ).

thf(member_pname_type,type,
    member_pname: fun_pn422929397l_bool ).

thf(member618553700_state_type,type,
    member618553700_state: fun_Ho1085560331l_bool ).

thf(member799430823e_bool_type,type,
    member799430823e_bool: fun_fu931343505l_bool ).

thf(member1062536460e_bool_type,type,
    member1062536460e_bool: fun_fu2083718837l_bool ).

thf(fa_type,type,
    fa: fun_Ho1996104121e_bool ).

thf(pn_type,type,
    pn: pname ).

thf(y_type,type,
    y: com ).

thf(505,axiom,
    ! [A: bool] :
      ( ( hBOOL @ A )
      | ( hBOOL @ ( hAPP_bool_bool @ fNot @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fNot_2_1_U) ).

thf(2630,plain,
    ! [A: bool] :
      ( ( hBOOL @ A )
      | ( hBOOL @ ( hAPP_bool_bool @ fNot @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).

thf(452,axiom,
    ! [A: fun_st1506752259e_bool,B: fun_st1506752259e_bool,C: com] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ bot_bo1715400655e_bool ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_c406083500_state @ hoare_Mirabelle_MGT @ C ) ) @ bot_bo1715400655e_bool ) ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_390430481_state @ bot_bo1715400655e_bool ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ A ) @ C ) @ B ) ) @ bot_bo1715400655e_bool ) ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ bot_bo1715400655e_bool ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ A ) @ C ) @ B ) ) @ bot_bo1715400655e_bool ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_383_MGF__complete) ).

thf(2452,plain,
    ! [A: fun_st1506752259e_bool,B: fun_st1506752259e_bool,C: com] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ bot_bo1715400655e_bool ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_c406083500_state @ hoare_Mirabelle_MGT @ C ) ) @ bot_bo1715400655e_bool ) ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_390430481_state @ bot_bo1715400655e_bool ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ A ) @ C ) @ B ) ) @ bot_bo1715400655e_bool ) ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ bot_bo1715400655e_bool ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ A ) @ C ) @ B ) ) @ bot_bo1715400655e_bool ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).

thf(187,axiom,
    ! [A: fun_pname_bool] :
      ( ( hAPP_f1297739591_pname @ the_elem_pname @ A )
      = ( hAPP_f1297739591_pname @ the_pname @ ( hAPP_f42430548e_bool @ ( cOMBB_530759491_pname @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ A ) ) @ ( hAPP_f180827860e_bool @ ( hAPP_f698292281e_bool @ cOMBC_1123258281e_bool @ insert_pname ) @ bot_bo844097828e_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_491_the__elem__def) ).

thf(1469,plain,
    ! [A: fun_pname_bool] :
      ( ( hAPP_f1297739591_pname @ the_elem_pname @ A )
      = ( hAPP_f1297739591_pname @ the_pname @ ( hAPP_f42430548e_bool @ ( cOMBB_530759491_pname @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ A ) ) @ ( hAPP_f180827860e_bool @ ( hAPP_f698292281e_bool @ cOMBC_1123258281e_bool @ insert_pname ) @ bot_bo844097828e_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(101,axiom,
    ! [A: pname,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ C ) ) )
    <=> ( ( A = B )
        | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_insert__iff) ).

thf(1168,plain,
    ! [A: pname,B: pname,C: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ C ) ) )
       => ( ( A = B )
          | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) ) )
      & ( ( ( A = B )
          | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(422,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( A = B )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_equalityD2) ).

thf(2336,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( A = B )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).

thf(542,axiom,
    ! [A: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ bot_bo1715400655e_bool ) )
     => ( A = bot_bo1715400655e_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_362_le__bot) ).

thf(2778,plain,
    ! [A: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ bot_bo1715400655e_bool ) )
     => ( A = bot_bo1715400655e_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).

thf(785,axiom,
    ! [A: fun_pn664418900_state,B: fun_pname_bool,C: fun_pname_bool] : ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ B ) @ C ) ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ A ) @ B ) ) @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_665_image__Int__subset) ).

thf(3666,plain,
    ! [A: fun_pn664418900_state,B: fun_pname_bool,C: fun_pname_bool] : ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ B ) @ C ) ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ A ) @ B ) ) @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).

thf(444,axiom,
    hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ bot_bo1715400655e_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_finite_OemptyI) ).

thf(2427,plain,
    hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ bot_bo1715400655e_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).

thf(482,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] : ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ B ) ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_628_inf__sup__ord_I2_J) ).

thf(2559,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] : ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ B ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).

thf(43,axiom,
    ! [A: fun_pn479984722e_bool,B: fun_pname_bool,C: pname] :
      ( ( hAPP_p61793385e_bool @ ( hAPP_f180827860e_bool @ ( hAPP_f698292281e_bool @ cOMBC_1123258281e_bool @ A ) @ B ) @ C )
      = ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_221) ).

thf(941,plain,
    ! [A: fun_pn479984722e_bool,B: fun_pname_bool,C: pname] :
      ( ( hAPP_p61793385e_bool @ ( hAPP_f180827860e_bool @ ( hAPP_f698292281e_bool @ cOMBC_1123258281e_bool @ A ) @ B ) @ C )
      = ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(758,axiom,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ C ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_UnE) ).

thf(3566,plain,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ C ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).

thf(282,axiom,
    ! [A: fun_fu1998731480e_bool,B: fun_st1506752259e_bool,C: state] :
      ( ( hAPP_s336103912e_bool @ ( hAPP_f249262236e_bool @ ( cOMBB_1476898461_state @ A ) @ B ) @ C )
      = ( hAPP_f1863945078e_bool @ A @ ( hAPP_s1806633685e_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc__fun_It_226) ).

thf(1818,plain,
    ! [A: fun_fu1998731480e_bool,B: fun_st1506752259e_bool,C: state] :
      ( ( hAPP_s336103912e_bool @ ( hAPP_f249262236e_bool @ ( cOMBB_1476898461_state @ A ) @ B ) @ C )
      = ( hAPP_f1863945078e_bool @ A @ ( hAPP_s1806633685e_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(212,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_441_le__supI1) ).

thf(1554,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(143,axiom,
    ! [A: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ A ) @ bot_bo844097828e_bool )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_457_sup__bot__right) ).

thf(1322,plain,
    ! [A: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ A ) @ bot_bo844097828e_bool )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(240,axiom,
    ! [A: hoare_1875481847_state,B: hoare_1875481847_state] :
      ( ( hAPP_H350317809_state @ ( hAPP_H743221337_state @ ( hAPP_b1347637997_state @ if_Hoa1541320583_state @ fFalse ) @ A ) @ B )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_000tc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc__Com__Ostate) ).

thf(1665,plain,
    ! [A: hoare_1875481847_state,B: hoare_1875481847_state] :
      ( ( hAPP_H350317809_state @ ( hAPP_H743221337_state @ ( hAPP_b1347637997_state @ if_Hoa1541320583_state @ fFalse ) @ A ) @ B )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(570,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( A = B )
     => ~ ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
         => ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_equalityE) ).

thf(2889,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( A = B )
     => ~ ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
         => ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).

thf(105,axiom,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ B ) @ ( hAPP_f759274231e_bool @ collect_pname @ C ) ) ) )
    <=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
        & ( hBOOL @ ( hAPP_pname_bool @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_586_Int__Collect) ).

thf(1190,plain,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ B ) @ ( hAPP_f759274231e_bool @ collect_pname @ C ) ) ) )
       => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
          & ( hBOOL @ ( hAPP_pname_bool @ C @ A ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
          & ( hBOOL @ ( hAPP_pname_bool @ C @ A ) ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ B ) @ ( hAPP_f759274231e_bool @ collect_pname @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(32,axiom,
    ! [A: pname,B: fun_pname_bool,C: fun_pn1208287926_pname,D: fun_fu1499449723_pname] :
      ( ( hBOOL @ ( finite89670078_pname @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
       => ( ( B != bot_bo844097828e_bool )
         => ( ( hAPP_f1297739591_pname @ D @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ B ) )
            = ( hAPP_pname_pname @ ( hAPP_p1170154830_pname @ C @ A ) @ ( hAPP_f1297739591_pname @ D @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_470_folding__one__idem_Oinsert__idem) ).

thf(909,plain,
    ! [A: pname,B: fun_pname_bool,C: fun_pn1208287926_pname,D: fun_fu1499449723_pname] :
      ( ( hBOOL @ ( finite89670078_pname @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
       => ( ( B != bot_bo844097828e_bool )
         => ( ( hAPP_f1297739591_pname @ D @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ B ) )
            = ( hAPP_pname_pname @ ( hAPP_p1170154830_pname @ C @ A ) @ ( hAPP_f1297739591_pname @ D @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(67,axiom,
    ! [A: com] :
      ( ( set_com @ ( some_com @ A ) )
      = ( hAPP_f1682609283m_bool @ ( hAPP_c566651504m_bool @ insert_com @ A ) @ bot_bot_fun_com_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_404_Option_Oset_Osimps_I2_J) ).

thf(1031,plain,
    ! [A: com] :
      ( ( set_com @ ( some_com @ A ) )
      = ( hAPP_f1682609283m_bool @ ( hAPP_c566651504m_bool @ insert_com @ A ) @ bot_bot_fun_com_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(28,axiom,
    ! [A: pname,B: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ B )
      = ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ ( hAPP_f759274231e_bool @ collect_pname @ ( hAPP_p61793385e_bool @ ( hAPP_f22061361e_bool @ cOMBC_1149511130e_bool @ fequal_pname ) @ A ) ) ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_insert__def) ).

thf(893,plain,
    ! [A: pname,B: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ B )
      = ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ ( hAPP_f759274231e_bool @ collect_pname @ ( hAPP_p61793385e_bool @ ( hAPP_f22061361e_bool @ cOMBC_1149511130e_bool @ fequal_pname ) @ A ) ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(289,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: pname] :
      ( ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f661147897e_bool @ cOMBC_1058051404l_bool @ member_pname ) @ A ) ) @ ( hAPP_f759274231e_bool @ ( hAPP_f661147897e_bool @ cOMBC_1058051404l_bool @ member_pname ) @ B ) ) @ C ) )
    <=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_590_inf__Int__eq) ).

thf(1840,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: pname] :
      ( ( ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f661147897e_bool @ cOMBC_1058051404l_bool @ member_pname ) @ A ) ) @ ( hAPP_f759274231e_bool @ ( hAPP_f661147897e_bool @ cOMBC_1058051404l_bool @ member_pname ) @ B ) ) @ C ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ A ) @ B ) ) ) )
      & ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ A ) @ B ) ) )
       => ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f661147897e_bool @ cOMBC_1058051404l_bool @ member_pname ) @ A ) ) @ ( hAPP_f759274231e_bool @ ( hAPP_f661147897e_bool @ cOMBC_1058051404l_bool @ member_pname ) @ B ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(350,axiom,
    ! [A: fun_Ho1996104121e_bool] : ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ bot_bo1715400655e_bool ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_366_bot__least) ).

thf(2077,plain,
    ! [A: fun_Ho1996104121e_bool] : ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ bot_bo1715400655e_bool ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(502,axiom,
    ! [A: fun_fu1296727421e_bool,B: hoare_1875481847_state,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ ( hAPP_f309954467l_bool @ cOMBC_685773310e_bool @ A ) @ B ) @ C )
      = ( hAPP_H1173941847e_bool @ ( hAPP_f121055253e_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Otriple_I_232) ).

thf(2622,plain,
    ! [A: fun_fu1296727421e_bool,B: hoare_1875481847_state,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ ( hAPP_f309954467l_bool @ cOMBC_685773310e_bool @ A ) @ B ) @ C )
      = ( hAPP_H1173941847e_bool @ ( hAPP_f121055253e_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).

thf(753,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_pn12888928e_bool,C: fun_pn12888928e_bool,D: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ ( hAPP_f1568887991_state @ ( hAPP_f891245078_state @ cOMBS_475568287_state @ ( hAPP_f2116202538_state @ ( hAPP_f1339343196_state @ cOMBS_1674056844_state @ ( hAPP_f275933352_state @ ( cOMBB_718493681_pname @ hoare_13225861_state ) @ B ) ) @ body_1 ) ) @ C ) ) @ D ) ) ) @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ ( hAPP_f1568887991_state @ ( hAPP_f891245078_state @ cOMBS_475568287_state @ ( hAPP_f2116202538_state @ ( hAPP_f1339343196_state @ cOMBS_1674056844_state @ ( hAPP_f275933352_state @ ( cOMBB_718493681_pname @ hoare_13225861_state ) @ B ) ) @ ( hAPP_f96342628me_com @ ( cOMBB_923936821_pname @ the_com ) @ body ) ) ) @ C ) ) @ D ) ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ A ) @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ ( hAPP_f1568887991_state @ ( hAPP_f891245078_state @ cOMBS_475568287_state @ ( hAPP_f2116202538_state @ ( hAPP_f1339343196_state @ cOMBS_1674056844_state @ ( hAPP_f275933352_state @ ( cOMBB_718493681_pname @ hoare_13225861_state ) @ B ) ) @ body_1 ) ) @ C ) ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_hoare__derivs_OBody) ).

thf(3549,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_pn12888928e_bool,C: fun_pn12888928e_bool,D: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ ( hAPP_f1568887991_state @ ( hAPP_f891245078_state @ cOMBS_475568287_state @ ( hAPP_f2116202538_state @ ( hAPP_f1339343196_state @ cOMBS_1674056844_state @ ( hAPP_f275933352_state @ ( cOMBB_718493681_pname @ hoare_13225861_state ) @ B ) ) @ body_1 ) ) @ C ) ) @ D ) ) ) @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ ( hAPP_f1568887991_state @ ( hAPP_f891245078_state @ cOMBS_475568287_state @ ( hAPP_f2116202538_state @ ( hAPP_f1339343196_state @ cOMBS_1674056844_state @ ( hAPP_f275933352_state @ ( cOMBB_718493681_pname @ hoare_13225861_state ) @ B ) ) @ ( hAPP_f96342628me_com @ ( cOMBB_923936821_pname @ the_com ) @ body ) ) ) @ C ) ) @ D ) ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ A ) @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ ( hAPP_f1568887991_state @ ( hAPP_f891245078_state @ cOMBS_475568287_state @ ( hAPP_f2116202538_state @ ( hAPP_f1339343196_state @ cOMBS_1674056844_state @ ( hAPP_f275933352_state @ ( cOMBB_718493681_pname @ hoare_13225861_state ) @ B ) ) @ body_1 ) ) @ C ) ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).

thf(705,axiom,
    ! [A: fun_pn664418900_state,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_p702226982_state @ A @ B ) ) @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ A ) @ C ) )
        = ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ A ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_insert__image) ).

thf(3377,plain,
    ! [A: fun_pn664418900_state,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_p702226982_state @ A @ B ) ) @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ A ) @ C ) )
        = ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).

thf(164,axiom,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ B ) @ C ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_UnE) ).

thf(1401,plain,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ B ) @ C ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(585,axiom,
    ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ ( hAPP_c406083500_state @ hoare_Mirabelle_MGT @ y ) ) @ fa ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_3) ).

thf(2947,plain,
    ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ ( hAPP_c406083500_state @ hoare_Mirabelle_MGT @ y ) ) @ fa ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).

thf(74,axiom,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_pname_bool @ B @ A ) ) @ ( hAPP_pname_bool @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_369_le__funD) ).

thf(1073,plain,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_pname_bool @ B @ A ) ) @ ( hAPP_pname_bool @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(109,axiom,
    ! [A: pname] :
      ( ( hAPP_f759274231e_bool @ collect_pname @ ( hAPP_p61793385e_bool @ ( hAPP_f22061361e_bool @ cOMBC_1149511130e_bool @ fequal_pname ) @ A ) )
      = ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ bot_bo844097828e_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_singleton__conv) ).

thf(1205,plain,
    ! [A: pname] :
      ( ( hAPP_f759274231e_bool @ collect_pname @ ( hAPP_p61793385e_bool @ ( hAPP_f22061361e_bool @ cOMBC_1149511130e_bool @ fequal_pname ) @ A ) )
      = ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ bot_bo844097828e_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(219,axiom,
    ! [A: pname] :
      ( ( hAPP_f759274231e_bool @ collect_pname @ ( hAPP_p61793385e_bool @ fequal_pname @ A ) )
      = ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ bot_bo844097828e_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_singleton__conv2) ).

thf(1591,plain,
    ! [A: pname] :
      ( ( hAPP_f759274231e_bool @ collect_pname @ ( hAPP_p61793385e_bool @ fequal_pname @ A ) )
      = ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ bot_bo844097828e_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(738,axiom,
    ! [A: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ bot_bo1715400655e_bool ) @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_460_sup__bot__left) ).

thf(3498,plain,
    ! [A: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ bot_bo1715400655e_bool ) @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).

thf(19,axiom,
    ! [A: fun_pn800050071e_bool,B: pname,C: pname] :
      ( ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ ( hAPP_f22061361e_bool @ cOMBC_1149511130e_bool @ A ) @ B ) @ C )
      = ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Com__Opname_000tc__HOL__Obool_U) ).

thf(861,plain,
    ! [A: fun_pn800050071e_bool,B: pname,C: pname] :
      ( ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ ( hAPP_f22061361e_bool @ cOMBC_1149511130e_bool @ A ) @ B ) @ C )
      = ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(193,axiom,
    ! [A: pname,B: pname,C: fun_pname_bool] :
      ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
       => ( B = A ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_insertCI) ).

thf(1486,plain,
    ! [A: pname,B: pname,C: fun_pname_bool] :
      ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
       => ( B = A ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(311,axiom,
    ! [A: hoare_1875481847_state] :
      ( ( hBOOL @ ( hAPP_H1173941847e_bool @ bot_bo1715400655e_bool @ A ) )
    <=> ( hBOOL @ bot_bot_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_376_bot__fun__def) ).

thf(1924,plain,
    ! [A: hoare_1875481847_state] :
      ( ( ( hBOOL @ ( hAPP_H1173941847e_bool @ bot_bo1715400655e_bool @ A ) )
       => ( hBOOL @ bot_bot_bool ) )
      & ( ( hBOOL @ bot_bot_bool )
       => ( hBOOL @ ( hAPP_H1173941847e_bool @ bot_bo1715400655e_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(59,axiom,
    ! [A: fun_pname_pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ ( hAPP_f759274231e_bool @ ( image_pname_pname @ A ) @ B ) ) )
       => ? [D: fun_pname_bool] :
            ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ D ) )
            & ( C
              = ( hAPP_f759274231e_bool @ ( image_pname_pname @ A ) @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_finite__subset__image) ).

thf(1005,plain,
    ! [A: fun_pname_pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ ( hAPP_f759274231e_bool @ ( image_pname_pname @ A ) @ B ) ) )
       => ? [D: fun_pname_bool] :
            ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ D ) )
            & ( C
              = ( hAPP_f759274231e_bool @ ( image_pname_pname @ A ) @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(583,axiom,
    ! [A: fun_Ho1085560331l_bool,B: fun_Ho1996104121e_bool,C: hoare_1875481847_state] :
      ( ( hAPP_H1173941847e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1795624711e_bool @ cOMBC_1099403170l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc__Com___231) ).

thf(2940,plain,
    ! [A: fun_Ho1085560331l_bool,B: fun_Ho1996104121e_bool,C: hoare_1875481847_state] :
      ( ( hAPP_H1173941847e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1795624711e_bool @ cOMBC_1099403170l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).

thf(166,axiom,
    ! [A: com,B: com] :
      ( ( semi @ A @ B )
     != skip ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_508_com_Osimps_I13_J) ).

thf(1406,plain,
    ! [A: com,B: com] :
      ( ( semi @ A @ B )
     != skip ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(547,axiom,
    ! [A: fun_Ho1996104121e_bool,B: hoare_1875481847_state,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ C ) )
     => ( ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ A ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ minus_589155914e_bool @ C ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_685_DiffI) ).

thf(2808,plain,
    ! [A: fun_Ho1996104121e_bool,B: hoare_1875481847_state,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ C ) )
     => ( ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ A ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ minus_589155914e_bool @ C ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).

thf(809,axiom,
    ! [A: fun_fu237807729l_bool,B: fun_fu689207471l_bool] :
      ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ B ) )
     => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ A @ bot_bo973479705l_bool ) )
       => ( ! [C: fun_Ho1996104121e_bool,D: fun_fu689207471l_bool] :
              ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ D ) )
             => ( ~ ( hBOOL @ ( hAPP_f1699935247l_bool @ ( hAPP_f640685261l_bool @ member1062536460e_bool @ C ) @ D ) )
               => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ A @ D ) )
                 => ( hBOOL @ ( hAPP_f1699935247l_bool @ A @ ( hAPP_f900945761l_bool @ ( hAPP_f872497439l_bool @ insert504309043e_bool @ C ) @ D ) ) ) ) ) )
         => ( hBOOL @ ( hAPP_f1699935247l_bool @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_finite__induct) ).

thf(3762,plain,
    ! [A: fun_fu237807729l_bool,B: fun_fu689207471l_bool] :
      ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ B ) )
     => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ A @ bot_bo973479705l_bool ) )
       => ( ! [C: fun_Ho1996104121e_bool,D: fun_fu689207471l_bool] :
              ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ D ) )
             => ( ~ ( hBOOL @ ( hAPP_f1699935247l_bool @ ( hAPP_f640685261l_bool @ member1062536460e_bool @ C ) @ D ) )
               => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ A @ D ) )
                 => ( hBOOL @ ( hAPP_f1699935247l_bool @ A @ ( hAPP_f900945761l_bool @ ( hAPP_f872497439l_bool @ insert504309043e_bool @ C ) @ D ) ) ) ) ) )
         => ( hBOOL @ ( hAPP_f1699935247l_bool @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).

thf(509,axiom,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool,C: fun_fu2101097872e_bool,D: fun_fu608906319e_bool] :
      ( ( hBOOL @ ( finite1268145088e_bool @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
       => ( ( A != bot_bo1649642514l_bool )
         => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ A ) @ B ) )
           => ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ C @ ( hAPP_f674760225e_bool @ D @ A ) ) @ ( hAPP_f674760225e_bool @ D @ B ) )
              = ( hAPP_f674760225e_bool @ D @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_465_folding__one__idem_Osubset__idem) ).

thf(2644,plain,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool,C: fun_fu2101097872e_bool,D: fun_fu608906319e_bool] :
      ( ( hBOOL @ ( finite1268145088e_bool @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
       => ( ( A != bot_bo1649642514l_bool )
         => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ A ) @ B ) )
           => ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ C @ ( hAPP_f674760225e_bool @ D @ A ) ) @ ( hAPP_f674760225e_bool @ D @ B ) )
              = ( hAPP_f674760225e_bool @ D @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).

thf(177,axiom,
    ! [A: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
     => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( hAPP_f559147733l_bool @ collec1974731493e_bool @ ( hAPP_f434788991l_bool @ ( hAPP_f1297925993l_bool @ cOMBC_1284144636l_bool @ ord_le313189616e_bool ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_finite__Collect__subsets) ).

thf(1443,plain,
    ! [A: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
     => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( hAPP_f559147733l_bool @ collec1974731493e_bool @ ( hAPP_f434788991l_bool @ ( hAPP_f1297925993l_bool @ cOMBC_1284144636l_bool @ ord_le313189616e_bool ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(715,axiom,
    ! [A: fun_fu689207471l_bool,B: fun_fu689207471l_bool,C: fun_fu947547457e_bool,D: fun_fu1163781179e_bool] :
      ( ( hBOOL @ ( finite1619424307e_bool @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ B ) )
       => ( ( A != bot_bo973479705l_bool )
         => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ ( hAPP_f1970936639l_bool @ ord_le724727525l_bool @ A ) @ B ) )
           => ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ C @ ( hAPP_f962122119e_bool @ D @ A ) ) @ ( hAPP_f962122119e_bool @ D @ B ) )
              = ( hAPP_f962122119e_bool @ D @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_466_folding__one__idem_Osubset__idem) ).

thf(3417,plain,
    ! [A: fun_fu689207471l_bool,B: fun_fu689207471l_bool,C: fun_fu947547457e_bool,D: fun_fu1163781179e_bool] :
      ( ( hBOOL @ ( finite1619424307e_bool @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ B ) )
       => ( ( A != bot_bo973479705l_bool )
         => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ ( hAPP_f1970936639l_bool @ ord_le724727525l_bool @ A ) @ B ) )
           => ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ C @ ( hAPP_f962122119e_bool @ D @ A ) ) @ ( hAPP_f962122119e_bool @ D @ B ) )
              = ( hAPP_f962122119e_bool @ D @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).

thf(256,axiom,
    ! [A: hoare_1875481847_state,B: pname] :
      ( ( hAPP_p702226982_state @ ( cOMBK_1032401873_pname @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc__Com__) ).

thf(1728,plain,
    ! [A: hoare_1875481847_state,B: pname] :
      ( ( hAPP_p702226982_state @ ( cOMBK_1032401873_pname @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(632,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ C ) )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_417_inf__sup__aci_I7_J) ).

thf(3108,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ C ) )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).

thf(322,axiom,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool,C: fun_Ho784854669_state,D: fun_fu385705929_state] :
      ( ( hBOOL @ ( finite1514162941_state @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ B ) )
       => ( ( B != bot_bo1715400655e_bool )
         => ( ( hAPP_f890249627_state @ D @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ B ) )
            = ( hAPP_H350317809_state @ ( hAPP_H743221337_state @ C @ A ) @ ( hAPP_f890249627_state @ D @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_471_folding__one__idem_Oinsert__idem) ).

thf(1971,plain,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool,C: fun_Ho784854669_state,D: fun_fu385705929_state] :
      ( ( hBOOL @ ( finite1514162941_state @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ B ) )
       => ( ( B != bot_bo1715400655e_bool )
         => ( ( hAPP_f890249627_state @ D @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ B ) )
            = ( hAPP_H350317809_state @ ( hAPP_H743221337_state @ C @ A ) @ ( hAPP_f890249627_state @ D @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(274,axiom,
    ( bot_bo973479705l_bool
    = ( hAPP_f900945761l_bool @ collec771609166e_bool @ ( cOMBK_1224513760e_bool @ fFalse ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_empty__def) ).

thf(1793,plain,
    ( bot_bo973479705l_bool
    = ( hAPP_f900945761l_bool @ collec771609166e_bool @ ( cOMBK_1224513760e_bool @ fFalse ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(711,axiom,
    ! [A: fun_Ho1996104121e_bool,B: hoare_1875481847_state,C: fun_Ho1996104121e_bool] :
      ( ( ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ C ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_UnCI) ).

thf(3402,plain,
    ! [A: fun_Ho1996104121e_bool,B: hoare_1875481847_state,C: fun_Ho1996104121e_bool] :
      ( ( ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ C ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).

thf(560,axiom,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_in__mono) ).

thf(2854,plain,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).

thf(606,axiom,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_581_IntD2) ).

thf(3017,plain,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).

thf(238,axiom,
    ! [A: com,B: com] :
      ( skip
     != ( semi @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_507_com_Osimps_I12_J) ).

thf(1655,plain,
    ! [A: com,B: com] :
      ( skip
     != ( semi @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(262,axiom,
    ! [A: fun_fu1173762305l_bool,B: fun_Ho1695028467e_bool,C: hoare_1875481847_state] :
      ( ( hAPP_H810811817l_bool @ ( hAPP_f2059405973l_bool @ ( cOMBB_2063006993_state @ A ) @ B ) @ C )
      = ( hAPP_f1873026899l_bool @ A @ ( hAPP_H117293375e_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Otriple_I_244) ).

thf(1756,plain,
    ! [A: fun_fu1173762305l_bool,B: fun_Ho1695028467e_bool,C: hoare_1875481847_state] :
      ( ( hAPP_H810811817l_bool @ ( hAPP_f2059405973l_bool @ ( cOMBB_2063006993_state @ A ) @ B ) @ C )
      = ( hAPP_f1873026899l_bool @ A @ ( hAPP_H117293375e_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(779,axiom,
    ! [A: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ bot_bo1715400655e_bool )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_Un__empty__right) ).

thf(3649,plain,
    ! [A: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ bot_bo1715400655e_bool )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).

thf(614,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_420_inf__sup__aci_I8_J) ).

thf(3044,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).

thf(722,axiom,
    ! [A: fun_pname_bool] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_order__refl) ).

thf(3446,plain,
    ! [A: fun_pname_bool] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).

thf(579,axiom,
    ! [A: fun_fu1430349052l_bool,B: fun_pn800050071e_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ A ) @ ( hAPP_f434788991l_bool @ ( image_47868345e_bool @ B ) @ C ) ) )
       => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_finite__surj) ).

thf(2933,plain,
    ! [A: fun_fu1430349052l_bool,B: fun_pn800050071e_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ A ) @ ( hAPP_f434788991l_bool @ ( image_47868345e_bool @ B ) @ C ) ) )
       => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).

thf(119,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_Un__upper2) ).

thf(1233,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(491,axiom,
    ! [A: fun_Ho1996104121e_bool] :
      ( ? [B: hoare_1875481847_state] : ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ A ) )
    <=> ( A != bot_bo1715400655e_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_ex__in__conv) ).

thf(2580,plain,
    ! [A: fun_Ho1996104121e_bool] :
      ( ( ? [B: hoare_1875481847_state] : ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ A ) )
       => ( A != bot_bo1715400655e_bool ) )
      & ( ( A != bot_bo1715400655e_bool )
       => ? [B: hoare_1875481847_state] : ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).

thf(573,axiom,
    ! [A: com] :
      ( ( hAPP_c406083500_state @ hoare_Mirabelle_MGT @ A )
      = ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ fequal_state ) @ A ) @ ( evalc @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_535_MGT__def) ).

thf(2901,plain,
    ! [A: com] :
      ( ( hAPP_c406083500_state @ hoare_Mirabelle_MGT @ A )
      = ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ fequal_state ) @ A ) @ ( evalc @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).

thf(151,axiom,
    ! [A: fun_fu689207471l_bool,B: fun_fu689207471l_bool] :
      ( ( hAPP_f900945761l_bool @ collec771609166e_bool @ ( hAPP_f900945761l_bool @ ( hAPP_f2051813877l_bool @ cOMBS_1451994324l_bool @ ( hAPP_f440042033l_bool @ ( cOMBB_532710323e_bool @ fdisj ) @ A ) ) @ B ) )
      = ( hAPP_f900945761l_bool @ ( hAPP_f19215249l_bool @ semila1703230395l_bool @ ( hAPP_f900945761l_bool @ collec771609166e_bool @ A ) ) @ ( hAPP_f900945761l_bool @ collec771609166e_bool @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_Collect__disj__eq) ).

thf(1354,plain,
    ! [A: fun_fu689207471l_bool,B: fun_fu689207471l_bool] :
      ( ( hAPP_f900945761l_bool @ collec771609166e_bool @ ( hAPP_f900945761l_bool @ ( hAPP_f2051813877l_bool @ cOMBS_1451994324l_bool @ ( hAPP_f440042033l_bool @ ( cOMBB_532710323e_bool @ fdisj ) @ A ) ) @ B ) )
      = ( hAPP_f900945761l_bool @ ( hAPP_f19215249l_bool @ semila1703230395l_bool @ ( hAPP_f900945761l_bool @ collec771609166e_bool @ A ) ) @ ( hAPP_f900945761l_bool @ collec771609166e_bool @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(76,axiom,
    ! [A: fun_fu689207471l_bool] :
      ( ( hAPP_f900945761l_bool @ collec771609166e_bool @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_Collect__def) ).

thf(1078,plain,
    ! [A: fun_fu689207471l_bool] :
      ( ( hAPP_f900945761l_bool @ collec771609166e_bool @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(173,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ A ) @ B ) ) )
    <=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
        & ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_finite__Un) ).

thf(1426,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ A ) @ B ) ) )
       => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
          & ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
          & ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ A ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(663,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ A ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_432_sup__least) ).

thf(3217,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ A ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).

thf(603,axiom,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool,C: fun_Ho784854669_state,D: fun_fu385705929_state] :
      ( ( hBOOL @ ( finite1782051386_state @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ B ) )
       => ( ( ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ minus_589155914e_bool @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ bot_bo1715400655e_bool ) )
              = bot_bo1715400655e_bool )
           => ( ( hAPP_f890249627_state @ D @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ B ) )
              = A ) )
          & ( ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ minus_589155914e_bool @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ bot_bo1715400655e_bool ) )
             != bot_bo1715400655e_bool )
           => ( ( hAPP_f890249627_state @ D @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ B ) )
              = ( hAPP_H350317809_state @ ( hAPP_H743221337_state @ C @ A ) @ ( hAPP_f890249627_state @ D @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ minus_589155914e_bool @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ bot_bo1715400655e_bool ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_681_folding__one_Oinsert__remove) ).

thf(3004,plain,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool,C: fun_Ho784854669_state,D: fun_fu385705929_state] :
      ( ( hBOOL @ ( finite1782051386_state @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ B ) )
       => ( ( ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ minus_589155914e_bool @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ bot_bo1715400655e_bool ) )
              = bot_bo1715400655e_bool )
           => ( ( hAPP_f890249627_state @ D @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ B ) )
              = A ) )
          & ( ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ minus_589155914e_bool @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ bot_bo1715400655e_bool ) )
             != bot_bo1715400655e_bool )
           => ( ( hAPP_f890249627_state @ D @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ B ) )
              = ( hAPP_H350317809_state @ ( hAPP_H743221337_state @ C @ A ) @ ( hAPP_f890249627_state @ D @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ minus_589155914e_bool @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ bot_bo1715400655e_bool ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).

thf(702,axiom,
    ! [A: fun_fu1604182422_state,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ ( hAPP_f1440968210e_bool @ ( image_1943894628_state @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_finite__imageI) ).

thf(3367,plain,
    ! [A: fun_fu1604182422_state,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ ( hAPP_f1440968210e_bool @ ( image_1943894628_state @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).

thf(447,axiom,
    ! [A: pname,B: state,C: state] :
      ( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ ( evalc @ ( hAPP_option_com_com @ the_com @ ( hAPP_p799580910on_com @ body @ A ) ) ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ ( evalc @ ( hAPP_pname_com @ body_1 @ A ) ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_536_evalc_OBody) ).

thf(2434,plain,
    ! [A: pname,B: state,C: state] :
      ( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ ( evalc @ ( hAPP_option_com_com @ the_com @ ( hAPP_p799580910on_com @ body @ A ) ) ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ ( evalc @ ( hAPP_pname_com @ body_1 @ A ) ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).

thf(297,axiom,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ B ) )
     => ( ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ minus_589155914e_bool @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ bot_bo1715400655e_bool ) ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_693_insert__Diff) ).

thf(1872,plain,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ B ) )
     => ( ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ minus_589155914e_bool @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ bot_bo1715400655e_bool ) ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(461,axiom,
    ! [A: bool,B: fun_Ho1996104121e_bool] :
      ( ( hAPP_f1408815105l_bool @ ( cOMBK_1224513760e_bool @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Hoare____Mirabelle____xlr) ).

thf(2476,plain,
    ! [A: bool,B: fun_Ho1996104121e_bool] :
      ( ( hAPP_f1408815105l_bool @ ( cOMBK_1224513760e_bool @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).

thf(504,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_fu689207471l_bool,C: fun_fu947547457e_bool,D: fun_fu1163781179e_bool] :
      ( ( hBOOL @ ( finite1619424307e_bool @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ B ) )
       => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ ( hAPP_f640685261l_bool @ member1062536460e_bool @ A ) @ B ) )
         => ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ C @ A ) @ ( hAPP_f962122119e_bool @ D @ B ) )
            = ( hAPP_f962122119e_bool @ D @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_484_folding__one__idem_Oin__idem) ).

thf(2627,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_fu689207471l_bool,C: fun_fu947547457e_bool,D: fun_fu1163781179e_bool] :
      ( ( hBOOL @ ( finite1619424307e_bool @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ B ) )
       => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ ( hAPP_f640685261l_bool @ member1062536460e_bool @ A ) @ B ) )
         => ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ C @ A ) @ ( hAPP_f962122119e_bool @ D @ B ) )
            = ( hAPP_f962122119e_bool @ D @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).

thf(329,axiom,
    ! [A: hoare_1875481847_state] :
      ( ( hAPP_f121055253e_bool @ collec1735317154_state @ ( hAPP_H117293375e_bool @ fequal391417144_state @ A ) )
      = ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ bot_bo1715400655e_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_singleton__conv2) ).

thf(1988,plain,
    ! [A: hoare_1875481847_state] :
      ( ( hAPP_f121055253e_bool @ collec1735317154_state @ ( hAPP_H117293375e_bool @ fequal391417144_state @ A ) )
      = ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ bot_bo1715400655e_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(455,axiom,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool,C: fun_Ho784854669_state,D: fun_fu385705929_state] :
      ( ( hBOOL @ ( finite1514162941_state @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ B ) )
       => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ B ) )
         => ( ( hAPP_H350317809_state @ ( hAPP_H743221337_state @ C @ A ) @ ( hAPP_f890249627_state @ D @ B ) )
            = ( hAPP_f890249627_state @ D @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_482_folding__one__idem_Oin__idem) ).

thf(2459,plain,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool,C: fun_Ho784854669_state,D: fun_fu385705929_state] :
      ( ( hBOOL @ ( finite1514162941_state @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ B ) )
       => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ B ) )
         => ( ( hAPP_H350317809_state @ ( hAPP_H743221337_state @ C @ A ) @ ( hAPP_f890249627_state @ D @ B ) )
            = ( hAPP_f890249627_state @ D @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).

thf(147,axiom,
    ! [A: pname,B: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ B )
      = ( hAPP_f759274231e_bool @ collect_pname @ ( hAPP_f759274231e_bool @ ( hAPP_f649174806e_bool @ cOMBS_568398431l_bool @ ( hAPP_f1402196763l_bool @ ( cOMBB_675860798_pname @ fdisj ) @ ( hAPP_p61793385e_bool @ ( hAPP_f22061361e_bool @ cOMBC_1149511130e_bool @ fequal_pname ) @ A ) ) ) @ ( hAPP_f759274231e_bool @ ( hAPP_f661147897e_bool @ cOMBC_1058051404l_bool @ member_pname ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_insert__compr) ).

thf(1342,plain,
    ! [A: pname,B: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ B )
      = ( hAPP_f759274231e_bool @ collect_pname @ ( hAPP_f759274231e_bool @ ( hAPP_f649174806e_bool @ cOMBS_568398431l_bool @ ( hAPP_f1402196763l_bool @ ( cOMBB_675860798_pname @ fdisj ) @ ( hAPP_p61793385e_bool @ ( hAPP_f22061361e_bool @ cOMBC_1149511130e_bool @ fequal_pname ) @ A ) ) ) @ ( hAPP_f759274231e_bool @ ( hAPP_f661147897e_bool @ cOMBC_1058051404l_bool @ member_pname ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(635,axiom,
    ! [A: fun_fu689207471l_bool,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ B ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ A @ bot_bo1715400655e_bool ) )
       => ( ! [C: hoare_1875481847_state,D: fun_Ho1996104121e_bool] :
              ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ D ) )
             => ( ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ C ) @ D ) )
               => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ A @ D ) )
                 => ( hBOOL @ ( hAPP_f1408815105l_bool @ A @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ C ) @ D ) ) ) ) ) )
         => ( hBOOL @ ( hAPP_f1408815105l_bool @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_finite__induct) ).

thf(3121,plain,
    ! [A: fun_fu689207471l_bool,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ B ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ A @ bot_bo1715400655e_bool ) )
       => ( ! [C: hoare_1875481847_state,D: fun_Ho1996104121e_bool] :
              ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ D ) )
             => ( ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ C ) @ D ) )
               => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ A @ D ) )
                 => ( hBOOL @ ( hAPP_f1408815105l_bool @ A @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ C ) @ D ) ) ) ) ) )
         => ( hBOOL @ ( hAPP_f1408815105l_bool @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).

thf(318,axiom,
    ! [A: fun_Ho1996104121e_bool,B: pname,C: fun_Ho1653816318_pname,D: hoare_1875481847_state] :
      ( ( B
        = ( hAPP_H139064010_pname @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ D ) @ A ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ ( hAPP_f1148778334e_bool @ ( image_720060442_pname @ C ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_image__eqI) ).

thf(1954,plain,
    ! [A: fun_Ho1996104121e_bool,B: pname,C: fun_Ho1653816318_pname,D: hoare_1875481847_state] :
      ( ( B
        = ( hAPP_H139064010_pname @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ D ) @ A ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ ( hAPP_f1148778334e_bool @ ( image_720060442_pname @ C ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(556,axiom,
    ! [A: fun_fu689207471l_bool,B: fun_fu689207471l_bool] :
      ( ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ B ) )
        | ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ A ) ) )
     => ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ ( hAPP_f900945761l_bool @ ( hAPP_f19215249l_bool @ semila1058800161l_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_563_finite__Int) ).

thf(2844,plain,
    ! [A: fun_fu689207471l_bool,B: fun_fu689207471l_bool] :
      ( ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ B ) )
        | ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ A ) ) )
     => ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ ( hAPP_f900945761l_bool @ ( hAPP_f19215249l_bool @ semila1058800161l_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).

thf(81,axiom,
    ! [A: fun_Ho1996104121e_bool] :
      ( ( hAPP_f900945761l_bool @ collec771609166e_bool @ ( hAPP_f1873026899l_bool @ ( hAPP_f2051277573l_bool @ cOMBC_195806106l_bool @ fequal259518520e_bool ) @ A ) )
      = ( hAPP_f900945761l_bool @ ( hAPP_f872497439l_bool @ insert504309043e_bool @ A ) @ bot_bo973479705l_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_singleton__conv) ).

thf(1095,plain,
    ! [A: fun_Ho1996104121e_bool] :
      ( ( hAPP_f900945761l_bool @ collec771609166e_bool @ ( hAPP_f1873026899l_bool @ ( hAPP_f2051277573l_bool @ cOMBC_195806106l_bool @ fequal259518520e_bool ) @ A ) )
      = ( hAPP_f900945761l_bool @ ( hAPP_f872497439l_bool @ insert504309043e_bool @ A ) @ bot_bo973479705l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(343,axiom,
    ! [A: fun_pn664418900_state,B: fun_pn664418900_state,C: fun_pname_bool,D: fun_pname_bool] :
      ( ( C = D )
     => ( ! [E: pname] :
            ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ E ) @ D ) )
           => ( ( hAPP_p702226982_state @ A @ E )
              = ( hAPP_p702226982_state @ B @ E ) ) )
       => ( ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ A ) @ C )
          = ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_520_image__cong) ).

thf(2046,plain,
    ! [A: fun_pn664418900_state,B: fun_pn664418900_state,C: fun_pname_bool,D: fun_pname_bool] :
      ( ( C = D )
     => ( ! [E: pname] :
            ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ E ) @ D ) )
           => ( ( hAPP_p702226982_state @ A @ E )
              = ( hAPP_p702226982_state @ B @ E ) ) )
       => ( ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ A ) @ C )
          = ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ B ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(392,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
     => ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ B ) @ A )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_642_inf__absorb2) ).

thf(2227,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
     => ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ B ) @ A )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(743,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_fu689207471l_bool,C: fun_fu947547457e_bool,D: fun_fu1163781179e_bool] :
      ( ( hBOOL @ ( finite792754358e_bool @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ B ) )
       => ( ~ ( hBOOL @ ( hAPP_f1699935247l_bool @ ( hAPP_f640685261l_bool @ member1062536460e_bool @ A ) @ B ) )
         => ( ( B != bot_bo973479705l_bool )
           => ( ( hAPP_f962122119e_bool @ D @ ( hAPP_f900945761l_bool @ ( hAPP_f872497439l_bool @ insert504309043e_bool @ A ) @ B ) )
              = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ C @ A ) @ ( hAPP_f962122119e_bool @ D @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_512_folding__one_Oinsert) ).

thf(3513,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_fu689207471l_bool,C: fun_fu947547457e_bool,D: fun_fu1163781179e_bool] :
      ( ( hBOOL @ ( finite792754358e_bool @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ B ) )
       => ( ~ ( hBOOL @ ( hAPP_f1699935247l_bool @ ( hAPP_f640685261l_bool @ member1062536460e_bool @ A ) @ B ) )
         => ( ( B != bot_bo973479705l_bool )
           => ( ( hAPP_f962122119e_bool @ D @ ( hAPP_f900945761l_bool @ ( hAPP_f872497439l_bool @ insert504309043e_bool @ A ) @ B ) )
              = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ C @ A ) @ ( hAPP_f962122119e_bool @ D @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).

thf(798,axiom,
    ( bot_bo1715400655e_bool
    = ( hAPP_f121055253e_bool @ collec1735317154_state @ ( cOMBK_2086958736_state @ fFalse ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_empty__def) ).

thf(3730,plain,
    ( bot_bo1715400655e_bool
    = ( hAPP_f121055253e_bool @ collec1735317154_state @ ( cOMBK_2086958736_state @ fFalse ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).

thf(222,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ! [C: pname] :
          ( ( hBOOL @ ( hAPP_pname_bool @ B @ C ) )
         => ( hBOOL @ ( hAPP_pname_bool @ A @ C ) ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_525_predicate1I) ).

thf(1601,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ! [C: pname] :
          ( ( hBOOL @ ( hAPP_pname_bool @ B @ C ) )
         => ( hBOOL @ ( hAPP_pname_bool @ A @ C ) ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(352,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ C ) )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ B ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_653_inf__sup__distrib1) ).

thf(2082,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ C ) )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ B ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(377,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ B )
        = bot_bo1715400655e_bool )
    <=> ! [C: hoare_1875481847_state] :
          ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ C ) @ A ) )
         => ! [D: hoare_1875481847_state] :
              ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ D ) @ B ) )
             => ( C != D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_567_disjoint__iff__not__equal) ).

thf(2173,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ B )
          = bot_bo1715400655e_bool )
       => ! [C: hoare_1875481847_state] :
            ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ C ) @ A ) )
           => ! [D: hoare_1875481847_state] :
                ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ D ) @ B ) )
               => ( C != D ) ) ) )
      & ( ! [C: hoare_1875481847_state] :
            ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ C ) @ A ) )
           => ! [D: hoare_1875481847_state] :
                ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ D ) @ B ) )
               => ( C != D ) ) )
       => ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ B )
          = bot_bo1715400655e_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(205,axiom,
    ! [A: fun_bo1549164019l_bool,B: fun_Ho1996104121e_bool,C: hoare_1875481847_state] :
      ( ( hAPP_H377399461l_bool @ ( hAPP_f932622461l_bool @ ( cOMBB_242064253_state @ A ) @ B ) @ C )
      = ( hAPP_b589554111l_bool @ A @ ( hAPP_H1173941847e_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_222) ).

thf(1529,plain,
    ! [A: fun_bo1549164019l_bool,B: fun_Ho1996104121e_bool,C: hoare_1875481847_state] :
      ( ( hAPP_H377399461l_bool @ ( hAPP_f932622461l_bool @ ( cOMBB_242064253_state @ A ) @ B ) @ C )
      = ( hAPP_b589554111l_bool @ A @ ( hAPP_H1173941847e_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(277,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
        | ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_564_finite__Int) ).

thf(1803,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
        | ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(301,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] : ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ B ) @ C ) ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_662_distrib__sup__le) ).

thf(1887,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] : ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ B ) @ C ) ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(590,axiom,
    ! [A: pname,B: fun_pn1208287926_pname,C: fun_fu1499449723_pname] :
      ( ( hBOOL @ ( finite1282449217_pname @ B @ C ) )
     => ( ( hAPP_f1297739591_pname @ C @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ bot_bo844097828e_bool ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_513_folding__one_Osingleton) ).

thf(2957,plain,
    ! [A: pname,B: fun_pn1208287926_pname,C: fun_fu1499449723_pname] :
      ( ( hBOOL @ ( finite1282449217_pname @ B @ C ) )
     => ( ( hAPP_f1297739591_pname @ C @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ bot_bo844097828e_bool ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).

thf(694,axiom,
    ! [A: fun_fu689207471l_bool] :
      ( ( bot_bo973479705l_bool
        = ( hAPP_f900945761l_bool @ collec771609166e_bool @ A ) )
    <=> ! [B: fun_Ho1996104121e_bool] :
          ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_empty__Collect__eq) ).

thf(3335,plain,
    ! [A: fun_fu689207471l_bool] :
      ( ( ( bot_bo973479705l_bool
          = ( hAPP_f900945761l_bool @ collec771609166e_bool @ A ) )
       => ! [B: fun_Ho1996104121e_bool] :
            ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ A @ B ) ) )
      & ( ! [B: fun_Ho1996104121e_bool] :
            ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ A @ B ) )
       => ( bot_bo973479705l_bool
          = ( hAPP_f900945761l_bool @ collec771609166e_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).

thf(106,axiom,
    ! [A: bool] :
      ( ( A = fTrue )
      | ( A = fFalse ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).

thf(1196,plain,
    ! [A: bool] :
      ( ( A = fTrue )
      | ( A = fFalse ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(630,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho784854669_state,C: fun_fu385705929_state] :
      ( ( hBOOL @ ( finite1782051386_state @ B @ C ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ A ) )
       => ( ( A != bot_bo1715400655e_bool )
         => ( ! [D: hoare_1875481847_state,E: hoare_1875481847_state] : ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ ( hAPP_H350317809_state @ ( hAPP_H743221337_state @ B @ D ) @ E ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ D ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ E ) @ bot_bo1715400655e_bool ) ) ) )
           => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ ( hAPP_f890249627_state @ C @ A ) ) @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_516_folding__one_Oclosed) ).

thf(3103,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho784854669_state,C: fun_fu385705929_state] :
      ( ( hBOOL @ ( finite1782051386_state @ B @ C ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ A ) )
       => ( ( A != bot_bo1715400655e_bool )
         => ( ! [D: hoare_1875481847_state,E: hoare_1875481847_state] : ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ ( hAPP_H350317809_state @ ( hAPP_H743221337_state @ B @ D ) @ E ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ D ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ E ) @ bot_bo1715400655e_bool ) ) ) )
           => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ ( hAPP_f890249627_state @ C @ A ) ) @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).

thf(30,axiom,
    ! [A: pname,B: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ B )
     != bot_bo844097828e_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_insert__not__empty) ).

thf(898,plain,
    ! [A: pname,B: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ B )
     != bot_bo844097828e_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(57,axiom,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_set__mp) ).

thf(1001,plain,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(528,axiom,
    ! [A: fun_Ho1996104121e_bool,B: hoare_1875481847_state,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_UnI1) ).

thf(2723,plain,
    ! [A: fun_Ho1996104121e_bool,B: hoare_1875481847_state,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).

thf(92,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_439_le__supI2) ).

thf(1127,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(467,axiom,
    ! [A: fun_fu237807729l_bool,B: fun_fu689207471l_bool] :
      ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ B ) )
     => ( ( B != bot_bo973479705l_bool )
       => ( ! [C: fun_Ho1996104121e_bool] : ( hBOOL @ ( hAPP_f1699935247l_bool @ A @ ( hAPP_f900945761l_bool @ ( hAPP_f872497439l_bool @ insert504309043e_bool @ C ) @ bot_bo973479705l_bool ) ) )
         => ( ! [C: fun_Ho1996104121e_bool,D: fun_fu689207471l_bool] :
                ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ D ) )
               => ( ( D != bot_bo973479705l_bool )
                 => ( ~ ( hBOOL @ ( hAPP_f1699935247l_bool @ ( hAPP_f640685261l_bool @ member1062536460e_bool @ C ) @ D ) )
                   => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ A @ D ) )
                     => ( hBOOL @ ( hAPP_f1699935247l_bool @ A @ ( hAPP_f900945761l_bool @ ( hAPP_f872497439l_bool @ insert504309043e_bool @ C ) @ D ) ) ) ) ) ) )
           => ( hBOOL @ ( hAPP_f1699935247l_bool @ A @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_477_finite__ne__induct) ).

thf(2491,plain,
    ! [A: fun_fu237807729l_bool,B: fun_fu689207471l_bool] :
      ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ B ) )
     => ( ( B != bot_bo973479705l_bool )
       => ( ! [C: fun_Ho1996104121e_bool] : ( hBOOL @ ( hAPP_f1699935247l_bool @ A @ ( hAPP_f900945761l_bool @ ( hAPP_f872497439l_bool @ insert504309043e_bool @ C ) @ bot_bo973479705l_bool ) ) )
         => ( ! [C: fun_Ho1996104121e_bool,D: fun_fu689207471l_bool] :
                ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ D ) )
               => ( ( D != bot_bo973479705l_bool )
                 => ( ~ ( hBOOL @ ( hAPP_f1699935247l_bool @ ( hAPP_f640685261l_bool @ member1062536460e_bool @ C ) @ D ) )
                   => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ A @ D ) )
                     => ( hBOOL @ ( hAPP_f1699935247l_bool @ A @ ( hAPP_f900945761l_bool @ ( hAPP_f872497439l_bool @ insert504309043e_bool @ C ) @ D ) ) ) ) ) ) )
           => ( hBOOL @ ( hAPP_f1699935247l_bool @ A @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).

thf(123,axiom,
    ! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
      ( ( hAPP_f559147733l_bool @ ( hAPP_f1320879424l_bool @ insert1325755072e_bool @ A ) @ B )
      = ( hAPP_f559147733l_bool @ collec1974731493e_bool @ ( hAPP_f559147733l_bool @ ( hAPP_f624840228l_bool @ cOMBS_350070575l_bool @ ( hAPP_f143162813l_bool @ ( cOMBB_2095475776e_bool @ fdisj ) @ ( hAPP_f434788991l_bool @ ( hAPP_f1297925993l_bool @ cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ A ) ) ) @ ( hAPP_f559147733l_bool @ ( hAPP_f1145991873l_bool @ cOMBC_1988546018l_bool @ member799430823e_bool ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_insert__compr) ).

thf(1243,plain,
    ! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
      ( ( hAPP_f559147733l_bool @ ( hAPP_f1320879424l_bool @ insert1325755072e_bool @ A ) @ B )
      = ( hAPP_f559147733l_bool @ collec1974731493e_bool @ ( hAPP_f559147733l_bool @ ( hAPP_f624840228l_bool @ cOMBS_350070575l_bool @ ( hAPP_f143162813l_bool @ ( cOMBB_2095475776e_bool @ fdisj ) @ ( hAPP_f434788991l_bool @ ( hAPP_f1297925993l_bool @ cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ A ) ) ) @ ( hAPP_f559147733l_bool @ ( hAPP_f1145991873l_bool @ cOMBC_1988546018l_bool @ member799430823e_bool ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(201,axiom,
    ! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ C ) )
      = ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ A ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_Un__insert__right) ).

thf(1518,plain,
    ! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ C ) )
      = ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(129,axiom,
    ! [A: fun_fu90736755l_bool,B: fun_fu689207471l_bool,C: fun_fu689207471l_bool] :
      ( ( hAPP_f1699935247l_bool @ ( hAPP_f1970936639l_bool @ ( hAPP_f1475014121l_bool @ cOMBC_686159718l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1699935247l_bool @ ( hAPP_f1970936639l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__) ).

thf(1265,plain,
    ! [A: fun_fu90736755l_bool,B: fun_fu689207471l_bool,C: fun_fu689207471l_bool] :
      ( ( hAPP_f1699935247l_bool @ ( hAPP_f1970936639l_bool @ ( hAPP_f1475014121l_bool @ cOMBC_686159718l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1699935247l_bool @ ( hAPP_f1970936639l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(249,axiom,
    ! [A: fun_pn422929397l_bool,B: fun_pname_bool,C: pname] :
      ( ( hAPP_pname_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f661147897e_bool @ cOMBC_1058051404l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob) ).

thf(1703,plain,
    ! [A: fun_pn422929397l_bool,B: fun_pname_bool,C: pname] :
      ( ( hAPP_pname_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f661147897e_bool @ cOMBC_1058051404l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(419,axiom,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_subset__insertI2) ).

thf(2328,plain,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

thf(609,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) ) @ C )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_415_sup_Oassoc) ).

thf(3029,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) ) @ C )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).

thf(778,axiom,
    ! [A: fun_pn664418900_state,B: fun_pname_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ C ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ C ) @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ A ) @ B ) ) )
       => ? [D: fun_pname_bool] :
            ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ D ) )
            & ( C
              = ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ A ) @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_finite__subset__image) ).

thf(3644,plain,
    ! [A: fun_pn664418900_state,B: fun_pname_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ C ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ C ) @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ A ) @ B ) ) )
       => ? [D: fun_pname_bool] :
            ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ D ) )
            & ( C
              = ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ A ) @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).

thf(514,axiom,
    ! [A: pname] :
      ( ( hBOOL @ ( hAPP_pname_bool @ bot_bo844097828e_bool @ A ) )
    <=> ( hBOOL @ bot_bot_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_373_bot__apply) ).

thf(2667,plain,
    ! [A: pname] :
      ( ( ( hBOOL @ ( hAPP_pname_bool @ bot_bo844097828e_bool @ A ) )
       => ( hBOOL @ bot_bot_bool ) )
      & ( ( hBOOL @ bot_bot_bool )
       => ( hBOOL @ ( hAPP_pname_bool @ bot_bo844097828e_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).

thf(695,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
    <=> ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_446_le__iff__sup) ).

thf(3342,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
       => ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B )
          = B ) )
      & ( ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B )
          = B )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).

thf(535,axiom,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool,C: fun_fu1430349052l_bool,D: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ C ) @ D ) )
     => ( ! [E: fun_pname_bool] :
            ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ E ) @ C ) )
           => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ B @ E ) )
             => ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ E ) ) ) )
       => ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ ( hAPP_f559147733l_bool @ ( hAPP_f230953622l_bool @ semila1130628874l_bool @ C ) @ ( hAPP_f559147733l_bool @ collec1974731493e_bool @ B ) ) ) @ ( hAPP_f559147733l_bool @ ( hAPP_f230953622l_bool @ semila1130628874l_bool @ D ) @ ( hAPP_f559147733l_bool @ collec1974731493e_bool @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_672_Int__Collect__mono) ).

thf(2755,plain,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool,C: fun_fu1430349052l_bool,D: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ C ) @ D ) )
     => ( ! [E: fun_pname_bool] :
            ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ E ) @ C ) )
           => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ B @ E ) )
             => ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ E ) ) ) )
       => ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ ( hAPP_f559147733l_bool @ ( hAPP_f230953622l_bool @ semila1130628874l_bool @ C ) @ ( hAPP_f559147733l_bool @ collec1974731493e_bool @ B ) ) ) @ ( hAPP_f559147733l_bool @ ( hAPP_f230953622l_bool @ semila1130628874l_bool @ D ) @ ( hAPP_f559147733l_bool @ collec1974731493e_bool @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).

thf(619,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ ( hAPP_f121055253e_bool @ collec1735317154_state @ ( hAPP_f121055253e_bool @ ( hAPP_f1300953505e_bool @ cOMBS_896408300l_bool @ ( hAPP_f932622461l_bool @ ( cOMBB_242064253_state @ fdisj ) @ A ) ) @ B ) ) ) )
    <=> ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ ( hAPP_f121055253e_bool @ collec1735317154_state @ A ) ) )
        & ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ ( hAPP_f121055253e_bool @ collec1735317154_state @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_finite__Collect__disjI) ).

thf(3061,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ ( hAPP_f121055253e_bool @ collec1735317154_state @ ( hAPP_f121055253e_bool @ ( hAPP_f1300953505e_bool @ cOMBS_896408300l_bool @ ( hAPP_f932622461l_bool @ ( cOMBB_242064253_state @ fdisj ) @ A ) ) @ B ) ) ) )
       => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ ( hAPP_f121055253e_bool @ collec1735317154_state @ A ) ) )
          & ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ ( hAPP_f121055253e_bool @ collec1735317154_state @ B ) ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ ( hAPP_f121055253e_bool @ collec1735317154_state @ A ) ) )
          & ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ ( hAPP_f121055253e_bool @ collec1735317154_state @ B ) ) ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ ( hAPP_f121055253e_bool @ collec1735317154_state @ ( hAPP_f121055253e_bool @ ( hAPP_f1300953505e_bool @ cOMBS_896408300l_bool @ ( hAPP_f932622461l_bool @ ( cOMBB_242064253_state @ fdisj ) @ A ) ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).

thf(523,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_st1506752259e_bool,C: fun_state_bool,D: com] : ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ ( hAPP_f1863945078e_bool @ ( hAPP_f915354021e_bool @ cOMBC_952831051e_bool @ ( hAPP_f1138284024e_bool @ ( cOMBB_20296667_state @ cOMBS_1378840469l_bool ) @ ( hAPP_f1283379615l_bool @ ( cOMBB_1759179140_state @ ( cOMBB_188601460_state @ fconj ) ) @ B ) ) ) @ ( hAPP_f1759915619e_bool @ ( cOMBB_160679318_state @ fNot ) @ C ) ) ) @ ( while @ C @ D ) ) @ B ) ) @ bot_bo1715400655e_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_489_LoopF) ).

thf(2708,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_st1506752259e_bool,C: fun_state_bool,D: com] : ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ ( hAPP_f1863945078e_bool @ ( hAPP_f915354021e_bool @ cOMBC_952831051e_bool @ ( hAPP_f1138284024e_bool @ ( cOMBB_20296667_state @ cOMBS_1378840469l_bool ) @ ( hAPP_f1283379615l_bool @ ( cOMBB_1759179140_state @ ( cOMBB_188601460_state @ fconj ) ) @ B ) ) ) @ ( hAPP_f1759915619e_bool @ ( cOMBB_160679318_state @ fNot ) @ C ) ) ) @ ( while @ C @ D ) ) @ B ) ) @ bot_bo1715400655e_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).

thf(449,axiom,
    ( ( hAPP_p799580910on_com @ body @ pn )
    = ( some_com @ y ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_5) ).

thf(2444,plain,
    ( ( hAPP_p799580910on_com @ body @ pn )
    = ( some_com @ y ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).

thf(770,axiom,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_579_IntD1) ).

thf(3612,plain,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).

thf(35,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ A ) @ B ) ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_605_Int__lower2) ).

thf(917,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ A ) @ B ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(752,axiom,
    ! [A: pname,B: pname] :
      ( ( ( hAPP_pname_com @ body_1 @ A )
        = ( hAPP_pname_com @ body_1 @ B ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_com_Osimps_I6_J) ).

thf(3542,plain,
    ! [A: pname,B: pname] :
      ( ( ( ( hAPP_pname_com @ body_1 @ A )
          = ( hAPP_pname_com @ body_1 @ B ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( ( hAPP_pname_com @ body_1 @ A )
          = ( hAPP_pname_com @ body_1 @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).

thf(677,axiom,
    ! [A: com,B: fun_state_bool,C: state] :
      ( ~ ( hBOOL @ ( hAPP_state_bool @ B @ C ) )
     => ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ ( evalc @ ( while @ B @ A ) ) @ C ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_539_evalc_OWhileFalse) ).

thf(3280,plain,
    ! [A: com,B: fun_state_bool,C: state] :
      ( ~ ( hBOOL @ ( hAPP_state_bool @ B @ C ) )
     => ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ ( evalc @ ( while @ B @ A ) ) @ C ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).

thf(804,axiom,
    ! [A: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ A ) )
     => ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ ( hAPP_f900945761l_bool @ collec771609166e_bool @ ( hAPP_f1873026899l_bool @ ( hAPP_f2051277573l_bool @ cOMBC_195806106l_bool @ ord_le233469699e_bool ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_finite__Collect__subsets) ).

thf(3744,plain,
    ! [A: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ A ) )
     => ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ ( hAPP_f900945761l_bool @ collec771609166e_bool @ ( hAPP_f1873026899l_bool @ ( hAPP_f2051277573l_bool @ cOMBC_195806106l_bool @ ord_le233469699e_bool ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).

thf(697,axiom,
    ! [A: fun_Ho1996104121e_bool] :
      ( ( hAPP_f890249627_state @ the_el1031305112_state @ A )
      = ( hAPP_f890249627_state @ the_Ho1017792262_state @ ( hAPP_f169892419e_bool @ ( cOMBB_1380679615_state @ ( hAPP_f1873026899l_bool @ fequal259518520e_bool @ A ) ) @ ( hAPP_f56162711e_bool @ ( hAPP_f392546175e_bool @ cOMBC_483615668e_bool @ insert694999549_state ) @ bot_bo1715400655e_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_492_the__elem__def) ).

thf(3353,plain,
    ! [A: fun_Ho1996104121e_bool] :
      ( ( hAPP_f890249627_state @ the_el1031305112_state @ A )
      = ( hAPP_f890249627_state @ the_Ho1017792262_state @ ( hAPP_f169892419e_bool @ ( cOMBB_1380679615_state @ ( hAPP_f1873026899l_bool @ fequal259518520e_bool @ A ) ) @ ( hAPP_f56162711e_bool @ ( hAPP_f392546175e_bool @ cOMBC_483615668e_bool @ insert694999549_state ) @ bot_bo1715400655e_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).

thf(457,axiom,
    ! [A: fun_pn664418900_state,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ ( hAPP_p702226982_state @ A @ B ) ) @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_imageI) ).

thf(2466,plain,
    ! [A: fun_pn664418900_state,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ ( hAPP_p702226982_state @ A @ B ) ) @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).

thf(487,axiom,
    ! [A: fun_Ho1996104121e_bool] : ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ A ) @ bot_bo1715400655e_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_empty) ).

thf(2571,plain,
    ! [A: fun_Ho1996104121e_bool] : ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ A ) @ bot_bo1715400655e_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).

thf(806,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B )
        = bot_bo1715400655e_bool )
    <=> ( ( A = bot_bo1715400655e_bool )
        & ( B = bot_bo1715400655e_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_456_sup__eq__bot__iff) ).

thf(3749,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B )
          = bot_bo1715400655e_bool )
       => ( ( A = bot_bo1715400655e_bool )
          & ( B = bot_bo1715400655e_bool ) ) )
      & ( ( ( A = bot_bo1715400655e_bool )
          & ( B = bot_bo1715400655e_bool ) )
       => ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B )
          = bot_bo1715400655e_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).

thf(625,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ B ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ B ) @ C ) ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ C ) @ A ) )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ C ) ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ C ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_592_Un__Int__crazy) ).

thf(3089,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ B ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ B ) @ C ) ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ C ) @ A ) )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ C ) ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ C ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).

thf(184,axiom,
    ! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_UnI2) ).

thf(1462,plain,
    ! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(94,axiom,
    ! [A: fun_pname_bool,B: pname] :
      ( ( ( hBOOL @ ( hAPP_pname_bool @ A @ B ) )
       => ( ( hAPP_f759274231e_bool @ collect_pname @ ( hAPP_f759274231e_bool @ ( hAPP_f649174806e_bool @ cOMBS_568398431l_bool @ ( hAPP_f1402196763l_bool @ ( cOMBB_675860798_pname @ fconj ) @ ( hAPP_p61793385e_bool @ fequal_pname @ B ) ) ) @ A ) )
          = ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ bot_bo844097828e_bool ) ) )
      & ( ~ ( hBOOL @ ( hAPP_pname_bool @ A @ B ) )
       => ( ( hAPP_f759274231e_bool @ collect_pname @ ( hAPP_f759274231e_bool @ ( hAPP_f649174806e_bool @ cOMBS_568398431l_bool @ ( hAPP_f1402196763l_bool @ ( cOMBB_675860798_pname @ fconj ) @ ( hAPP_p61793385e_bool @ fequal_pname @ B ) ) ) @ A ) )
          = bot_bo844097828e_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_Collect__conv__if2) ).

thf(1132,plain,
    ! [A: fun_pname_bool,B: pname] :
      ( ( ( hBOOL @ ( hAPP_pname_bool @ A @ B ) )
       => ( ( hAPP_f759274231e_bool @ collect_pname @ ( hAPP_f759274231e_bool @ ( hAPP_f649174806e_bool @ cOMBS_568398431l_bool @ ( hAPP_f1402196763l_bool @ ( cOMBB_675860798_pname @ fconj ) @ ( hAPP_p61793385e_bool @ fequal_pname @ B ) ) ) @ A ) )
          = ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ bot_bo844097828e_bool ) ) )
      & ( ~ ( hBOOL @ ( hAPP_pname_bool @ A @ B ) )
       => ( ( hAPP_f759274231e_bool @ collect_pname @ ( hAPP_f759274231e_bool @ ( hAPP_f649174806e_bool @ cOMBS_568398431l_bool @ ( hAPP_f1402196763l_bool @ ( cOMBB_675860798_pname @ fconj ) @ ( hAPP_p61793385e_bool @ fequal_pname @ B ) ) ) @ A ) )
          = bot_bo844097828e_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(276,axiom,
    ! [A: fun_bool_bool,B: fun_pname_bool,C: pname] :
      ( ( hAPP_pname_bool @ ( hAPP_f759274231e_bool @ ( cOMBB_647938656_pname @ A ) @ B ) @ C )
      = ( hAPP_bool_bool @ A @ ( hAPP_pname_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname_U) ).

thf(1800,plain,
    ! [A: fun_bool_bool,B: fun_pname_bool,C: pname] :
      ( ( hAPP_pname_bool @ ( hAPP_f759274231e_bool @ ( cOMBB_647938656_pname @ A ) @ B ) @ C )
      = ( hAPP_bool_bool @ A @ ( hAPP_pname_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(376,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ! [D: fun_Ho1996104121e_bool,E: fun_Ho1996104121e_bool,F: fun_Ho1996104121e_bool] :
          ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ D ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ E ) @ F ) )
          = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ D ) @ E ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ D ) @ F ) ) )
     => ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ B ) @ C ) )
        = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_674_distrib__imp1) ).

thf(2169,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ! [D: fun_Ho1996104121e_bool,E: fun_Ho1996104121e_bool,F: fun_Ho1996104121e_bool] :
          ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ D ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ E ) @ F ) )
          = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ D ) @ E ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ D ) @ F ) ) )
     => ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ B ) @ C ) )
        = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(96,axiom,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ B ) @ C ) ) )
    <=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
        | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_Un__iff) ).

thf(1147,plain,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ B ) @ C ) ) )
       => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
          | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
          | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ B ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(480,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ A ) )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_order__antisym) ).

thf(2552,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ A ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).

thf(142,axiom,
    ! [A: fun_pn1580610524on_com,B: fun_pname_option_com,C: pname] :
      ( ( hAPP_p799580910on_com @ ( hAPP_f2123220539on_com @ ( hAPP_f1673966486on_com @ cOMBS_904531235on_com @ A ) @ B ) @ C )
      = ( hAPP_o356497025on_com @ ( hAPP_p1086945780on_com @ A @ C ) @ ( hAPP_p799580910on_com @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__Option__Ooption_Itc__Com__Ocom_J_) ).

thf(1319,plain,
    ! [A: fun_pn1580610524on_com,B: fun_pname_option_com,C: pname] :
      ( ( hAPP_p799580910on_com @ ( hAPP_f2123220539on_com @ ( hAPP_f1673966486on_com @ cOMBS_904531235on_com @ A ) @ B ) @ C )
      = ( hAPP_o356497025on_com @ ( hAPP_p1086945780on_com @ A @ C ) @ ( hAPP_p799580910on_com @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(539,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho784854669_state,D: fun_fu385705929_state] :
      ( ( hBOOL @ ( finite1514162941_state @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ B ) )
       => ( ( B != bot_bo1715400655e_bool )
         => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ A ) )
           => ( ( A != bot_bo1715400655e_bool )
             => ( ( hAPP_f890249627_state @ D @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ A ) )
                = ( hAPP_H350317809_state @ ( hAPP_H743221337_state @ C @ ( hAPP_f890249627_state @ D @ B ) ) @ ( hAPP_f890249627_state @ D @ A ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_464_folding__one__idem_Ounion__idem) ).

thf(2767,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho784854669_state,D: fun_fu385705929_state] :
      ( ( hBOOL @ ( finite1514162941_state @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ B ) )
       => ( ( B != bot_bo1715400655e_bool )
         => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ A ) )
           => ( ( A != bot_bo1715400655e_bool )
             => ( ( hAPP_f890249627_state @ D @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ A ) )
                = ( hAPP_H350317809_state @ ( hAPP_H743221337_state @ C @ ( hAPP_f890249627_state @ D @ B ) ) @ ( hAPP_f890249627_state @ D @ A ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).

thf(225,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
     => ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ A ) @ B )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_603_Int__absorb2) ).

thf(1609,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
     => ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ A ) @ B )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(433,axiom,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ B )
      = ( hAPP_f121055253e_bool @ collec1735317154_state @ ( hAPP_f121055253e_bool @ ( hAPP_f1300953505e_bool @ cOMBS_896408300l_bool @ ( hAPP_f932622461l_bool @ ( cOMBB_242064253_state @ fdisj ) @ ( hAPP_H117293375e_bool @ ( hAPP_f2101312745e_bool @ cOMBC_1972244470e_bool @ fequal391417144_state ) @ A ) ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1795624711e_bool @ cOMBC_1099403170l_bool @ member618553700_state ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_insert__compr) ).

thf(2373,plain,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ B )
      = ( hAPP_f121055253e_bool @ collec1735317154_state @ ( hAPP_f121055253e_bool @ ( hAPP_f1300953505e_bool @ cOMBS_896408300l_bool @ ( hAPP_f932622461l_bool @ ( cOMBB_242064253_state @ fdisj ) @ ( hAPP_H117293375e_bool @ ( hAPP_f2101312745e_bool @ cOMBC_1972244470e_bool @ fequal391417144_state ) @ A ) ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1795624711e_bool @ cOMBC_1099403170l_bool @ member618553700_state ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).

thf(800,axiom,
    ! [A: hoare_1875481847_state,B: hoare_1875481847_state] :
      ( ~ ( hBOOL @ ( hAPP_H1173941847e_bool @ ( hAPP_H117293375e_bool @ fequal391417144_state @ A ) @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc__Com) ).

thf(3734,plain,
    ! [A: hoare_1875481847_state,B: hoare_1875481847_state] :
      ( ~ ( hBOOL @ ( hAPP_H1173941847e_bool @ ( hAPP_H117293375e_bool @ fequal391417144_state @ A ) @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).

thf(372,axiom,
    ! [A: fun_pn249986828l_bool,B: fun_Ho1996104121e_bool,C: pname] :
      ( ( hAPP_pname_bool @ ( hAPP_f1148778334e_bool @ ( hAPP_f1967984667e_bool @ cOMBC_1788166607l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1408815105l_bool @ ( hAPP_p1265998686l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Hoare____Mirabelle____xl) ).

thf(2158,plain,
    ! [A: fun_pn249986828l_bool,B: fun_Ho1996104121e_bool,C: pname] :
      ( ( hAPP_pname_bool @ ( hAPP_f1148778334e_bool @ ( hAPP_f1967984667e_bool @ cOMBC_1788166607l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1408815105l_bool @ ( hAPP_p1265998686l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(268,axiom,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
      ( ( hAPP_f559147733l_bool @ collec1974731493e_bool @ ( hAPP_f559147733l_bool @ ( hAPP_f624840228l_bool @ cOMBS_350070575l_bool @ ( hAPP_f143162813l_bool @ ( cOMBB_2095475776e_bool @ fdisj ) @ A ) ) @ B ) )
      = ( hAPP_f559147733l_bool @ ( hAPP_f230953622l_bool @ semila1782091504l_bool @ ( hAPP_f559147733l_bool @ collec1974731493e_bool @ A ) ) @ ( hAPP_f559147733l_bool @ collec1974731493e_bool @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_Collect__disj__eq) ).

thf(1773,plain,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
      ( ( hAPP_f559147733l_bool @ collec1974731493e_bool @ ( hAPP_f559147733l_bool @ ( hAPP_f624840228l_bool @ cOMBS_350070575l_bool @ ( hAPP_f143162813l_bool @ ( cOMBB_2095475776e_bool @ fdisj ) @ A ) ) @ B ) )
      = ( hAPP_f559147733l_bool @ ( hAPP_f230953622l_bool @ semila1782091504l_bool @ ( hAPP_f559147733l_bool @ collec1974731493e_bool @ A ) ) @ ( hAPP_f559147733l_bool @ collec1974731493e_bool @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(154,axiom,
    ! [A: fun_bo79750167on_com,B: fun_pname_bool,C: pname] :
      ( ( hAPP_p1164893188on_com @ ( hAPP_f755519727on_com @ ( cOMBB_1394247784_pname @ A ) @ B ) @ C )
      = ( hAPP_b1679505845on_com @ A @ ( hAPP_pname_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__Option__Ooption_Itc__Com_) ).

thf(1362,plain,
    ! [A: fun_bo79750167on_com,B: fun_pname_bool,C: pname] :
      ( ( hAPP_p1164893188on_com @ ( hAPP_f755519727on_com @ ( cOMBB_1394247784_pname @ A ) @ B ) @ C )
      = ( hAPP_b1679505845on_com @ A @ ( hAPP_pname_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(298,axiom,
    ! [A: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ bot_bo1715400655e_bool ) @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_Un__empty__left) ).

thf(1875,plain,
    ! [A: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ bot_bo1715400655e_bool ) @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(559,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_xt1_I6_J) ).

thf(2852,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).

thf(3,axiom,
    ! [A: option_com,B: option_com] :
      ( ( hAPP_o356497025on_com @ ( hAPP_o334540577on_com @ ( hAPP_b1679505845on_com @ if_option_com @ fTrue ) @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_000tc__Option__Ooption_Itc__Com__Ocom_J_T) ).

thf(817,plain,
    ! [A: option_com,B: option_com] :
      ( ( hAPP_o356497025on_com @ ( hAPP_o334540577on_com @ ( hAPP_b1679505845on_com @ if_option_com @ fTrue ) @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(519,axiom,
    ! [A: hoare_1875481847_state,B: hoare_1875481847_state,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ C ) )
      = ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_insert__commute) ).

thf(2691,plain,
    ! [A: hoare_1875481847_state,B: hoare_1875481847_state,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ C ) )
      = ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).

thf(31,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
    <=> ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ A ) @ B )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_445_le__iff__sup) ).

thf(902,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
       => ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ A ) @ B )
          = B ) )
      & ( ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ A ) @ B )
          = B )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(728,axiom,
    ! [A: fun_fu385705929_state,B: fun_fu689207471l_bool] :
      ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ B ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ ( hAPP_f962122119e_bool @ ( image_1669234411_state @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_finite__imageI) ).

thf(3463,plain,
    ! [A: fun_fu385705929_state,B: fun_fu689207471l_bool] :
      ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ B ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ ( hAPP_f962122119e_bool @ ( image_1669234411_state @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).

thf(704,axiom,
    ! [A: fun_fu689207471l_bool,B: fun_fu1296727421e_bool,C: fun_fu947547457e_bool,D: fun_fu1163781179e_bool] :
      ( ( hBOOL @ ( finite1619424307e_bool @ C @ D ) )
     => ( ! [E: fun_Ho1996104121e_bool,F: fun_Ho1996104121e_bool] :
            ( ( hAPP_f121055253e_bool @ B @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ C @ E ) @ F ) )
            = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ C @ ( hAPP_f121055253e_bool @ B @ E ) ) @ ( hAPP_f121055253e_bool @ B @ F ) ) )
       => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ A ) )
         => ( ( A != bot_bo973479705l_bool )
           => ( ( hAPP_f121055253e_bool @ B @ ( hAPP_f962122119e_bool @ D @ A ) )
              = ( hAPP_f962122119e_bool @ D @ ( hAPP_f900945761l_bool @ ( image_1852024517e_bool @ B ) @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_486_folding__one__idem_Ohom__commute) ).

thf(3374,plain,
    ! [A: fun_fu689207471l_bool,B: fun_fu1296727421e_bool,C: fun_fu947547457e_bool,D: fun_fu1163781179e_bool] :
      ( ( hBOOL @ ( finite1619424307e_bool @ C @ D ) )
     => ( ! [E: fun_Ho1996104121e_bool,F: fun_Ho1996104121e_bool] :
            ( ( hAPP_f121055253e_bool @ B @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ C @ E ) @ F ) )
            = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ C @ ( hAPP_f121055253e_bool @ B @ E ) ) @ ( hAPP_f121055253e_bool @ B @ F ) ) )
       => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ A ) )
         => ( ( A != bot_bo973479705l_bool )
           => ( ( hAPP_f121055253e_bool @ B @ ( hAPP_f962122119e_bool @ D @ A ) )
              = ( hAPP_f962122119e_bool @ D @ ( hAPP_f900945761l_bool @ ( image_1852024517e_bool @ B ) @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).

thf(88,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ B )
      = ( hAPP_f121055253e_bool @ collec1735317154_state @ ( hAPP_f121055253e_bool @ ( hAPP_f1300953505e_bool @ cOMBS_896408300l_bool @ ( hAPP_f932622461l_bool @ ( cOMBB_242064253_state @ fconj ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1795624711e_bool @ cOMBC_1099403170l_bool @ member618553700_state ) @ A ) ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1795624711e_bool @ cOMBC_1099403170l_bool @ member618553700_state ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_573_Int__def) ).

thf(1115,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ B )
      = ( hAPP_f121055253e_bool @ collec1735317154_state @ ( hAPP_f121055253e_bool @ ( hAPP_f1300953505e_bool @ cOMBS_896408300l_bool @ ( hAPP_f932622461l_bool @ ( cOMBB_242064253_state @ fconj ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1795624711e_bool @ cOMBC_1099403170l_bool @ member618553700_state ) @ A ) ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1795624711e_bool @ cOMBC_1099403170l_bool @ member618553700_state ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(731,axiom,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( hAPP_f559147733l_bool @ collec1974731493e_bool @ ( hAPP_f559147733l_bool @ ( hAPP_f624840228l_bool @ cOMBS_350070575l_bool @ ( hAPP_f143162813l_bool @ ( cOMBB_2095475776e_bool @ fdisj ) @ A ) ) @ B ) ) ) )
    <=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( hAPP_f559147733l_bool @ collec1974731493e_bool @ A ) ) )
        & ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( hAPP_f559147733l_bool @ collec1974731493e_bool @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_finite__Collect__disjI) ).

thf(3470,plain,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
      ( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( hAPP_f559147733l_bool @ collec1974731493e_bool @ ( hAPP_f559147733l_bool @ ( hAPP_f624840228l_bool @ cOMBS_350070575l_bool @ ( hAPP_f143162813l_bool @ ( cOMBB_2095475776e_bool @ fdisj ) @ A ) ) @ B ) ) ) )
       => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( hAPP_f559147733l_bool @ collec1974731493e_bool @ A ) ) )
          & ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( hAPP_f559147733l_bool @ collec1974731493e_bool @ B ) ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( hAPP_f559147733l_bool @ collec1974731493e_bool @ A ) ) )
          & ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( hAPP_f559147733l_bool @ collec1974731493e_bool @ B ) ) ) )
       => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( hAPP_f559147733l_bool @ collec1974731493e_bool @ ( hAPP_f559147733l_bool @ ( hAPP_f624840228l_bool @ cOMBS_350070575l_bool @ ( hAPP_f143162813l_bool @ ( cOMBB_2095475776e_bool @ fdisj ) @ A ) ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).

thf(689,axiom,
    ! [A: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ A ) )
    <=> ( ( A = bot_bo1715400655e_bool )
        | ? [B: fun_Ho1996104121e_bool,C: hoare_1875481847_state] :
            ( ( A
              = ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ C ) @ B ) )
            & ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_finite_Osimps) ).

thf(3312,plain,
    ! [A: fun_Ho1996104121e_bool] :
      ( ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ A ) )
       => ( ( A = bot_bo1715400655e_bool )
          | ? [B: fun_Ho1996104121e_bool,C: hoare_1875481847_state] :
              ( ( A
                = ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ C ) @ B ) )
              & ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ B ) ) ) ) )
      & ( ( ( A = bot_bo1715400655e_bool )
          | ? [B: fun_Ho1996104121e_bool,C: hoare_1875481847_state] :
              ( ( A
                = ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ C ) @ B ) )
              & ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ B ) ) ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).

thf(782,axiom,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ B ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ C ) )
      = ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ B ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_618_insert__inter__insert) ).

thf(3657,plain,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ B ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ C ) )
      = ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).

thf(313,axiom,
    ! [A: fun_fu235184776_pname,B: fun_fu689207471l_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ ( hAPP_f75069804e_bool @ ( image_1169820240_pname @ A ) @ B ) ) )
       => ? [D: fun_fu689207471l_bool] :
            ( ( hBOOL @ ( hAPP_f1699935247l_bool @ ( hAPP_f1970936639l_bool @ ord_le724727525l_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ D ) )
            & ( C
              = ( hAPP_f75069804e_bool @ ( image_1169820240_pname @ A ) @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_finite__subset__image) ).

thf(1931,plain,
    ! [A: fun_fu235184776_pname,B: fun_fu689207471l_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ ( hAPP_f75069804e_bool @ ( image_1169820240_pname @ A ) @ B ) ) )
       => ? [D: fun_fu689207471l_bool] :
            ( ( hBOOL @ ( hAPP_f1699935247l_bool @ ( hAPP_f1970936639l_bool @ ord_le724727525l_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ D ) )
            & ( C
              = ( hAPP_f75069804e_bool @ ( image_1169820240_pname @ A ) @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(412,axiom,
    ! [A: pname,B: option_pname] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( set_pname @ B ) ) )
    <=> ( B
        = ( some_pname @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_405_elem__set) ).

thf(2301,plain,
    ! [A: pname,B: option_pname] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( set_pname @ B ) ) )
       => ( B
          = ( some_pname @ A ) ) )
      & ( ( B
          = ( some_pname @ A ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( set_pname @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(281,axiom,
    ! [A: pname,B: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ ( hAPP_f759274231e_bool @ collect_pname @ B ) )
      = ( hAPP_f759274231e_bool @ collect_pname @ ( hAPP_f759274231e_bool @ ( hAPP_f649174806e_bool @ cOMBS_568398431l_bool @ ( hAPP_f1402196763l_bool @ ( cOMBB_675860798_pname @ fimplies ) @ ( hAPP_f759274231e_bool @ ( cOMBB_647938656_pname @ fNot ) @ ( hAPP_p61793385e_bool @ ( hAPP_f22061361e_bool @ cOMBC_1149511130e_bool @ fequal_pname ) @ A ) ) ) ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_insert__Collect) ).

thf(1815,plain,
    ! [A: pname,B: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ ( hAPP_f759274231e_bool @ collect_pname @ B ) )
      = ( hAPP_f759274231e_bool @ collect_pname @ ( hAPP_f759274231e_bool @ ( hAPP_f649174806e_bool @ cOMBS_568398431l_bool @ ( hAPP_f1402196763l_bool @ ( cOMBB_675860798_pname @ fimplies ) @ ( hAPP_f759274231e_bool @ ( cOMBB_647938656_pname @ fNot ) @ ( hAPP_p61793385e_bool @ ( hAPP_f22061361e_bool @ cOMBC_1149511130e_bool @ fequal_pname ) @ A ) ) ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(335,axiom,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_finite__insert) ).

thf(2007,plain,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool] :
      ( ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ B ) ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ B ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(390,axiom,
    ! [A: fun_Ho1653816318_pname,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f1148778334e_bool @ ( image_720060442_pname @ A ) @ B ) ) @ ( hAPP_f1148778334e_bool @ ( image_720060442_pname @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_image__mono) ).

thf(2222,plain,
    ! [A: fun_Ho1653816318_pname,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f1148778334e_bool @ ( image_720060442_pname @ A ) @ B ) ) @ ( hAPP_f1148778334e_bool @ ( image_720060442_pname @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(38,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_fu410713561e_bool,D: fun_pname_bool] :
      ( ( B
        = ( hAPP_f759274231e_bool @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ D ) )
       => ( ! [E: fun_pname_bool,F: fun_pname_bool] :
              ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ F ) @ E ) )
             => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f759274231e_bool @ C @ F ) ) @ ( hAPP_f759274231e_bool @ C @ E ) ) ) )
         => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f759274231e_bool @ C @ A ) ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_546_xt1_I15_J) ).

thf(924,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_fu410713561e_bool,D: fun_pname_bool] :
      ( ( B
        = ( hAPP_f759274231e_bool @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ D ) )
       => ( ! [E: fun_pname_bool,F: fun_pname_bool] :
              ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ F ) @ E ) )
             => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f759274231e_bool @ C @ F ) ) @ ( hAPP_f759274231e_bool @ C @ E ) ) ) )
         => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f759274231e_bool @ C @ A ) ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(500,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ A ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_434_le__supI) ).

thf(2616,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ A ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).

thf(747,axiom,
    ! [A: fun_fu689207471l_bool,B: fun_fu689207471l_bool] :
      ( ( hBOOL @ ( hAPP_f1699935247l_bool @ ( hAPP_f1970936639l_bool @ ord_le724727525l_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ B ) )
       => ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_finite__subset) ).

thf(3524,plain,
    ! [A: fun_fu689207471l_bool,B: fun_fu689207471l_bool] :
      ( ( hBOOL @ ( hAPP_f1699935247l_bool @ ( hAPP_f1970936639l_bool @ ord_le724727525l_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ B ) )
       => ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).

thf(709,axiom,
    ! [A: fun_fu1604182422_state,B: fun_fu1430349052l_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ C ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ C ) @ ( hAPP_f1440968210e_bool @ ( image_1943894628_state @ A ) @ B ) ) )
       => ? [D: fun_fu1430349052l_bool] :
            ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ D ) )
            & ( C
              = ( hAPP_f1440968210e_bool @ ( image_1943894628_state @ A ) @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_finite__subset__image) ).

thf(3393,plain,
    ! [A: fun_fu1604182422_state,B: fun_fu1430349052l_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ C ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ C ) @ ( hAPP_f1440968210e_bool @ ( image_1943894628_state @ A ) @ B ) ) )
       => ? [D: fun_fu1430349052l_bool] :
            ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ D ) )
            & ( C
              = ( hAPP_f1440968210e_bool @ ( image_1943894628_state @ A ) @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).

thf(683,axiom,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
      ( ! [C: fun_pname_bool] :
          ( ( hBOOL @ ( hAPP_f1664156314l_bool @ B @ C ) )
         => ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ C ) ) )
     => ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ ( hAPP_f559147733l_bool @ collec1974731493e_bool @ B ) ) @ ( hAPP_f559147733l_bool @ collec1974731493e_bool @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_523_Collect__mono) ).

thf(3295,plain,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
      ( ! [C: fun_pname_bool] :
          ( ( hBOOL @ ( hAPP_f1664156314l_bool @ B @ C ) )
         => ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ C ) ) )
     => ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ ( hAPP_f559147733l_bool @ collec1974731493e_bool @ B ) ) @ ( hAPP_f559147733l_bool @ collec1974731493e_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).

thf(773,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ ( hAPP_f121055253e_bool @ collec1735317154_state @ B ) ) )
        | ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ ( hAPP_f121055253e_bool @ collec1735317154_state @ A ) ) ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ ( hAPP_f121055253e_bool @ collec1735317154_state @ ( hAPP_f121055253e_bool @ ( hAPP_f1300953505e_bool @ cOMBS_896408300l_bool @ ( hAPP_f932622461l_bool @ ( cOMBB_242064253_state @ fconj ) @ B ) ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_finite__Collect__conjI) ).

thf(3621,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ ( hAPP_f121055253e_bool @ collec1735317154_state @ B ) ) )
        | ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ ( hAPP_f121055253e_bool @ collec1735317154_state @ A ) ) ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ ( hAPP_f121055253e_bool @ collec1735317154_state @ ( hAPP_f121055253e_bool @ ( hAPP_f1300953505e_bool @ cOMBS_896408300l_bool @ ( hAPP_f932622461l_bool @ ( cOMBB_242064253_state @ fconj ) @ B ) ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).

thf(243,axiom,
    ! [A: fun_st277393160e_bool,B: fun_state_bool,C: state] :
      ( ( hAPP_s1806633685e_bool @ ( hAPP_f1863945078e_bool @ ( hAPP_f915354021e_bool @ cOMBC_952831051e_bool @ A ) @ B ) @ C )
      = ( hAPP_f1759915619e_bool @ ( hAPP_s1226857760e_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Ostate_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Ob) ).

thf(1677,plain,
    ! [A: fun_st277393160e_bool,B: fun_state_bool,C: state] :
      ( ( hAPP_s1806633685e_bool @ ( hAPP_f1863945078e_bool @ ( hAPP_f915354021e_bool @ cOMBC_952831051e_bool @ A ) @ B ) @ C )
      = ( hAPP_f1759915619e_bool @ ( hAPP_s1226857760e_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(481,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( B = C )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_351_ord__eq__le__trans) ).

thf(2555,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( B = C )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).

thf(50,axiom,
    ! [A: fun_pname_bool,B: pname] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_subset__insertI) ).

thf(966,plain,
    ! [A: fun_pname_bool,B: pname] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(644,axiom,
    ! [A: state,B: state] :
      ( ~ ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ fequal_state @ A ) @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Com__Ostate_T) ).

thf(3152,plain,
    ! [A: state,B: state] :
      ( ~ ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ fequal_state @ A ) @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).

thf(358,axiom,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ minus_589155914e_bool @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ bot_bo1715400655e_bool ) ) )
      = ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_697_insert__Diff__single) ).

thf(2105,plain,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ minus_589155914e_bool @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ bot_bo1715400655e_bool ) ) )
      = ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(623,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ A ) )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_equalityI) ).

thf(3075,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ A ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).

thf(180,axiom,
    ! [A: bool,B: pname] :
      ( ( hAPP_pname_bool @ ( cOMBK_bool_pname @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Com__Opname_U) ).

thf(1450,plain,
    ! [A: bool,B: pname] :
      ( ( hAPP_pname_bool @ ( cOMBK_bool_pname @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(86,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_447_sup__ge2) ).

thf(1109,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(234,axiom,
    ! [A: fun_pn1673019570on_com,B: fun_pname_option_com,C: pname] :
      ( ( hAPP_p1086945780on_com @ ( hAPP_f648377725on_com @ ( hAPP_f2093196134on_com @ cOMBS_1529518335on_com @ A ) @ B ) @ C )
      = ( hAPP_o334540577on_com @ ( hAPP_p1164893188on_com @ A @ C ) @ ( hAPP_p799580910on_com @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__Option__Ooption_Itc__Com__Ocom_J__227) ).

thf(1632,plain,
    ! [A: fun_pn1673019570on_com,B: fun_pname_option_com,C: pname] :
      ( ( hAPP_p1086945780on_com @ ( hAPP_f648377725on_com @ ( hAPP_f2093196134on_com @ cOMBS_1529518335on_com @ A ) @ B ) @ C )
      = ( hAPP_o334540577on_com @ ( hAPP_p1164893188on_com @ A @ C ) @ ( hAPP_p799580910on_com @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(245,axiom,
    ! [A: fun_st2063251938l_bool,B: bool,C: state] :
      ( ( hAPP_state_bool @ ( hAPP_b2019457360e_bool @ ( hAPP_f167292325e_bool @ cOMBC_231445413l_bool @ A ) @ B ) @ C )
      = ( hAPP_bool_bool @ ( hAPP_s58564346l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Ostate_000tc__HOL__Obool_000tc__HOL__Obool_U) ).

thf(1682,plain,
    ! [A: fun_st2063251938l_bool,B: bool,C: state] :
      ( ( hAPP_state_bool @ ( hAPP_b2019457360e_bool @ ( hAPP_f167292325e_bool @ cOMBC_231445413l_bool @ A ) @ B ) @ C )
      = ( hAPP_bool_bool @ ( hAPP_s58564346l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(9,axiom,
    ! [A: fun_bo840793679_state,B: fun_pname_bool,C: pname] :
      ( ( hAPP_p1513527868_state @ ( hAPP_f980169511_state @ ( cOMBB_1989814576_pname @ A ) @ B ) @ C )
      = ( hAPP_b1347637997_state @ A @ ( hAPP_pname_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__Hoare____Mirabelle____xlr) ).

thf(834,plain,
    ! [A: fun_bo840793679_state,B: fun_pname_bool,C: pname] :
      ( ( hAPP_p1513527868_state @ ( hAPP_f980169511_state @ ( cOMBB_1989814576_pname @ A ) @ B ) @ C )
      = ( hAPP_b1347637997_state @ A @ ( hAPP_pname_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(160,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
    <=> ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ A ) @ B )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_subset__Un__eq) ).

thf(1383,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
       => ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ A ) @ B )
          = B ) )
      & ( ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ A ) @ B )
          = B )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(63,axiom,
    ! [A: pname,B: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ B )
      = ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ bot_bo844097828e_bool ) ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_insert__is__Un) ).

thf(1020,plain,
    ! [A: pname,B: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ B )
      = ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ bot_bo844097828e_bool ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(398,axiom,
    ! [A: com,B: fun_st1506752259e_bool,C: fun_Ho1996104121e_bool,D: fun_st1506752259e_bool,E: com,F: fun_st1506752259e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ C ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ D ) @ E ) @ F ) ) @ bot_bo1715400655e_bool ) ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ C ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ F ) @ A ) @ B ) ) @ bot_bo1715400655e_bool ) ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ C ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ D ) @ ( semi @ E @ A ) ) @ B ) ) @ bot_bo1715400655e_bool ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_490_Comp) ).

thf(2254,plain,
    ! [A: com,B: fun_st1506752259e_bool,C: fun_Ho1996104121e_bool,D: fun_st1506752259e_bool,E: com,F: fun_st1506752259e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ C ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ D ) @ E ) @ F ) ) @ bot_bo1715400655e_bool ) ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ C ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ F ) @ A ) @ B ) ) @ bot_bo1715400655e_bool ) ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ C ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ D ) @ ( semi @ E @ A ) ) @ B ) ) @ bot_bo1715400655e_bool ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

thf(134,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( hAPP_f759274231e_bool @ collect_pname @ ( hAPP_f759274231e_bool @ ( hAPP_f649174806e_bool @ cOMBS_568398431l_bool @ ( hAPP_f1402196763l_bool @ ( cOMBB_675860798_pname @ fdisj ) @ A ) ) @ B ) ) ) )
    <=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( hAPP_f759274231e_bool @ collect_pname @ A ) ) )
        & ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( hAPP_f759274231e_bool @ collect_pname @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_finite__Collect__disjI) ).

thf(1283,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( hAPP_f759274231e_bool @ collect_pname @ ( hAPP_f759274231e_bool @ ( hAPP_f649174806e_bool @ cOMBS_568398431l_bool @ ( hAPP_f1402196763l_bool @ ( cOMBB_675860798_pname @ fdisj ) @ A ) ) @ B ) ) ) )
       => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( hAPP_f759274231e_bool @ collect_pname @ A ) ) )
          & ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( hAPP_f759274231e_bool @ collect_pname @ B ) ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( hAPP_f759274231e_bool @ collect_pname @ A ) ) )
          & ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( hAPP_f759274231e_bool @ collect_pname @ B ) ) ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( hAPP_f759274231e_bool @ collect_pname @ ( hAPP_f759274231e_bool @ ( hAPP_f649174806e_bool @ cOMBS_568398431l_bool @ ( hAPP_f1402196763l_bool @ ( cOMBB_675860798_pname @ fdisj ) @ A ) ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(349,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( A = B )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_355_order__eq__refl) ).

thf(2073,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( A = B )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(470,axiom,
    ! [A: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ bot_bo1715400655e_bool ) )
    <=> ( A = bot_bo1715400655e_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_subset__empty) ).

thf(2508,plain,
    ! [A: fun_Ho1996104121e_bool] :
      ( ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ bot_bo1715400655e_bool ) )
       => ( A = bot_bo1715400655e_bool ) )
      & ( ( A = bot_bo1715400655e_bool )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ bot_bo1715400655e_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).

thf(304,axiom,
    ! [A: pname] :
      ( skip
     != ( hAPP_pname_com @ body_1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_479_com_Osimps_I18_J) ).

thf(1896,plain,
    ! [A: pname] :
      ( skip
     != ( hAPP_pname_com @ body_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(740,axiom,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ B ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_finite_OinsertI) ).

thf(3505,plain,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ B ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).

thf(443,axiom,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ ( hAPP_f121055253e_bool @ collec1735317154_state @ B ) )
      = ( hAPP_f121055253e_bool @ collec1735317154_state @ ( hAPP_f121055253e_bool @ ( hAPP_f1300953505e_bool @ cOMBS_896408300l_bool @ ( hAPP_f932622461l_bool @ ( cOMBB_242064253_state @ fimplies ) @ ( hAPP_f121055253e_bool @ ( cOMBB_1424001755_state @ fNot ) @ ( hAPP_H117293375e_bool @ ( hAPP_f2101312745e_bool @ cOMBC_1972244470e_bool @ fequal391417144_state ) @ A ) ) ) ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_insert__Collect) ).

thf(2424,plain,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ ( hAPP_f121055253e_bool @ collec1735317154_state @ B ) )
      = ( hAPP_f121055253e_bool @ collec1735317154_state @ ( hAPP_f121055253e_bool @ ( hAPP_f1300953505e_bool @ cOMBS_896408300l_bool @ ( hAPP_f932622461l_bool @ ( cOMBB_242064253_state @ fimplies ) @ ( hAPP_f121055253e_bool @ ( cOMBB_1424001755_state @ fNot ) @ ( hAPP_H117293375e_bool @ ( hAPP_f2101312745e_bool @ cOMBC_1972244470e_bool @ fequal391417144_state ) @ A ) ) ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).

thf(541,axiom,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( hAPP_f559147733l_bool @ ( hAPP_f230953622l_bool @ semila1782091504l_bool @ A ) @ B ) ) )
    <=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) )
        & ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_finite__Un) ).

thf(2772,plain,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
      ( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( hAPP_f559147733l_bool @ ( hAPP_f230953622l_bool @ semila1782091504l_bool @ A ) @ B ) ) )
       => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) )
          & ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) )
          & ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) ) )
       => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( hAPP_f559147733l_bool @ ( hAPP_f230953622l_bool @ semila1782091504l_bool @ A ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).

thf(150,axiom,
    ! [A: pname,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
     => ( ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ minus_1015773161e_bool @ B ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ bot_bo844097828e_bool ) ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_692_insert__Diff) ).

thf(1351,plain,
    ! [A: pname,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
     => ( ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ minus_1015773161e_bool @ B ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ bot_bo844097828e_bool ) ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(56,axiom,
    ! [A: fun_fu1173762305l_bool,B: fun_pn760644914e_bool,C: pname] :
      ( ( hAPP_p1265998686l_bool @ ( hAPP_f98146217l_bool @ ( cOMBB_2094848682_pname @ A ) @ B ) @ C )
      = ( hAPP_f1873026899l_bool @ A @ ( hAPP_p1537966538e_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Otriple_I_240) ).

thf(998,plain,
    ! [A: fun_fu1173762305l_bool,B: fun_pn760644914e_bool,C: pname] :
      ( ( hAPP_p1265998686l_bool @ ( hAPP_f98146217l_bool @ ( cOMBB_2094848682_pname @ A ) @ B ) @ C )
      = ( hAPP_f1873026899l_bool @ A @ ( hAPP_p1537966538e_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(533,axiom,
    ! [A: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_425_sup__idem) ).

thf(2750,plain,
    ! [A: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).

thf(665,axiom,
    ! [A: fun_fu689207471l_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ C ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ C ) @ B ) )
       => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ A @ bot_bo1715400655e_bool ) )
         => ( ! [D: hoare_1875481847_state,E: fun_Ho1996104121e_bool] :
                ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ E ) )
               => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ D ) @ B ) )
                 => ( ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ D ) @ E ) )
                   => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ A @ E ) )
                     => ( hBOOL @ ( hAPP_f1408815105l_bool @ A @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ D ) @ E ) ) ) ) ) ) )
           => ( hBOOL @ ( hAPP_f1408815105l_bool @ A @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_finite__subset__induct) ).

thf(3226,plain,
    ! [A: fun_fu689207471l_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ C ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ C ) @ B ) )
       => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ A @ bot_bo1715400655e_bool ) )
         => ( ! [D: hoare_1875481847_state,E: fun_Ho1996104121e_bool] :
                ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ E ) )
               => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ D ) @ B ) )
                 => ( ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ D ) @ E ) )
                   => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ A @ E ) )
                     => ( hBOOL @ ( hAPP_f1408815105l_bool @ A @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ D ) @ E ) ) ) ) ) ) )
           => ( hBOOL @ ( hAPP_f1408815105l_bool @ A @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).

thf(593,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) ) @ C ) )
    <=> ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ C ) )
        & ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_444_le__sup__iff) ).

thf(2965,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) ) @ C ) )
       => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ C ) )
          & ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ C ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ C ) )
          & ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ C ) ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).

thf(651,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho784854669_state,D: fun_fu385705929_state] :
      ( ( hBOOL @ ( finite1782051386_state @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ B ) )
       => ( ( B != bot_bo1715400655e_bool )
         => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ A ) )
           => ( ( A != bot_bo1715400655e_bool )
             => ( ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ B ) @ A )
                  = bot_bo1715400655e_bool )
               => ( ( hAPP_f890249627_state @ D @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ A ) )
                  = ( hAPP_H350317809_state @ ( hAPP_H743221337_state @ C @ ( hAPP_f890249627_state @ D @ B ) ) @ ( hAPP_f890249627_state @ D @ A ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_557_folding__one_Ounion__disjoint) ).

thf(3184,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho784854669_state,D: fun_fu385705929_state] :
      ( ( hBOOL @ ( finite1782051386_state @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ B ) )
       => ( ( B != bot_bo1715400655e_bool )
         => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ A ) )
           => ( ( A != bot_bo1715400655e_bool )
             => ( ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ B ) @ A )
                  = bot_bo1715400655e_bool )
               => ( ( hAPP_f890249627_state @ D @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ A ) )
                  = ( hAPP_H350317809_state @ ( hAPP_H743221337_state @ C @ ( hAPP_f890249627_state @ D @ B ) ) @ ( hAPP_f890249627_state @ D @ A ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).

thf(431,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ! [C: hoare_1875481847_state] :
          ( ( hBOOL @ ( hAPP_H1173941847e_bool @ B @ C ) )
         => ( hBOOL @ ( hAPP_H1173941847e_bool @ A @ C ) ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_526_predicate1I) ).

thf(2367,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ! [C: hoare_1875481847_state] :
          ( ( hBOOL @ ( hAPP_H1173941847e_bool @ B @ C ) )
         => ( hBOOL @ ( hAPP_H1173941847e_bool @ A @ C ) ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).

thf(750,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ A ) @ B ) )
      | ( hBOOL @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_3_1_U) ).

thf(3537,plain,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ A ) @ B ) )
      | ( hBOOL @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).

thf(501,axiom,
    ! [A: pname] :
      ( ( hBOOL @ ( hAPP_com_bool @ wt @ ( hAPP_pname_com @ body_1 @ A ) ) )
     => ~ ! [B: com] :
            ( ( hAPP_p799580910on_com @ body @ A )
           != ( some_com @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_WTs__elim__cases_I7_J) ).

thf(2618,plain,
    ! [A: pname] :
      ( ( hBOOL @ ( hAPP_com_bool @ wt @ ( hAPP_pname_com @ body_1 @ A ) ) )
     => ~ ! [B: com] :
            ( ( hAPP_p799580910on_com @ body @ A )
           != ( some_com @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).

thf(554,axiom,
    ! [A: fun_Ho1996104121e_bool,B: hoare_1875481847_state,C: fun_Ho1996104121e_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ C ) )
     => ( ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ A ) )
       => ( ( ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ C )
            = ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ A ) )
        <=> ( C = A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_insert__ident) ).

thf(2833,plain,
    ! [A: fun_Ho1996104121e_bool,B: hoare_1875481847_state,C: fun_Ho1996104121e_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ C ) )
     => ( ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ A ) )
       => ( ( ( ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ C )
              = ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ A ) )
           => ( C = A ) )
          & ( ( C = A )
           => ( ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ C )
              = ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).

thf(407,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ A ) )
      <=> ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_353_order__antisym__conv) ).

thf(2281,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
     => ( ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ A ) )
         => ( B = A ) )
        & ( ( B = A )
         => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

thf(563,axiom,
    ! [A: fun_fu1430349052l_bool] :
      ( ( bot_bo1649642514l_bool
        = ( hAPP_f559147733l_bool @ collec1974731493e_bool @ A ) )
    <=> ! [B: fun_pname_bool] :
          ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_empty__Collect__eq) ).

thf(2861,plain,
    ! [A: fun_fu1430349052l_bool] :
      ( ( ( bot_bo1649642514l_bool
          = ( hAPP_f559147733l_bool @ collec1974731493e_bool @ A ) )
       => ! [B: fun_pname_bool] :
            ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ B ) ) )
      & ( ! [B: fun_pname_bool] :
            ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ B ) )
       => ( bot_bo1649642514l_bool
          = ( hAPP_f559147733l_bool @ collec1974731493e_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).

thf(113,axiom,
    ! [A: fun_Ho1695028467e_bool,B: fun_pn664418900_state,C: pname] :
      ( ( hAPP_p1537966538e_bool @ ( hAPP_f1601283355e_bool @ ( cOMBB_2037342654_pname @ A ) @ B ) @ C )
      = ( hAPP_H117293375e_bool @ A @ ( hAPP_p702226982_state @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc__Com__) ).

thf(1215,plain,
    ! [A: fun_Ho1695028467e_bool,B: fun_pn664418900_state,C: pname] :
      ( ( hAPP_p1537966538e_bool @ ( hAPP_f1601283355e_bool @ ( cOMBB_2037342654_pname @ A ) @ B ) @ C )
      = ( hAPP_H117293375e_bool @ A @ ( hAPP_p702226982_state @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(204,axiom,
    ! [A: fun_fu1430349052l_bool] :
      ( ( hAPP_f559147733l_bool @ collec1974731493e_bool @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_Collect__def) ).

thf(1526,plain,
    ! [A: fun_fu1430349052l_bool] :
      ( ( hAPP_f559147733l_bool @ collec1974731493e_bool @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(366,axiom,
    ! [A: fun_fu1296727421e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool,D: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ C ) @ D ) )
     => ( ( ( hAPP_f121055253e_bool @ A @ C )
          = B )
       => ( ! [E: fun_Ho1996104121e_bool,F: fun_Ho1996104121e_bool] :
              ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ F ) @ E ) )
             => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f121055253e_bool @ A @ F ) ) @ ( hAPP_f121055253e_bool @ A @ E ) ) ) )
         => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ ( hAPP_f121055253e_bool @ A @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_549_xt1_I16_J) ).

thf(2137,plain,
    ! [A: fun_fu1296727421e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool,D: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ C ) @ D ) )
     => ( ( ( hAPP_f121055253e_bool @ A @ C )
          = B )
       => ( ! [E: fun_Ho1996104121e_bool,F: fun_Ho1996104121e_bool] :
              ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ F ) @ E ) )
             => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f121055253e_bool @ A @ F ) ) @ ( hAPP_f121055253e_bool @ A @ E ) ) ) )
         => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ ( hAPP_f121055253e_bool @ A @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(148,axiom,
    ! [A: fun_pname_bool] :
      ( ( hAPP_f559147733l_bool @ collec1974731493e_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ A ) )
      = ( hAPP_f559147733l_bool @ ( hAPP_f1320879424l_bool @ insert1325755072e_bool @ A ) @ bot_bo1649642514l_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_singleton__conv2) ).

thf(1345,plain,
    ! [A: fun_pname_bool] :
      ( ( hAPP_f559147733l_bool @ collec1974731493e_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ A ) )
      = ( hAPP_f559147733l_bool @ ( hAPP_f1320879424l_bool @ insert1325755072e_bool @ A ) @ bot_bo1649642514l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(507,axiom,
    ! [A: fun_Ho1653816318_pname,B: fun_pname_bool,C: fun_Ho1996104121e_bool] :
      ( ! [D: hoare_1875481847_state] :
          ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ D ) @ C ) )
         => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( hAPP_H139064010_pname @ A @ D ) ) @ B ) ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f1148778334e_bool @ ( image_720060442_pname @ A ) @ C ) ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_image__subsetI) ).

thf(2639,plain,
    ! [A: fun_Ho1653816318_pname,B: fun_pname_bool,C: fun_Ho1996104121e_bool] :
      ( ! [D: hoare_1875481847_state] :
          ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ D ) @ C ) )
         => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( hAPP_H139064010_pname @ A @ D ) ) @ B ) ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f1148778334e_bool @ ( image_720060442_pname @ A ) @ C ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).

thf(84,axiom,
    ! [A: pname,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_insertI2) ).

thf(1104,plain,
    ! [A: pname,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(15,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool @ collect_pname @ ( hAPP_f759274231e_bool @ ( hAPP_f649174806e_bool @ cOMBS_568398431l_bool @ ( hAPP_f1402196763l_bool @ ( cOMBB_675860798_pname @ fdisj ) @ A ) ) @ B ) )
      = ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ ( hAPP_f759274231e_bool @ collect_pname @ A ) ) @ ( hAPP_f759274231e_bool @ collect_pname @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_Collect__disj__eq) ).

thf(849,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool @ collect_pname @ ( hAPP_f759274231e_bool @ ( hAPP_f649174806e_bool @ cOMBS_568398431l_bool @ ( hAPP_f1402196763l_bool @ ( cOMBB_675860798_pname @ fdisj ) @ A ) ) @ B ) )
      = ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ ( hAPP_f759274231e_bool @ collect_pname @ A ) ) @ ( hAPP_f759274231e_bool @ collect_pname @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(768,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_equalityI) ).

thf(3606,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).

thf(202,axiom,
    ! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ A ) ) )
      <=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_subset__insert) ).

thf(1521,plain,
    ! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ A ) ) )
         => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ A ) ) )
        & ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ A ) )
         => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(742,axiom,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool,C: fun_Ho784854669_state,D: fun_fu385705929_state] :
      ( ( hBOOL @ ( finite1782051386_state @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ B ) )
       => ( ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ B ) )
         => ( ( B != bot_bo1715400655e_bool )
           => ( ( hAPP_f890249627_state @ D @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ B ) )
              = ( hAPP_H350317809_state @ ( hAPP_H743221337_state @ C @ A ) @ ( hAPP_f890249627_state @ D @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_510_folding__one_Oinsert) ).

thf(3510,plain,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool,C: fun_Ho784854669_state,D: fun_fu385705929_state] :
      ( ( hBOOL @ ( finite1782051386_state @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ B ) )
       => ( ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ B ) )
         => ( ( B != bot_bo1715400655e_bool )
           => ( ( hAPP_f890249627_state @ D @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ B ) )
              = ( hAPP_H350317809_state @ ( hAPP_H743221337_state @ C @ A ) @ ( hAPP_f890249627_state @ D @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).

thf(215,axiom,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ B ) ) @ C ) )
    <=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) )
        & ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_insert__subset) ).

thf(1564,plain,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ B ) ) @ C ) )
       => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) )
          & ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) )
          & ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ B ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(588,axiom,
    hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ fa ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).

thf(2954,plain,
    hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ fa ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).

thf(223,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pn1208287926_pname,D: fun_fu1499449723_pname] :
      ( ( hBOOL @ ( finite1282449217_pname @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
       => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
         => ( ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ B ) @ A )
             != bot_bo844097828e_bool )
           => ( ( hAPP_pname_pname @ ( hAPP_p1170154830_pname @ C @ ( hAPP_f1297739591_pname @ D @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ B ) @ A ) ) ) @ ( hAPP_f1297739591_pname @ D @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ B ) @ A ) ) )
              = ( hAPP_pname_pname @ ( hAPP_p1170154830_pname @ C @ ( hAPP_f1297739591_pname @ D @ B ) ) @ ( hAPP_f1297739591_pname @ D @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_552_folding__one_Ounion__inter) ).

thf(1604,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pn1208287926_pname,D: fun_fu1499449723_pname] :
      ( ( hBOOL @ ( finite1282449217_pname @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
       => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
         => ( ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ B ) @ A )
             != bot_bo844097828e_bool )
           => ( ( hAPP_pname_pname @ ( hAPP_p1170154830_pname @ C @ ( hAPP_f1297739591_pname @ D @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ B ) @ A ) ) ) @ ( hAPP_f1297739591_pname @ D @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ B ) @ A ) ) )
              = ( hAPP_pname_pname @ ( hAPP_p1170154830_pname @ C @ ( hAPP_f1297739591_pname @ D @ B ) ) @ ( hAPP_f1297739591_pname @ D @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(628,axiom,
    ! [A: fun_Ho1996104121e_bool,B: com,C: fun_st1506752259e_bool,D: fun_st1506752259e_bool] :
      ( ! [E: state,F: state] :
          ( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ D @ E ) @ F ) )
         => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ ( cOMBK_631994958_state @ ( hAPP_s1806633685e_bool @ ( hAPP_f817621513e_bool @ cOMBC_2027030106e_bool @ fequal_state ) @ F ) ) ) @ B ) @ ( cOMBK_631994958_state @ ( hAPP_s1806633685e_bool @ C @ E ) ) ) ) @ bot_bo1715400655e_bool ) ) ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ D ) @ B ) @ C ) ) @ bot_bo1715400655e_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_379_escape) ).

thf(3097,plain,
    ! [A: fun_Ho1996104121e_bool,B: com,C: fun_st1506752259e_bool,D: fun_st1506752259e_bool] :
      ( ! [E: state,F: state] :
          ( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ D @ E ) @ F ) )
         => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ ( cOMBK_631994958_state @ ( hAPP_s1806633685e_bool @ ( hAPP_f817621513e_bool @ cOMBC_2027030106e_bool @ fequal_state ) @ F ) ) ) @ B ) @ ( cOMBK_631994958_state @ ( hAPP_s1806633685e_bool @ C @ E ) ) ) ) @ bot_bo1715400655e_bool ) ) ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ D ) @ B ) @ C ) ) @ bot_bo1715400655e_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).

thf(605,axiom,
    ! [A: fun_fu689207471l_bool,B: fun_fu689207471l_bool] :
      ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ ( hAPP_f900945761l_bool @ ( hAPP_f19215249l_bool @ semila1703230395l_bool @ A ) @ B ) ) )
    <=> ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ A ) )
        & ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_finite__Un) ).

thf(3011,plain,
    ! [A: fun_fu689207471l_bool,B: fun_fu689207471l_bool] :
      ( ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ ( hAPP_f900945761l_bool @ ( hAPP_f19215249l_bool @ semila1703230395l_bool @ A ) @ B ) ) )
       => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ A ) )
          & ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ B ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ A ) )
          & ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ B ) ) )
       => ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ ( hAPP_f900945761l_bool @ ( hAPP_f19215249l_bool @ semila1703230395l_bool @ A ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).

thf(72,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ A ) @ B ) ) @ C ) )
     => ~ ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ C ) )
         => ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_427_le__supE) ).

thf(1067,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ A ) @ B ) ) @ C ) )
     => ~ ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ C ) )
         => ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(724,axiom,
    ! [A: fun_pn664418900_state,B: fun_pname_bool] :
      ( ( ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ A ) @ B )
        = bot_bo1715400655e_bool )
    <=> ( B = bot_bo844097828e_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_image__is__empty) ).

thf(3450,plain,
    ! [A: fun_pn664418900_state,B: fun_pname_bool] :
      ( ( ( ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ A ) @ B )
          = bot_bo1715400655e_bool )
       => ( B = bot_bo844097828e_bool ) )
      & ( ( B = bot_bo844097828e_bool )
       => ( ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ A ) @ B )
          = bot_bo1715400655e_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).

thf(726,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_st1506752259e_bool,C: pname,D: fun_st1506752259e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ B ) @ ( hAPP_option_com_com @ the_com @ ( hAPP_p799580910on_com @ body @ C ) ) ) @ D ) ) @ bot_bo1715400655e_bool ) ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ B ) @ ( hAPP_pname_com @ body_1 @ C ) ) @ D ) ) @ bot_bo1715400655e_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_weak__Body) ).

thf(3459,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_st1506752259e_bool,C: pname,D: fun_st1506752259e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ B ) @ ( hAPP_option_com_com @ the_com @ ( hAPP_p799580910on_com @ body @ C ) ) ) @ D ) ) @ bot_bo1715400655e_bool ) ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ B ) @ ( hAPP_pname_com @ body_1 @ C ) ) @ D ) ) @ bot_bo1715400655e_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).

thf(685,axiom,
    ! [A: pname,B: hoare_1875481847_state,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ C ) )
     => ( ( hAPP_f1148778334e_bool @ ( image_720060442_pname @ ( cOMBK_1595564845_state @ A ) ) @ C )
        = ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ bot_bo844097828e_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_image__constant) ).

thf(3301,plain,
    ! [A: pname,B: hoare_1875481847_state,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ C ) )
     => ( ( hAPP_f1148778334e_bool @ ( image_720060442_pname @ ( cOMBK_1595564845_state @ A ) ) @ C )
        = ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ bot_bo844097828e_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).

thf(383,axiom,
    ! [A: fun_fu689207471l_bool,B: fun_fu689207471l_bool,C: fun_fu947547457e_bool,D: fun_fu1163781179e_bool] :
      ( ( hBOOL @ ( finite1619424307e_bool @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ B ) )
       => ( ( B != bot_bo973479705l_bool )
         => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ A ) )
           => ( ( A != bot_bo973479705l_bool )
             => ( ( hAPP_f962122119e_bool @ D @ ( hAPP_f900945761l_bool @ ( hAPP_f19215249l_bool @ semila1703230395l_bool @ B ) @ A ) )
                = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ C @ ( hAPP_f962122119e_bool @ D @ B ) ) @ ( hAPP_f962122119e_bool @ D @ A ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_462_folding__one__idem_Ounion__idem) ).

thf(2204,plain,
    ! [A: fun_fu689207471l_bool,B: fun_fu689207471l_bool,C: fun_fu947547457e_bool,D: fun_fu1163781179e_bool] :
      ( ( hBOOL @ ( finite1619424307e_bool @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ B ) )
       => ( ( B != bot_bo973479705l_bool )
         => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ A ) )
           => ( ( A != bot_bo973479705l_bool )
             => ( ( hAPP_f962122119e_bool @ D @ ( hAPP_f900945761l_bool @ ( hAPP_f19215249l_bool @ semila1703230395l_bool @ B ) @ A ) )
                = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ C @ ( hAPP_f962122119e_bool @ D @ B ) ) @ ( hAPP_f962122119e_bool @ D @ A ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(489,axiom,
    ! [A: fun_Ho1996104121e_bool,B: hoare_1875481847_state,C: fun_Ho1996104121e_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ C ) )
     => ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ A ) ) @ C )
        = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_614_Int__insert__left__if0) ).

thf(2574,plain,
    ! [A: fun_Ho1996104121e_bool,B: hoare_1875481847_state,C: fun_Ho1996104121e_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ C ) )
     => ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ A ) ) @ C )
        = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).

thf(176,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f661147897e_bool @ cOMBC_1058051404l_bool @ member_pname ) @ A ) ) @ ( hAPP_f759274231e_bool @ ( hAPP_f661147897e_bool @ cOMBC_1058051404l_bool @ member_pname ) @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_395_pred__subset__eq) ).

thf(1438,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f661147897e_bool @ cOMBC_1058051404l_bool @ member_pname ) @ A ) ) @ ( hAPP_f759274231e_bool @ ( hAPP_f661147897e_bool @ cOMBC_1058051404l_bool @ member_pname ) @ B ) ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f661147897e_bool @ cOMBC_1058051404l_bool @ member_pname ) @ A ) ) @ ( hAPP_f759274231e_bool @ ( hAPP_f661147897e_bool @ cOMBC_1058051404l_bool @ member_pname ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(107,axiom,
    ! [A: fun_pn1610849624_state,B: fun_pn12888928e_bool,C: pname] :
      ( ( hAPP_p702226982_state @ ( hAPP_f1568887991_state @ ( hAPP_f891245078_state @ cOMBS_475568287_state @ A ) @ B ) @ C )
      = ( hAPP_f1595846909_state @ ( hAPP_p1985340144_state @ A @ C ) @ ( hAPP_p1637813682e_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc) ).

thf(1199,plain,
    ! [A: fun_pn1610849624_state,B: fun_pn12888928e_bool,C: pname] :
      ( ( hAPP_p702226982_state @ ( hAPP_f1568887991_state @ ( hAPP_f891245078_state @ cOMBS_475568287_state @ A ) @ B ) @ C )
      = ( hAPP_f1595846909_state @ ( hAPP_p1985340144_state @ A @ C ) @ ( hAPP_p1637813682e_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(374,axiom,
    ! [A: fun_fu689207471l_bool,B: fun_fu689207471l_bool,C: fun_fu947547457e_bool,D: fun_fu1163781179e_bool] :
      ( ( hBOOL @ ( finite792754358e_bool @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ B ) )
       => ( ( B != bot_bo973479705l_bool )
         => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ A ) )
           => ( ( A != bot_bo973479705l_bool )
             => ( ( ( hAPP_f900945761l_bool @ ( hAPP_f19215249l_bool @ semila1058800161l_bool @ B ) @ A )
                  = bot_bo973479705l_bool )
               => ( ( hAPP_f962122119e_bool @ D @ ( hAPP_f900945761l_bool @ ( hAPP_f19215249l_bool @ semila1703230395l_bool @ B ) @ A ) )
                  = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ C @ ( hAPP_f962122119e_bool @ D @ B ) ) @ ( hAPP_f962122119e_bool @ D @ A ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_555_folding__one_Ounion__disjoint) ).

thf(2164,plain,
    ! [A: fun_fu689207471l_bool,B: fun_fu689207471l_bool,C: fun_fu947547457e_bool,D: fun_fu1163781179e_bool] :
      ( ( hBOOL @ ( finite792754358e_bool @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ B ) )
       => ( ( B != bot_bo973479705l_bool )
         => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ A ) )
           => ( ( A != bot_bo973479705l_bool )
             => ( ( ( hAPP_f900945761l_bool @ ( hAPP_f19215249l_bool @ semila1058800161l_bool @ B ) @ A )
                  = bot_bo973479705l_bool )
               => ( ( hAPP_f962122119e_bool @ D @ ( hAPP_f900945761l_bool @ ( hAPP_f19215249l_bool @ semila1703230395l_bool @ B ) @ A ) )
                  = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ C @ ( hAPP_f962122119e_bool @ D @ B ) ) @ ( hAPP_f962122119e_bool @ D @ A ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(140,axiom,
    ! [A: fun_state_bool,B: state] :
      ( ( hAPP_s1806633685e_bool @ ( cOMBK_631994958_state @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc__Com__O) ).

thf(1311,plain,
    ! [A: fun_state_bool,B: state] :
      ( ( hAPP_s1806633685e_bool @ ( cOMBK_631994958_state @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(810,axiom,
    ! [A: state,B: com,C: state,D: state] :
      ( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ ( evalc @ B ) @ C ) @ D ) )
     => ( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ ( evalc @ B ) @ C ) @ A ) )
       => ( A = D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_543_com__det) ).

thf(3767,plain,
    ! [A: state,B: com,C: state,D: state] :
      ( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ ( evalc @ B ) @ C ) @ D ) )
     => ( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ ( evalc @ B ) @ C ) @ A ) )
       => ( A = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).

thf(394,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ collec1735317154_state @ ( hAPP_f121055253e_bool @ ( hAPP_f1300953505e_bool @ cOMBS_896408300l_bool @ ( hAPP_f932622461l_bool @ ( cOMBB_242064253_state @ fdisj ) @ A ) ) @ B ) )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ ( hAPP_f121055253e_bool @ collec1735317154_state @ A ) ) @ ( hAPP_f121055253e_bool @ collec1735317154_state @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_Collect__disj__eq) ).

thf(2232,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ collec1735317154_state @ ( hAPP_f121055253e_bool @ ( hAPP_f1300953505e_bool @ cOMBS_896408300l_bool @ ( hAPP_f932622461l_bool @ ( cOMBB_242064253_state @ fdisj ) @ A ) ) @ B ) )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ ( hAPP_f121055253e_bool @ collec1735317154_state @ A ) ) @ ( hAPP_f121055253e_bool @ collec1735317154_state @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).

thf(411,axiom,
    ! [A: pname,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
    <=> ( hBOOL @ ( hAPP_pname_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_mem__def) ).

thf(2296,plain,
    ! [A: pname,B: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_pname_bool @ B @ A ) ) )
      & ( ( hBOOL @ ( hAPP_pname_bool @ B @ A ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(617,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: hoare_1875481847_state] :
      ( ( hBOOL @ ( hAPP_H1173941847e_bool @ B @ C ) )
     => ( hBOOL @ ( hAPP_H1173941847e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_393_sup1I2) ).

thf(3054,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: hoare_1875481847_state] :
      ( ( hBOOL @ ( hAPP_H1173941847e_bool @ B @ C ) )
     => ( hBOOL @ ( hAPP_H1173941847e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).

thf(513,axiom,
    ! [A: fun_pname_bool] :
      ( ( ( hAPP_f759274231e_bool @ collect_pname @ A )
        = bot_bo844097828e_bool )
    <=> ! [B: pname] :
          ~ ( hBOOL @ ( hAPP_pname_bool @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_Collect__empty__eq) ).

thf(2660,plain,
    ! [A: fun_pname_bool] :
      ( ( ( ( hAPP_f759274231e_bool @ collect_pname @ A )
          = bot_bo844097828e_bool )
       => ! [B: pname] :
            ~ ( hBOOL @ ( hAPP_pname_bool @ A @ B ) ) )
      & ( ! [B: pname] :
            ~ ( hBOOL @ ( hAPP_pname_bool @ A @ B ) )
       => ( ( hAPP_f759274231e_bool @ collect_pname @ A )
          = bot_bo844097828e_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).

thf(266,axiom,
    ! [A: fun_pname_bool,B: fun_fu1499449723_pname,C: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( hAPP_f674760225e_bool @ ( image_1283814551_pname @ B ) @ C ) ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_finite__surj) ).

thf(1768,plain,
    ! [A: fun_pname_bool,B: fun_fu1499449723_pname,C: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( hAPP_f674760225e_bool @ ( image_1283814551_pname @ B ) @ C ) ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(295,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool,D: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ D ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ C ) @ A ) ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ D ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_Un__mono) ).

thf(1868,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool,D: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ D ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ C ) @ A ) ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ D ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(611,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ A ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ C ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_600_Int__greatest) ).

thf(3037,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ A ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ C ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).

thf(99,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ A ) @ B ) ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_627_inf__sup__ord_I2_J) ).

thf(1163,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ A ) @ B ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(132,axiom,
    ! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
      ( ( hAPP_f559147733l_bool @ ( hAPP_f1320879424l_bool @ insert1325755072e_bool @ A ) @ B )
      = ( hAPP_f559147733l_bool @ collec1974731493e_bool @ ( hAPP_f559147733l_bool @ ( hAPP_f624840228l_bool @ cOMBS_350070575l_bool @ ( hAPP_f143162813l_bool @ ( cOMBB_2095475776e_bool @ fdisj ) @ ( hAPP_f434788991l_bool @ ( hAPP_f1297925993l_bool @ cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ A ) ) ) @ ( hAPP_f559147733l_bool @ ( hAPP_f1145991873l_bool @ cOMBC_1988546018l_bool @ member799430823e_bool ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_insert__compr__raw) ).

thf(1274,plain,
    ! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
      ( ( hAPP_f559147733l_bool @ ( hAPP_f1320879424l_bool @ insert1325755072e_bool @ A ) @ B )
      = ( hAPP_f559147733l_bool @ collec1974731493e_bool @ ( hAPP_f559147733l_bool @ ( hAPP_f624840228l_bool @ cOMBS_350070575l_bool @ ( hAPP_f143162813l_bool @ ( cOMBB_2095475776e_bool @ fdisj ) @ ( hAPP_f434788991l_bool @ ( hAPP_f1297925993l_bool @ cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ A ) ) ) @ ( hAPP_f559147733l_bool @ ( hAPP_f1145991873l_bool @ cOMBC_1988546018l_bool @ member799430823e_bool ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(305,axiom,
    ! [A: fun_fu1176632176e_bool,B: hoare_1875481847_state,C: fun_pname_bool] :
      ( ( hAPP_f1664156314l_bool @ ( hAPP_H434980226l_bool @ ( hAPP_f492176169l_bool @ cOMBC_620146361e_bool @ A ) @ B ) @ C )
      = ( hAPP_H1173941847e_bool @ ( hAPP_f1291720380e_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Hoare_) ).

thf(1900,plain,
    ! [A: fun_fu1176632176e_bool,B: hoare_1875481847_state,C: fun_pname_bool] :
      ( ( hAPP_f1664156314l_bool @ ( hAPP_H434980226l_bool @ ( hAPP_f492176169l_bool @ cOMBC_620146361e_bool @ A ) @ B ) @ C )
      = ( hAPP_H1173941847e_bool @ ( hAPP_f1291720380e_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(116,axiom,
    ! [A: pname,B: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ B ) )
      = ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_insert__absorb2) ).

thf(1223,plain,
    ! [A: pname,B: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ B ) )
      = ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(445,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ B ) )
        | ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ A ) ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_565_finite__Int) ).

thf(2428,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ B ) )
        | ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ A ) ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).

thf(6,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
     => ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ A ) @ B )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_Un__absorb1) ).

thf(825,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
     => ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ A ) @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(396,axiom,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ B ) )
     => ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ minus_589155914e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ B ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ bot_bo1715400655e_bool ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_695_Diff__insert__absorb) ).

thf(2249,plain,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ B ) )
     => ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ minus_589155914e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ B ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ bot_bo1715400655e_bool ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(477,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] : ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_Un__upper2) ).

thf(2541,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] : ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).

thf(494,axiom,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ B ) )
     => ~ ! [C: fun_Ho1996104121e_bool] :
            ( ( B
              = ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ C ) )
           => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_530_Set_Oset__insert) ).

thf(2596,plain,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ B ) )
     => ~ ! [C: fun_Ho1996104121e_bool] :
            ( ( B
              = ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ C ) )
           => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).

thf(216,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ A ) @ B )
        = bot_bo844097828e_bool )
    <=> ( ( A = bot_bo844097828e_bool )
        & ( B = bot_bo844097828e_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_455_sup__eq__bot__iff) ).

thf(1570,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ A ) @ B )
          = bot_bo844097828e_bool )
       => ( ( A = bot_bo844097828e_bool )
          & ( B = bot_bo844097828e_bool ) ) )
      & ( ( ( A = bot_bo844097828e_bool )
          & ( B = bot_bo844097828e_bool ) )
       => ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ A ) @ B )
          = bot_bo844097828e_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(368,axiom,
    ! [A: pname,B: com] :
      ( ( hBOOL @ wT_bodies )
     => ( ( ( hAPP_p799580910on_com @ body @ A )
          = ( some_com @ B ) )
       => ( hBOOL @ ( hAPP_com_bool @ wt @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_WT__bodiesD) ).

thf(2147,plain,
    ! [A: pname,B: com] :
      ( ( hBOOL @ wT_bodies )
     => ( ( ( hAPP_p799580910on_com @ body @ A )
          = ( some_com @ B ) )
       => ( hBOOL @ ( hAPP_com_bool @ wt @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(803,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_subset__trans) ).

thf(3742,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).

thf(496,axiom,
    ! [A: fun_Ho1695028467e_bool,B: fun_fu385705929_state,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1185879473e_bool @ ( cOMBB_1094554675e_bool @ A ) @ B ) @ C )
      = ( hAPP_H117293375e_bool @ A @ ( hAPP_f890249627_state @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc__Com___241) ).

thf(2606,plain,
    ! [A: fun_Ho1695028467e_bool,B: fun_fu385705929_state,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1185879473e_bool @ ( cOMBB_1094554675e_bool @ A ) @ B ) @ C )
      = ( hAPP_H117293375e_bool @ A @ ( hAPP_f890249627_state @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).

thf(680,axiom,
    ! [A: state,B: com,C: state,D: fun_state_bool,E: state] :
      ( ( hBOOL @ ( hAPP_state_bool @ D @ E ) )
     => ( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ ( evalc @ B ) @ E ) @ C ) )
       => ( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ ( evalc @ ( while @ D @ B ) ) @ C ) @ A ) )
         => ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ ( evalc @ ( while @ D @ B ) ) @ E ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_540_evalc_OWhileTrue) ).

thf(3286,plain,
    ! [A: state,B: com,C: state,D: fun_state_bool,E: state] :
      ( ( hBOOL @ ( hAPP_state_bool @ D @ E ) )
     => ( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ ( evalc @ B ) @ E ) @ C ) )
       => ( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ ( evalc @ ( while @ D @ B ) ) @ C ) @ A ) )
         => ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ ( evalc @ ( while @ D @ B ) ) @ E ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).

thf(608,axiom,
    ! [A: com,B: option_com] :
      ( ( hBOOL @ ( hAPP_f990396704l_bool @ ( hAPP_c667411853l_bool @ member_com @ A ) @ ( set_com @ B ) ) )
    <=> ( B
        = ( some_com @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_407_elem__set) ).

thf(3022,plain,
    ! [A: com,B: option_com] :
      ( ( ( hBOOL @ ( hAPP_f990396704l_bool @ ( hAPP_c667411853l_bool @ member_com @ A ) @ ( set_com @ B ) ) )
       => ( B
          = ( some_com @ A ) ) )
      & ( ( B
          = ( some_com @ A ) )
       => ( hBOOL @ ( hAPP_f990396704l_bool @ ( hAPP_c667411853l_bool @ member_com @ A ) @ ( set_com @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).

thf(197,axiom,
    ! [A: fun_fu802393907l_bool,B: fun_Ho14659478e_bool,C: hoare_1875481847_state] :
      ( ( hAPP_H434980226l_bool @ ( hAPP_f745653815l_bool @ ( cOMBB_582022205_state @ A ) @ B ) @ C )
      = ( hAPP_f434788991l_bool @ A @ ( hAPP_H785152948e_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_233) ).

thf(1502,plain,
    ! [A: fun_fu802393907l_bool,B: fun_Ho14659478e_bool,C: hoare_1875481847_state] :
      ( ( hAPP_H434980226l_bool @ ( hAPP_f745653815l_bool @ ( cOMBB_582022205_state @ A ) @ B ) @ C )
      = ( hAPP_f434788991l_bool @ A @ ( hAPP_H785152948e_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(261,axiom,
    ! [A: fun_pn800050071e_bool,B: fun_pname_bool,C: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ C ) @ ( hAPP_f434788991l_bool @ ( image_47868345e_bool @ A ) @ B ) ) )
       => ? [D: fun_pname_bool] :
            ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ D ) )
            & ( C
              = ( hAPP_f434788991l_bool @ ( image_47868345e_bool @ A ) @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_finite__subset__image) ).

thf(1751,plain,
    ! [A: fun_pn800050071e_bool,B: fun_pname_bool,C: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ C ) @ ( hAPP_f434788991l_bool @ ( image_47868345e_bool @ A ) @ B ) ) )
       => ? [D: fun_pname_bool] :
            ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ D ) )
            & ( C
              = ( hAPP_f434788991l_bool @ ( image_47868345e_bool @ A ) @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(4,axiom,
    ! [A: fun_fu802393907l_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ( hAPP_f1297925993l_bool @ cOMBC_1284144636l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It) ).

thf(820,plain,
    ! [A: fun_fu802393907l_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ( hAPP_f1297925993l_bool @ cOMBC_1284144636l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(284,axiom,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ B ) @ C ) ) )
     => ~ ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
         => ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_560_IntE) ).

thf(1824,plain,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ B ) @ C ) ) )
     => ~ ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
         => ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(229,axiom,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_580_IntD2) ).

thf(1619,plain,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(659,axiom,
    ! [A: hoare_1875481847_state,B: hoare_1875481847_state] :
      ( ( ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ bot_bo1715400655e_bool )
        = ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ bot_bo1715400655e_bool ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_singleton__inject) ).

thf(3207,plain,
    ! [A: hoare_1875481847_state,B: hoare_1875481847_state] :
      ( ( ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ bot_bo1715400655e_bool )
        = ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ bot_bo1715400655e_bool ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).

thf(788,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B )
        = bot_bo1715400655e_bool )
    <=> ( ( A = bot_bo1715400655e_bool )
        & ( B = bot_bo1715400655e_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_Un__empty) ).

thf(3682,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B )
          = bot_bo1715400655e_bool )
       => ( ( A = bot_bo1715400655e_bool )
          & ( B = bot_bo1715400655e_bool ) ) )
      & ( ( ( A = bot_bo1715400655e_bool )
          & ( B = bot_bo1715400655e_bool ) )
       => ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B )
          = bot_bo1715400655e_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).

thf(814,axiom,
    ! [A: hoare_1875481847_state,B: hoare_1875481847_state,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ C ) ) )
    <=> ( ( A = B )
        | ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_insert__iff) ).

thf(3778,plain,
    ! [A: hoare_1875481847_state,B: hoare_1875481847_state,C: fun_Ho1996104121e_bool] :
      ( ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ C ) ) )
       => ( ( A = B )
          | ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ C ) ) ) )
      & ( ( ( A = B )
          | ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ C ) ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).

thf(121,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ B ) @ A ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_433_le__supI) ).

thf(1238,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ B ) @ A ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(337,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( A = B )
    <=> ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
        & ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_set__eq__subset) ).

thf(2015,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( ( A = B )
       => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
          & ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ A ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
          & ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ A ) ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(648,axiom,
    ! [A: fun_state_bool,B: com,C: state,D: state] :
      ( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ ( evalc @ ( while @ A @ B ) ) @ C ) @ D ) )
     => ( ( ( D = C )
         => ( hBOOL @ ( hAPP_state_bool @ A @ C ) ) )
       => ~ ( ( hBOOL @ ( hAPP_state_bool @ A @ C ) )
           => ! [E: state] :
                ( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ ( evalc @ B ) @ C ) @ E ) )
               => ~ ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ ( evalc @ ( while @ A @ B ) ) @ E ) @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_545_evalc__WHILE__case) ).

thf(3166,plain,
    ! [A: fun_state_bool,B: com,C: state,D: state] :
      ( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ ( evalc @ ( while @ A @ B ) ) @ C ) @ D ) )
     => ( ( ( D = C )
         => ( hBOOL @ ( hAPP_state_bool @ A @ C ) ) )
       => ~ ( ( hBOOL @ ( hAPP_state_bool @ A @ C ) )
           => ! [E: state] :
                ( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ ( evalc @ B ) @ C ) @ E ) )
               => ~ ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ ( evalc @ ( while @ A @ B ) ) @ E ) @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).

thf(14,axiom,
    ! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ A ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ C ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_558_IntI) ).

thf(847,plain,
    ! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ A ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ C ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(772,axiom,
    ! [A: fun_fu689207471l_bool,B: fun_fu689207471l_bool] :
      ( ! [C: fun_Ho1996104121e_bool] :
          ( ( hBOOL @ ( hAPP_f1408815105l_bool @ B @ C ) )
         => ( hBOOL @ ( hAPP_f1408815105l_bool @ A @ C ) ) )
     => ( hBOOL @ ( hAPP_f1699935247l_bool @ ( hAPP_f1970936639l_bool @ ord_le724727525l_bool @ ( hAPP_f900945761l_bool @ collec771609166e_bool @ B ) ) @ ( hAPP_f900945761l_bool @ collec771609166e_bool @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_524_Collect__mono) ).

thf(3618,plain,
    ! [A: fun_fu689207471l_bool,B: fun_fu689207471l_bool] :
      ( ! [C: fun_Ho1996104121e_bool] :
          ( ( hBOOL @ ( hAPP_f1408815105l_bool @ B @ C ) )
         => ( hBOOL @ ( hAPP_f1408815105l_bool @ A @ C ) ) )
     => ( hBOOL @ ( hAPP_f1699935247l_bool @ ( hAPP_f1970936639l_bool @ ord_le724727525l_bool @ ( hAPP_f900945761l_bool @ collec771609166e_bool @ B ) ) @ ( hAPP_f900945761l_bool @ collec771609166e_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).

thf(155,axiom,
    ! [A: pname,B: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ B )
      = ( hAPP_f759274231e_bool @ collect_pname @ ( hAPP_f759274231e_bool @ ( hAPP_f649174806e_bool @ cOMBS_568398431l_bool @ ( hAPP_f1402196763l_bool @ ( cOMBB_675860798_pname @ fdisj ) @ ( hAPP_p61793385e_bool @ ( hAPP_f22061361e_bool @ cOMBC_1149511130e_bool @ fequal_pname ) @ A ) ) ) @ ( hAPP_f759274231e_bool @ ( hAPP_f661147897e_bool @ cOMBC_1058051404l_bool @ member_pname ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_insert__compr__raw) ).

thf(1365,plain,
    ! [A: pname,B: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ B )
      = ( hAPP_f759274231e_bool @ collect_pname @ ( hAPP_f759274231e_bool @ ( hAPP_f649174806e_bool @ cOMBS_568398431l_bool @ ( hAPP_f1402196763l_bool @ ( cOMBB_675860798_pname @ fdisj ) @ ( hAPP_p61793385e_bool @ ( hAPP_f22061361e_bool @ cOMBC_1149511130e_bool @ fequal_pname ) @ A ) ) ) @ ( hAPP_f759274231e_bool @ ( hAPP_f661147897e_bool @ cOMBC_1058051404l_bool @ member_pname ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(16,axiom,
    ! [A: hoare_1875481847_state] :
      ~ ! [B: fun_st1506752259e_bool,C: com,D: fun_st1506752259e_bool] :
          ( A
         != ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ B ) @ C ) @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_519_triple_Oexhaust) ).

thf(852,plain,
    ! [A: hoare_1875481847_state] :
      ~ ! [B: fun_st1506752259e_bool,C: com,D: fun_st1506752259e_bool] :
          ( A
         != ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ B ) @ C ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(696,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( A = B )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_354_order__eq__refl) ).

thf(3349,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( A = B )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).

thf(317,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ B ) ) @ C )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ C ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_656_sup__inf__distrib2) ).

thf(1951,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ B ) ) @ C )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ C ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(795,axiom,
    ! [A: fun_state_bool,B: com,C: pname] :
      ( ( while @ A @ B )
     != ( hAPP_pname_com @ body_1 @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_500_com_Osimps_I58_J) ).

thf(3718,plain,
    ! [A: fun_state_bool,B: com,C: pname] :
      ( ( while @ A @ B )
     != ( hAPP_pname_com @ body_1 @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).

thf(111,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_326_Un__upper1) ).

thf(1210,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(531,axiom,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ B ) @ C ) ) )
    <=> ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ B ) )
        & ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_577_Int__iff) ).

thf(2741,plain,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ B ) @ C ) ) )
       => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ B ) )
          & ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ C ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ B ) )
          & ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ C ) ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ B ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).

thf(162,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
    <=> ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ A ) @ B )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_631_le__iff__inf) ).

thf(1392,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
       => ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ A ) @ B )
          = A ) )
      & ( ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ A ) @ B )
          = A )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(136,axiom,
    ! [A: fun_pn1243268074_state,B: fun_pn664418900_state,C: pname] :
      ( ( hAPP_p1279250276_state @ ( hAPP_f1087244981_state @ ( hAPP_f294490838_state @ cOMBS_602905655_state @ A ) @ B ) @ C )
      = ( hAPP_H743221337_state @ ( hAPP_p1513527868_state @ A @ C ) @ ( hAPP_p702226982_state @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__Hoare____Mirabelle____xlrqixeqwe__238) ).

thf(1291,plain,
    ! [A: fun_pn1243268074_state,B: fun_pn664418900_state,C: pname] :
      ( ( hAPP_p1279250276_state @ ( hAPP_f1087244981_state @ ( hAPP_f294490838_state @ cOMBS_602905655_state @ A ) @ B ) @ C )
      = ( hAPP_H743221337_state @ ( hAPP_p1513527868_state @ A @ C ) @ ( hAPP_p702226982_state @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(12,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pn1208287926_pname,D: fun_fu1499449723_pname] :
      ( ( hBOOL @ ( finite89670078_pname @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
       => ( ( A != bot_bo844097828e_bool )
         => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
           => ( ( hAPP_pname_pname @ ( hAPP_p1170154830_pname @ C @ ( hAPP_f1297739591_pname @ D @ A ) ) @ ( hAPP_f1297739591_pname @ D @ B ) )
              = ( hAPP_f1297739591_pname @ D @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_467_folding__one__idem_Osubset__idem) ).

thf(842,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pn1208287926_pname,D: fun_fu1499449723_pname] :
      ( ( hBOOL @ ( finite89670078_pname @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
       => ( ( A != bot_bo844097828e_bool )
         => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
           => ( ( hAPP_pname_pname @ ( hAPP_p1170154830_pname @ C @ ( hAPP_f1297739591_pname @ D @ A ) ) @ ( hAPP_f1297739591_pname @ D @ B ) )
              = ( hAPP_f1297739591_pname @ D @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(764,axiom,
    ( ( hBOOL @ hoare_1239590103gleton )
   => ! [A: state] :
        ~ ! [B: state] : ( B = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_411_single__stateE) ).

thf(3595,plain,
    ( ( hBOOL @ hoare_1239590103gleton )
   => ! [A: state] :
        ~ ! [B: state] : ( B = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).

thf(85,axiom,
    ! [A: fun_fu1658206819l_bool,B: fun_st1506752259e_bool,C: state] :
      ( ( hAPP_s2001034685l_bool @ ( hAPP_f1283379615l_bool @ ( cOMBB_1759179140_state @ A ) @ B ) @ C )
      = ( hAPP_f1259673775l_bool @ A @ ( hAPP_s1806633685e_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc__fun_It) ).

thf(1106,plain,
    ! [A: fun_fu1658206819l_bool,B: fun_st1506752259e_bool,C: state] :
      ( ( hAPP_s2001034685l_bool @ ( hAPP_f1283379615l_bool @ ( cOMBB_1759179140_state @ A ) @ B ) @ C )
      = ( hAPP_f1259673775l_bool @ A @ ( hAPP_s1806633685e_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(678,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ A ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ C ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_644_le__infI) ).

thf(3282,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ A ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ C ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).

thf(172,axiom,
    ! [A: fun_pname_bool,B: fun_fu1430349052l_bool,C: fun_fu2101097872e_bool,D: fun_fu608906319e_bool] :
      ( ( hBOOL @ ( finite1268145088e_bool @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
       => ( ( B != bot_bo1649642514l_bool )
         => ( ( hAPP_f674760225e_bool @ D @ ( hAPP_f559147733l_bool @ ( hAPP_f1320879424l_bool @ insert1325755072e_bool @ A ) @ B ) )
            = ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ C @ A ) @ ( hAPP_f674760225e_bool @ D @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_472_folding__one__idem_Oinsert__idem) ).

thf(1423,plain,
    ! [A: fun_pname_bool,B: fun_fu1430349052l_bool,C: fun_fu2101097872e_bool,D: fun_fu608906319e_bool] :
      ( ( hBOOL @ ( finite1268145088e_bool @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
       => ( ( B != bot_bo1649642514l_bool )
         => ( ( hAPP_f674760225e_bool @ D @ ( hAPP_f559147733l_bool @ ( hAPP_f1320879424l_bool @ insert1325755072e_bool @ A ) @ B ) )
            = ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ C @ A ) @ ( hAPP_f674760225e_bool @ D @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(687,axiom,
    ! [A: fun_fu689207471l_bool,B: fun_fu689207471l_bool] :
      ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ B ) )
     => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ A ) )
       => ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ ( hAPP_f900945761l_bool @ ( hAPP_f19215249l_bool @ semila1703230395l_bool @ B ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_finite__UnI) ).

thf(3307,plain,
    ! [A: fun_fu689207471l_bool,B: fun_fu689207471l_bool] :
      ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ B ) )
     => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ A ) )
       => ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ ( hAPP_f900945761l_bool @ ( hAPP_f19215249l_bool @ semila1703230395l_bool @ B ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).

thf(321,axiom,
    ! [A: fun_fu689207471l_bool,B: fun_fu689207471l_bool,C: fun_fu947547457e_bool,D: fun_fu1163781179e_bool] :
      ( ( hBOOL @ ( finite792754358e_bool @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ B ) )
       => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ A ) )
         => ( ( ( hAPP_f900945761l_bool @ ( hAPP_f19215249l_bool @ semila1058800161l_bool @ B ) @ A )
             != bot_bo973479705l_bool )
           => ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ C @ ( hAPP_f962122119e_bool @ D @ ( hAPP_f900945761l_bool @ ( hAPP_f19215249l_bool @ semila1703230395l_bool @ B ) @ A ) ) ) @ ( hAPP_f962122119e_bool @ D @ ( hAPP_f900945761l_bool @ ( hAPP_f19215249l_bool @ semila1058800161l_bool @ B ) @ A ) ) )
              = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ C @ ( hAPP_f962122119e_bool @ D @ B ) ) @ ( hAPP_f962122119e_bool @ D @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_551_folding__one_Ounion__inter) ).

thf(1968,plain,
    ! [A: fun_fu689207471l_bool,B: fun_fu689207471l_bool,C: fun_fu947547457e_bool,D: fun_fu1163781179e_bool] :
      ( ( hBOOL @ ( finite792754358e_bool @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ B ) )
       => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ A ) )
         => ( ( ( hAPP_f900945761l_bool @ ( hAPP_f19215249l_bool @ semila1058800161l_bool @ B ) @ A )
             != bot_bo973479705l_bool )
           => ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ C @ ( hAPP_f962122119e_bool @ D @ ( hAPP_f900945761l_bool @ ( hAPP_f19215249l_bool @ semila1703230395l_bool @ B ) @ A ) ) ) @ ( hAPP_f962122119e_bool @ D @ ( hAPP_f900945761l_bool @ ( hAPP_f19215249l_bool @ semila1058800161l_bool @ B ) @ A ) ) )
              = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ C @ ( hAPP_f962122119e_bool @ D @ B ) ) @ ( hAPP_f962122119e_bool @ D @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(485,axiom,
    ! [A: fun_pn12888928e_bool,B: fun_pn12888928e_bool,C: fun_Ho1996104121e_bool,D: fun_pn12888928e_bool,E: fun_pname_com,F: fun_pn12888928e_bool,G: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ G ) )
     => ( ! [H: pname] :
            ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ C ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ ( hAPP_p1637813682e_bool @ D @ H ) ) @ ( hAPP_pname_com @ E @ H ) ) @ ( hAPP_p1637813682e_bool @ F @ H ) ) ) @ bot_bo1715400655e_bool ) ) )
           => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ C ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ ( hAPP_p1637813682e_bool @ A @ H ) ) @ ( hAPP_pname_com @ E @ H ) ) @ ( hAPP_p1637813682e_bool @ B @ H ) ) ) @ bot_bo1715400655e_bool ) ) ) )
       => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ C ) @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ ( hAPP_f1568887991_state @ ( hAPP_f891245078_state @ cOMBS_475568287_state @ ( hAPP_f2116202538_state @ ( hAPP_f1339343196_state @ cOMBS_1674056844_state @ ( hAPP_f275933352_state @ ( cOMBB_718493681_pname @ hoare_13225861_state ) @ D ) ) @ E ) ) @ F ) ) @ G ) ) )
         => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ C ) @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ ( hAPP_f1568887991_state @ ( hAPP_f891245078_state @ cOMBS_475568287_state @ ( hAPP_f2116202538_state @ ( hAPP_f1339343196_state @ cOMBS_1674056844_state @ ( hAPP_f275933352_state @ ( cOMBB_718493681_pname @ hoare_13225861_state ) @ A ) ) @ E ) ) @ B ) ) @ G ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_378_finite__pointwise) ).

thf(2565,plain,
    ! [A: fun_pn12888928e_bool,B: fun_pn12888928e_bool,C: fun_Ho1996104121e_bool,D: fun_pn12888928e_bool,E: fun_pname_com,F: fun_pn12888928e_bool,G: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ G ) )
     => ( ! [H: pname] :
            ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ C ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ ( hAPP_p1637813682e_bool @ D @ H ) ) @ ( hAPP_pname_com @ E @ H ) ) @ ( hAPP_p1637813682e_bool @ F @ H ) ) ) @ bot_bo1715400655e_bool ) ) )
           => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ C ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ ( hAPP_p1637813682e_bool @ A @ H ) ) @ ( hAPP_pname_com @ E @ H ) ) @ ( hAPP_p1637813682e_bool @ B @ H ) ) ) @ bot_bo1715400655e_bool ) ) ) )
       => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ C ) @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ ( hAPP_f1568887991_state @ ( hAPP_f891245078_state @ cOMBS_475568287_state @ ( hAPP_f2116202538_state @ ( hAPP_f1339343196_state @ cOMBS_1674056844_state @ ( hAPP_f275933352_state @ ( cOMBB_718493681_pname @ hoare_13225861_state ) @ D ) ) @ E ) ) @ F ) ) @ G ) ) )
         => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ C ) @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ ( hAPP_f1568887991_state @ ( hAPP_f891245078_state @ cOMBS_475568287_state @ ( hAPP_f2116202538_state @ ( hAPP_f1339343196_state @ cOMBS_1674056844_state @ ( hAPP_f275933352_state @ ( cOMBB_718493681_pname @ hoare_13225861_state ) @ A ) ) @ E ) ) @ B ) ) @ G ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).

thf(656,axiom,
    ! [A: fun_fu1499449723_pname,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( hAPP_f674760225e_bool @ ( image_1283814551_pname @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_finite__imageI) ).

thf(3198,plain,
    ! [A: fun_fu1499449723_pname,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( hAPP_f674760225e_bool @ ( image_1283814551_pname @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).

thf(347,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_442_le__supI1) ).

thf(2068,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(231,axiom,
    ! [A: fun_bo1549164019l_bool,B: fun_state_bool,C: state] :
      ( ( hAPP_s58564346l_bool @ ( hAPP_f1259673775l_bool @ ( cOMBB_188601460_state @ A ) @ B ) @ C )
      = ( hAPP_b589554111l_bool @ A @ ( hAPP_state_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_218) ).

thf(1624,plain,
    ! [A: fun_bo1549164019l_bool,B: fun_state_bool,C: state] :
      ( ( hAPP_s58564346l_bool @ ( hAPP_f1259673775l_bool @ ( cOMBB_188601460_state @ A ) @ B ) @ C )
      = ( hAPP_b589554111l_bool @ A @ ( hAPP_state_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(381,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] : ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ B ) ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_624_inf__sup__ord_I1_J) ).

thf(2200,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] : ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ B ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(497,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ B ) ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_638_le__infI2) ).

thf(2609,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ B ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).

thf(288,axiom,
    ! [A: fun_pname_bool] :
      ( ! [B: pname] :
          ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ A ) )
     => ( A = bot_bo844097828e_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_531_equals0I) ).

thf(1836,plain,
    ! [A: fun_pname_bool] :
      ( ! [B: pname] :
          ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ A ) )
     => ( A = bot_bo844097828e_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(272,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_fu689207471l_bool] :
      ( ( hAPP_f900945761l_bool @ ( hAPP_f872497439l_bool @ insert504309043e_bool @ A ) @ ( hAPP_f900945761l_bool @ collec771609166e_bool @ B ) )
      = ( hAPP_f900945761l_bool @ collec771609166e_bool @ ( hAPP_f900945761l_bool @ ( hAPP_f2051813877l_bool @ cOMBS_1451994324l_bool @ ( hAPP_f440042033l_bool @ ( cOMBB_532710323e_bool @ fimplies ) @ ( hAPP_f900945761l_bool @ ( cOMBB_469839573e_bool @ fNot ) @ ( hAPP_f1873026899l_bool @ ( hAPP_f2051277573l_bool @ cOMBC_195806106l_bool @ fequal259518520e_bool ) @ A ) ) ) ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_insert__Collect) ).

thf(1787,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_fu689207471l_bool] :
      ( ( hAPP_f900945761l_bool @ ( hAPP_f872497439l_bool @ insert504309043e_bool @ A ) @ ( hAPP_f900945761l_bool @ collec771609166e_bool @ B ) )
      = ( hAPP_f900945761l_bool @ collec771609166e_bool @ ( hAPP_f900945761l_bool @ ( hAPP_f2051813877l_bool @ cOMBS_1451994324l_bool @ ( hAPP_f440042033l_bool @ ( cOMBB_532710323e_bool @ fimplies ) @ ( hAPP_f900945761l_bool @ ( cOMBB_469839573e_bool @ fNot ) @ ( hAPP_f1873026899l_bool @ ( hAPP_f2051277573l_bool @ cOMBC_195806106l_bool @ fequal259518520e_bool ) @ A ) ) ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(327,axiom,
    ! [A: fun_pname_bool,B: fun_pname_pname,C: fun_pn1208287926_pname,D: fun_fu1499449723_pname] :
      ( ( hBOOL @ ( finite89670078_pname @ C @ D ) )
     => ( ! [E: pname,F: pname] :
            ( ( hAPP_pname_pname @ B @ ( hAPP_pname_pname @ ( hAPP_p1170154830_pname @ C @ E ) @ F ) )
            = ( hAPP_pname_pname @ ( hAPP_p1170154830_pname @ C @ ( hAPP_pname_pname @ B @ E ) ) @ ( hAPP_pname_pname @ B @ F ) ) )
       => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
         => ( ( A != bot_bo844097828e_bool )
           => ( ( hAPP_pname_pname @ B @ ( hAPP_f1297739591_pname @ D @ A ) )
              = ( hAPP_f1297739591_pname @ D @ ( hAPP_f759274231e_bool @ ( image_pname_pname @ B ) @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_487_folding__one__idem_Ohom__commute) ).

thf(1983,plain,
    ! [A: fun_pname_bool,B: fun_pname_pname,C: fun_pn1208287926_pname,D: fun_fu1499449723_pname] :
      ( ( hBOOL @ ( finite89670078_pname @ C @ D ) )
     => ( ! [E: pname,F: pname] :
            ( ( hAPP_pname_pname @ B @ ( hAPP_pname_pname @ ( hAPP_p1170154830_pname @ C @ E ) @ F ) )
            = ( hAPP_pname_pname @ ( hAPP_p1170154830_pname @ C @ ( hAPP_pname_pname @ B @ E ) ) @ ( hAPP_pname_pname @ B @ F ) ) )
       => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
         => ( ( A != bot_bo844097828e_bool )
           => ( ( hAPP_pname_pname @ B @ ( hAPP_f1297739591_pname @ D @ A ) )
              = ( hAPP_f1297739591_pname @ D @ ( hAPP_f759274231e_bool @ ( image_pname_pname @ B ) @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(361,axiom,
    ! [A: pname,B: pname] :
      ( ( A != B )
      | ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ fequal_pname @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Com__Opname_T) ).

thf(2115,plain,
    ! [A: pname,B: pname] :
      ( ( A != B )
      | ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ fequal_pname @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(127,axiom,
    ! [A: fun_bo1549164019l_bool,B: fun_pname_bool,C: pname] :
      ( ( hAPP_p393069232l_bool @ ( hAPP_f1402196763l_bool @ ( cOMBB_675860798_pname @ A ) @ B ) @ C )
      = ( hAPP_b589554111l_bool @ A @ ( hAPP_pname_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo) ).

thf(1259,plain,
    ! [A: fun_bo1549164019l_bool,B: fun_pname_bool,C: pname] :
      ( ( hAPP_p393069232l_bool @ ( hAPP_f1402196763l_bool @ ( cOMBB_675860798_pname @ A ) @ B ) @ C )
      = ( hAPP_b589554111l_bool @ A @ ( hAPP_pname_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(62,axiom,
    ! [A: fun_Ho1996104121e_bool] :
      ( ( hAPP_f900945761l_bool @ collec771609166e_bool @ ( hAPP_f1873026899l_bool @ fequal259518520e_bool @ A ) )
      = ( hAPP_f900945761l_bool @ ( hAPP_f872497439l_bool @ insert504309043e_bool @ A ) @ bot_bo973479705l_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_singleton__conv2) ).

thf(1017,plain,
    ! [A: fun_Ho1996104121e_bool] :
      ( ( hAPP_f900945761l_bool @ collec771609166e_bool @ ( hAPP_f1873026899l_bool @ fequal259518520e_bool @ A ) )
      = ( hAPP_f900945761l_bool @ ( hAPP_f872497439l_bool @ insert504309043e_bool @ A ) @ bot_bo973479705l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(90,axiom,
    ! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ A ) ) @ C )
        = ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ A ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_613_Int__insert__left__if0) ).

thf(1121,plain,
    ! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ A ) ) @ C )
        = ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(87,axiom,
    ! [A: pname,B: fun_pname_bool] :
      ( ( B = bot_bo844097828e_bool )
     => ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_equals0D) ).

thf(1111,plain,
    ! [A: pname,B: fun_pname_bool] :
      ( ( B = bot_bo844097828e_bool )
     => ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(195,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ A ) @ B ) ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_637_le__infI2) ).

thf(1498,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ A ) @ B ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(520,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_423_inf__sup__aci_I5_J) ).

thf(2694,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).

thf(792,axiom,
    ! [A: fun_Ho1996104121e_bool,B: hoare_1875481847_state,C: fun_Ho1996104121e_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ C ) )
     => ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ C ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ A ) )
        = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ C ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_616_Int__insert__right__if0) ).

thf(3704,plain,
    ! [A: fun_Ho1996104121e_bool,B: hoare_1875481847_state,C: fun_Ho1996104121e_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ C ) )
     => ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ C ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ A ) )
        = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ C ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).

thf(745,axiom,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ B ) @ C ) ) )
     => ~ ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ B ) )
         => ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_561_IntE) ).

thf(3518,plain,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ B ) @ C ) ) )
     => ~ ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ B ) )
         => ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).

thf(299,axiom,
    ! [A: fun_Ho1653816318_pname,B: fun_Ho1996104121e_bool] :
      ( ( bot_bo844097828e_bool
        = ( hAPP_f1148778334e_bool @ ( image_720060442_pname @ A ) @ B ) )
    <=> ( B = bot_bo1715400655e_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_empty__is__image) ).

thf(1878,plain,
    ! [A: fun_Ho1653816318_pname,B: fun_Ho1996104121e_bool] :
      ( ( ( bot_bo844097828e_bool
          = ( hAPP_f1148778334e_bool @ ( image_720060442_pname @ A ) @ B ) )
       => ( B = bot_bo1715400655e_bool ) )
      & ( ( B = bot_bo1715400655e_bool )
       => ( bot_bo844097828e_bool
          = ( hAPP_f1148778334e_bool @ ( image_720060442_pname @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(805,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) )
       => ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_xt1_I5_J) ).

thf(3746,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).

thf(624,axiom,
    ! [A: fun_fu689207471l_bool,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ B ) )
     => ( ( B != bot_bo1715400655e_bool )
       => ( ! [C: hoare_1875481847_state] : ( hBOOL @ ( hAPP_f1408815105l_bool @ A @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ C ) @ bot_bo1715400655e_bool ) ) )
         => ( ! [C: hoare_1875481847_state,D: fun_Ho1996104121e_bool] :
                ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ D ) )
               => ( ( D != bot_bo1715400655e_bool )
                 => ( ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ C ) @ D ) )
                   => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ A @ D ) )
                     => ( hBOOL @ ( hAPP_f1408815105l_bool @ A @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ C ) @ D ) ) ) ) ) ) )
           => ( hBOOL @ ( hAPP_f1408815105l_bool @ A @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_475_finite__ne__induct) ).

thf(3078,plain,
    ! [A: fun_fu689207471l_bool,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ B ) )
     => ( ( B != bot_bo1715400655e_bool )
       => ( ! [C: hoare_1875481847_state] : ( hBOOL @ ( hAPP_f1408815105l_bool @ A @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ C ) @ bot_bo1715400655e_bool ) ) )
         => ( ! [C: hoare_1875481847_state,D: fun_Ho1996104121e_bool] :
                ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ D ) )
               => ( ( D != bot_bo1715400655e_bool )
                 => ( ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ C ) @ D ) )
                   => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ A @ D ) )
                     => ( hBOOL @ ( hAPP_f1408815105l_bool @ A @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ C ) @ D ) ) ) ) ) ) )
           => ( hBOOL @ ( hAPP_f1408815105l_bool @ A @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).

thf(89,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
     => ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ B ) @ A )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_601_Int__absorb1) ).

thf(1118,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
     => ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ B ) @ A )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(658,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ B )
      | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fimplies_2_1_U) ).

thf(3205,plain,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ B )
      | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).

thf(649,axiom,
    ! [A: fun_fu689207471l_bool,B: fun_fu689207471l_bool] :
      ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ ( hAPP_f900945761l_bool @ collec771609166e_bool @ ( hAPP_f900945761l_bool @ ( hAPP_f2051813877l_bool @ cOMBS_1451994324l_bool @ ( hAPP_f440042033l_bool @ ( cOMBB_532710323e_bool @ fdisj ) @ A ) ) @ B ) ) ) )
    <=> ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ ( hAPP_f900945761l_bool @ collec771609166e_bool @ A ) ) )
        & ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ ( hAPP_f900945761l_bool @ collec771609166e_bool @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_finite__Collect__disjI) ).

thf(3176,plain,
    ! [A: fun_fu689207471l_bool,B: fun_fu689207471l_bool] :
      ( ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ ( hAPP_f900945761l_bool @ collec771609166e_bool @ ( hAPP_f900945761l_bool @ ( hAPP_f2051813877l_bool @ cOMBS_1451994324l_bool @ ( hAPP_f440042033l_bool @ ( cOMBB_532710323e_bool @ fdisj ) @ A ) ) @ B ) ) ) )
       => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ ( hAPP_f900945761l_bool @ collec771609166e_bool @ A ) ) )
          & ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ ( hAPP_f900945761l_bool @ collec771609166e_bool @ B ) ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ ( hAPP_f900945761l_bool @ collec771609166e_bool @ A ) ) )
          & ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ ( hAPP_f900945761l_bool @ collec771609166e_bool @ B ) ) ) )
       => ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ ( hAPP_f900945761l_bool @ collec771609166e_bool @ ( hAPP_f900945761l_bool @ ( hAPP_f2051813877l_bool @ cOMBS_1451994324l_bool @ ( hAPP_f440042033l_bool @ ( cOMBB_532710323e_bool @ fdisj ) @ A ) ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).

thf(153,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_finite__subset) ).

thf(1360,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(314,axiom,
    ! [A: com,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ hoare_1239590103gleton )
     => ( ! [C: pname] :
            ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ ( dom_pname_com @ body ) ) )
           => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_c406083500_state @ hoare_Mirabelle_MGT @ ( hAPP_pname_com @ body_1 @ C ) ) ) @ bot_bo1715400655e_bool ) ) ) )
       => ( ( hBOOL @ ( hAPP_com_bool @ wt @ A ) )
         => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_c406083500_state @ hoare_Mirabelle_MGT @ A ) ) @ bot_bo1715400655e_bool ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_MGF__lemma1) ).

thf(1936,plain,
    ! [A: com,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ hoare_1239590103gleton )
     => ( ! [C: pname] :
            ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ ( dom_pname_com @ body ) ) )
           => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_c406083500_state @ hoare_Mirabelle_MGT @ ( hAPP_pname_com @ body_1 @ C ) ) ) @ bot_bo1715400655e_bool ) ) ) )
       => ( ( hBOOL @ ( hAPP_com_bool @ wt @ A ) )
         => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_c406083500_state @ hoare_Mirabelle_MGT @ A ) ) @ bot_bo1715400655e_bool ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(730,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ B ) ) @ C )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ C ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_593_Un__Int__distrib2) ).

thf(3467,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ B ) ) @ C )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ C ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).

thf(791,axiom,
    ! [A: fun_Ho14659478e_bool,B: fun_Ho1996104121e_bool,C: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ C ) @ ( hAPP_f1628972376l_bool @ ( image_412748388e_bool @ A ) @ B ) ) )
       => ? [D: fun_Ho1996104121e_bool] :
            ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ D ) )
            & ( C
              = ( hAPP_f1628972376l_bool @ ( image_412748388e_bool @ A ) @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_finite__subset__image) ).

thf(3699,plain,
    ! [A: fun_Ho14659478e_bool,B: fun_Ho1996104121e_bool,C: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ C ) @ ( hAPP_f1628972376l_bool @ ( image_412748388e_bool @ A ) @ B ) ) )
       => ? [D: fun_Ho1996104121e_bool] :
            ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ D ) )
            & ( C
              = ( hAPP_f1628972376l_bool @ ( image_412748388e_bool @ A ) @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).

thf(79,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ A ) @ B )
      = ( hAPP_f759274231e_bool @ collect_pname @ ( hAPP_f759274231e_bool @ ( hAPP_f649174806e_bool @ cOMBS_568398431l_bool @ ( hAPP_f1402196763l_bool @ ( cOMBB_675860798_pname @ fdisj ) @ ( hAPP_f759274231e_bool @ ( hAPP_f661147897e_bool @ cOMBC_1058051404l_bool @ member_pname ) @ A ) ) ) @ ( hAPP_f759274231e_bool @ ( hAPP_f661147897e_bool @ cOMBC_1058051404l_bool @ member_pname ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_Un__def) ).

thf(1089,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ A ) @ B )
      = ( hAPP_f759274231e_bool @ collect_pname @ ( hAPP_f759274231e_bool @ ( hAPP_f649174806e_bool @ cOMBS_568398431l_bool @ ( hAPP_f1402196763l_bool @ ( cOMBB_675860798_pname @ fdisj ) @ ( hAPP_f759274231e_bool @ ( hAPP_f661147897e_bool @ cOMBC_1058051404l_bool @ member_pname ) @ A ) ) ) @ ( hAPP_f759274231e_bool @ ( hAPP_f661147897e_bool @ cOMBC_1058051404l_bool @ member_pname ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(771,axiom,
    ! [A: fun_pname_bool,B: fun_pn664418900_state,C: fun_pn664418900_state,D: fun_pname_bool] :
      ( ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ ( hAPP_f1981552043_state @ ( hAPP_f1875279510_state @ cOMBS_629630867_state @ ( hAPP_f1087244981_state @ ( hAPP_f294490838_state @ cOMBS_602905655_state @ ( hAPP_f980169511_state @ ( cOMBB_1989814576_pname @ if_Hoa1541320583_state ) @ A ) ) @ B ) ) @ C ) ) @ D )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ B ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ D ) @ ( hAPP_f759274231e_bool @ collect_pname @ A ) ) ) ) @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ C ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ D ) @ ( hAPP_f759274231e_bool @ collect_pname @ ( hAPP_f759274231e_bool @ ( cOMBB_647938656_pname @ fNot ) @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_668_if__image__distrib) ).

thf(3615,plain,
    ! [A: fun_pname_bool,B: fun_pn664418900_state,C: fun_pn664418900_state,D: fun_pname_bool] :
      ( ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ ( hAPP_f1981552043_state @ ( hAPP_f1875279510_state @ cOMBS_629630867_state @ ( hAPP_f1087244981_state @ ( hAPP_f294490838_state @ cOMBS_602905655_state @ ( hAPP_f980169511_state @ ( cOMBB_1989814576_pname @ if_Hoa1541320583_state ) @ A ) ) @ B ) ) @ C ) ) @ D )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ B ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ D ) @ ( hAPP_f759274231e_bool @ collect_pname @ A ) ) ) ) @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ C ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ D ) @ ( hAPP_f759274231e_bool @ collect_pname @ ( hAPP_f759274231e_bool @ ( cOMBB_647938656_pname @ fNot ) @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).

thf(734,axiom,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ B ) ) @ C ) )
    <=> ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ C ) )
        & ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_insert__subset) ).

thf(3482,plain,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ B ) ) @ C ) )
       => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ C ) )
          & ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ C ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ C ) )
          & ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ C ) ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ B ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).

thf(264,axiom,
    ! [A: pname,B: pname,C: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ C ) )
      = ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_insert__commute) ).

thf(1762,plain,
    ! [A: pname,B: pname,C: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ C ) )
      = ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(471,axiom,
    ! [A: fun_Ho1996104121e_bool] :
      ( ( bot_bo1715400655e_bool
        = ( hAPP_f121055253e_bool @ collec1735317154_state @ A ) )
    <=> ! [B: hoare_1875481847_state] :
          ~ ( hBOOL @ ( hAPP_H1173941847e_bool @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_empty__Collect__eq) ).

thf(2515,plain,
    ! [A: fun_Ho1996104121e_bool] :
      ( ( ( bot_bo1715400655e_bool
          = ( hAPP_f121055253e_bool @ collec1735317154_state @ A ) )
       => ! [B: hoare_1875481847_state] :
            ~ ( hBOOL @ ( hAPP_H1173941847e_bool @ A @ B ) ) )
      & ( ! [B: hoare_1875481847_state] :
            ~ ( hBOOL @ ( hAPP_H1173941847e_bool @ A @ B ) )
       => ( bot_bo1715400655e_bool
          = ( hAPP_f121055253e_bool @ collec1735317154_state @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).

thf(714,axiom,
    ! [A: fun_pname_option_com,B: pname,C: com] :
      ( ( ( hAPP_p799580910on_com @ A @ B )
        = ( some_com @ C ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ ( dom_pname_com @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_domI) ).

thf(3413,plain,
    ! [A: fun_pname_option_com,B: pname,C: com] :
      ( ( ( hAPP_p799580910on_com @ A @ B )
        = ( some_com @ C ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ ( dom_pname_com @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).

thf(490,axiom,
    ! [A: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_426_sup_Oidem) ).

thf(2577,plain,
    ! [A: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).

thf(71,axiom,
    ! [A: option_com,B: option_com] :
      ( ( hAPP_o356497025on_com @ ( hAPP_o334540577on_com @ ( hAPP_b1679505845on_com @ if_option_com @ fFalse ) @ A ) @ B )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_000tc__Option__Ooption_Itc__Com__Ocom_J_T) ).

thf(1064,plain,
    ! [A: option_com,B: option_com] :
      ( ( hAPP_o356497025on_com @ ( hAPP_o334540577on_com @ ( hAPP_b1679505845on_com @ if_option_com @ fFalse ) @ A ) @ B )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(253,axiom,
    ! [A: bool] :
      ( ( A = fTrue )
      | ( A = fFalse ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_If_000tc__Option__Ooption_Itc__Com__Ocom_J_T) ).

thf(1719,plain,
    ! [A: bool] :
      ( ( A = fTrue )
      | ( A = fFalse ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(476,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( A = B )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_equalityD2) ).

thf(2537,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( A = B )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).

thf(26,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ A ) @ B ) ) @ C ) )
    <=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ C ) )
        & ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_443_le__sup__iff) ).

thf(884,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ A ) @ B ) ) @ C ) )
       => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ C ) )
          & ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ C ) )
          & ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ A ) @ B ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(239,axiom,
    ! [A: fun_fu1430349052l_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ B ) )
       => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ bot_bo844097828e_bool ) )
         => ( ! [D: pname,E: fun_pname_bool] :
                ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ E ) )
               => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ B ) )
                 => ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ E ) )
                   => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ E ) )
                     => ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ D ) @ E ) ) ) ) ) ) )
           => ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_finite__subset__induct) ).

thf(1659,plain,
    ! [A: fun_fu1430349052l_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ B ) )
       => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ bot_bo844097828e_bool ) )
         => ( ! [D: pname,E: fun_pname_bool] :
                ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ E ) )
               => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ B ) )
                 => ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ E ) )
                   => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ E ) )
                     => ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ D ) @ E ) ) ) ) ) ) )
           => ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(601,axiom,
    ! [A: fun_Ho1996104121e_bool,B: hoare_1875481847_state,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ C ) ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ bot_bo1715400655e_bool ) ) )
        & ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_derivs__insertD) ).

thf(3000,plain,
    ! [A: fun_Ho1996104121e_bool,B: hoare_1875481847_state,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ C ) ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ bot_bo1715400655e_bool ) ) )
        & ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).

thf(40,axiom,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ B ) ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ C ) )
      = ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ B ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_617_insert__inter__insert) ).

thf(933,plain,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ B ) ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ C ) )
      = ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(553,axiom,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ minus_589155914e_bool @ B ) @ C ) ) )
     => ~ ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ B ) )
         => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_687_DiffE) ).

thf(2830,plain,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ minus_589155914e_bool @ B ) @ C ) ) )
     => ~ ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ B ) )
         => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).

thf(794,axiom,
    ! [A: pname,B: fun_state_bool,C: com] :
      ( ( hAPP_pname_com @ body_1 @ A )
     != ( while @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_499_com_Osimps_I59_J) ).

thf(3714,plain,
    ! [A: pname,B: fun_state_bool,C: com] :
      ( ( hAPP_pname_com @ body_1 @ A )
     != ( while @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).

thf(564,axiom,
    ! [A: fun_Ho1110608055e_bool,B: fun_Ho1996104121e_bool,C: hoare_1875481847_state] :
      ( ( hAPP_H117293375e_bool @ ( hAPP_f56162711e_bool @ ( hAPP_f392546175e_bool @ cOMBC_483615668e_bool @ A ) @ B ) @ C )
      = ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc__Com___242) ).

thf(2868,plain,
    ! [A: fun_Ho1110608055e_bool,B: fun_Ho1996104121e_bool,C: hoare_1875481847_state] :
      ( ( hAPP_H117293375e_bool @ ( hAPP_f56162711e_bool @ ( hAPP_f392546175e_bool @ cOMBC_483615668e_bool @ A ) @ B ) @ C )
      = ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).

thf(75,axiom,
    ! [A: pname,B: hoare_1875481847_state] :
      ( ( hAPP_H139064010_pname @ ( cOMBK_1595564845_state @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__Com__Opname_000tc__Hoare____Mirabelle____xlrqixeqwe_) ).

thf(1075,plain,
    ! [A: pname,B: hoare_1875481847_state] :
      ( ( hAPP_H139064010_pname @ ( cOMBK_1595564845_state @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(425,axiom,
    ! [A: fun_fu1499449723_pname,B: fun_fu1430349052l_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( hAPP_f674760225e_bool @ ( image_1283814551_pname @ A ) @ B ) ) )
       => ? [C: fun_pname_bool] :
            ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( hAPP_f559147733l_bool @ collec1974731493e_bool @ ( hAPP_f559147733l_bool @ ( hAPP_f624840228l_bool @ cOMBS_350070575l_bool @ ( hAPP_f143162813l_bool @ ( cOMBB_2095475776e_bool @ fconj ) @ ( hAPP_f559147733l_bool @ ( hAPP_f1145991873l_bool @ cOMBC_1988546018l_bool @ member799430823e_bool ) @ B ) ) ) @ ( hAPP_p338031245l_bool @ ( hAPP_f2082757169l_bool @ cOMBC_1004116266e_bool @ ( hAPP_f1385420507e_bool @ ( cOMBB_598082538e_bool @ fequal_pname ) @ A ) ) @ ( hAPP_f1297739591_pname @ A @ C ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_pigeonhole__infinite) ).

thf(2349,plain,
    ! [A: fun_fu1499449723_pname,B: fun_fu1430349052l_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( hAPP_f674760225e_bool @ ( image_1283814551_pname @ A ) @ B ) ) )
       => ? [C: fun_pname_bool] :
            ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( hAPP_f559147733l_bool @ collec1974731493e_bool @ ( hAPP_f559147733l_bool @ ( hAPP_f624840228l_bool @ cOMBS_350070575l_bool @ ( hAPP_f143162813l_bool @ ( cOMBB_2095475776e_bool @ fconj ) @ ( hAPP_f559147733l_bool @ ( hAPP_f1145991873l_bool @ cOMBC_1988546018l_bool @ member799430823e_bool ) @ B ) ) ) @ ( hAPP_p338031245l_bool @ ( hAPP_f2082757169l_bool @ cOMBC_1004116266e_bool @ ( hAPP_f1385420507e_bool @ ( cOMBB_598082538e_bool @ fequal_pname ) @ A ) ) @ ( hAPP_f1297739591_pname @ A @ C ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).

thf(353,axiom,
    ! [A: fun_bool_bool,B: fun_Ho1996104121e_bool,C: hoare_1875481847_state] :
      ( ( hAPP_H1173941847e_bool @ ( hAPP_f121055253e_bool @ ( cOMBB_1424001755_state @ A ) @ B ) @ C )
      = ( hAPP_bool_bool @ A @ ( hAPP_H1173941847e_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Hoare____Mirabel) ).

thf(2085,plain,
    ! [A: fun_bool_bool,B: fun_Ho1996104121e_bool,C: hoare_1875481847_state] :
      ( ( hAPP_H1173941847e_bool @ ( hAPP_f121055253e_bool @ ( cOMBB_1424001755_state @ A ) @ B ) @ C )
      = ( hAPP_bool_bool @ A @ ( hAPP_H1173941847e_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(416,axiom,
    ! [A: fun_pname_bool,B: fun_fu1430349052l_bool,C: fun_fu2101097872e_bool,D: fun_fu608906319e_bool] :
      ( ( hBOOL @ ( finite1626890877e_bool @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
       => ( ( ( ( hAPP_f559147733l_bool @ ( hAPP_f230953622l_bool @ minus_1290075917l_bool @ B ) @ ( hAPP_f559147733l_bool @ ( hAPP_f1320879424l_bool @ insert1325755072e_bool @ A ) @ bot_bo1649642514l_bool ) )
              = bot_bo1649642514l_bool )
           => ( ( hAPP_f674760225e_bool @ D @ ( hAPP_f559147733l_bool @ ( hAPP_f1320879424l_bool @ insert1325755072e_bool @ A ) @ B ) )
              = A ) )
          & ( ( ( hAPP_f559147733l_bool @ ( hAPP_f230953622l_bool @ minus_1290075917l_bool @ B ) @ ( hAPP_f559147733l_bool @ ( hAPP_f1320879424l_bool @ insert1325755072e_bool @ A ) @ bot_bo1649642514l_bool ) )
             != bot_bo1649642514l_bool )
           => ( ( hAPP_f674760225e_bool @ D @ ( hAPP_f559147733l_bool @ ( hAPP_f1320879424l_bool @ insert1325755072e_bool @ A ) @ B ) )
              = ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ C @ A ) @ ( hAPP_f674760225e_bool @ D @ ( hAPP_f559147733l_bool @ ( hAPP_f230953622l_bool @ minus_1290075917l_bool @ B ) @ ( hAPP_f559147733l_bool @ ( hAPP_f1320879424l_bool @ insert1325755072e_bool @ A ) @ bot_bo1649642514l_bool ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_682_folding__one_Oinsert__remove) ).

thf(2317,plain,
    ! [A: fun_pname_bool,B: fun_fu1430349052l_bool,C: fun_fu2101097872e_bool,D: fun_fu608906319e_bool] :
      ( ( hBOOL @ ( finite1626890877e_bool @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
       => ( ( ( ( hAPP_f559147733l_bool @ ( hAPP_f230953622l_bool @ minus_1290075917l_bool @ B ) @ ( hAPP_f559147733l_bool @ ( hAPP_f1320879424l_bool @ insert1325755072e_bool @ A ) @ bot_bo1649642514l_bool ) )
              = bot_bo1649642514l_bool )
           => ( ( hAPP_f674760225e_bool @ D @ ( hAPP_f559147733l_bool @ ( hAPP_f1320879424l_bool @ insert1325755072e_bool @ A ) @ B ) )
              = A ) )
          & ( ( ( hAPP_f559147733l_bool @ ( hAPP_f230953622l_bool @ minus_1290075917l_bool @ B ) @ ( hAPP_f559147733l_bool @ ( hAPP_f1320879424l_bool @ insert1325755072e_bool @ A ) @ bot_bo1649642514l_bool ) )
             != bot_bo1649642514l_bool )
           => ( ( hAPP_f674760225e_bool @ D @ ( hAPP_f559147733l_bool @ ( hAPP_f1320879424l_bool @ insert1325755072e_bool @ A ) @ B ) )
              = ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ C @ A ) @ ( hAPP_f674760225e_bool @ D @ ( hAPP_f559147733l_bool @ ( hAPP_f230953622l_bool @ minus_1290075917l_bool @ B ) @ ( hAPP_f559147733l_bool @ ( hAPP_f1320879424l_bool @ insert1325755072e_bool @ A ) @ bot_bo1649642514l_bool ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).

thf(543,axiom,
    ! [A: fun_fu689207471l_bool] :
      ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ A ) )
    <=> ( ( A = bot_bo973479705l_bool )
        | ? [B: fun_fu689207471l_bool,C: fun_Ho1996104121e_bool] :
            ( ( A
              = ( hAPP_f900945761l_bool @ ( hAPP_f872497439l_bool @ insert504309043e_bool @ C ) @ B ) )
            & ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_finite_Osimps) ).

thf(2781,plain,
    ! [A: fun_fu689207471l_bool] :
      ( ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ A ) )
       => ( ( A = bot_bo973479705l_bool )
          | ? [B: fun_fu689207471l_bool,C: fun_Ho1996104121e_bool] :
              ( ( A
                = ( hAPP_f900945761l_bool @ ( hAPP_f872497439l_bool @ insert504309043e_bool @ C ) @ B ) )
              & ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ B ) ) ) ) )
      & ( ( ( A = bot_bo973479705l_bool )
          | ? [B: fun_fu689207471l_bool,C: fun_Ho1996104121e_bool] :
              ( ( A
                = ( hAPP_f900945761l_bool @ ( hAPP_f872497439l_bool @ insert504309043e_bool @ C ) @ B ) )
              & ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ B ) ) ) )
       => ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).

thf(813,axiom,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool,C: fun_fu2101097872e_bool,D: fun_fu608906319e_bool] :
      ( ( hBOOL @ ( finite1626890877e_bool @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
       => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) )
         => ( ( ( hAPP_f559147733l_bool @ ( hAPP_f230953622l_bool @ semila1130628874l_bool @ B ) @ A )
             != bot_bo1649642514l_bool )
           => ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ C @ ( hAPP_f674760225e_bool @ D @ ( hAPP_f559147733l_bool @ ( hAPP_f230953622l_bool @ semila1782091504l_bool @ B ) @ A ) ) ) @ ( hAPP_f674760225e_bool @ D @ ( hAPP_f559147733l_bool @ ( hAPP_f230953622l_bool @ semila1130628874l_bool @ B ) @ A ) ) )
              = ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ C @ ( hAPP_f674760225e_bool @ D @ B ) ) @ ( hAPP_f674760225e_bool @ D @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_550_folding__one_Ounion__inter) ).

thf(3775,plain,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool,C: fun_fu2101097872e_bool,D: fun_fu608906319e_bool] :
      ( ( hBOOL @ ( finite1626890877e_bool @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
       => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) )
         => ( ( ( hAPP_f559147733l_bool @ ( hAPP_f230953622l_bool @ semila1130628874l_bool @ B ) @ A )
             != bot_bo1649642514l_bool )
           => ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ C @ ( hAPP_f674760225e_bool @ D @ ( hAPP_f559147733l_bool @ ( hAPP_f230953622l_bool @ semila1782091504l_bool @ B ) @ A ) ) ) @ ( hAPP_f674760225e_bool @ D @ ( hAPP_f559147733l_bool @ ( hAPP_f230953622l_bool @ semila1130628874l_bool @ B ) @ A ) ) )
              = ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ C @ ( hAPP_f674760225e_bool @ D @ B ) ) @ ( hAPP_f674760225e_bool @ D @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).

thf(641,axiom,
    hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ ( hAPP_f2031411714_state @ ( cOMBB_1364904209_pname @ hoare_Mirabelle_MGT ) @ body_1 ) ) @ ( dom_pname_com @ body ) ) ) @ fa ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_6) ).

thf(3141,plain,
    hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ ( hAPP_f2031411714_state @ ( cOMBB_1364904209_pname @ hoare_Mirabelle_MGT ) @ body_1 ) ) @ ( dom_pname_com @ body ) ) ) @ fa ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).

thf(713,axiom,
    ! [A: fun_fu399576434l_bool,B: fun_fu1430349052l_bool,C: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ C ) @ B ) )
       => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ bot_bo1649642514l_bool ) )
         => ( ! [D: fun_pname_bool,E: fun_fu1430349052l_bool] :
                ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ E ) )
               => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ D ) @ B ) )
                 => ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ D ) @ E ) )
                   => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ E ) )
                     => ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ ( hAPP_f559147733l_bool @ ( hAPP_f1320879424l_bool @ insert1325755072e_bool @ D ) @ E ) ) ) ) ) ) )
           => ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_finite__subset__induct) ).

thf(3407,plain,
    ! [A: fun_fu399576434l_bool,B: fun_fu1430349052l_bool,C: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ C ) @ B ) )
       => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ bot_bo1649642514l_bool ) )
         => ( ! [D: fun_pname_bool,E: fun_fu1430349052l_bool] :
                ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ E ) )
               => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ D ) @ B ) )
                 => ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ D ) @ E ) )
                   => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ E ) )
                     => ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ ( hAPP_f559147733l_bool @ ( hAPP_f1320879424l_bool @ insert1325755072e_bool @ D ) @ E ) ) ) ) ) ) )
           => ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).

thf(483,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool,D: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ C ) @ D ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ C ) @ A ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ D ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_430_sup__mono) ).

thf(2561,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool,D: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ C ) @ D ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ C ) @ A ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ D ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).

thf(660,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ minus_1015773161e_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_690_finite__Diff) ).

thf(3210,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ minus_1015773161e_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).

thf(169,axiom,
    ! [A: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ bot_bo844097828e_bool ) @ A )
      = bot_bo844097828e_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_570_Int__empty__left) ).

thf(1414,plain,
    ! [A: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ bot_bo844097828e_bool ) @ A )
      = bot_bo844097828e_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(344,axiom,
    ! [A: fun_bo1549164019l_bool,B: fun_fu689207471l_bool,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f78029435l_bool @ ( hAPP_f440042033l_bool @ ( cOMBB_532710323e_bool @ A ) @ B ) @ C )
      = ( hAPP_b589554111l_bool @ A @ ( hAPP_f1408815105l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_229) ).

thf(2053,plain,
    ! [A: fun_bo1549164019l_bool,B: fun_fu689207471l_bool,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f78029435l_bool @ ( hAPP_f440042033l_bool @ ( cOMBB_532710323e_bool @ A ) @ B ) @ C )
      = ( hAPP_b589554111l_bool @ A @ ( hAPP_f1408815105l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(248,axiom,
    ! [A: pname,B: pname] :
      ( ( ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ bot_bo844097828e_bool )
        = ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ bot_bo844097828e_bool ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_singleton__inject) ).

thf(1700,plain,
    ! [A: pname,B: pname] :
      ( ( ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ bot_bo844097828e_bool )
        = ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ bot_bo844097828e_bool ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(499,axiom,
    ! [A: fun_st1506752259e_bool,B: fun_Ho1996104121e_bool,C: fun_st1506752259e_bool,D: com,E: fun_st1506752259e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ C ) @ D ) @ E ) ) @ bot_bo1715400655e_bool ) ) )
     => ( ! [F: state,G: state] :
            ( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ E @ F ) @ G ) )
           => ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ A @ F ) @ G ) ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ C ) @ D ) @ A ) ) @ bot_bo1715400655e_bool ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_382_conseq2) ).

thf(2613,plain,
    ! [A: fun_st1506752259e_bool,B: fun_Ho1996104121e_bool,C: fun_st1506752259e_bool,D: com,E: fun_st1506752259e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ C ) @ D ) @ E ) ) @ bot_bo1715400655e_bool ) ) )
     => ( ! [F: state,G: state] :
            ( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ E @ F ) @ G ) )
           => ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ A @ F ) @ G ) ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ C ) @ D ) @ A ) ) @ bot_bo1715400655e_bool ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).

thf(610,axiom,
    ! [A: hoare_1875481847_state,B: hoare_1875481847_state,C: fun_Ho1996104121e_bool] :
      ( ( ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ C ) )
       => ( B = A ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_insertCI) ).

thf(3032,plain,
    ! [A: hoare_1875481847_state,B: hoare_1875481847_state,C: fun_Ho1996104121e_bool] :
      ( ( ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ C ) )
       => ( B = A ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).

thf(359,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ! [C: hoare_1875481847_state] :
          ( ( hBOOL @ ( hAPP_H1173941847e_bool @ B @ C ) )
         => ( hBOOL @ ( hAPP_H1173941847e_bool @ A @ C ) ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f121055253e_bool @ collec1735317154_state @ B ) ) @ ( hAPP_f121055253e_bool @ collec1735317154_state @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_521_Collect__mono) ).

thf(2108,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ! [C: hoare_1875481847_state] :
          ( ( hBOOL @ ( hAPP_H1173941847e_bool @ B @ C ) )
         => ( hBOOL @ ( hAPP_H1173941847e_bool @ A @ C ) ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f121055253e_bool @ collec1735317154_state @ B ) ) @ ( hAPP_f121055253e_bool @ collec1735317154_state @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(340,axiom,
    ! [A: fun_Ho1996104121e_bool,B: com] :
      ( ( hBOOL @ hoare_1239590103gleton )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ ( hAPP_f1935169308e_bool @ ( cOMBB_1036740637_state @ ( cOMBB_1911358915_state @ fAll_state ) ) @ ( hAPP_f249262236e_bool @ ( cOMBB_1476898461_state @ ( hAPP_f915354021e_bool @ cOMBC_952831051e_bool @ ( hAPP_f1138284024e_bool @ ( cOMBB_20296667_state @ cOMBS_1378840469l_bool ) @ ( hAPP_f1283379615l_bool @ ( cOMBB_1759179140_state @ ( cOMBB_188601460_state @ fimplies ) ) @ ( evalc @ B ) ) ) ) ) @ fequal_state ) ) ) @ B ) @ fequal_state ) ) @ bot_bo1715400655e_bool ) ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_c406083500_state @ hoare_Mirabelle_MGT @ B ) ) @ bot_bo1715400655e_bool ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_533_MGT__alternD) ).

thf(2038,plain,
    ! [A: fun_Ho1996104121e_bool,B: com] :
      ( ( hBOOL @ hoare_1239590103gleton )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ ( hAPP_f1935169308e_bool @ ( cOMBB_1036740637_state @ ( cOMBB_1911358915_state @ fAll_state ) ) @ ( hAPP_f249262236e_bool @ ( cOMBB_1476898461_state @ ( hAPP_f915354021e_bool @ cOMBC_952831051e_bool @ ( hAPP_f1138284024e_bool @ ( cOMBB_20296667_state @ cOMBS_1378840469l_bool ) @ ( hAPP_f1283379615l_bool @ ( cOMBB_1759179140_state @ ( cOMBB_188601460_state @ fimplies ) ) @ ( evalc @ B ) ) ) ) ) @ fequal_state ) ) ) @ B ) @ fequal_state ) ) @ bot_bo1715400655e_bool ) ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_c406083500_state @ hoare_Mirabelle_MGT @ B ) ) @ bot_bo1715400655e_bool ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(302,axiom,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool] :
      ( ( B = bot_bo1715400655e_bool )
     => ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_equals0D) ).

thf(1889,plain,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool] :
      ( ( B = bot_bo1715400655e_bool )
     => ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(755,axiom,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ B )
      = ( hAPP_f121055253e_bool @ collec1735317154_state @ ( hAPP_f121055253e_bool @ ( hAPP_f1300953505e_bool @ cOMBS_896408300l_bool @ ( hAPP_f932622461l_bool @ ( cOMBB_242064253_state @ fdisj ) @ ( hAPP_H117293375e_bool @ ( hAPP_f2101312745e_bool @ cOMBC_1972244470e_bool @ fequal391417144_state ) @ A ) ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1795624711e_bool @ cOMBC_1099403170l_bool @ member618553700_state ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_insert__compr__raw) ).

thf(3555,plain,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ B )
      = ( hAPP_f121055253e_bool @ collec1735317154_state @ ( hAPP_f121055253e_bool @ ( hAPP_f1300953505e_bool @ cOMBS_896408300l_bool @ ( hAPP_f932622461l_bool @ ( cOMBB_242064253_state @ fdisj ) @ ( hAPP_H117293375e_bool @ ( hAPP_f2101312745e_bool @ cOMBC_1972244470e_bool @ fequal391417144_state ) @ A ) ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1795624711e_bool @ cOMBC_1099403170l_bool @ member618553700_state ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).

thf(226,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: pname] :
      ( ( hBOOL @ ( hAPP_pname_bool @ B @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) )
       => ( hBOOL @ ( hAPP_pname_bool @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_389_rev__predicate1D) ).

thf(1612,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: pname] :
      ( ( hBOOL @ ( hAPP_pname_bool @ B @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) )
       => ( hBOOL @ ( hAPP_pname_bool @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(511,axiom,
    ! [A: fun_fu1430349052l_bool] :
      ( ( ( hAPP_f559147733l_bool @ collec1974731493e_bool @ A )
        = bot_bo1649642514l_bool )
    <=> ! [B: fun_pname_bool] :
          ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_Collect__empty__eq) ).

thf(2649,plain,
    ! [A: fun_fu1430349052l_bool] :
      ( ( ( ( hAPP_f559147733l_bool @ collec1974731493e_bool @ A )
          = bot_bo1649642514l_bool )
       => ! [B: fun_pname_bool] :
            ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ B ) ) )
      & ( ! [B: fun_pname_bool] :
            ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ B ) )
       => ( ( hAPP_f559147733l_bool @ collec1974731493e_bool @ A )
          = bot_bo1649642514l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).

thf(52,axiom,
    ! [A: fun_fu1499449723_pname,B: fun_fu1430349052l_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ ( hAPP_f674760225e_bool @ ( image_1283814551_pname @ A ) @ B ) ) )
       => ? [D: fun_fu1430349052l_bool] :
            ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ D ) )
            & ( C
              = ( hAPP_f674760225e_bool @ ( image_1283814551_pname @ A ) @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_finite__subset__image) ).

thf(970,plain,
    ! [A: fun_fu1499449723_pname,B: fun_fu1430349052l_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ ( hAPP_f674760225e_bool @ ( image_1283814551_pname @ A ) @ B ) ) )
       => ? [D: fun_fu1430349052l_bool] :
            ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ D ) )
            & ( C
              = ( hAPP_f674760225e_bool @ ( image_1283814551_pname @ A ) @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(10,axiom,
    ( bot_bo844097828e_bool
    = ( hAPP_f759274231e_bool @ collect_pname @ ( cOMBK_bool_pname @ fFalse ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_empty__def) ).

thf(837,plain,
    ( bot_bo844097828e_bool
    = ( hAPP_f759274231e_bool @ collect_pname @ ( cOMBK_bool_pname @ fFalse ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(269,axiom,
    ! [A: pname,B: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ minus_1015773161e_bool @ B ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ bot_bo844097828e_bool ) ) )
      = ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_696_insert__Diff__single) ).

thf(1776,plain,
    ! [A: pname,B: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ minus_1015773161e_bool @ B ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ bot_bo844097828e_bool ) ) )
      = ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(781,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ! [C: hoare_1875481847_state] :
          ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ C ) @ B ) )
         => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ C ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_subsetI) ).

thf(3654,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ! [C: hoare_1875481847_state] :
          ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ C ) @ B ) )
         => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ C ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).

thf(125,axiom,
    ! [A: fun_pname_bool,B: pname] :
      ( ( ( hBOOL @ ( hAPP_pname_bool @ A @ B ) )
       => ( ( hAPP_f759274231e_bool @ collect_pname @ ( hAPP_f759274231e_bool @ ( hAPP_f649174806e_bool @ cOMBS_568398431l_bool @ ( hAPP_f1402196763l_bool @ ( cOMBB_675860798_pname @ fconj ) @ ( hAPP_p61793385e_bool @ ( hAPP_f22061361e_bool @ cOMBC_1149511130e_bool @ fequal_pname ) @ B ) ) ) @ A ) )
          = ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ bot_bo844097828e_bool ) ) )
      & ( ~ ( hBOOL @ ( hAPP_pname_bool @ A @ B ) )
       => ( ( hAPP_f759274231e_bool @ collect_pname @ ( hAPP_f759274231e_bool @ ( hAPP_f649174806e_bool @ cOMBS_568398431l_bool @ ( hAPP_f1402196763l_bool @ ( cOMBB_675860798_pname @ fconj ) @ ( hAPP_p61793385e_bool @ ( hAPP_f22061361e_bool @ cOMBC_1149511130e_bool @ fequal_pname ) @ B ) ) ) @ A ) )
          = bot_bo844097828e_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_Collect__conv__if) ).

thf(1249,plain,
    ! [A: fun_pname_bool,B: pname] :
      ( ( ( hBOOL @ ( hAPP_pname_bool @ A @ B ) )
       => ( ( hAPP_f759274231e_bool @ collect_pname @ ( hAPP_f759274231e_bool @ ( hAPP_f649174806e_bool @ cOMBS_568398431l_bool @ ( hAPP_f1402196763l_bool @ ( cOMBB_675860798_pname @ fconj ) @ ( hAPP_p61793385e_bool @ ( hAPP_f22061361e_bool @ cOMBC_1149511130e_bool @ fequal_pname ) @ B ) ) ) @ A ) )
          = ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ bot_bo844097828e_bool ) ) )
      & ( ~ ( hBOOL @ ( hAPP_pname_bool @ A @ B ) )
       => ( ( hAPP_f759274231e_bool @ collect_pname @ ( hAPP_f759274231e_bool @ ( hAPP_f649174806e_bool @ cOMBS_568398431l_bool @ ( hAPP_f1402196763l_bool @ ( cOMBB_675860798_pname @ fconj ) @ ( hAPP_p61793385e_bool @ ( hAPP_f22061361e_bool @ cOMBC_1149511130e_bool @ fequal_pname ) @ B ) ) ) @ A ) )
          = bot_bo844097828e_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(465,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_pn664418900_state,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ B ) @ C ) ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_finite__surj) ).

thf(2487,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_pn664418900_state,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ B ) @ C ) ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).

thf(370,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) ) @ C )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ C ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ B ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_655_inf__sup__distrib2) ).

thf(2153,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) ) @ C )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ C ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(427,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ B ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_rev__finite__subset) ).

thf(2355,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ B ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).

thf(669,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: hoare_1875481847_state] :
      ( ( hBOOL @ ( hAPP_H1173941847e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1795624711e_bool @ cOMBC_1099403170l_bool @ member618553700_state ) @ A ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1795624711e_bool @ cOMBC_1099403170l_bool @ member618553700_state ) @ B ) ) @ C ) )
    <=> ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ C ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_398_sup__Un__eq) ).

thf(3247,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: hoare_1875481847_state] :
      ( ( ( hBOOL @ ( hAPP_H1173941847e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1795624711e_bool @ cOMBC_1099403170l_bool @ member618553700_state ) @ A ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1795624711e_bool @ cOMBC_1099403170l_bool @ member618553700_state ) @ B ) ) @ C ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ C ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) ) ) )
      & ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ C ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) ) )
       => ( hBOOL @ ( hAPP_H1173941847e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1795624711e_bool @ cOMBC_1099403170l_bool @ member618553700_state ) @ A ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1795624711e_bool @ cOMBC_1099403170l_bool @ member618553700_state ) @ B ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).

thf(693,axiom,
    ! [A: fun_Ho1695028467e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ B ) )
     => ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ ( hAPP_f1873026899l_bool @ ( image_896278159e_bool @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_finite__imageI) ).

thf(3333,plain,
    ! [A: fun_Ho1695028467e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ B ) )
     => ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ ( hAPP_f1873026899l_bool @ ( image_896278159e_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).

thf(325,axiom,
    hBOOL @ ( hAPP_com_bool @ wt @ skip ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_480_WT_OSkip) ).

thf(1979,plain,
    hBOOL @ ( hAPP_com_bool @ wt @ skip ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(701,axiom,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ B )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ bot_bo1715400655e_bool ) ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_insert__is__Un) ).

thf(3364,plain,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ B )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ bot_bo1715400655e_bool ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).

thf(263,axiom,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
      ( ( hAPP_f559147733l_bool @ ( hAPP_f230953622l_bool @ semila1130628874l_bool @ A ) @ B )
      = ( hAPP_f559147733l_bool @ collec1974731493e_bool @ ( hAPP_f559147733l_bool @ ( hAPP_f624840228l_bool @ cOMBS_350070575l_bool @ ( hAPP_f143162813l_bool @ ( cOMBB_2095475776e_bool @ fconj ) @ ( hAPP_f559147733l_bool @ ( hAPP_f1145991873l_bool @ cOMBC_1988546018l_bool @ member799430823e_bool ) @ A ) ) ) @ ( hAPP_f559147733l_bool @ ( hAPP_f1145991873l_bool @ cOMBC_1988546018l_bool @ member799430823e_bool ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_574_Int__def) ).

thf(1759,plain,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
      ( ( hAPP_f559147733l_bool @ ( hAPP_f230953622l_bool @ semila1130628874l_bool @ A ) @ B )
      = ( hAPP_f559147733l_bool @ collec1974731493e_bool @ ( hAPP_f559147733l_bool @ ( hAPP_f624840228l_bool @ cOMBS_350070575l_bool @ ( hAPP_f143162813l_bool @ ( cOMBB_2095475776e_bool @ fconj ) @ ( hAPP_f559147733l_bool @ ( hAPP_f1145991873l_bool @ cOMBC_1988546018l_bool @ member799430823e_bool ) @ A ) ) ) @ ( hAPP_f559147733l_bool @ ( hAPP_f1145991873l_bool @ cOMBC_1988546018l_bool @ member799430823e_bool ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(138,axiom,
    ! [A: hoare_1875481847_state,B: hoare_1875481847_state] :
      ( ( hAPP_H350317809_state @ ( hAPP_H743221337_state @ ( hAPP_b1347637997_state @ if_Hoa1541320583_state @ fTrue ) @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_000tc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc__Com__Ostate) ).

thf(1297,plain,
    ! [A: hoare_1875481847_state,B: hoare_1875481847_state] :
      ( ( hAPP_H350317809_state @ ( hAPP_H743221337_state @ ( hAPP_b1347637997_state @ if_Hoa1541320583_state @ fTrue ) @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(636,axiom,
    ! [A: fun_pn800050071e_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( hAPP_f434788991l_bool @ ( image_47868345e_bool @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_finite__imageI) ).

thf(3126,plain,
    ! [A: fun_pn800050071e_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( hAPP_f434788991l_bool @ ( image_47868345e_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).

thf(815,axiom,
    ! [A: bool,B: bool] :
      ( ( hBOOL @ B )
      | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fimplies_1_1_U) ).

thf(3787,plain,
    ! [A: bool,B: bool] :
      ( ( hBOOL @ B )
      | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).

thf(208,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pn1208287926_pname,D: fun_fu1499449723_pname] :
      ( ( hBOOL @ ( finite1282449217_pname @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
       => ( ( B != bot_bo844097828e_bool )
         => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
           => ( ( A != bot_bo844097828e_bool )
             => ( ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ B ) @ A )
                  = bot_bo844097828e_bool )
               => ( ( hAPP_f1297739591_pname @ D @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ B ) @ A ) )
                  = ( hAPP_pname_pname @ ( hAPP_p1170154830_pname @ C @ ( hAPP_f1297739591_pname @ D @ B ) ) @ ( hAPP_f1297739591_pname @ D @ A ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_556_folding__one_Ounion__disjoint) ).

thf(1539,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pn1208287926_pname,D: fun_fu1499449723_pname] :
      ( ( hBOOL @ ( finite1282449217_pname @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
       => ( ( B != bot_bo844097828e_bool )
         => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
           => ( ( A != bot_bo844097828e_bool )
             => ( ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ B ) @ A )
                  = bot_bo844097828e_bool )
               => ( ( hAPP_f1297739591_pname @ D @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ B ) @ A ) )
                  = ( hAPP_pname_pname @ ( hAPP_p1170154830_pname @ C @ ( hAPP_f1297739591_pname @ D @ B ) ) @ ( hAPP_f1297739591_pname @ D @ A ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(182,axiom,
    ! [A: pname] :
      ( ( set_pname @ ( some_pname @ A ) )
      = ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ bot_bo844097828e_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_402_Option_Oset_Osimps_I2_J) ).

thf(1456,plain,
    ! [A: pname] :
      ( ( set_pname @ ( some_pname @ A ) )
      = ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ bot_bo844097828e_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(811,axiom,
    ! [A: fun_Ho1653816318_pname,B: hoare_1875481847_state,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f1148778334e_bool @ ( image_720060442_pname @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ C ) )
      = ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ ( hAPP_H139064010_pname @ A @ B ) ) @ ( hAPP_f1148778334e_bool @ ( image_720060442_pname @ A ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_image__insert) ).

thf(3770,plain,
    ! [A: fun_Ho1653816318_pname,B: hoare_1875481847_state,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f1148778334e_bool @ ( image_720060442_pname @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ C ) )
      = ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ ( hAPP_H139064010_pname @ A @ B ) ) @ ( hAPP_f1148778334e_bool @ ( image_720060442_pname @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).

thf(241,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ A ) @ B ) ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_629_inf__le2) ).

thf(1668,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ A ) @ B ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(323,axiom,
    ! [A: com,B: com] :
      ( ( hBOOL @ ( hAPP_com_bool @ wt @ ( semi @ A @ B ) ) )
     => ~ ( ( hBOOL @ ( hAPP_com_bool @ wt @ A ) )
         => ~ ( hBOOL @ ( hAPP_com_bool @ wt @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_494_WTs__elim__cases_I4_J) ).

thf(1974,plain,
    ! [A: com,B: com] :
      ( ( hBOOL @ ( hAPP_com_bool @ wt @ ( semi @ A @ B ) ) )
     => ~ ( ( hBOOL @ ( hAPP_com_bool @ wt @ A ) )
         => ~ ( hBOOL @ ( hAPP_com_bool @ wt @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(469,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ B ) @ C ) )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_595_Un__Int__distrib) ).

thf(2505,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ B ) @ C ) )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).

thf(708,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ fequal259518520e_bool @ A ) @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Otriple) ).

thf(3390,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ fequal259518520e_bool @ A ) @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).

thf(292,axiom,
    ! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
       => ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ A ) ) @ C )
          = ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ A ) @ C ) ) ) )
      & ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
       => ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ A ) ) @ C )
          = ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_619_Int__insert__left) ).

thf(1852,plain,
    ! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
       => ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ A ) ) @ C )
          = ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ A ) @ C ) ) ) )
      & ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
       => ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ A ) ) @ C )
          = ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(549,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) ) @ C )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_413_sup__assoc) ).

thf(2813,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) ) @ C )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).

thf(521,axiom,
    ! [A: fun_fu235184776_pname,B: fun_fu689207471l_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ B ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( hAPP_f75069804e_bool @ ( image_1169820240_pname @ A ) @ B ) ) )
       => ? [C: fun_Ho1996104121e_bool] :
            ( ( hBOOL @ ( hAPP_f1699935247l_bool @ ( hAPP_f640685261l_bool @ member1062536460e_bool @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ ( hAPP_f900945761l_bool @ collec771609166e_bool @ ( hAPP_f900945761l_bool @ ( hAPP_f2051813877l_bool @ cOMBS_1451994324l_bool @ ( hAPP_f440042033l_bool @ ( cOMBB_532710323e_bool @ fconj ) @ ( hAPP_f900945761l_bool @ ( hAPP_f1846363427l_bool @ cOMBC_1909905718l_bool @ member1062536460e_bool ) @ B ) ) ) @ ( hAPP_p1265998686l_bool @ ( hAPP_f662360091l_bool @ cOMBC_217340069e_bool @ ( hAPP_f585615743e_bool @ ( cOMBB_184405641e_bool @ fequal_pname ) @ A ) ) @ ( hAPP_f1542224800_pname @ A @ C ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_pigeonhole__infinite) ).

thf(2697,plain,
    ! [A: fun_fu235184776_pname,B: fun_fu689207471l_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ B ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( hAPP_f75069804e_bool @ ( image_1169820240_pname @ A ) @ B ) ) )
       => ? [C: fun_Ho1996104121e_bool] :
            ( ( hBOOL @ ( hAPP_f1699935247l_bool @ ( hAPP_f640685261l_bool @ member1062536460e_bool @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ ( hAPP_f900945761l_bool @ collec771609166e_bool @ ( hAPP_f900945761l_bool @ ( hAPP_f2051813877l_bool @ cOMBS_1451994324l_bool @ ( hAPP_f440042033l_bool @ ( cOMBB_532710323e_bool @ fconj ) @ ( hAPP_f900945761l_bool @ ( hAPP_f1846363427l_bool @ cOMBC_1909905718l_bool @ member1062536460e_bool ) @ B ) ) ) @ ( hAPP_p1265998686l_bool @ ( hAPP_f662360091l_bool @ cOMBC_217340069e_bool @ ( hAPP_f585615743e_bool @ ( cOMBB_184405641e_bool @ fequal_pname ) @ A ) ) @ ( hAPP_f1542224800_pname @ A @ C ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).

thf(124,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool @ collect_pname @ ( hAPP_f759274231e_bool @ ( hAPP_f649174806e_bool @ cOMBS_568398431l_bool @ ( hAPP_f1402196763l_bool @ ( cOMBB_675860798_pname @ fconj ) @ A ) ) @ B ) )
      = ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ ( hAPP_f759274231e_bool @ collect_pname @ A ) ) @ ( hAPP_f759274231e_bool @ collect_pname @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_583_Collect__conj__eq) ).

thf(1246,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool @ collect_pname @ ( hAPP_f759274231e_bool @ ( hAPP_f649174806e_bool @ cOMBS_568398431l_bool @ ( hAPP_f1402196763l_bool @ ( cOMBB_675860798_pname @ fconj ) @ A ) ) @ B ) )
      = ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ ( hAPP_f759274231e_bool @ collect_pname @ A ) ) @ ( hAPP_f759274231e_bool @ collect_pname @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(232,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ A ) @ B ) ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_607_Int__lower1) ).

thf(1627,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ A ) @ B ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(432,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) ) @ C ) )
     => ~ ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ C ) )
         => ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_428_le__supE) ).

thf(2370,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) ) @ C ) )
     => ~ ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ C ) )
         => ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

thf(662,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] : ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_452_sup__ge1) ).

thf(3215,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] : ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).

thf(732,axiom,
    ! [A: fun_pname_bool,B: fun_Ho1653816318_pname,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( hAPP_f1148778334e_bool @ ( image_720060442_pname @ B ) @ C ) ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_finite__surj) ).

thf(3476,plain,
    ! [A: fun_pname_bool,B: fun_Ho1653816318_pname,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( hAPP_f1148778334e_bool @ ( image_720060442_pname @ B ) @ C ) ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).

thf(330,axiom,
    ! [A: hoare_1875481847_state] :
      ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ bot_bo1715400655e_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_empty__iff) ).

thf(1991,plain,
    ! [A: hoare_1875481847_state] :
      ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ bot_bo1715400655e_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(108,axiom,
    ! [A: fun_pn760644914e_bool,B: hoare_1875481847_state,C: pname] :
      ( ( hAPP_pname_bool @ ( hAPP_H785152948e_bool @ ( hAPP_f1564627769e_bool @ cOMBC_951029257e_bool @ A ) @ B ) @ C )
      = ( hAPP_H1173941847e_bool @ ( hAPP_p1537966538e_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Hoare____Mirabelle____xlrqixeqwe_) ).

thf(1202,plain,
    ! [A: fun_pn760644914e_bool,B: hoare_1875481847_state,C: pname] :
      ( ( hAPP_pname_bool @ ( hAPP_H785152948e_bool @ ( hAPP_f1564627769e_bool @ cOMBC_951029257e_bool @ A ) @ B ) @ C )
      = ( hAPP_H1173941847e_bool @ ( hAPP_p1537966538e_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(762,axiom,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
       => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_finite__subset) ).

thf(3592,plain,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
       => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).

thf(592,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] : ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_448_sup__ge2) ).

thf(2963,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] : ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).

thf(200,axiom,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool,C: fun_fu2101097872e_bool,D: fun_fu608906319e_bool] :
      ( ( hBOOL @ ( finite1268145088e_bool @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
       => ( ( B != bot_bo1649642514l_bool )
         => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) )
           => ( ( A != bot_bo1649642514l_bool )
             => ( ( hAPP_f674760225e_bool @ D @ ( hAPP_f559147733l_bool @ ( hAPP_f230953622l_bool @ semila1782091504l_bool @ B ) @ A ) )
                = ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ C @ ( hAPP_f674760225e_bool @ D @ B ) ) @ ( hAPP_f674760225e_bool @ D @ A ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_461_folding__one__idem_Ounion__idem) ).

thf(1515,plain,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool,C: fun_fu2101097872e_bool,D: fun_fu608906319e_bool] :
      ( ( hBOOL @ ( finite1268145088e_bool @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
       => ( ( B != bot_bo1649642514l_bool )
         => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) )
           => ( ( A != bot_bo1649642514l_bool )
             => ( ( hAPP_f674760225e_bool @ D @ ( hAPP_f559147733l_bool @ ( hAPP_f230953622l_bool @ semila1782091504l_bool @ B ) @ A ) )
                = ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ C @ ( hAPP_f674760225e_bool @ D @ B ) ) @ ( hAPP_f674760225e_bool @ D @ A ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(65,axiom,
    ! [A: fun_Ho14659478e_bool,B: pname,C: hoare_1875481847_state] :
      ( ( hAPP_H1173941847e_bool @ ( hAPP_p1537966538e_bool @ ( hAPP_f1188413809e_bool @ cOMBC_1259060397e_bool @ A ) @ B ) @ C )
      = ( hAPP_pname_bool @ ( hAPP_H785152948e_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc__Com__) ).

thf(1026,plain,
    ! [A: fun_Ho14659478e_bool,B: pname,C: hoare_1875481847_state] :
      ( ( hAPP_H1173941847e_bool @ ( hAPP_p1537966538e_bool @ ( hAPP_f1188413809e_bool @ cOMBC_1259060397e_bool @ A ) @ B ) @ C )
      = ( hAPP_pname_bool @ ( hAPP_H785152948e_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(717,axiom,
    ! [A: fun_st1506752259e_bool,B: fun_st1506752259e_bool,C: fun_Ho1996104121e_bool,D: fun_st1506752259e_bool,E: com,F: fun_st1506752259e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ C ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ D ) @ E ) @ F ) ) @ bot_bo1715400655e_bool ) ) )
     => ( ! [G: state,H: state] :
            ( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ B @ G ) @ H ) )
           => ! [I: state] :
                ( ! [J: state] :
                    ( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ D @ J ) @ H ) )
                   => ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ F @ J ) @ I ) ) )
               => ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ A @ G ) @ I ) ) ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ C ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ B ) @ E ) @ A ) ) @ bot_bo1715400655e_bool ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_399_conseq12) ).

thf(3422,plain,
    ! [A: fun_st1506752259e_bool,B: fun_st1506752259e_bool,C: fun_Ho1996104121e_bool,D: fun_st1506752259e_bool,E: com,F: fun_st1506752259e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ C ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ D ) @ E ) @ F ) ) @ bot_bo1715400655e_bool ) ) )
     => ( ! [G: state,H: state] :
            ( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ B @ G ) @ H ) )
           => ! [I: state] :
                ( ! [J: state] :
                    ( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ D @ J ) @ H ) )
                   => ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ F @ J ) @ I ) ) )
               => ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ A @ G ) @ I ) ) ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ C ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ B ) @ E ) @ A ) ) @ bot_bo1715400655e_bool ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).

thf(474,axiom,
    ! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( hAPP_f559147733l_bool @ ( hAPP_f1320879424l_bool @ insert1325755072e_bool @ A ) @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_finite__insert) ).

thf(2529,plain,
    ! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
      ( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( hAPP_f559147733l_bool @ ( hAPP_f1320879424l_bool @ insert1325755072e_bool @ A ) @ B ) ) )
       => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
       => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( hAPP_f559147733l_bool @ ( hAPP_f1320879424l_bool @ insert1325755072e_bool @ A ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).

thf(78,axiom,
    ! [A: fun_bool_bool,B: fun_state_bool,C: state] :
      ( ( hAPP_state_bool @ ( hAPP_f1759915619e_bool @ ( cOMBB_160679318_state @ A ) @ B ) @ C )
      = ( hAPP_bool_bool @ A @ ( hAPP_state_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Ostate_U) ).

thf(1086,plain,
    ! [A: fun_bool_bool,B: fun_state_bool,C: state] :
      ( ( hAPP_state_bool @ ( hAPP_f1759915619e_bool @ ( cOMBB_160679318_state @ A ) @ B ) @ C )
      = ( hAPP_bool_bool @ A @ ( hAPP_state_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(42,axiom,
    ! [A: pname] :
      ( ( hAPP_f1297739591_pname @ the_elem_pname @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ bot_bo844097828e_bool ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_the__elem__eq) ).

thf(938,plain,
    ! [A: pname] :
      ( ( hAPP_f1297739591_pname @ the_elem_pname @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ bot_bo844097828e_bool ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(757,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: hoare_1875481847_state] :
      ( ( ~ ( hBOOL @ ( hAPP_H1173941847e_bool @ B @ C ) )
       => ( hBOOL @ ( hAPP_H1173941847e_bool @ A @ C ) ) )
     => ( hBOOL @ ( hAPP_H1173941847e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_385_sup1CI) ).

thf(3563,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: hoare_1875481847_state] :
      ( ( ~ ( hBOOL @ ( hAPP_H1173941847e_bool @ B @ C ) )
       => ( hBOOL @ ( hAPP_H1173941847e_bool @ A @ C ) ) )
     => ( hBOOL @ ( hAPP_H1173941847e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).

thf(537,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( ( C = A )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_ord__le__eq__trans) ).

thf(2761,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( ( C = A )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).

thf(270,axiom,
    ! [A: pname,B: fun_pname_bool,C: fun_pn1208287926_pname,D: fun_fu1499449723_pname] :
      ( ( hBOOL @ ( finite1282449217_pname @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
       => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
         => ( ( ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ minus_1015773161e_bool @ B ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ bot_bo844097828e_bool ) )
                = bot_bo844097828e_bool )
             => ( ( hAPP_f1297739591_pname @ D @ B )
                = A ) )
            & ( ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ minus_1015773161e_bool @ B ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ bot_bo844097828e_bool ) )
               != bot_bo844097828e_bool )
             => ( ( hAPP_f1297739591_pname @ D @ B )
                = ( hAPP_pname_pname @ ( hAPP_p1170154830_pname @ C @ A ) @ ( hAPP_f1297739591_pname @ D @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ minus_1015773161e_bool @ B ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ bot_bo844097828e_bool ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_676_folding__one_Oremove) ).

thf(1779,plain,
    ! [A: pname,B: fun_pname_bool,C: fun_pn1208287926_pname,D: fun_fu1499449723_pname] :
      ( ( hBOOL @ ( finite1282449217_pname @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
       => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
         => ( ( ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ minus_1015773161e_bool @ B ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ bot_bo844097828e_bool ) )
                = bot_bo844097828e_bool )
             => ( ( hAPP_f1297739591_pname @ D @ B )
                = A ) )
            & ( ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ minus_1015773161e_bool @ B ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ bot_bo844097828e_bool ) )
               != bot_bo844097828e_bool )
             => ( ( hAPP_f1297739591_pname @ D @ B )
                = ( hAPP_pname_pname @ ( hAPP_p1170154830_pname @ C @ A ) @ ( hAPP_f1297739591_pname @ D @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ minus_1015773161e_bool @ B ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ bot_bo844097828e_bool ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(774,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool,D: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ C ) @ D ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ C ) @ A ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ D ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_598_Int__mono) ).

thf(3624,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool,D: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ C ) @ D ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ C ) @ A ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ D ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).

thf(544,axiom,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
      ( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
        | ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) ) )
     => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( hAPP_f559147733l_bool @ ( hAPP_f230953622l_bool @ semila1130628874l_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_562_finite__Int) ).

thf(2793,plain,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
      ( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
        | ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) ) )
     => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( hAPP_f559147733l_bool @ ( hAPP_f230953622l_bool @ semila1130628874l_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).

thf(653,axiom,
    ! [A: fun_Ho760178998l_bool,B: fun_pname_bool,C: hoare_1875481847_state] :
      ( ( hAPP_H1173941847e_bool @ ( hAPP_f1291720380e_bool @ ( hAPP_f406856233e_bool @ cOMBC_2049654457l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1664156314l_bool @ ( hAPP_H434980226l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc__Com___223) ).

thf(3190,plain,
    ! [A: fun_Ho760178998l_bool,B: fun_pname_bool,C: hoare_1875481847_state] :
      ( ( hAPP_H1173941847e_bool @ ( hAPP_f1291720380e_bool @ ( hAPP_f406856233e_bool @ cOMBC_2049654457l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1664156314l_bool @ ( hAPP_H434980226l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).

thf(332,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_st1506752259e_bool] : ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ B ) @ skip ) @ B ) ) @ bot_bo1715400655e_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_469_hoare__derivs_OSkip) ).

thf(1996,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_st1506752259e_bool] : ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ B ) @ skip ) @ B ) ) @ bot_bo1715400655e_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(787,axiom,
    ! [A: fun_Ho1996104121e_bool,B: hoare_1875481847_state,C: fun_Ho1996104121e_bool] :
      ( ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ C ) )
       => ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ C ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ A ) )
          = ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ C ) @ A ) ) ) )
      & ( ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ C ) )
       => ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ C ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ A ) )
          = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_622_Int__insert__right) ).

thf(3675,plain,
    ! [A: fun_Ho1996104121e_bool,B: hoare_1875481847_state,C: fun_Ho1996104121e_bool] :
      ( ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ C ) )
       => ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ C ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ A ) )
          = ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ C ) @ A ) ) ) )
      & ( ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ C ) )
       => ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ C ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ A ) )
          = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).

thf(307,axiom,
    ! [A: fun_fu235184776_pname,B: fun_fu689207471l_bool] :
      ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ B ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( hAPP_f75069804e_bool @ ( image_1169820240_pname @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_finite__imageI) ).

thf(1906,plain,
    ! [A: fun_fu235184776_pname,B: fun_fu689207471l_bool] :
      ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ B ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( hAPP_f75069804e_bool @ ( image_1169820240_pname @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(783,axiom,
    ! [A: hoare_1875481847_state] :
      ( ( hAPP_f121055253e_bool @ collec1735317154_state @ ( hAPP_H117293375e_bool @ ( hAPP_f2101312745e_bool @ cOMBC_1972244470e_bool @ fequal391417144_state ) @ A ) )
      = ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ bot_bo1715400655e_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_singleton__conv) ).

thf(3660,plain,
    ! [A: hoare_1875481847_state] :
      ( ( hAPP_f121055253e_bool @ collec1735317154_state @ ( hAPP_H117293375e_bool @ ( hAPP_f2101312745e_bool @ cOMBC_1972244470e_bool @ fequal391417144_state ) @ A ) )
      = ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ bot_bo1715400655e_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).

thf(793,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
    <=> ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ B )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_632_le__iff__inf) ).

thf(3707,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
       => ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ B )
          = A ) )
      & ( ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ B )
          = A )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).

thf(638,axiom,
    ( ( hBOOL @ hoare_1239590103gleton )
  <=> ? [A: state,B: state] : ( A != B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_412_state__not__singleton__def) ).

thf(3130,plain,
    ( ( ( hBOOL @ hoare_1239590103gleton )
     => ? [A: state,B: state] : ( A != B ) )
    & ( ? [A: state,B: state] : ( A != B )
     => ( hBOOL @ hoare_1239590103gleton ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).

thf(517,axiom,
    ! [A: hoare_1875481847_state] :
      ( ( hAPP_f890249627_state @ the_el1031305112_state @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ bot_bo1715400655e_bool ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_the__elem__eq) ).

thf(2677,plain,
    ! [A: hoare_1875481847_state] :
      ( ( hAPP_f890249627_state @ the_el1031305112_state @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ bot_bo1715400655e_bool ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).

thf(613,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ B )
      | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fdisj_1_1_U) ).

thf(3042,plain,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ B )
      | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).

thf(525,axiom,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
     => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( hAPP_f559147733l_bool @ ( hAPP_f230953622l_bool @ minus_1290075917l_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_688_finite__Diff) ).

thf(2717,plain,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
     => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( hAPP_f559147733l_bool @ ( hAPP_f230953622l_bool @ minus_1290075917l_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).

thf(210,axiom,
    ! [A: fun_pname_bool,B: fun_pn1208287926_pname,C: fun_fu1499449723_pname] :
      ( ( hBOOL @ ( finite1282449217_pname @ B @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
       => ( ( A != bot_bo844097828e_bool )
         => ( ! [D: pname,E: pname] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( hAPP_pname_pname @ ( hAPP_p1170154830_pname @ B @ D ) @ E ) ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ D ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ E ) @ bot_bo844097828e_bool ) ) ) )
           => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( hAPP_f1297739591_pname @ C @ A ) ) @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_515_folding__one_Oclosed) ).

thf(1548,plain,
    ! [A: fun_pname_bool,B: fun_pn1208287926_pname,C: fun_fu1499449723_pname] :
      ( ( hBOOL @ ( finite1282449217_pname @ B @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
       => ( ( A != bot_bo844097828e_bool )
         => ( ! [D: pname,E: pname] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( hAPP_pname_pname @ ( hAPP_p1170154830_pname @ B @ D ) @ E ) ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ D ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ E ) @ bot_bo844097828e_bool ) ) ) )
           => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( hAPP_f1297739591_pname @ C @ A ) ) @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(17,axiom,
    ! [A: fun_st1483075957e_bool,B: bool,C: state] :
      ( ( hAPP_s1806633685e_bool @ ( hAPP_b1095269219e_bool @ ( hAPP_f701449317e_bool @ cOMBC_471052088e_bool @ A ) @ B ) @ C )
      = ( hAPP_b2019457360e_bool @ ( hAPP_s1874344717e_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Ostate_000tc__HOL__Obool_000tc__fun_Itc__Com__O) ).

thf(856,plain,
    ! [A: fun_st1483075957e_bool,B: bool,C: state] :
      ( ( hAPP_s1806633685e_bool @ ( hAPP_b1095269219e_bool @ ( hAPP_f701449317e_bool @ cOMBC_471052088e_bool @ A ) @ B ) @ C )
      = ( hAPP_b2019457360e_bool @ ( hAPP_s1874344717e_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(633,axiom,
    hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ bot_bo844097828e_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_finite_OemptyI) ).

thf(3111,plain,
    hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ bot_bo844097828e_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).

thf(434,axiom,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ B ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_insert__mono) ).

thf(2376,plain,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ B ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).

thf(646,axiom,
    ! [A: fun_pn800050071e_bool,B: fun_pname_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( hAPP_f434788991l_bool @ ( image_47868345e_bool @ A ) @ B ) ) )
       => ? [C: pname] :
            ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( hAPP_f759274231e_bool @ collect_pname @ ( hAPP_f759274231e_bool @ ( hAPP_f649174806e_bool @ cOMBS_568398431l_bool @ ( hAPP_f1402196763l_bool @ ( cOMBB_675860798_pname @ fconj ) @ ( hAPP_f759274231e_bool @ ( hAPP_f661147897e_bool @ cOMBC_1058051404l_bool @ member_pname ) @ B ) ) ) @ ( hAPP_f759274231e_bool @ ( hAPP_f661147897e_bool @ cOMBC_1058051404l_bool @ ( hAPP_f567934427l_bool @ ( cOMBB_408569982_pname @ fequal533582459e_bool ) @ A ) ) @ ( hAPP_p61793385e_bool @ A @ C ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_pigeonhole__infinite) ).

thf(3158,plain,
    ! [A: fun_pn800050071e_bool,B: fun_pname_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( hAPP_f434788991l_bool @ ( image_47868345e_bool @ A ) @ B ) ) )
       => ? [C: pname] :
            ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( hAPP_f759274231e_bool @ collect_pname @ ( hAPP_f759274231e_bool @ ( hAPP_f649174806e_bool @ cOMBS_568398431l_bool @ ( hAPP_f1402196763l_bool @ ( cOMBB_675860798_pname @ fconj ) @ ( hAPP_f759274231e_bool @ ( hAPP_f661147897e_bool @ cOMBC_1058051404l_bool @ member_pname ) @ B ) ) ) @ ( hAPP_f759274231e_bool @ ( hAPP_f661147897e_bool @ cOMBC_1058051404l_bool @ ( hAPP_f567934427l_bool @ ( cOMBB_408569982_pname @ fequal533582459e_bool ) @ A ) ) @ ( hAPP_p61793385e_bool @ A @ C ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).

thf(395,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ? [D: hoare_1875481847_state] :
          ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ D ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ C ) ) )
          & ( hBOOL @ ( hAPP_H1173941847e_bool @ A @ D ) ) )
    <=> ( ? [D: hoare_1875481847_state] :
            ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_H1173941847e_bool @ A @ D ) ) )
        | ? [D: hoare_1875481847_state] :
            ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ D ) @ C ) )
            & ( hBOOL @ ( hAPP_H1173941847e_bool @ A @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_bex__Un) ).

thf(2235,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( ? [D: hoare_1875481847_state] :
            ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ D ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ C ) ) )
            & ( hBOOL @ ( hAPP_H1173941847e_bool @ A @ D ) ) )
       => ( ? [D: hoare_1875481847_state] :
              ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ D ) @ B ) )
              & ( hBOOL @ ( hAPP_H1173941847e_bool @ A @ D ) ) )
          | ? [D: hoare_1875481847_state] :
              ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ D ) @ C ) )
              & ( hBOOL @ ( hAPP_H1173941847e_bool @ A @ D ) ) ) ) )
      & ( ( ? [D: hoare_1875481847_state] :
              ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ D ) @ B ) )
              & ( hBOOL @ ( hAPP_H1173941847e_bool @ A @ D ) ) )
          | ? [D: hoare_1875481847_state] :
              ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ D ) @ C ) )
              & ( hBOOL @ ( hAPP_H1173941847e_bool @ A @ D ) ) ) )
       => ? [D: hoare_1875481847_state] :
            ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ D ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ C ) ) )
            & ( hBOOL @ ( hAPP_H1173941847e_bool @ A @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).

thf(367,axiom,
    ! [A: fun_fu1040518284e_bool,B: pname,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f1408815105l_bool @ ( hAPP_p1265998686l_bool @ ( hAPP_f662360091l_bool @ cOMBC_217340069e_bool @ A ) @ B ) @ C )
      = ( hAPP_pname_bool @ ( hAPP_f1148778334e_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Otriple_I) ).

thf(2144,plain,
    ! [A: fun_fu1040518284e_bool,B: pname,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f1408815105l_bool @ ( hAPP_p1265998686l_bool @ ( hAPP_f662360091l_bool @ cOMBC_217340069e_bool @ A ) @ B ) @ C )
      = ( hAPP_pname_bool @ ( hAPP_f1148778334e_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(581,axiom,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_H1173941847e_bool @ B @ A ) )
       => ( hBOOL @ ( hAPP_H1173941847e_bool @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_392_predicate1D) ).

thf(2936,plain,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_H1173941847e_bool @ B @ A ) )
       => ( hBOOL @ ( hAPP_H1173941847e_bool @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).

thf(530,axiom,
    ! [A: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) )
    <=> ( ( A = bot_bo1649642514l_bool )
        | ? [B: fun_fu1430349052l_bool,C: fun_pname_bool] :
            ( ( A
              = ( hAPP_f559147733l_bool @ ( hAPP_f1320879424l_bool @ insert1325755072e_bool @ C ) @ B ) )
            & ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_finite_Osimps) ).

thf(2729,plain,
    ! [A: fun_fu1430349052l_bool] :
      ( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) )
       => ( ( A = bot_bo1649642514l_bool )
          | ? [B: fun_fu1430349052l_bool,C: fun_pname_bool] :
              ( ( A
                = ( hAPP_f559147733l_bool @ ( hAPP_f1320879424l_bool @ insert1325755072e_bool @ C ) @ B ) )
              & ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) ) ) ) )
      & ( ( ( A = bot_bo1649642514l_bool )
          | ? [B: fun_fu1430349052l_bool,C: fun_pname_bool] :
              ( ( A
                = ( hAPP_f559147733l_bool @ ( hAPP_f1320879424l_bool @ insert1325755072e_bool @ C ) @ B ) )
              & ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) ) ) )
       => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).

thf(574,axiom,
    ! [A: state,B: state] :
      ( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ ( evalc @ skip ) @ A ) @ B ) )
     => ( B = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_538_evalc__elim__cases_I1_J) ).

thf(2904,plain,
    ! [A: state,B: state] :
      ( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ ( evalc @ skip ) @ A ) @ B ) )
     => ( B = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).

thf(244,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ B ) @ A ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_431_sup__least) ).

thf(1680,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ B ) @ A ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(736,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ C ) )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_Un__left__commute) ).

thf(3491,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ C ) )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).

thf(192,axiom,
    ! [A: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ bot_bo844097828e_bool ) @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_459_sup__bot__left) ).

thf(1483,plain,
    ! [A: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ bot_bo844097828e_bool ) @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(97,axiom,
    ! [A: fun_pn800050071e_bool,B: fun_pname_pname,C: pname] :
      ( ( hAPP_p61793385e_bool @ ( hAPP_f1336811455e_bool @ ( cOMBB_542850580_pname @ A ) @ B ) @ C )
      = ( hAPP_p61793385e_bool @ A @ ( hAPP_pname_pname @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob) ).

thf(1154,plain,
    ! [A: fun_pn800050071e_bool,B: fun_pname_pname,C: pname] :
      ( ( hAPP_p61793385e_bool @ ( hAPP_f1336811455e_bool @ ( cOMBB_542850580_pname @ A ) @ B ) @ C )
      = ( hAPP_p61793385e_bool @ A @ ( hAPP_pname_pname @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(287,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ! [C: pname] :
          ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ B ) )
         => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_subsetI) ).

thf(1833,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ! [C: pname] :
          ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ B ) )
         => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(621,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ C ) )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_416_sup__left__commute) ).

thf(3070,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ C ) )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).

thf(310,axiom,
    ! [A: hoare_1875481847_state,B: fun_pn664418900_state,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ B ) @ C ) ) )
    <=> ? [D: pname] :
          ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ C ) )
          & ( A
            = ( hAPP_p702226982_state @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_image__iff) ).

thf(1916,plain,
    ! [A: hoare_1875481847_state,B: fun_pn664418900_state,C: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ B ) @ C ) ) )
       => ? [D: pname] :
            ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ C ) )
            & ( A
              = ( hAPP_p702226982_state @ B @ D ) ) ) )
      & ( ? [D: pname] :
            ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ C ) )
            & ( A
              = ( hAPP_p702226982_state @ B @ D ) ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ B ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(668,axiom,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ C ) ) )
    <=> ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ B ) )
        | ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_Un__iff) ).

thf(3240,plain,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ C ) ) )
       => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ B ) )
          | ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ C ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ B ) )
          | ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ C ) ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).

thf(597,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) ) @ C )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_414_inf__sup__aci_I6_J) ).

thf(2981,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) ) @ C )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).

thf(466,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] : ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ B ) ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_608_Int__lower1) ).

thf(2489,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] : ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ B ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).

thf(23,axiom,
    ! [A: pname] :
      ( ( hBOOL @ ( hAPP_pname_bool @ bot_bo844097828e_bool @ A ) )
    <=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ bot_bo844097828e_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_387_bot__empty__eq) ).

thf(875,plain,
    ! [A: pname] :
      ( ( ( hBOOL @ ( hAPP_pname_bool @ bot_bo844097828e_bool @ A ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ bot_bo844097828e_bool ) ) )
      & ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ bot_bo844097828e_bool ) )
       => ( hBOOL @ ( hAPP_pname_bool @ bot_bo844097828e_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(275,axiom,
    ! [A: fun_fu1430349052l_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ bot_bo844097828e_bool ) )
       => ( ! [C: pname,D: fun_pname_bool] :
              ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ D ) )
             => ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ D ) )
               => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ D ) )
                 => ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ C ) @ D ) ) ) ) ) )
         => ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_finite__induct) ).

thf(1795,plain,
    ! [A: fun_fu1430349052l_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ bot_bo844097828e_bool ) )
       => ( ! [C: pname,D: fun_pname_bool] :
              ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ D ) )
             => ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ D ) )
               => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ D ) )
                 => ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ C ) @ D ) ) ) ) ) )
         => ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(767,axiom,
    ! [A: pname,B: fun_Ho1996104121e_bool,C: fun_pn12888928e_bool,D: fun_pn12888928e_bool,E: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ ( hAPP_f1568887991_state @ ( hAPP_f891245078_state @ cOMBS_475568287_state @ ( hAPP_f2116202538_state @ ( hAPP_f1339343196_state @ cOMBS_1674056844_state @ ( hAPP_f275933352_state @ ( cOMBB_718493681_pname @ hoare_13225861_state ) @ C ) ) @ body_1 ) ) @ D ) ) @ E ) ) ) @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ ( hAPP_f1568887991_state @ ( hAPP_f891245078_state @ cOMBS_475568287_state @ ( hAPP_f2116202538_state @ ( hAPP_f1339343196_state @ cOMBS_1674056844_state @ ( hAPP_f275933352_state @ ( cOMBB_718493681_pname @ hoare_13225861_state ) @ C ) ) @ ( hAPP_f96342628me_com @ ( cOMBB_923936821_pname @ the_com ) @ body ) ) ) @ D ) ) @ E ) ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ E ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ ( hAPP_p1637813682e_bool @ C @ A ) ) @ ( hAPP_pname_com @ body_1 @ A ) ) @ ( hAPP_p1637813682e_bool @ D @ A ) ) ) @ bot_bo1715400655e_bool ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_360_Body1) ).

thf(3604,plain,
    ! [A: pname,B: fun_Ho1996104121e_bool,C: fun_pn12888928e_bool,D: fun_pn12888928e_bool,E: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ ( hAPP_f1568887991_state @ ( hAPP_f891245078_state @ cOMBS_475568287_state @ ( hAPP_f2116202538_state @ ( hAPP_f1339343196_state @ cOMBS_1674056844_state @ ( hAPP_f275933352_state @ ( cOMBB_718493681_pname @ hoare_13225861_state ) @ C ) ) @ body_1 ) ) @ D ) ) @ E ) ) ) @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ ( hAPP_f1568887991_state @ ( hAPP_f891245078_state @ cOMBS_475568287_state @ ( hAPP_f2116202538_state @ ( hAPP_f1339343196_state @ cOMBS_1674056844_state @ ( hAPP_f275933352_state @ ( cOMBB_718493681_pname @ hoare_13225861_state ) @ C ) ) @ ( hAPP_f96342628me_com @ ( cOMBB_923936821_pname @ the_com ) @ body ) ) ) @ D ) ) @ E ) ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ E ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ ( hAPP_p1637813682e_bool @ C @ A ) ) @ ( hAPP_pname_com @ body_1 @ A ) ) @ ( hAPP_p1637813682e_bool @ D @ A ) ) ) @ bot_bo1715400655e_bool ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).

thf(320,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) ) @ C )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_Un__assoc) ).

thf(1965,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) ) @ C )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(91,axiom,
    ! [A: com] :
      ( ( hAPP_option_com_com @ the_com @ ( some_com @ A ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_the_Osimps) ).

thf(1124,plain,
    ! [A: com] :
      ( ( hAPP_option_com_com @ the_com @ ( some_com @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(765,axiom,
    ! [A: fun_Ho1996104121e_bool] : ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_subset__refl) ).

thf(3599,plain,
    ! [A: fun_Ho1996104121e_bool] : ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).

thf(53,axiom,
    ! [A: com,B: com,C: com,D: com] :
      ( ( ( semi @ A @ B )
        = ( semi @ C @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_497_com_Osimps_I3_J) ).

thf(975,plain,
    ! [A: com,B: com,C: com,D: com] :
      ( ( ( ( semi @ A @ B )
          = ( semi @ C @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( semi @ A @ B )
          = ( semi @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(707,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ B ) @ C ) )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_654_sup__inf__distrib1) ).

thf(3387,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ B ) @ C ) )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).

thf(652,axiom,
    ! [A: pname,B: pname] :
      ( ~ ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ fequal_pname @ A ) @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Com__Opname_T) ).

thf(3187,plain,
    ! [A: pname,B: pname] :
      ( ~ ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ fequal_pname @ A ) @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).

thf(562,axiom,
    ! [A: pname,B: state,C: state] :
      ( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ ( evalc @ ( hAPP_pname_com @ body_1 @ A ) ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ ( evalc @ ( hAPP_option_com_com @ the_com @ ( hAPP_p799580910on_com @ body @ A ) ) ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_537_evalc__elim__cases_I6_J) ).

thf(2859,plain,
    ! [A: pname,B: state,C: state] :
      ( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ ( evalc @ ( hAPP_pname_com @ body_1 @ A ) ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ ( evalc @ ( hAPP_option_com_com @ the_com @ ( hAPP_p799580910on_com @ body @ A ) ) ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).

thf(582,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ A ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_thin) ).

thf(2938,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ A ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).

thf(271,axiom,
    ! [A: fun_pn800050071e_bool,B: fun_fu235184776_pname,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f1148778334e_bool @ ( hAPP_f585615743e_bool @ ( cOMBB_184405641e_bool @ A ) @ B ) @ C )
      = ( hAPP_p61793385e_bool @ A @ ( hAPP_f1542224800_pname @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_230) ).

thf(1784,plain,
    ! [A: fun_pn800050071e_bool,B: fun_fu235184776_pname,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f1148778334e_bool @ ( hAPP_f585615743e_bool @ ( cOMBB_184405641e_bool @ A ) @ B ) @ C )
      = ( hAPP_p61793385e_bool @ A @ ( hAPP_f1542224800_pname @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(671,axiom,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ B ) )
     => ? [C: fun_Ho1996104121e_bool] :
          ( ( B
            = ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ C ) )
          & ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_528_mk__disjoint__insert) ).

thf(3255,plain,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ B ) )
     => ? [C: fun_Ho1996104121e_bool] :
          ( ( B
            = ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ C ) )
          & ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).

thf(769,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
     => ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_438_sup__absorb2) ).

thf(3609,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
     => ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).

thf(558,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho784854669_state,D: fun_fu385705929_state] :
      ( ( hBOOL @ ( finite1782051386_state @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ B ) )
       => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ A ) )
         => ( ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ B ) @ A )
             != bot_bo1715400655e_bool )
           => ( ( hAPP_H350317809_state @ ( hAPP_H743221337_state @ C @ ( hAPP_f890249627_state @ D @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ A ) ) ) @ ( hAPP_f890249627_state @ D @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ B ) @ A ) ) )
              = ( hAPP_H350317809_state @ ( hAPP_H743221337_state @ C @ ( hAPP_f890249627_state @ D @ B ) ) @ ( hAPP_f890249627_state @ D @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_553_folding__one_Ounion__inter) ).

thf(2849,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho784854669_state,D: fun_fu385705929_state] :
      ( ( hBOOL @ ( finite1782051386_state @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ B ) )
       => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ A ) )
         => ( ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ B ) @ A )
             != bot_bo1715400655e_bool )
           => ( ( hAPP_H350317809_state @ ( hAPP_H743221337_state @ C @ ( hAPP_f890249627_state @ D @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ A ) ) ) @ ( hAPP_f890249627_state @ D @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ B ) @ A ) ) )
              = ( hAPP_H350317809_state @ ( hAPP_H743221337_state @ C @ ( hAPP_f890249627_state @ D @ B ) ) @ ( hAPP_f890249627_state @ D @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).

thf(807,axiom,
    hBOOL @ wT_bodies,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).

thf(3758,plain,
    hBOOL @ wT_bodies,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).

thf(312,axiom,
    ! [A: fun_pname_bool] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_subset__refl) ).

thf(1929,plain,
    ! [A: fun_pname_bool] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(516,axiom,
    ! [A: fun_fu1173762305l_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ( hAPP_f2051277573l_bool @ cOMBC_195806106l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Otriple_I_235) ).

thf(2674,plain,
    ! [A: fun_fu1173762305l_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ( hAPP_f2051277573l_bool @ cOMBC_195806106l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).

thf(486,axiom,
    ! [A: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ bot_bo1715400655e_bool )
      = bot_bo1715400655e_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_658_inf__bot__right) ).

thf(2568,plain,
    ! [A: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ bot_bo1715400655e_bool )
      = bot_bo1715400655e_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).

thf(207,axiom,
    ! [A: pname,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
     => ? [C: fun_pname_bool] :
          ( ( B
            = ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ C ) )
          & ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_527_mk__disjoint__insert) ).

thf(1535,plain,
    ! [A: pname,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
     => ? [C: fun_pname_bool] :
          ( ( B
            = ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ C ) )
          & ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(599,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ B ) @ C ) ) )
    <=> ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
        & ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_634_le__inf__iff) ).

thf(2991,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ B ) @ C ) ) )
       => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
          & ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ C ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
          & ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ C ) ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ B ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).

thf(47,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( hAPP_f759274231e_bool @ collect_pname @ B ) ) )
        | ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( hAPP_f759274231e_bool @ collect_pname @ A ) ) ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( hAPP_f759274231e_bool @ collect_pname @ ( hAPP_f759274231e_bool @ ( hAPP_f649174806e_bool @ cOMBS_568398431l_bool @ ( hAPP_f1402196763l_bool @ ( cOMBB_675860798_pname @ fconj ) @ B ) ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_finite__Collect__conjI) ).

thf(958,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( hAPP_f759274231e_bool @ collect_pname @ B ) ) )
        | ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( hAPP_f759274231e_bool @ collect_pname @ A ) ) ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( hAPP_f759274231e_bool @ collect_pname @ ( hAPP_f759274231e_bool @ ( hAPP_f649174806e_bool @ cOMBS_568398431l_bool @ ( hAPP_f1402196763l_bool @ ( cOMBB_675860798_pname @ fconj ) @ B ) ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(165,axiom,
    ! [A: fun_fu1430349052l_bool,B: fun_pn800050071e_bool,C: pname] :
      ( ( hAPP_pname_bool @ ( hAPP_f42430548e_bool @ ( cOMBB_530759491_pname @ A ) @ B ) @ C )
      = ( hAPP_f1664156314l_bool @ A @ ( hAPP_p61793385e_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__O) ).

thf(1403,plain,
    ! [A: fun_fu1430349052l_bool,B: fun_pn800050071e_bool,C: pname] :
      ( ( hAPP_pname_bool @ ( hAPP_f42430548e_bool @ ( cOMBB_530759491_pname @ A ) @ B ) @ C )
      = ( hAPP_f1664156314l_bool @ A @ ( hAPP_p61793385e_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(126,axiom,
    ! [A: fun_fu31783638l_bool,B: fun_fu1430349052l_bool,C: fun_pname_bool] :
      ( ( hAPP_f1664156314l_bool @ ( hAPP_f559147733l_bool @ ( hAPP_f624840228l_bool @ cOMBS_350070575l_bool @ A ) @ B ) @ C )
      = ( hAPP_bool_bool @ ( hAPP_f1476298914l_bool @ A @ C ) @ ( hAPP_f1664156314l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__O) ).

thf(1256,plain,
    ! [A: fun_fu31783638l_bool,B: fun_fu1430349052l_bool,C: fun_pname_bool] :
      ( ( hAPP_f1664156314l_bool @ ( hAPP_f559147733l_bool @ ( hAPP_f624840228l_bool @ cOMBS_350070575l_bool @ A ) @ B ) @ C )
      = ( hAPP_bool_bool @ ( hAPP_f1476298914l_bool @ A @ C ) @ ( hAPP_f1664156314l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(117,axiom,
    ! [A: fun_state_bool,B: com] :
      ( ( while @ A @ B )
     != skip ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_503_com_Osimps_I17_J) ).

thf(1226,plain,
    ! [A: fun_state_bool,B: com] :
      ( ( while @ A @ B )
     != skip ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(373,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
     => ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ B )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_640_inf__absorb1) ).

thf(2161,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
     => ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ B )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(95,axiom,
    ! [A: com,B: com] :
      ( ( ( some_com @ A )
        = ( some_com @ B ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_358_option_Oinject) ).

thf(1139,plain,
    ! [A: com,B: com] :
      ( ( ( ( some_com @ A )
          = ( some_com @ B ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( ( some_com @ A )
          = ( some_com @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(379,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_fu689207471l_bool,C: fun_fu947547457e_bool,D: fun_fu1163781179e_bool] :
      ( ( hBOOL @ ( finite792754358e_bool @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ B ) )
       => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ ( hAPP_f640685261l_bool @ member1062536460e_bool @ A ) @ B ) )
         => ( ( ( ( hAPP_f900945761l_bool @ ( hAPP_f19215249l_bool @ minus_1959767774l_bool @ B ) @ ( hAPP_f900945761l_bool @ ( hAPP_f872497439l_bool @ insert504309043e_bool @ A ) @ bot_bo973479705l_bool ) )
                = bot_bo973479705l_bool )
             => ( ( hAPP_f962122119e_bool @ D @ B )
                = A ) )
            & ( ( ( hAPP_f900945761l_bool @ ( hAPP_f19215249l_bool @ minus_1959767774l_bool @ B ) @ ( hAPP_f900945761l_bool @ ( hAPP_f872497439l_bool @ insert504309043e_bool @ A ) @ bot_bo973479705l_bool ) )
               != bot_bo973479705l_bool )
             => ( ( hAPP_f962122119e_bool @ D @ B )
                = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ C @ A ) @ ( hAPP_f962122119e_bool @ D @ ( hAPP_f900945761l_bool @ ( hAPP_f19215249l_bool @ minus_1959767774l_bool @ B ) @ ( hAPP_f900945761l_bool @ ( hAPP_f872497439l_bool @ insert504309043e_bool @ A ) @ bot_bo973479705l_bool ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_679_folding__one_Oremove) ).

thf(2193,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_fu689207471l_bool,C: fun_fu947547457e_bool,D: fun_fu1163781179e_bool] :
      ( ( hBOOL @ ( finite792754358e_bool @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ B ) )
       => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ ( hAPP_f640685261l_bool @ member1062536460e_bool @ A ) @ B ) )
         => ( ( ( ( hAPP_f900945761l_bool @ ( hAPP_f19215249l_bool @ minus_1959767774l_bool @ B ) @ ( hAPP_f900945761l_bool @ ( hAPP_f872497439l_bool @ insert504309043e_bool @ A ) @ bot_bo973479705l_bool ) )
                = bot_bo973479705l_bool )
             => ( ( hAPP_f962122119e_bool @ D @ B )
                = A ) )
            & ( ( ( hAPP_f900945761l_bool @ ( hAPP_f19215249l_bool @ minus_1959767774l_bool @ B ) @ ( hAPP_f900945761l_bool @ ( hAPP_f872497439l_bool @ insert504309043e_bool @ A ) @ bot_bo973479705l_bool ) )
               != bot_bo973479705l_bool )
             => ( ( hAPP_f962122119e_bool @ D @ B )
                = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ C @ A ) @ ( hAPP_f962122119e_bool @ D @ ( hAPP_f900945761l_bool @ ( hAPP_f19215249l_bool @ minus_1959767774l_bool @ B ) @ ( hAPP_f900945761l_bool @ ( hAPP_f872497439l_bool @ insert504309043e_bool @ A ) @ bot_bo973479705l_bool ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(389,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] : ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_454_inf__sup__ord_I3_J) ).

thf(2220,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] : ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(616,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) ) @ C )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ C ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ B ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_594_Int__Un__distrib2) ).

thf(3051,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) ) @ C )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ C ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).

thf(784,axiom,
    ! [A: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ bot_bo1715400655e_bool ) @ A )
      = bot_bo1715400655e_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_660_inf__bot__left) ).

thf(3663,plain,
    ! [A: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ bot_bo1715400655e_bool ) @ A )
      = bot_bo1715400655e_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).

thf(763,axiom,
    hBOOL @ hoare_1239590103gleton,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

thf(3594,plain,
    hBOOL @ hoare_1239590103gleton,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).

thf(145,axiom,
    ! [A: fun_fu1430349052l_bool,B: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ B ) )
       => ( ( hAPP_f559147733l_bool @ collec1974731493e_bool @ ( hAPP_f559147733l_bool @ ( hAPP_f624840228l_bool @ cOMBS_350070575l_bool @ ( hAPP_f143162813l_bool @ ( cOMBB_2095475776e_bool @ fconj ) @ ( hAPP_f434788991l_bool @ ( hAPP_f1297925993l_bool @ cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ B ) ) ) @ A ) )
          = ( hAPP_f559147733l_bool @ ( hAPP_f1320879424l_bool @ insert1325755072e_bool @ B ) @ bot_bo1649642514l_bool ) ) )
      & ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ B ) )
       => ( ( hAPP_f559147733l_bool @ collec1974731493e_bool @ ( hAPP_f559147733l_bool @ ( hAPP_f624840228l_bool @ cOMBS_350070575l_bool @ ( hAPP_f143162813l_bool @ ( cOMBB_2095475776e_bool @ fconj ) @ ( hAPP_f434788991l_bool @ ( hAPP_f1297925993l_bool @ cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ B ) ) ) @ A ) )
          = bot_bo1649642514l_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_Collect__conv__if) ).

thf(1332,plain,
    ! [A: fun_fu1430349052l_bool,B: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ B ) )
       => ( ( hAPP_f559147733l_bool @ collec1974731493e_bool @ ( hAPP_f559147733l_bool @ ( hAPP_f624840228l_bool @ cOMBS_350070575l_bool @ ( hAPP_f143162813l_bool @ ( cOMBB_2095475776e_bool @ fconj ) @ ( hAPP_f434788991l_bool @ ( hAPP_f1297925993l_bool @ cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ B ) ) ) @ A ) )
          = ( hAPP_f559147733l_bool @ ( hAPP_f1320879424l_bool @ insert1325755072e_bool @ B ) @ bot_bo1649642514l_bool ) ) )
      & ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ B ) )
       => ( ( hAPP_f559147733l_bool @ collec1974731493e_bool @ ( hAPP_f559147733l_bool @ ( hAPP_f624840228l_bool @ cOMBS_350070575l_bool @ ( hAPP_f143162813l_bool @ ( cOMBB_2095475776e_bool @ fconj ) @ ( hAPP_f434788991l_bool @ ( hAPP_f1297925993l_bool @ cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ B ) ) ) @ A ) )
          = bot_bo1649642514l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(80,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
     => ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ A ) @ B )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_437_sup__absorb2) ).

thf(1092,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
     => ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ A ) @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(265,axiom,
    ! [A: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ bot_bo844097828e_bool ) )
     => ( A = bot_bo844097828e_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_361_le__bot) ).

thf(1765,plain,
    ! [A: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ bot_bo844097828e_bool ) )
     => ( A = bot_bo844097828e_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(686,axiom,
    ! [A: fun_pname_pname,B: fun_pname_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( hAPP_f759274231e_bool @ ( image_pname_pname @ A ) @ B ) ) )
       => ? [C: pname] :
            ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( hAPP_f759274231e_bool @ collect_pname @ ( hAPP_f759274231e_bool @ ( hAPP_f649174806e_bool @ cOMBS_568398431l_bool @ ( hAPP_f1402196763l_bool @ ( cOMBB_675860798_pname @ fconj ) @ ( hAPP_f759274231e_bool @ ( hAPP_f661147897e_bool @ cOMBC_1058051404l_bool @ member_pname ) @ B ) ) ) @ ( hAPP_p61793385e_bool @ ( hAPP_f22061361e_bool @ cOMBC_1149511130e_bool @ ( hAPP_f1336811455e_bool @ ( cOMBB_542850580_pname @ fequal_pname ) @ A ) ) @ ( hAPP_pname_pname @ A @ C ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_pigeonhole__infinite) ).

thf(3304,plain,
    ! [A: fun_pname_pname,B: fun_pname_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( hAPP_f759274231e_bool @ ( image_pname_pname @ A ) @ B ) ) )
       => ? [C: pname] :
            ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( hAPP_f759274231e_bool @ collect_pname @ ( hAPP_f759274231e_bool @ ( hAPP_f649174806e_bool @ cOMBS_568398431l_bool @ ( hAPP_f1402196763l_bool @ ( cOMBB_675860798_pname @ fconj ) @ ( hAPP_f759274231e_bool @ ( hAPP_f661147897e_bool @ cOMBC_1058051404l_bool @ member_pname ) @ B ) ) ) @ ( hAPP_p61793385e_bool @ ( hAPP_f22061361e_bool @ cOMBC_1149511130e_bool @ ( hAPP_f1336811455e_bool @ ( cOMBB_542850580_pname @ fequal_pname ) @ A ) ) @ ( hAPP_pname_pname @ A @ C ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).

thf(759,axiom,
    ! [A: fun_Ho1896286681l_bool,B: fun_Ho1996104121e_bool,C: hoare_1875481847_state] :
      ( ( hAPP_H1173941847e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1300953505e_bool @ cOMBS_896408300l_bool @ A ) @ B ) @ C )
      = ( hAPP_bool_bool @ ( hAPP_H377399461l_bool @ A @ C ) @ ( hAPP_H1173941847e_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc__Com__) ).

thf(3568,plain,
    ! [A: fun_Ho1896286681l_bool,B: fun_Ho1996104121e_bool,C: hoare_1875481847_state] :
      ( ( hAPP_H1173941847e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1300953505e_bool @ cOMBS_896408300l_bool @ A ) @ B ) @ C )
      = ( hAPP_bool_bool @ ( hAPP_H377399461l_bool @ A @ C ) @ ( hAPP_H1173941847e_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).

thf(488,axiom,
    hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ bot_bo1649642514l_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_finite_OemptyI) ).

thf(2573,plain,
    hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ bot_bo1649642514l_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).

thf(812,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ B ) @ A ) ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_636_le__infI1) ).

thf(3773,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ B ) @ A ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).

thf(41,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ B ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_finite__UnI) ).

thf(936,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ B ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(339,axiom,
    ! [A: pname,B: fun_pname_bool,C: pname] :
      ( ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ B ) @ C ) )
    <=> ( ( A = C )
        | ( hBOOL @ ( hAPP_pname_bool @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_insert__code) ).

thf(2029,plain,
    ! [A: pname,B: fun_pname_bool,C: pname] :
      ( ( ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ B ) @ C ) )
       => ( ( A = C )
          | ( hBOOL @ ( hAPP_pname_bool @ B @ C ) ) ) )
      & ( ( ( A = C )
          | ( hBOOL @ ( hAPP_pname_bool @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(418,axiom,
    ! [A: fun_Ho1996104121e_bool] : ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ bot_bo1715400655e_bool ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_empty__subsetI) ).

thf(2326,plain,
    ! [A: fun_Ho1996104121e_bool] : ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ bot_bo1715400655e_bool ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

thf(131,axiom,
    ! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
      ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_UnCI) ).

thf(1271,plain,
    ! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
      ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(413,axiom,
    ! [A: fun_fu689207471l_bool,B: fun_fu689207471l_bool] :
      ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ B ) )
     => ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ ( hAPP_f900945761l_bool @ ( hAPP_f19215249l_bool @ minus_1959767774l_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_689_finite__Diff) ).

thf(2308,plain,
    ! [A: fun_fu689207471l_bool,B: fun_fu689207471l_bool] :
      ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ B ) )
     => ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ ( hAPP_f900945761l_bool @ ( hAPP_f19215249l_bool @ minus_1959767774l_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(157,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ A ) @ B ) ) @ C )
        = ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ B ) @ C ) ) )
    <=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_666_Un__Int__assoc__eq) ).

thf(1371,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ A ) @ B ) ) @ C )
          = ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ B ) @ C ) ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ A ) ) )
      & ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ A ) )
       => ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ A ) @ B ) ) @ C )
          = ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ B ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(235,axiom,
    ! [A: fun_state_bool,B: com,C: com,D: com] :
      ( ( while @ A @ B )
     != ( semi @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_496_com_Osimps_I47_J) ).

thf(1635,plain,
    ! [A: fun_state_bool,B: com,C: com,D: com] :
      ( ( while @ A @ B )
     != ( semi @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(580,axiom,
    hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ fa ) @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ ( hAPP_f2031411714_state @ ( cOMBB_1364904209_pname @ hoare_Mirabelle_MGT ) @ ( hAPP_f96342628me_com @ ( cOMBB_923936821_pname @ the_com ) @ body ) ) ) @ ( dom_pname_com @ body ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_4) ).

thf(2935,plain,
    hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ fa ) @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ ( hAPP_f2031411714_state @ ( cOMBB_1364904209_pname @ hoare_Mirabelle_MGT ) @ ( hAPP_f96342628me_com @ ( cOMBB_923936821_pname @ the_com ) @ body ) ) ) @ ( dom_pname_com @ body ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).

thf(536,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] : ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ B ) ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_626_inf__le1) ).

thf(2759,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] : ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ B ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).

thf(534,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ A ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ C ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_646_inf__greatest) ).

thf(2753,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ A ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ C ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).

thf(454,axiom,
    ! [A: fun_state_bool,B: com] :
      ( ( hBOOL @ ( hAPP_com_bool @ wt @ ( while @ A @ B ) ) )
     => ( hBOOL @ ( hAPP_com_bool @ wt @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_493_WTs__elim__cases_I6_J) ).

thf(2457,plain,
    ! [A: fun_state_bool,B: com] :
      ( ( hBOOL @ ( hAPP_com_bool @ wt @ ( while @ A @ B ) ) )
     => ( hBOOL @ ( hAPP_com_bool @ wt @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).

thf(36,axiom,
    ! [A: fun_fu410713561e_bool,B: pname,C: fun_pname_bool] :
      ( ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ ( hAPP_f2082757169l_bool @ cOMBC_1004116266e_bool @ A ) @ B ) @ C )
      = ( hAPP_pname_bool @ ( hAPP_f759274231e_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__O) ).

thf(919,plain,
    ! [A: fun_fu410713561e_bool,B: pname,C: fun_pname_bool] :
      ( ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ ( hAPP_f2082757169l_bool @ cOMBC_1004116266e_bool @ A ) @ B ) @ C )
      = ( hAPP_pname_bool @ ( hAPP_f759274231e_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(185,axiom,
    ! [A: fun_pn250273176l_bool,B: fun_pname_bool,C: pname] :
      ( ( hAPP_pname_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f649174806e_bool @ cOMBS_568398431l_bool @ A ) @ B ) @ C )
      = ( hAPP_bool_bool @ ( hAPP_p393069232l_bool @ A @ C ) @ ( hAPP_pname_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool_U) ).

thf(1464,plain,
    ! [A: fun_pn250273176l_bool,B: fun_pname_bool,C: pname] :
      ( ( hAPP_pname_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f649174806e_bool @ cOMBS_568398431l_bool @ A ) @ B ) @ C )
      = ( hAPP_bool_bool @ ( hAPP_p393069232l_bool @ A @ C ) @ ( hAPP_pname_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(460,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ B ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ A ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_finite__UnI) ).

thf(2474,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ B ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ A ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).

thf(45,axiom,
    ! [A: com,B: com,C: fun_state_bool,D: com] :
      ( ( semi @ A @ B )
     != ( while @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_495_com_Osimps_I46_J) ).

thf(947,plain,
    ! [A: com,B: com,C: fun_state_bool,D: com] :
      ( ( semi @ A @ B )
     != ( while @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(424,axiom,
    ! [A: hoare_1875481847_state,B: fun_Ho784854669_state,C: fun_fu385705929_state] :
      ( ( hBOOL @ ( finite1782051386_state @ B @ C ) )
     => ( ( hAPP_f890249627_state @ C @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ bot_bo1715400655e_bool ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_514_folding__one_Osingleton) ).

thf(2346,plain,
    ! [A: hoare_1875481847_state,B: fun_Ho784854669_state,C: fun_fu385705929_state] :
      ( ( hBOOL @ ( finite1782051386_state @ B @ C ) )
     => ( ( hAPP_f890249627_state @ C @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ bot_bo1715400655e_bool ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).

thf(351,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ B ) @ C ) ) )
     => ~ ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
         => ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_650_le__infE) ).

thf(2079,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ B ) @ C ) ) )
     => ~ ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
         => ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(8,axiom,
    ! [A: fun_fu1047394976e_bool,B: fun_st2116860965l_bool,C: state] :
      ( ( hAPP_s1226857760e_bool @ ( hAPP_f1138284024e_bool @ ( cOMBB_20296667_state @ A ) @ B ) @ C )
      = ( hAPP_f644196280e_bool @ A @ ( hAPP_s2001034685l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__HOL__Obool_Mtc__H_234) ).

thf(831,plain,
    ! [A: fun_fu1047394976e_bool,B: fun_st2116860965l_bool,C: state] :
      ( ( hAPP_s1226857760e_bool @ ( hAPP_f1138284024e_bool @ ( cOMBB_20296667_state @ A ) @ B ) @ C )
      = ( hAPP_f644196280e_bool @ A @ ( hAPP_s2001034685l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(776,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool,D: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ C ) @ D ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ C ) @ A ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ D ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_648_inf__mono) ).

thf(3631,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool,D: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ C ) @ D ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ C ) @ A ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ D ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).

thf(754,axiom,
    ! [A: pname,B: fun_Ho1653816318_pname,C: hoare_1875481847_state,D: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ C ) @ D ) )
     => ( ( A
          = ( hAPP_H139064010_pname @ B @ C ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( hAPP_f1148778334e_bool @ ( image_720060442_pname @ B ) @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_rev__image__eqI) ).

thf(3551,plain,
    ! [A: pname,B: fun_Ho1653816318_pname,C: hoare_1875481847_state,D: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ C ) @ D ) )
     => ( ( A
          = ( hAPP_H139064010_pname @ B @ C ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( hAPP_f1148778334e_bool @ ( image_720060442_pname @ B ) @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).

thf(278,axiom,
    ! [A: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool @ collect_pname @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_Collect__def) ).

thf(1806,plain,
    ! [A: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool @ collect_pname @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(203,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ B ) @ A ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_Un__least) ).

thf(1524,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ B ) @ A ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(675,axiom,
    ! [A: hoare_1875481847_state,B: fun_pname_bool] :
      ( ( ( B = bot_bo844097828e_bool )
       => ( ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ ( cOMBK_1032401873_pname @ A ) ) @ B )
          = bot_bo1715400655e_bool ) )
      & ( ( B != bot_bo844097828e_bool )
       => ( ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ ( cOMBK_1032401873_pname @ A ) ) @ B )
          = ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ bot_bo1715400655e_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_image__constant__conv) ).

thf(3270,plain,
    ! [A: hoare_1875481847_state,B: fun_pname_bool] :
      ( ( ( B = bot_bo844097828e_bool )
       => ( ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ ( cOMBK_1032401873_pname @ A ) ) @ B )
          = bot_bo1715400655e_bool ) )
      & ( ( B != bot_bo844097828e_bool )
       => ( ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ ( cOMBK_1032401873_pname @ A ) ) @ B )
          = ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ bot_bo1715400655e_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).

thf(799,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_440_le__supI2) ).

thf(3732,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).

thf(589,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ B )
      | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fdisj_2_1_U) ).

thf(2955,plain,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ B )
      | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).

thf(254,axiom,
    ! [A: fun_fu404278912_state,B: fun_pn12888928e_bool,C: pname] :
      ( ( hAPP_p2012996835_state @ ( hAPP_f275933352_state @ ( cOMBB_718493681_pname @ A ) @ B ) @ C )
      = ( hAPP_f1930074316_state @ A @ ( hAPP_p1637813682e_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__Com__Ostate_Mtc___243) ).

thf(1722,plain,
    ! [A: fun_fu404278912_state,B: fun_pn12888928e_bool,C: pname] :
      ( ( hAPP_p2012996835_state @ ( hAPP_f275933352_state @ ( cOMBB_718493681_pname @ A ) @ B ) @ C )
      = ( hAPP_f1930074316_state @ A @ ( hAPP_p1637813682e_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(555,axiom,
    ! [A: fun_Ho1695028467e_bool,B: fun_Ho1996104121e_bool,C: fun_fu689207471l_bool] :
      ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ ( hAPP_f1970936639l_bool @ ord_le724727525l_bool @ C ) @ ( hAPP_f1873026899l_bool @ ( image_896278159e_bool @ A ) @ B ) ) )
       => ? [D: fun_Ho1996104121e_bool] :
            ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ D ) )
            & ( C
              = ( hAPP_f1873026899l_bool @ ( image_896278159e_bool @ A ) @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_finite__subset__image) ).

thf(2839,plain,
    ! [A: fun_Ho1695028467e_bool,B: fun_Ho1996104121e_bool,C: fun_fu689207471l_bool] :
      ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ ( hAPP_f1970936639l_bool @ ord_le724727525l_bool @ C ) @ ( hAPP_f1873026899l_bool @ ( image_896278159e_bool @ A ) @ B ) ) )
       => ? [D: fun_Ho1996104121e_bool] :
            ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ D ) )
            & ( C
              = ( hAPP_f1873026899l_bool @ ( image_896278159e_bool @ A ) @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).

thf(584,axiom,
    ! [A: state,B: state] :
      ( ( A != B )
      | ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ fequal_state @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Com__Ostate_T) ).

thf(2943,plain,
    ! [A: state,B: state] :
      ( ( A != B )
      | ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ fequal_state @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).

thf(24,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_rev__finite__subset) ).

thf(880,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(565,axiom,
    ! [A: fun_Ho1996104121e_bool] :
      ( ! [B: hoare_1875481847_state] :
          ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ A ) )
     => ( A = bot_bo1715400655e_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_532_equals0I) ).

thf(2871,plain,
    ! [A: fun_Ho1996104121e_bool] :
      ( ! [B: hoare_1875481847_state] :
          ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ A ) )
     => ( A = bot_bo1715400655e_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).

thf(527,axiom,
    ! [A: bool] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ fNot @ A ) )
      | ~ ( hBOOL @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fNot_1_1_U) ).

thf(2721,plain,
    ! [A: bool] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ fNot @ A ) )
      | ~ ( hBOOL @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).

thf(362,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( A != B )
      | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T) ).

thf(2119,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( A != B )
      | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(369,axiom,
    ! [A: state] : ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ ( evalc @ skip ) @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_542_evalc_OSkip) ).

thf(2151,plain,
    ! [A: state] : ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ ( evalc @ skip ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(508,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ ( hAPP_f2031411714_state @ ( cOMBB_1364904209_pname @ hoare_Mirabelle_MGT ) @ body_1 ) ) @ B ) ) ) @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ ( hAPP_f2031411714_state @ ( cOMBB_1364904209_pname @ hoare_Mirabelle_MGT ) @ ( hAPP_f96342628me_com @ ( cOMBB_923936821_pname @ the_com ) @ body ) ) ) @ B ) ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ A ) @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ ( hAPP_f2031411714_state @ ( cOMBB_1364904209_pname @ hoare_Mirabelle_MGT ) @ body_1 ) ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_MGT__Body) ).

thf(2642,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ ( hAPP_f2031411714_state @ ( cOMBB_1364904209_pname @ hoare_Mirabelle_MGT ) @ body_1 ) ) @ B ) ) ) @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ ( hAPP_f2031411714_state @ ( cOMBB_1364904209_pname @ hoare_Mirabelle_MGT ) @ ( hAPP_f96342628me_com @ ( cOMBB_923936821_pname @ the_com ) @ body ) ) ) @ B ) ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ A ) @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ ( hAPP_f2031411714_state @ ( cOMBB_1364904209_pname @ hoare_Mirabelle_MGT ) @ body_1 ) ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).

thf(645,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_424_sup_Ocommute) ).

thf(3155,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).

thf(631,axiom,
    ! [A: hoare_1875481847_state,B: hoare_1875481847_state,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_insertI2) ).

thf(3106,plain,
    ! [A: hoare_1875481847_state,B: hoare_1875481847_state,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).

thf(209,axiom,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ B ) @ C ) ) )
    <=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
        & ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_576_Int__iff) ).

thf(1542,plain,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ B ) @ C ) ) )
       => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
          & ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
          & ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ B ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(561,axiom,
    ! [A: fun_Ho14659478e_bool,B: fun_Ho1996104121e_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ B ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( hAPP_f1628972376l_bool @ ( image_412748388e_bool @ A ) @ B ) ) )
       => ? [C: hoare_1875481847_state] :
            ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ ( hAPP_f121055253e_bool @ collec1735317154_state @ ( hAPP_f121055253e_bool @ ( hAPP_f1300953505e_bool @ cOMBS_896408300l_bool @ ( hAPP_f932622461l_bool @ ( cOMBB_242064253_state @ fconj ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1795624711e_bool @ cOMBC_1099403170l_bool @ member618553700_state ) @ B ) ) ) @ ( hAPP_f1291720380e_bool @ ( hAPP_f406856233e_bool @ cOMBC_2049654457l_bool @ ( hAPP_f745653815l_bool @ ( cOMBB_582022205_state @ fequal533582459e_bool ) @ A ) ) @ ( hAPP_H785152948e_bool @ A @ C ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_pigeonhole__infinite) ).

thf(2856,plain,
    ! [A: fun_Ho14659478e_bool,B: fun_Ho1996104121e_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ B ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( hAPP_f1628972376l_bool @ ( image_412748388e_bool @ A ) @ B ) ) )
       => ? [C: hoare_1875481847_state] :
            ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ ( hAPP_f121055253e_bool @ collec1735317154_state @ ( hAPP_f121055253e_bool @ ( hAPP_f1300953505e_bool @ cOMBS_896408300l_bool @ ( hAPP_f932622461l_bool @ ( cOMBB_242064253_state @ fconj ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1795624711e_bool @ cOMBC_1099403170l_bool @ member618553700_state ) @ B ) ) ) @ ( hAPP_f1291720380e_bool @ ( hAPP_f406856233e_bool @ cOMBC_2049654457l_bool @ ( hAPP_f745653815l_bool @ ( cOMBB_582022205_state @ fequal533582459e_bool ) @ A ) ) @ ( hAPP_H785152948e_bool @ A @ C ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).

thf(640,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_651_inf__sup__absorb) ).

thf(3138,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).

thf(435,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) ) )
    <=> ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ A ) )
        & ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_finite__Un) ).

thf(2378,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) ) )
       => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ A ) )
          & ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ B ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ A ) )
          & ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ B ) ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).

thf(650,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ A ) @ B ) )
      | ~ ( hBOOL @ A )
      | ( hBOOL @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fimplies_3_1_U) ).

thf(3182,plain,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ A ) @ B ) )
      | ~ ( hBOOL @ A )
      | ( hBOOL @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).

thf(571,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ! [C: hoare_1875481847_state] : ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_H1173941847e_bool @ A @ C ) ) @ ( hAPP_H1173941847e_bool @ B @ C ) ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_401_le__funI) ).

thf(2896,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ! [C: hoare_1875481847_state] : ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_H1173941847e_bool @ A @ C ) ) @ ( hAPP_H1173941847e_bool @ B @ C ) ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).

thf(27,axiom,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ minus_1015773161e_bool @ B ) @ C ) ) )
     => ~ ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
         => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_686_DiffE) ).

thf(890,plain,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ minus_1015773161e_bool @ B ) @ C ) ) )
     => ~ ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
         => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(664,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ B ) ) @ C )
        = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ C ) ) )
    <=> ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ C ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_667_Un__Int__assoc__eq) ).

thf(3219,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ B ) ) @ C )
          = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ C ) ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ C ) @ A ) ) )
      & ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ C ) @ A ) )
       => ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ B ) ) @ C )
          = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).

thf(506,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( A = B )
     => ~ ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
         => ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_equalityE) ).

thf(2632,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( A = B )
     => ~ ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
         => ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).

thf(146,axiom,
    ! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ C ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ A ) )
        = ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_611_Int__insert__right__if1) ).

thf(1339,plain,
    ! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ C ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ A ) )
        = ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(1,conjecture,
    hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ ( hAPP_f2031411714_state @ ( cOMBB_1364904209_pname @ hoare_Mirabelle_MGT ) @ body_1 ) ) @ ( dom_pname_com @ body ) ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_c406083500_state @ hoare_Mirabelle_MGT @ y ) ) @ bot_bo1715400655e_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_7) ).

thf(2,negated_conjecture,
    ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ ( hAPP_f2031411714_state @ ( cOMBB_1364904209_pname @ hoare_Mirabelle_MGT ) @ body_1 ) ) @ ( dom_pname_com @ body ) ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_c406083500_state @ hoare_Mirabelle_MGT @ y ) ) @ bot_bo1715400655e_bool ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(816,plain,
    ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ ( hAPP_f2031411714_state @ ( cOMBB_1364904209_pname @ hoare_Mirabelle_MGT ) @ body_1 ) ) @ ( dom_pname_com @ body ) ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_c406083500_state @ hoare_Mirabelle_MGT @ y ) ) @ bot_bo1715400655e_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(402,axiom,
    ! [A: fun_st1506752259e_bool,B: fun_Ho1996104121e_bool,C: fun_st1506752259e_bool,D: com,E: fun_st1506752259e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ C ) @ D ) @ E ) ) @ bot_bo1715400655e_bool ) ) )
     => ( ! [F: state,G: state] :
            ( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ A @ F ) @ G ) )
           => ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ C @ F ) @ G ) ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ A ) @ D ) @ E ) ) @ bot_bo1715400655e_bool ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_381_conseq1) ).

thf(2267,plain,
    ! [A: fun_st1506752259e_bool,B: fun_Ho1996104121e_bool,C: fun_st1506752259e_bool,D: com,E: fun_st1506752259e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ C ) @ D ) @ E ) ) @ bot_bo1715400655e_bool ) ) )
     => ( ! [F: state,G: state] :
            ( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ A @ F ) @ G ) )
           => ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ C @ F ) @ G ) ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ A ) @ D ) @ E ) ) @ bot_bo1715400655e_bool ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(450,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
     => ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_436_sup__absorb1) ).

thf(2446,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
     => ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).

thf(144,axiom,
    ! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
       => ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ C ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ A ) )
          = ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ C ) @ A ) ) ) )
      & ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
       => ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ C ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ A ) )
          = ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_621_Int__insert__right) ).

thf(1325,plain,
    ! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
       => ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ C ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ A ) )
          = ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ C ) @ A ) ) ) )
      & ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
       => ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ C ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ A ) )
          = ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(684,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1455141843_state,C: fun_Ho784854669_state,D: fun_fu385705929_state] :
      ( ( hBOOL @ ( finite1514162941_state @ C @ D ) )
     => ( ! [E: hoare_1875481847_state,F: hoare_1875481847_state] :
            ( ( hAPP_H350317809_state @ B @ ( hAPP_H350317809_state @ ( hAPP_H743221337_state @ C @ E ) @ F ) )
            = ( hAPP_H350317809_state @ ( hAPP_H743221337_state @ C @ ( hAPP_H350317809_state @ B @ E ) ) @ ( hAPP_H350317809_state @ B @ F ) ) )
       => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ A ) )
         => ( ( A != bot_bo1715400655e_bool )
           => ( ( hAPP_H350317809_state @ B @ ( hAPP_f890249627_state @ D @ A ) )
              = ( hAPP_f890249627_state @ D @ ( hAPP_f121055253e_bool @ ( image_436941729_state @ B ) @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_488_folding__one__idem_Ohom__commute) ).

thf(3298,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1455141843_state,C: fun_Ho784854669_state,D: fun_fu385705929_state] :
      ( ( hBOOL @ ( finite1514162941_state @ C @ D ) )
     => ( ! [E: hoare_1875481847_state,F: hoare_1875481847_state] :
            ( ( hAPP_H350317809_state @ B @ ( hAPP_H350317809_state @ ( hAPP_H743221337_state @ C @ E ) @ F ) )
            = ( hAPP_H350317809_state @ ( hAPP_H743221337_state @ C @ ( hAPP_H350317809_state @ B @ E ) ) @ ( hAPP_H350317809_state @ B @ F ) ) )
       => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ A ) )
         => ( ( A != bot_bo1715400655e_bool )
           => ( ( hAPP_H350317809_state @ B @ ( hAPP_f890249627_state @ D @ A ) )
              = ( hAPP_f890249627_state @ D @ ( hAPP_f121055253e_bool @ ( image_436941729_state @ B ) @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).

thf(397,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] : ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ B ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ C ) ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_664_distrib__inf__le) ).

thf(2252,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] : ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ B ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ C ) ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(102,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_fu689207471l_bool] :
      ( ( hAPP_f900945761l_bool @ ( hAPP_f872497439l_bool @ insert504309043e_bool @ A ) @ B )
      = ( hAPP_f900945761l_bool @ collec771609166e_bool @ ( hAPP_f900945761l_bool @ ( hAPP_f2051813877l_bool @ cOMBS_1451994324l_bool @ ( hAPP_f440042033l_bool @ ( cOMBB_532710323e_bool @ fdisj ) @ ( hAPP_f1873026899l_bool @ ( hAPP_f2051277573l_bool @ cOMBC_195806106l_bool @ fequal259518520e_bool ) @ A ) ) ) @ ( hAPP_f900945761l_bool @ ( hAPP_f1846363427l_bool @ cOMBC_1909905718l_bool @ member1062536460e_bool ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_insert__compr__raw) ).

thf(1177,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_fu689207471l_bool] :
      ( ( hAPP_f900945761l_bool @ ( hAPP_f872497439l_bool @ insert504309043e_bool @ A ) @ B )
      = ( hAPP_f900945761l_bool @ collec771609166e_bool @ ( hAPP_f900945761l_bool @ ( hAPP_f2051813877l_bool @ cOMBS_1451994324l_bool @ ( hAPP_f440042033l_bool @ ( cOMBB_532710323e_bool @ fdisj ) @ ( hAPP_f1873026899l_bool @ ( hAPP_f2051277573l_bool @ cOMBC_195806106l_bool @ fequal259518520e_bool ) @ A ) ) ) @ ( hAPP_f900945761l_bool @ ( hAPP_f1846363427l_bool @ cOMBC_1909905718l_bool @ member1062536460e_bool ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(595,axiom,
    ! [A: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ bot_bo1715400655e_bool )
      = bot_bo1715400655e_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_569_Int__empty__right) ).

thf(2974,plain,
    ! [A: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ bot_bo1715400655e_bool )
      = bot_bo1715400655e_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).

thf(70,axiom,
    ! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ C ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ A ) )
        = ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ C ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_615_Int__insert__right__if0) ).

thf(1061,plain,
    ! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ C ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ A ) )
        = ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ C ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(247,axiom,
    ! [A: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
    <=> ( ( A = bot_bo844097828e_bool )
        | ? [B: fun_pname_bool,C: pname] :
            ( ( A
              = ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ C ) @ B ) )
            & ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_finite_Osimps) ).

thf(1688,plain,
    ! [A: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
       => ( ( A = bot_bo844097828e_bool )
          | ? [B: fun_pname_bool,C: pname] :
              ( ( A
                = ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ C ) @ B ) )
              & ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) ) ) ) )
      & ( ( ( A = bot_bo844097828e_bool )
          | ? [B: fun_pname_bool,C: pname] :
              ( ( A
                = ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ C ) @ B ) )
              & ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) ) ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(415,axiom,
    ! [A: fun_pname_bool,B: fun_pname_option_com,C: fun_pname_option_com] :
      ( ( dom_pname_com @ ( hAPP_f2123220539on_com @ ( hAPP_f1673966486on_com @ cOMBS_904531235on_com @ ( hAPP_f648377725on_com @ ( hAPP_f2093196134on_com @ cOMBS_1529518335on_com @ ( hAPP_f755519727on_com @ ( cOMBB_1394247784_pname @ if_option_com ) @ A ) ) @ B ) ) @ C ) )
      = ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ ( dom_pname_com @ B ) ) @ ( hAPP_f759274231e_bool @ collect_pname @ A ) ) ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ ( dom_pname_com @ C ) ) @ ( hAPP_f759274231e_bool @ collect_pname @ ( hAPP_f759274231e_bool @ ( cOMBB_647938656_pname @ fNot ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_669_dom__if) ).

thf(2314,plain,
    ! [A: fun_pname_bool,B: fun_pname_option_com,C: fun_pname_option_com] :
      ( ( dom_pname_com @ ( hAPP_f2123220539on_com @ ( hAPP_f1673966486on_com @ cOMBS_904531235on_com @ ( hAPP_f648377725on_com @ ( hAPP_f2093196134on_com @ cOMBS_1529518335on_com @ ( hAPP_f755519727on_com @ ( cOMBB_1394247784_pname @ if_option_com ) @ A ) ) @ B ) ) @ C ) )
      = ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ ( dom_pname_com @ B ) ) @ ( hAPP_f759274231e_bool @ collect_pname @ A ) ) ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ ( dom_pname_com @ C ) ) @ ( hAPP_f759274231e_bool @ collect_pname @ ( hAPP_f759274231e_bool @ ( cOMBB_647938656_pname @ fNot ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

thf(786,axiom,
    ! [A: fun_Ho1653816318_pname,B: fun_Ho1996104121e_bool] :
      ( ( ( hAPP_f1148778334e_bool @ ( image_720060442_pname @ A ) @ B )
        = bot_bo844097828e_bool )
    <=> ( B = bot_bo1715400655e_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_image__is__empty) ).

thf(3668,plain,
    ! [A: fun_Ho1653816318_pname,B: fun_Ho1996104121e_bool] :
      ( ( ( ( hAPP_f1148778334e_bool @ ( image_720060442_pname @ A ) @ B )
          = bot_bo844097828e_bool )
       => ( B = bot_bo1715400655e_bool ) )
      & ( ( B = bot_bo1715400655e_bool )
       => ( ( hAPP_f1148778334e_bool @ ( image_720060442_pname @ A ) @ B )
          = bot_bo844097828e_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).

thf(503,axiom,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool] : ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_insertI1) ).

thf(2625,plain,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool] : ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).

thf(360,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool,D: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ C ) @ D ) )
     => ( ! [E: hoare_1875481847_state] :
            ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ E ) @ C ) )
           => ( ( hBOOL @ ( hAPP_H1173941847e_bool @ B @ E ) )
             => ( hBOOL @ ( hAPP_H1173941847e_bool @ A @ E ) ) ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ C ) @ ( hAPP_f121055253e_bool @ collec1735317154_state @ B ) ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ D ) @ ( hAPP_f121055253e_bool @ collec1735317154_state @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_671_Int__Collect__mono) ).

thf(2111,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool,D: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ C ) @ D ) )
     => ( ! [E: hoare_1875481847_state] :
            ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ E ) @ C ) )
           => ( ( hBOOL @ ( hAPP_H1173941847e_bool @ B @ E ) )
             => ( hBOOL @ ( hAPP_H1173941847e_bool @ A @ E ) ) ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ C ) @ ( hAPP_f121055253e_bool @ collec1735317154_state @ B ) ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ D ) @ ( hAPP_f121055253e_bool @ collec1735317154_state @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(622,axiom,
    ! [A: fun_fu1430349052l_bool,B: fun_Ho14659478e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ C ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ A ) @ ( hAPP_f1628972376l_bool @ ( image_412748388e_bool @ B ) @ C ) ) )
       => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_finite__surj) ).

thf(3073,plain,
    ! [A: fun_fu1430349052l_bool,B: fun_Ho14659478e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ C ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ A ) @ ( hAPP_f1628972376l_bool @ ( image_412748388e_bool @ B ) @ C ) ) )
       => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).

thf(283,axiom,
    ! [A: pname,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
     => ( ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ B )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_insert__absorb) ).

thf(1821,plain,
    ! [A: pname,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
     => ( ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(257,axiom,
    ! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
      ( ( hAPP_f559147733l_bool @ ( hAPP_f1320879424l_bool @ insert1325755072e_bool @ A ) @ B )
      = ( hAPP_f559147733l_bool @ ( hAPP_f230953622l_bool @ semila1782091504l_bool @ ( hAPP_f559147733l_bool @ collec1974731493e_bool @ ( hAPP_f434788991l_bool @ ( hAPP_f1297925993l_bool @ cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ A ) ) ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_331_insert__def) ).

thf(1731,plain,
    ! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
      ( ( hAPP_f559147733l_bool @ ( hAPP_f1320879424l_bool @ insert1325755072e_bool @ A ) @ B )
      = ( hAPP_f559147733l_bool @ ( hAPP_f230953622l_bool @ semila1782091504l_bool @ ( hAPP_f559147733l_bool @ collec1974731493e_bool @ ( hAPP_f434788991l_bool @ ( hAPP_f1297925993l_bool @ cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ A ) ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(493,axiom,
    ! [A: hoare_1875481847_state,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ ( cOMBK_1032401873_pname @ A ) ) @ C )
        = ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ bot_bo1715400655e_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_image__constant) ).

thf(2593,plain,
    ! [A: hoare_1875481847_state,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ ( cOMBK_1032401873_pname @ A ) ) @ C )
        = ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ bot_bo1715400655e_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).

thf(66,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ A ) @ B ) ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_625_inf__le1) ).

thf(1029,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ A ) @ B ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(213,axiom,
    ! [A: pname,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_finite__insert) ).

thf(1556,plain,
    ! [A: pname,B: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ B ) ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(510,axiom,
    ! [A: fun_Ho1996104121e_bool,B: hoare_1875481847_state] : ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_subset__insertI) ).

thf(2647,plain,
    ! [A: fun_Ho1996104121e_bool,B: hoare_1875481847_state] : ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).

thf(524,axiom,
    ! [A: fun_Ho1996104121e_bool,B: hoare_1875481847_state] :
      ( ( ( hBOOL @ ( hAPP_H1173941847e_bool @ A @ B ) )
       => ( ( hAPP_f121055253e_bool @ collec1735317154_state @ ( hAPP_f121055253e_bool @ ( hAPP_f1300953505e_bool @ cOMBS_896408300l_bool @ ( hAPP_f932622461l_bool @ ( cOMBB_242064253_state @ fconj ) @ ( hAPP_H117293375e_bool @ fequal391417144_state @ B ) ) ) @ A ) )
          = ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ bot_bo1715400655e_bool ) ) )
      & ( ~ ( hBOOL @ ( hAPP_H1173941847e_bool @ A @ B ) )
       => ( ( hAPP_f121055253e_bool @ collec1735317154_state @ ( hAPP_f121055253e_bool @ ( hAPP_f1300953505e_bool @ cOMBS_896408300l_bool @ ( hAPP_f932622461l_bool @ ( cOMBB_242064253_state @ fconj ) @ ( hAPP_H117293375e_bool @ fequal391417144_state @ B ) ) ) @ A ) )
          = bot_bo1715400655e_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_Collect__conv__if2) ).

thf(2710,plain,
    ! [A: fun_Ho1996104121e_bool,B: hoare_1875481847_state] :
      ( ( ( hBOOL @ ( hAPP_H1173941847e_bool @ A @ B ) )
       => ( ( hAPP_f121055253e_bool @ collec1735317154_state @ ( hAPP_f121055253e_bool @ ( hAPP_f1300953505e_bool @ cOMBS_896408300l_bool @ ( hAPP_f932622461l_bool @ ( cOMBB_242064253_state @ fconj ) @ ( hAPP_H117293375e_bool @ fequal391417144_state @ B ) ) ) @ A ) )
          = ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ bot_bo1715400655e_bool ) ) )
      & ( ~ ( hBOOL @ ( hAPP_H1173941847e_bool @ A @ B ) )
       => ( ( hAPP_f121055253e_bool @ collec1735317154_state @ ( hAPP_f121055253e_bool @ ( hAPP_f1300953505e_bool @ cOMBS_896408300l_bool @ ( hAPP_f932622461l_bool @ ( cOMBB_242064253_state @ fconj ) @ ( hAPP_H117293375e_bool @ fequal391417144_state @ B ) ) ) @ A ) )
          = bot_bo1715400655e_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).

thf(576,axiom,
    ! [A: fun_pn664418900_state,B: fun_pname_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ A ) @ B ) ) )
       => ? [C: pname] :
            ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( hAPP_f759274231e_bool @ collect_pname @ ( hAPP_f759274231e_bool @ ( hAPP_f649174806e_bool @ cOMBS_568398431l_bool @ ( hAPP_f1402196763l_bool @ ( cOMBB_675860798_pname @ fconj ) @ ( hAPP_f759274231e_bool @ ( hAPP_f661147897e_bool @ cOMBC_1058051404l_bool @ member_pname ) @ B ) ) ) @ ( hAPP_H785152948e_bool @ ( hAPP_f1564627769e_bool @ cOMBC_951029257e_bool @ ( hAPP_f1601283355e_bool @ ( cOMBB_2037342654_pname @ fequal391417144_state ) @ A ) ) @ ( hAPP_p702226982_state @ A @ C ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_pigeonhole__infinite) ).

thf(2911,plain,
    ! [A: fun_pn664418900_state,B: fun_pname_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ A ) @ B ) ) )
       => ? [C: pname] :
            ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( hAPP_f759274231e_bool @ collect_pname @ ( hAPP_f759274231e_bool @ ( hAPP_f649174806e_bool @ cOMBS_568398431l_bool @ ( hAPP_f1402196763l_bool @ ( cOMBB_675860798_pname @ fconj ) @ ( hAPP_f759274231e_bool @ ( hAPP_f661147897e_bool @ cOMBC_1058051404l_bool @ member_pname ) @ B ) ) ) @ ( hAPP_H785152948e_bool @ ( hAPP_f1564627769e_bool @ cOMBC_951029257e_bool @ ( hAPP_f1601283355e_bool @ ( cOMBB_2037342654_pname @ fequal391417144_state ) @ A ) ) @ ( hAPP_p702226982_state @ A @ C ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).

thf(33,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_453_inf__sup__ord_I3_J) ).

thf(912,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(430,axiom,
    ! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
     => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( hAPP_f559147733l_bool @ ( hAPP_f1320879424l_bool @ insert1325755072e_bool @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_finite_OinsertI) ).

thf(2365,plain,
    ! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
     => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( hAPP_f559147733l_bool @ ( hAPP_f1320879424l_bool @ insert1325755072e_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).

thf(189,axiom,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ B ) ) @ C )
      = ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ B ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_Un__insert__left) ).

thf(1474,plain,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ B ) ) @ C )
      = ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(386,axiom,
    ! [A: fun_Ho1695028467e_bool,B: fun_fu1604182422_state,C: fun_pname_bool] :
      ( ( hAPP_f1291720380e_bool @ ( hAPP_f1703905905e_bool @ ( cOMBB_93797312e_bool @ A ) @ B ) @ C )
      = ( hAPP_H117293375e_bool @ A @ ( hAPP_f168815540_state @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc__Com___236) ).

thf(2212,plain,
    ! [A: fun_Ho1695028467e_bool,B: fun_fu1604182422_state,C: fun_pname_bool] :
      ( ( hAPP_f1291720380e_bool @ ( hAPP_f1703905905e_bool @ ( cOMBB_93797312e_bool @ A ) @ B ) @ C )
      = ( hAPP_H117293375e_bool @ A @ ( hAPP_f168815540_state @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(808,axiom,
    ! [A: fun_co2032091866_state,B: fun_pname_com,C: pname] :
      ( ( hAPP_p702226982_state @ ( hAPP_f2031411714_state @ ( cOMBB_1364904209_pname @ A ) @ B ) @ C )
      = ( hAPP_c406083500_state @ A @ ( hAPP_pname_com @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Com__Ocom_000tc__Hoare____Mirabelle____xlrqixeqwe__O) ).

thf(3759,plain,
    ! [A: fun_co2032091866_state,B: fun_pname_com,C: pname] :
      ( ( hAPP_p702226982_state @ ( hAPP_f2031411714_state @ ( cOMBB_1364904209_pname @ A ) @ B ) @ C )
      = ( hAPP_c406083500_state @ A @ ( hAPP_pname_com @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).

thf(178,axiom,
    ! [A: pname] :
      ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ bot_bo844097828e_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_empty__iff) ).

thf(1445,plain,
    ! [A: pname] :
      ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ bot_bo844097828e_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(54,axiom,
    ! [A: fun_pname_bool] :
      ( ( A != bot_bo844097828e_bool )
    <=> ? [B: pname,C: fun_pname_bool] :
          ( ( A
            = ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ C ) )
          & ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_nonempty__iff) ).

thf(986,plain,
    ! [A: fun_pname_bool] :
      ( ( ( A != bot_bo844097828e_bool )
       => ? [B: pname,C: fun_pname_bool] :
            ( ( A
              = ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ C ) )
            & ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) ) ) )
      & ( ? [B: pname,C: fun_pname_bool] :
            ( ( A
              = ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ C ) )
            & ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) ) )
       => ( A != bot_bo844097828e_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(175,axiom,
    ! [A: fun_fu689207471l_bool,B: fun_fu689207471l_bool] :
      ( ( hAPP_f900945761l_bool @ ( hAPP_f19215249l_bool @ semila1703230395l_bool @ A ) @ B )
      = ( hAPP_f900945761l_bool @ collec771609166e_bool @ ( hAPP_f900945761l_bool @ ( hAPP_f2051813877l_bool @ cOMBS_1451994324l_bool @ ( hAPP_f440042033l_bool @ ( cOMBB_532710323e_bool @ fdisj ) @ ( hAPP_f900945761l_bool @ ( hAPP_f1846363427l_bool @ cOMBC_1909905718l_bool @ member1062536460e_bool ) @ A ) ) ) @ ( hAPP_f900945761l_bool @ ( hAPP_f1846363427l_bool @ cOMBC_1909905718l_bool @ member1062536460e_bool ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_Un__def) ).

thf(1435,plain,
    ! [A: fun_fu689207471l_bool,B: fun_fu689207471l_bool] :
      ( ( hAPP_f900945761l_bool @ ( hAPP_f19215249l_bool @ semila1703230395l_bool @ A ) @ B )
      = ( hAPP_f900945761l_bool @ collec771609166e_bool @ ( hAPP_f900945761l_bool @ ( hAPP_f2051813877l_bool @ cOMBS_1451994324l_bool @ ( hAPP_f440042033l_bool @ ( cOMBB_532710323e_bool @ fdisj ) @ ( hAPP_f900945761l_bool @ ( hAPP_f1846363427l_bool @ cOMBC_1909905718l_bool @ member1062536460e_bool ) @ A ) ) ) @ ( hAPP_f900945761l_bool @ ( hAPP_f1846363427l_bool @ cOMBC_1909905718l_bool @ member1062536460e_bool ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(357,axiom,
    ! [A: com,B: com,C: pname] :
      ( ( semi @ A @ B )
     != ( hAPP_pname_com @ body_1 @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_505_com_Osimps_I48_J) ).

thf(2101,plain,
    ! [A: com,B: com,C: pname] :
      ( ( semi @ A @ B )
     != ( hAPP_pname_com @ body_1 @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(437,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( B = C )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_xt1_I3_J) ).

thf(2390,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( B = C )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).

thf(83,axiom,
    ! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_set__rev__mp) ).

thf(1102,plain,
    ! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(371,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: hoare_1875481847_state] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ C ) @ bot_bo1715400655e_bool ) ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ B ) @ A ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ C ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_hoare__derivs_Oinsert) ).

thf(2156,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: hoare_1875481847_state] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ C ) @ bot_bo1715400655e_bool ) ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ B ) @ A ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ C ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(384,axiom,
    ! [A: fun_st1506752259e_bool,B: pname,C: fun_st1506752259e_bool,D: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ A ) @ ( hAPP_pname_com @ body_1 @ B ) ) @ C ) ) @ D ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ A ) @ ( hAPP_option_com_com @ the_com @ ( hAPP_p799580910on_com @ body @ B ) ) ) @ C ) ) @ bot_bo1715400655e_bool ) ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ D ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ A ) @ ( hAPP_pname_com @ body_1 @ B ) ) @ C ) ) @ bot_bo1715400655e_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_377_BodyN) ).

thf(2207,plain,
    ! [A: fun_st1506752259e_bool,B: pname,C: fun_st1506752259e_bool,D: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ A ) @ ( hAPP_pname_com @ body_1 @ B ) ) @ C ) ) @ D ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ A ) @ ( hAPP_option_com_com @ the_com @ ( hAPP_p799580910on_com @ body @ B ) ) ) @ C ) ) @ bot_bo1715400655e_bool ) ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ D ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ A ) @ ( hAPP_pname_com @ body_1 @ B ) ) @ C ) ) @ bot_bo1715400655e_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(37,axiom,
    ! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ A ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ minus_1015773161e_bool @ C ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_684_DiffI) ).

thf(922,plain,
    ! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ A ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ minus_1015773161e_bool @ C ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(598,axiom,
    ! [A: com,B: fun_com_bool,C: option_com] :
      ( ! [D: com] :
          ( ( hBOOL @ ( hAPP_f990396704l_bool @ ( hAPP_c667411853l_bool @ member_com @ D ) @ ( set_com @ C ) ) )
         => ( hBOOL @ ( hAPP_com_bool @ B @ D ) ) )
     => ( ( C
          = ( some_com @ A ) )
       => ( hBOOL @ ( hAPP_com_bool @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_408_ospec) ).

thf(2984,plain,
    ! [A: com,B: fun_com_bool,C: option_com] :
      ( ! [D: com] :
          ( ( hBOOL @ ( hAPP_f990396704l_bool @ ( hAPP_c667411853l_bool @ member_com @ D ) @ ( set_com @ C ) ) )
         => ( hBOOL @ ( hAPP_com_bool @ B @ D ) ) )
     => ( ( C
          = ( some_com @ A ) )
       => ( hBOOL @ ( hAPP_com_bool @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).

thf(706,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
    <=> ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_323_subset__Un__eq) ).

thf(3380,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
       => ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B )
          = B ) )
      & ( ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B )
          = B )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).

thf(751,axiom,
    ! [A: com,B: com,C: state,D: state] :
      ( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ ( evalc @ ( semi @ A @ B ) ) @ C ) @ D ) )
     => ~ ! [E: state] :
            ( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ ( evalc @ A ) @ C ) @ E ) )
           => ~ ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ ( evalc @ B ) @ E ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_544_evalc__elim__cases_I4_J) ).

thf(3539,plain,
    ! [A: com,B: com,C: state,D: state] :
      ( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ ( evalc @ ( semi @ A @ B ) ) @ C ) @ D ) )
     => ~ ! [E: state] :
            ( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ ( evalc @ A ) @ C ) @ E ) )
           => ~ ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ ( evalc @ B ) @ E ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).

thf(540,axiom,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_H1173941847e_bool @ B @ A ) ) @ ( hAPP_H1173941847e_bool @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_370_le__funD) ).

thf(2770,plain,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_H1173941847e_bool @ B @ A ) ) @ ( hAPP_H1173941847e_bool @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).

thf(529,axiom,
    ! [A: pname,B: com,C: com] :
      ( ( hAPP_pname_com @ body_1 @ A )
     != ( semi @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_504_com_Osimps_I49_J) ).

thf(2725,plain,
    ! [A: pname,B: com,C: com] :
      ( ( hAPP_pname_com @ body_1 @ A )
     != ( semi @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).

thf(220,axiom,
    ! [A: bool] :
      ( ( A = fTrue )
      | ( A = fFalse ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_If_000tc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc__Com__Ostate) ).

thf(1594,plain,
    ! [A: bool] :
      ( ( A = fTrue )
      | ( A = fFalse ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(538,axiom,
    ! [A: com,B: com] :
      ( ( hBOOL @ ( hAPP_com_bool @ wt @ B ) )
     => ( ( hBOOL @ ( hAPP_com_bool @ wt @ A ) )
       => ( hBOOL @ ( hAPP_com_bool @ wt @ ( semi @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_506_WT_OSemi) ).

thf(2765,plain,
    ! [A: com,B: com] :
      ( ( hBOOL @ ( hAPP_com_bool @ wt @ B ) )
     => ( ( hBOOL @ ( hAPP_com_bool @ wt @ A ) )
       => ( hBOOL @ ( hAPP_com_bool @ wt @ ( semi @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).

thf(463,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ A ) )
       => ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_xt1_I5_J) ).

thf(2481,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ A ) )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).

thf(190,axiom,
    ! [A: pname,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ C ) ) )
     => ( ( A != B )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_insertE) ).

thf(1477,plain,
    ! [A: pname,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ C ) ) )
     => ( ( A != B )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(642,axiom,
    ! [A: fun_fu854396771l_bool,B: fun_fu689207471l_bool,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f1408815105l_bool @ ( hAPP_f900945761l_bool @ ( hAPP_f2051813877l_bool @ cOMBS_1451994324l_bool @ A ) @ B ) @ C )
      = ( hAPP_bool_bool @ ( hAPP_f78029435l_bool @ A @ C ) @ ( hAPP_f1408815105l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Otriple_I) ).

thf(3142,plain,
    ! [A: fun_fu854396771l_bool,B: fun_fu689207471l_bool,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f1408815105l_bool @ ( hAPP_f900945761l_bool @ ( hAPP_f2051813877l_bool @ cOMBS_1451994324l_bool @ A ) @ B ) @ C )
      = ( hAPP_bool_bool @ ( hAPP_f78029435l_bool @ A @ C ) @ ( hAPP_f1408815105l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).

thf(604,axiom,
    ! [A: fun_Ho1996104121e_bool,B: hoare_1875481847_state,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_set__rev__mp) ).

thf(3009,plain,
    ! [A: fun_Ho1996104121e_bool,B: hoare_1875481847_state,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).

thf(355,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] : ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ B ) ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_606_Int__lower2) ).

thf(2096,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] : ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ B ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(654,axiom,
    ! [A: fun_pn760644914e_bool,B: fun_pname_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ ( hAPP_f1522632684l_bool @ ( image_1165561978e_bool @ A ) @ B ) ) )
       => ? [C: pname] :
            ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( hAPP_f759274231e_bool @ collect_pname @ ( hAPP_f759274231e_bool @ ( hAPP_f649174806e_bool @ cOMBS_568398431l_bool @ ( hAPP_f1402196763l_bool @ ( cOMBB_675860798_pname @ fconj ) @ ( hAPP_f759274231e_bool @ ( hAPP_f661147897e_bool @ cOMBC_1058051404l_bool @ member_pname ) @ B ) ) ) @ ( hAPP_f1148778334e_bool @ ( hAPP_f1967984667e_bool @ cOMBC_1788166607l_bool @ ( hAPP_f98146217l_bool @ ( cOMBB_2094848682_pname @ fequal259518520e_bool ) @ A ) ) @ ( hAPP_p1537966538e_bool @ A @ C ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_pigeonhole__infinite) ).

thf(3193,plain,
    ! [A: fun_pn760644914e_bool,B: fun_pname_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ ( hAPP_f1522632684l_bool @ ( image_1165561978e_bool @ A ) @ B ) ) )
       => ? [C: pname] :
            ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( hAPP_f759274231e_bool @ collect_pname @ ( hAPP_f759274231e_bool @ ( hAPP_f649174806e_bool @ cOMBS_568398431l_bool @ ( hAPP_f1402196763l_bool @ ( cOMBB_675860798_pname @ fconj ) @ ( hAPP_f759274231e_bool @ ( hAPP_f661147897e_bool @ cOMBC_1058051404l_bool @ member_pname ) @ B ) ) ) @ ( hAPP_f1148778334e_bool @ ( hAPP_f1967984667e_bool @ cOMBC_1788166607l_bool @ ( hAPP_f98146217l_bool @ ( cOMBB_2094848682_pname @ fequal259518520e_bool ) @ A ) ) @ ( hAPP_p1537966538e_bool @ A @ C ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).

thf(110,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ A ) @ B ) ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ A ) @ C ) ) ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_663_distrib__inf__le) ).

thf(1208,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ A ) @ B ) ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ A ) @ C ) ) ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(186,axiom,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_pname_bool @ B @ A ) )
       => ( hBOOL @ ( hAPP_pname_bool @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_391_predicate1D) ).

thf(1467,plain,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_pname_bool @ B @ A ) )
       => ( hBOOL @ ( hAPP_pname_bool @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(682,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] : ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ B ) ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_630_inf__le2) ).

thf(3293,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] : ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ B ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).

thf(133,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ B ) @ C ) ) )
    <=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
        & ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_633_le__inf__iff) ).

thf(1277,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ B ) @ C ) ) )
       => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
          & ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ C ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
          & ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ C ) ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ B ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(451,axiom,
    ! [A: fun_Ho1996104121e_bool,B: hoare_1875481847_state,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ C ) )
     => ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ A ) ) @ C )
        = ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_610_Int__insert__left__if1) ).

thf(2449,plain,
    ! [A: fun_Ho1996104121e_bool,B: hoare_1875481847_state,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ C ) )
     => ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ A ) ) @ C )
        = ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).

thf(77,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: pname] :
      ( ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f661147897e_bool @ cOMBC_1058051404l_bool @ member_pname ) @ A ) ) @ ( hAPP_f759274231e_bool @ ( hAPP_f661147897e_bool @ cOMBC_1058051404l_bool @ member_pname ) @ B ) ) @ C ) )
    <=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_397_sup__Un__eq) ).

thf(1081,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: pname] :
      ( ( ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f661147897e_bool @ cOMBC_1058051404l_bool @ member_pname ) @ A ) ) @ ( hAPP_f759274231e_bool @ ( hAPP_f661147897e_bool @ cOMBC_1058051404l_bool @ member_pname ) @ B ) ) @ C ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ A ) @ B ) ) ) )
      & ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ A ) @ B ) ) )
       => ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f661147897e_bool @ cOMBC_1058051404l_bool @ member_pname ) @ A ) ) @ ( hAPP_f759274231e_bool @ ( hAPP_f661147897e_bool @ cOMBC_1058051404l_bool @ member_pname ) @ B ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(382,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] : ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_Un__upper1) ).

thf(2202,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] : ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(188,axiom,
    ( bot_bo1649642514l_bool
    = ( hAPP_f559147733l_bool @ collec1974731493e_bool @ ( cOMBK_1857069011e_bool @ fFalse ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_empty__def) ).

thf(1472,plain,
    ( bot_bo1649642514l_bool
    = ( hAPP_f559147733l_bool @ collec1974731493e_bool @ ( cOMBK_1857069011e_bool @ fFalse ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(211,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ B ) @ C ) ) )
     => ~ ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
         => ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_649_le__infE) ).

thf(1551,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ B ) @ C ) ) )
     => ~ ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
         => ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(760,axiom,
    ! [A: fun_Ho1653816318_pname,B: fun_Ho1996104121e_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ ( hAPP_f1148778334e_bool @ ( image_720060442_pname @ A ) @ B ) ) )
       => ? [D: fun_Ho1996104121e_bool] :
            ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ D ) )
            & ( C
              = ( hAPP_f1148778334e_bool @ ( image_720060442_pname @ A ) @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_finite__subset__image) ).

thf(3571,plain,
    ! [A: fun_Ho1653816318_pname,B: fun_Ho1996104121e_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ ( hAPP_f1148778334e_bool @ ( image_720060442_pname @ A ) @ B ) ) )
       => ? [D: fun_Ho1996104121e_bool] :
            ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ D ) )
            & ( C
              = ( hAPP_f1148778334e_bool @ ( image_720060442_pname @ A ) @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).

thf(721,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_pn12888928e_bool,C: fun_pn12888928e_bool,D: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_390430481_state @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ ( hAPP_f1568887991_state @ ( hAPP_f891245078_state @ cOMBS_475568287_state @ ( hAPP_f2116202538_state @ ( hAPP_f1339343196_state @ cOMBS_1674056844_state @ ( hAPP_f275933352_state @ ( cOMBB_718493681_pname @ hoare_13225861_state ) @ B ) ) @ body_1 ) ) @ C ) ) @ D ) ) ) @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ ( hAPP_f1568887991_state @ ( hAPP_f891245078_state @ cOMBS_475568287_state @ ( hAPP_f2116202538_state @ ( hAPP_f1339343196_state @ cOMBS_1674056844_state @ ( hAPP_f275933352_state @ ( cOMBB_718493681_pname @ hoare_13225861_state ) @ B ) ) @ ( hAPP_f96342628me_com @ ( cOMBB_923936821_pname @ the_com ) @ body ) ) ) @ C ) ) @ D ) ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_390430481_state @ A ) @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ ( hAPP_f1568887991_state @ ( hAPP_f891245078_state @ cOMBS_475568287_state @ ( hAPP_f2116202538_state @ ( hAPP_f1339343196_state @ cOMBS_1674056844_state @ ( hAPP_f275933352_state @ ( cOMBB_718493681_pname @ hoare_13225861_state ) @ B ) ) @ body_1 ) ) @ C ) ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_380_Body__sound__lemma) ).

thf(3444,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_pn12888928e_bool,C: fun_pn12888928e_bool,D: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_390430481_state @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ ( hAPP_f1568887991_state @ ( hAPP_f891245078_state @ cOMBS_475568287_state @ ( hAPP_f2116202538_state @ ( hAPP_f1339343196_state @ cOMBS_1674056844_state @ ( hAPP_f275933352_state @ ( cOMBB_718493681_pname @ hoare_13225861_state ) @ B ) ) @ body_1 ) ) @ C ) ) @ D ) ) ) @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ ( hAPP_f1568887991_state @ ( hAPP_f891245078_state @ cOMBS_475568287_state @ ( hAPP_f2116202538_state @ ( hAPP_f1339343196_state @ cOMBS_1674056844_state @ ( hAPP_f275933352_state @ ( cOMBB_718493681_pname @ hoare_13225861_state ) @ B ) ) @ ( hAPP_f96342628me_com @ ( cOMBB_923936821_pname @ the_com ) @ body ) ) ) @ C ) ) @ D ) ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_390430481_state @ A ) @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ ( hAPP_f1568887991_state @ ( hAPP_f891245078_state @ cOMBS_475568287_state @ ( hAPP_f2116202538_state @ ( hAPP_f1339343196_state @ cOMBS_1674056844_state @ ( hAPP_f275933352_state @ ( cOMBB_718493681_pname @ hoare_13225861_state ) @ B ) ) @ body_1 ) ) @ C ) ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).

thf(68,axiom,
    ! [A: fun_state_bool,B: com,C: fun_state_bool,D: com] :
      ( ( ( while @ A @ B )
        = ( while @ C @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_498_com_Osimps_I5_J) ).

thf(1034,plain,
    ! [A: fun_state_bool,B: com,C: fun_state_bool,D: com] :
      ( ( ( ( while @ A @ B )
          = ( while @ C @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( while @ A @ B )
          = ( while @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(577,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ! [D: hoare_1875481847_state] :
          ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ D ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ C ) ) )
         => ( hBOOL @ ( hAPP_H1173941847e_bool @ A @ D ) ) )
    <=> ( ! [D: hoare_1875481847_state] :
            ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ D ) @ B ) )
           => ( hBOOL @ ( hAPP_H1173941847e_bool @ A @ D ) ) )
        & ! [D: hoare_1875481847_state] :
            ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ D ) @ C ) )
           => ( hBOOL @ ( hAPP_H1173941847e_bool @ A @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_ball__Un) ).

thf(2914,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( ! [D: hoare_1875481847_state] :
            ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ D ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ C ) ) )
           => ( hBOOL @ ( hAPP_H1173941847e_bool @ A @ D ) ) )
       => ( ! [D: hoare_1875481847_state] :
              ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ D ) @ B ) )
             => ( hBOOL @ ( hAPP_H1173941847e_bool @ A @ D ) ) )
          & ! [D: hoare_1875481847_state] :
              ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ D ) @ C ) )
             => ( hBOOL @ ( hAPP_H1173941847e_bool @ A @ D ) ) ) ) )
      & ( ( ! [D: hoare_1875481847_state] :
              ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ D ) @ B ) )
             => ( hBOOL @ ( hAPP_H1173941847e_bool @ A @ D ) ) )
          & ! [D: hoare_1875481847_state] :
              ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ D ) @ C ) )
             => ( hBOOL @ ( hAPP_H1173941847e_bool @ A @ D ) ) ) )
       => ! [D: hoare_1875481847_state] :
            ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ D ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ C ) ) )
           => ( hBOOL @ ( hAPP_H1173941847e_bool @ A @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).

thf(550,axiom,
    ! [A: fun_fu399576434l_bool,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ bot_bo1649642514l_bool ) )
       => ( ! [C: fun_pname_bool,D: fun_fu1430349052l_bool] :
              ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ D ) )
             => ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ C ) @ D ) )
               => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ D ) )
                 => ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ ( hAPP_f559147733l_bool @ ( hAPP_f1320879424l_bool @ insert1325755072e_bool @ C ) @ D ) ) ) ) ) )
         => ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_finite__induct) ).

thf(2816,plain,
    ! [A: fun_fu399576434l_bool,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ bot_bo1649642514l_bool ) )
       => ( ! [C: fun_pname_bool,D: fun_fu1430349052l_bool] :
              ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ D ) )
             => ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ C ) @ D ) )
               => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ D ) )
                 => ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ ( hAPP_f559147733l_bool @ ( hAPP_f1320879424l_bool @ insert1325755072e_bool @ C ) @ D ) ) ) ) ) )
         => ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).

thf(279,axiom,
    ! [A: pname,B: fun_pname_bool,C: fun_pn1208287926_pname,D: fun_fu1499449723_pname] :
      ( ( hBOOL @ ( finite1282449217_pname @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
       => ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
         => ( ( B != bot_bo844097828e_bool )
           => ( ( hAPP_f1297739591_pname @ D @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ B ) )
              = ( hAPP_pname_pname @ ( hAPP_p1170154830_pname @ C @ A ) @ ( hAPP_f1297739591_pname @ D @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_509_folding__one_Oinsert) ).

thf(1809,plain,
    ! [A: pname,B: fun_pname_bool,C: fun_pn1208287926_pname,D: fun_fu1499449723_pname] :
      ( ( hBOOL @ ( finite1282449217_pname @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
       => ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
         => ( ( B != bot_bo844097828e_bool )
           => ( ( hAPP_f1297739591_pname @ D @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ B ) )
              = ( hAPP_pname_pname @ ( hAPP_p1170154830_pname @ C @ A ) @ ( hAPP_f1297739591_pname @ D @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(587,axiom,
    ! [A: fun_pname_bool,B: fun_fu235184776_pname,C: fun_fu689207471l_bool] :
      ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( hAPP_f75069804e_bool @ ( image_1169820240_pname @ B ) @ C ) ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_finite__surj) ).

thf(2952,plain,
    ! [A: fun_pname_bool,B: fun_fu235184776_pname,C: fun_fu689207471l_bool] :
      ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( hAPP_f75069804e_bool @ ( image_1169820240_pname @ B ) @ C ) ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).

thf(761,axiom,
    ! [A: hoare_1875481847_state,B: hoare_1875481847_state,C: hoare_1875481847_state,D: hoare_1875481847_state] :
      ( ( ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ bot_bo1715400655e_bool ) )
        = ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ C ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ D ) @ bot_bo1715400655e_bool ) ) )
    <=> ( ( ( A = C )
          & ( B = D ) )
        | ( ( A = D )
          & ( B = C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_doubleton__eq__iff) ).

thf(3576,plain,
    ! [A: hoare_1875481847_state,B: hoare_1875481847_state,C: hoare_1875481847_state,D: hoare_1875481847_state] :
      ( ( ( ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ bot_bo1715400655e_bool ) )
          = ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ C ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ D ) @ bot_bo1715400655e_bool ) ) )
       => ( ( ( A = C )
            & ( B = D ) )
          | ( ( A = D )
            & ( B = C ) ) ) )
      & ( ( ( ( A = C )
            & ( B = D ) )
          | ( ( A = D )
            & ( B = C ) ) )
       => ( ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ bot_bo1715400655e_bool ) )
          = ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ C ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ D ) @ bot_bo1715400655e_bool ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).

thf(44,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
     => ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ B ) @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_435_sup__absorb1) ).

thf(944,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
     => ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ B ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(647,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: hoare_1875481847_state] :
      ( ( hBOOL @ ( hAPP_H1173941847e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) @ C ) )
    <=> ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ semila1168014441p_bool @ ( hAPP_H1173941847e_bool @ A @ C ) ) @ ( hAPP_H1173941847e_bool @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_409_sup__fun__def) ).

thf(3161,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: hoare_1875481847_state] :
      ( ( ( hBOOL @ ( hAPP_H1173941847e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) @ C ) )
       => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ semila1168014441p_bool @ ( hAPP_H1173941847e_bool @ A @ C ) ) @ ( hAPP_H1173941847e_bool @ B @ C ) ) ) )
      & ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ semila1168014441p_bool @ ( hAPP_H1173941847e_bool @ A @ C ) ) @ ( hAPP_H1173941847e_bool @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_H1173941847e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).

thf(171,axiom,
    ! [A: fun_fu689207471l_bool,B: fun_fu689207471l_bool] :
      ( ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ ( hAPP_f900945761l_bool @ collec771609166e_bool @ B ) ) )
        | ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ ( hAPP_f900945761l_bool @ collec771609166e_bool @ A ) ) ) )
     => ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ ( hAPP_f900945761l_bool @ collec771609166e_bool @ ( hAPP_f900945761l_bool @ ( hAPP_f2051813877l_bool @ cOMBS_1451994324l_bool @ ( hAPP_f440042033l_bool @ ( cOMBB_532710323e_bool @ fconj ) @ B ) ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_finite__Collect__conjI) ).

thf(1420,plain,
    ! [A: fun_fu689207471l_bool,B: fun_fu689207471l_bool] :
      ( ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ ( hAPP_f900945761l_bool @ collec771609166e_bool @ B ) ) )
        | ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ ( hAPP_f900945761l_bool @ collec771609166e_bool @ A ) ) ) )
     => ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ ( hAPP_f900945761l_bool @ collec771609166e_bool @ ( hAPP_f900945761l_bool @ ( hAPP_f2051813877l_bool @ cOMBS_1451994324l_bool @ ( hAPP_f440042033l_bool @ ( cOMBB_532710323e_bool @ fconj ) @ B ) ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(421,axiom,
    ! [A: fun_pn664418900_state,B: pname,C: fun_pname_bool] :
      ( ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ C ) )
      = ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_p702226982_state @ A @ B ) ) @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ A ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_image__insert) ).

thf(2333,plain,
    ! [A: fun_pn664418900_state,B: pname,C: fun_pname_bool] :
      ( ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ C ) )
      = ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_p702226982_state @ A @ B ) ) @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).

thf(399,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool,D: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ C ) @ D ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ C ) @ A ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ D ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_Un__mono) ).

thf(2256,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool,D: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ C ) @ D ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ C ) @ A ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ D ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(676,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_341_order__trans) ).

thf(3278,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).

thf(319,axiom,
    ! [A: fun_Ho1996104121e_bool] :
      ( ! [B: hoare_1875481847_state] :
          ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ A ) )
    <=> ( A = bot_bo1715400655e_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_all__not__in__conv) ).

thf(1958,plain,
    ! [A: fun_Ho1996104121e_bool] :
      ( ( ! [B: hoare_1875481847_state] :
            ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ A ) )
       => ( A = bot_bo1715400655e_bool ) )
      & ( ( A = bot_bo1715400655e_bool )
       => ! [B: hoare_1875481847_state] :
            ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(51,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ C ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_645_inf__greatest) ).

thf(968,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ C ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(5,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ A ) @ B ) ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_623_inf__sup__ord_I1_J) ).

thf(823,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ A ) @ B ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(290,axiom,
    ! [A: pname,B: fun_pname_bool] :
      ( bot_bo844097828e_bool
     != ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_empty__not__insert) ).

thf(1845,plain,
    ! [A: pname,B: fun_pname_bool] :
      ( bot_bo844097828e_bool
     != ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(260,axiom,
    ! [A: fun_fu1430349052l_bool,B: fun_fu2101097872e_bool,C: fun_fu608906319e_bool] :
      ( ( hBOOL @ ( finite1626890877e_bool @ B @ C ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) )
       => ( ( A != bot_bo1649642514l_bool )
         => ( ! [D: fun_pname_bool,E: fun_pname_bool] : ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ B @ D ) @ E ) ) @ ( hAPP_f559147733l_bool @ ( hAPP_f1320879424l_bool @ insert1325755072e_bool @ D ) @ ( hAPP_f559147733l_bool @ ( hAPP_f1320879424l_bool @ insert1325755072e_bool @ E ) @ bot_bo1649642514l_bool ) ) ) )
           => ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ ( hAPP_f674760225e_bool @ C @ A ) ) @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_517_folding__one_Oclosed) ).

thf(1748,plain,
    ! [A: fun_fu1430349052l_bool,B: fun_fu2101097872e_bool,C: fun_fu608906319e_bool] :
      ( ( hBOOL @ ( finite1626890877e_bool @ B @ C ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) )
       => ( ( A != bot_bo1649642514l_bool )
         => ( ! [D: fun_pname_bool,E: fun_pname_bool] : ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ B @ D ) @ E ) ) @ ( hAPP_f559147733l_bool @ ( hAPP_f1320879424l_bool @ insert1325755072e_bool @ D ) @ ( hAPP_f559147733l_bool @ ( hAPP_f1320879424l_bool @ insert1325755072e_bool @ E ) @ bot_bo1649642514l_bool ) ) ) )
           => ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ ( hAPP_f674760225e_bool @ C @ A ) ) @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(596,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( A = B )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_equalityD1) ).

thf(2977,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( A = B )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).

thf(336,axiom,
    ! [A: hoare_1875481847_state] :
      ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ bot_bo1715400655e_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_emptyE) ).

thf(2012,plain,
    ! [A: hoare_1875481847_state] :
      ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ bot_bo1715400655e_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(492,axiom,
    ! [A: pname] :
      ( ( hBOOL @ ( hAPP_pname_bool @ bot_bo844097828e_bool @ A ) )
    <=> ( hBOOL @ bot_bot_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_375_bot__fun__def) ).

thf(2588,plain,
    ! [A: pname] :
      ( ( ( hBOOL @ ( hAPP_pname_bool @ bot_bo844097828e_bool @ A ) )
       => ( hBOOL @ bot_bot_bool ) )
      & ( ( hBOOL @ bot_bot_bool )
       => ( hBOOL @ ( hAPP_pname_bool @ bot_bo844097828e_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).

thf(156,axiom,
    ! [A: fun_bool_bool,B: fun_fu1430349052l_bool,C: fun_pname_bool] :
      ( ( hAPP_f1664156314l_bool @ ( hAPP_f559147733l_bool @ ( cOMBB_307249310e_bool @ A ) @ B ) @ C )
      = ( hAPP_bool_bool @ A @ ( hAPP_f1664156314l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Op) ).

thf(1368,plain,
    ! [A: fun_bool_bool,B: fun_fu1430349052l_bool,C: fun_pname_bool] :
      ( ( hAPP_f1664156314l_bool @ ( hAPP_f559147733l_bool @ ( cOMBB_307249310e_bool @ A ) @ B ) @ C )
      = ( hAPP_bool_bool @ A @ ( hAPP_f1664156314l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(551,axiom,
    ! [A: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) )
     => ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ ( hAPP_f783502055l_bool @ collec1613912337l_bool @ ( hAPP_f510955609l_bool @ ( hAPP_f1879335953l_bool @ cOMBC_7971162l_bool @ ord_le675606854l_bool ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_finite__Collect__subsets) ).

thf(2821,plain,
    ! [A: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) )
     => ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ ( hAPP_f783502055l_bool @ collec1613912337l_bool @ ( hAPP_f510955609l_bool @ ( hAPP_f1879335953l_bool @ cOMBC_7971162l_bool @ ord_le675606854l_bool ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).

thf(118,axiom,
    ! [A: bool,B: fun_pname_bool] :
      ( ( hAPP_f1664156314l_bool @ ( cOMBK_1857069011e_bool @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obo) ).

thf(1230,plain,
    ! [A: bool,B: fun_pname_bool] :
      ( ( hAPP_f1664156314l_bool @ ( cOMBK_1857069011e_bool @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(82,axiom,
    ! [A: pname,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
     => ~ ! [C: fun_pname_bool] :
            ( ( B
              = ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ C ) )
           => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_529_Set_Oset__insert) ).

thf(1098,plain,
    ! [A: pname,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
     => ~ ! [C: fun_pname_bool] :
            ( ( B
              = ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ C ) )
           => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(567,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ collec1735317154_state @ ( hAPP_f121055253e_bool @ ( hAPP_f1300953505e_bool @ cOMBS_896408300l_bool @ ( hAPP_f932622461l_bool @ ( cOMBB_242064253_state @ fconj ) @ A ) ) @ B ) )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ ( hAPP_f121055253e_bool @ collec1735317154_state @ A ) ) @ ( hAPP_f121055253e_bool @ collec1735317154_state @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_582_Collect__conj__eq) ).

thf(2882,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ collec1735317154_state @ ( hAPP_f121055253e_bool @ ( hAPP_f1300953505e_bool @ cOMBS_896408300l_bool @ ( hAPP_f932622461l_bool @ ( cOMBB_242064253_state @ fconj ) @ A ) ) @ B ) )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ ( hAPP_f121055253e_bool @ collec1735317154_state @ A ) ) @ ( hAPP_f121055253e_bool @ collec1735317154_state @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).

thf(58,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_449_inf__sup__ord_I4_J) ).

thf(1003,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(801,axiom,
    ! [A: fun_fu689207471l_bool,B: fun_Ho1695028467e_bool,C: hoare_1875481847_state] :
      ( ( hAPP_H1173941847e_bool @ ( hAPP_f169892419e_bool @ ( cOMBB_1380679615_state @ A ) @ B ) @ C )
      = ( hAPP_f1408815105l_bool @ A @ ( hAPP_H117293375e_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Otriple_I) ).

thf(3737,plain,
    ! [A: fun_fu689207471l_bool,B: fun_Ho1695028467e_bool,C: hoare_1875481847_state] :
      ( ( hAPP_H1173941847e_bool @ ( hAPP_f169892419e_bool @ ( cOMBB_1380679615_state @ A ) @ B ) @ C )
      = ( hAPP_f1408815105l_bool @ A @ ( hAPP_H117293375e_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).

thf(267,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_fu689207471l_bool] :
      ( ( hAPP_f900945761l_bool @ ( hAPP_f872497439l_bool @ insert504309043e_bool @ A ) @ B )
      = ( hAPP_f900945761l_bool @ collec771609166e_bool @ ( hAPP_f900945761l_bool @ ( hAPP_f2051813877l_bool @ cOMBS_1451994324l_bool @ ( hAPP_f440042033l_bool @ ( cOMBB_532710323e_bool @ fdisj ) @ ( hAPP_f1873026899l_bool @ ( hAPP_f2051277573l_bool @ cOMBC_195806106l_bool @ fequal259518520e_bool ) @ A ) ) ) @ ( hAPP_f900945761l_bool @ ( hAPP_f1846363427l_bool @ cOMBC_1909905718l_bool @ member1062536460e_bool ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_insert__compr) ).

thf(1770,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_fu689207471l_bool] :
      ( ( hAPP_f900945761l_bool @ ( hAPP_f872497439l_bool @ insert504309043e_bool @ A ) @ B )
      = ( hAPP_f900945761l_bool @ collec771609166e_bool @ ( hAPP_f900945761l_bool @ ( hAPP_f2051813877l_bool @ cOMBS_1451994324l_bool @ ( hAPP_f440042033l_bool @ ( cOMBB_532710323e_bool @ fdisj ) @ ( hAPP_f1873026899l_bool @ ( hAPP_f2051277573l_bool @ cOMBC_195806106l_bool @ fequal259518520e_bool ) @ A ) ) ) @ ( hAPP_f900945761l_bool @ ( hAPP_f1846363427l_bool @ cOMBC_1909905718l_bool @ member1062536460e_bool ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(439,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] : ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_450_inf__sup__ord_I4_J) ).

thf(2397,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] : ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).

thf(741,axiom,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ B ) ) @ C )
      = ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_Un__insert__left) ).

thf(3507,plain,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ B ) ) @ C )
      = ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).

thf(73,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_fu689207471l_bool] :
      ( ( hAPP_f900945761l_bool @ ( hAPP_f872497439l_bool @ insert504309043e_bool @ A ) @ B )
      = ( hAPP_f900945761l_bool @ ( hAPP_f19215249l_bool @ semila1703230395l_bool @ ( hAPP_f900945761l_bool @ collec771609166e_bool @ ( hAPP_f1873026899l_bool @ ( hAPP_f2051277573l_bool @ cOMBC_195806106l_bool @ fequal259518520e_bool ) @ A ) ) ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_insert__def) ).

thf(1070,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_fu689207471l_bool] :
      ( ( hAPP_f900945761l_bool @ ( hAPP_f872497439l_bool @ insert504309043e_bool @ A ) @ B )
      = ( hAPP_f900945761l_bool @ ( hAPP_f19215249l_bool @ semila1703230395l_bool @ ( hAPP_f900945761l_bool @ collec771609166e_bool @ ( hAPP_f1873026899l_bool @ ( hAPP_f2051277573l_bool @ cOMBC_195806106l_bool @ fequal259518520e_bool ) @ A ) ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(634,axiom,
    ! [A: fun_Ho1996104121e_bool] :
      ( ( A != bot_bo1715400655e_bool )
    <=> ? [B: hoare_1875481847_state,C: fun_Ho1996104121e_bool] :
          ( ( A
            = ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ C ) )
          & ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_nonempty__iff) ).

thf(3112,plain,
    ! [A: fun_Ho1996104121e_bool] :
      ( ( ( A != bot_bo1715400655e_bool )
       => ? [B: hoare_1875481847_state,C: fun_Ho1996104121e_bool] :
            ( ( A
              = ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ C ) )
            & ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ C ) ) ) )
      & ( ? [B: hoare_1875481847_state,C: fun_Ho1996104121e_bool] :
            ( ( A
              = ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ C ) )
            & ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ C ) ) )
       => ( A != bot_bo1715400655e_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).

thf(22,axiom,
    ! [A: bool,B: hoare_1875481847_state] :
      ( ( hAPP_H1173941847e_bool @ ( cOMBK_2086958736_state @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Hoare____Mirabelle____xlrqixeqwe__) ).

thf(872,plain,
    ! [A: bool,B: hoare_1875481847_state] :
      ( ( hAPP_H1173941847e_bool @ ( cOMBK_2086958736_state @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(723,axiom,
    ! [A: com,B: state,C: com,D: state,E: state] :
      ( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ ( evalc @ C ) @ D ) @ E ) )
     => ( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ ( evalc @ A ) @ E ) @ B ) )
       => ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ ( evalc @ ( semi @ C @ A ) ) @ D ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_541_evalc_OSemi) ).

thf(3448,plain,
    ! [A: com,B: state,C: com,D: state,E: state] :
      ( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ ( evalc @ C ) @ D ) @ E ) )
     => ( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ ( evalc @ A ) @ E ) @ B ) )
       => ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ ( evalc @ ( semi @ C @ A ) ) @ D ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).

thf(174,axiom,
    ! [A: fun_fu689207471l_bool,B: fun_fu689207471l_bool] :
      ( ( hAPP_f900945761l_bool @ collec771609166e_bool @ ( hAPP_f900945761l_bool @ ( hAPP_f2051813877l_bool @ cOMBS_1451994324l_bool @ ( hAPP_f440042033l_bool @ ( cOMBB_532710323e_bool @ fconj ) @ A ) ) @ B ) )
      = ( hAPP_f900945761l_bool @ ( hAPP_f19215249l_bool @ semila1058800161l_bool @ ( hAPP_f900945761l_bool @ collec771609166e_bool @ A ) ) @ ( hAPP_f900945761l_bool @ collec771609166e_bool @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_585_Collect__conj__eq) ).

thf(1432,plain,
    ! [A: fun_fu689207471l_bool,B: fun_fu689207471l_bool] :
      ( ( hAPP_f900945761l_bool @ collec771609166e_bool @ ( hAPP_f900945761l_bool @ ( hAPP_f2051813877l_bool @ cOMBS_1451994324l_bool @ ( hAPP_f440042033l_bool @ ( cOMBB_532710323e_bool @ fconj ) @ A ) ) @ B ) )
      = ( hAPP_f900945761l_bool @ ( hAPP_f19215249l_bool @ semila1058800161l_bool @ ( hAPP_f900945761l_bool @ collec771609166e_bool @ A ) ) @ ( hAPP_f900945761l_bool @ collec771609166e_bool @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(796,axiom,
    ! [A: fun_Ho1996104121e_bool,B: hoare_1875481847_state] :
      ( ( ( hBOOL @ ( hAPP_H1173941847e_bool @ A @ B ) )
       => ( ( hAPP_f121055253e_bool @ collec1735317154_state @ ( hAPP_f121055253e_bool @ ( hAPP_f1300953505e_bool @ cOMBS_896408300l_bool @ ( hAPP_f932622461l_bool @ ( cOMBB_242064253_state @ fconj ) @ ( hAPP_H117293375e_bool @ ( hAPP_f2101312745e_bool @ cOMBC_1972244470e_bool @ fequal391417144_state ) @ B ) ) ) @ A ) )
          = ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ bot_bo1715400655e_bool ) ) )
      & ( ~ ( hBOOL @ ( hAPP_H1173941847e_bool @ A @ B ) )
       => ( ( hAPP_f121055253e_bool @ collec1735317154_state @ ( hAPP_f121055253e_bool @ ( hAPP_f1300953505e_bool @ cOMBS_896408300l_bool @ ( hAPP_f932622461l_bool @ ( cOMBB_242064253_state @ fconj ) @ ( hAPP_H117293375e_bool @ ( hAPP_f2101312745e_bool @ cOMBC_1972244470e_bool @ fequal391417144_state ) @ B ) ) ) @ A ) )
          = bot_bo1715400655e_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_Collect__conv__if) ).

thf(3722,plain,
    ! [A: fun_Ho1996104121e_bool,B: hoare_1875481847_state] :
      ( ( ( hBOOL @ ( hAPP_H1173941847e_bool @ A @ B ) )
       => ( ( hAPP_f121055253e_bool @ collec1735317154_state @ ( hAPP_f121055253e_bool @ ( hAPP_f1300953505e_bool @ cOMBS_896408300l_bool @ ( hAPP_f932622461l_bool @ ( cOMBB_242064253_state @ fconj ) @ ( hAPP_H117293375e_bool @ ( hAPP_f2101312745e_bool @ cOMBC_1972244470e_bool @ fequal391417144_state ) @ B ) ) ) @ A ) )
          = ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ bot_bo1715400655e_bool ) ) )
      & ( ~ ( hBOOL @ ( hAPP_H1173941847e_bool @ A @ B ) )
       => ( ( hAPP_f121055253e_bool @ collec1735317154_state @ ( hAPP_f121055253e_bool @ ( hAPP_f1300953505e_bool @ cOMBS_896408300l_bool @ ( hAPP_f932622461l_bool @ ( cOMBB_242064253_state @ fconj ) @ ( hAPP_H117293375e_bool @ ( hAPP_f2101312745e_bool @ cOMBC_1972244470e_bool @ fequal391417144_state ) @ B ) ) ) @ A ) )
          = bot_bo1715400655e_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).

thf(286,axiom,
    ! [A: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ A ) @ bot_bo844097828e_bool )
      = bot_bo844097828e_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_568_Int__empty__right) ).

thf(1830,plain,
    ! [A: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ A ) @ bot_bo844097828e_bool )
      = bot_bo844097828e_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(417,axiom,
    ! [A: hoare_1875481847_state,B: fun_pn664418900_state,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ B ) @ C ) ) )
     => ~ ! [D: pname] :
            ( ( A
              = ( hAPP_p702226982_state @ B @ D ) )
           => ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_imageE) ).

thf(2322,plain,
    ! [A: hoare_1875481847_state,B: fun_pn664418900_state,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ B ) @ C ) ) )
     => ~ ! [D: pname] :
            ( ( A
              = ( hAPP_p702226982_state @ B @ D ) )
           => ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

thf(217,axiom,
    ! [A: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ bot_bo844097828e_bool ) @ A )
      = bot_bo844097828e_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_659_inf__bot__left) ).

thf(1579,plain,
    ! [A: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ bot_bo844097828e_bool ) @ A )
      = bot_bo844097828e_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(512,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ! [D: fun_Ho1996104121e_bool,E: fun_Ho1996104121e_bool,F: fun_Ho1996104121e_bool] :
          ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ D ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ E ) @ F ) )
          = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ D ) @ E ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ D ) @ F ) ) )
     => ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ C ) )
        = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ B ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_675_distrib__imp2) ).

thf(2656,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ! [D: fun_Ho1996104121e_bool,E: fun_Ho1996104121e_bool,F: fun_Ho1996104121e_bool] :
          ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ D ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ E ) @ F ) )
          = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ D ) @ E ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ D ) @ F ) ) )
     => ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ C ) )
        = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ B ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).

thf(607,axiom,
    ! [A: pname,B: fun_pname_option_com] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( dom_pname_com @ B ) ) )
     => ? [C: com] :
          ( ( hAPP_p799580910on_com @ B @ A )
          = ( some_com @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_domD) ).

thf(3019,plain,
    ! [A: pname,B: fun_pname_option_com] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( dom_pname_com @ B ) ) )
     => ? [C: com] :
          ( ( hAPP_p799580910on_com @ B @ A )
          = ( some_com @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).

thf(532,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ A ) @ B ) )
      | ( hBOOL @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_2_1_U) ).

thf(2747,plain,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ A ) @ B ) )
      | ( hBOOL @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).

thf(273,axiom,
    ! [A: fun_fu93307442l_bool,B: fun_st1506752259e_bool,C: state] :
      ( ( hAPP_state_bool @ ( hAPP_f1012183542e_bool @ ( cOMBB_1911358915_state @ A ) @ B ) @ C )
      = ( hAPP_f327114704l_bool @ A @ ( hAPP_s1806633685e_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc__HOL__O) ).

thf(1790,plain,
    ! [A: fun_fu93307442l_bool,B: fun_st1506752259e_bool,C: state] :
      ( ( hAPP_state_bool @ ( hAPP_f1012183542e_bool @ ( cOMBB_1911358915_state @ A ) @ B ) @ C )
      = ( hAPP_f327114704l_bool @ A @ ( hAPP_s1806633685e_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(252,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ! [C: pname] :
          ( ( hBOOL @ ( hAPP_pname_bool @ B @ C ) )
         => ( hBOOL @ ( hAPP_pname_bool @ A @ C ) ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f759274231e_bool @ collect_pname @ B ) ) @ ( hAPP_f759274231e_bool @ collect_pname @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_522_Collect__mono) ).

thf(1716,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ! [C: pname] :
          ( ( hBOOL @ ( hAPP_pname_bool @ B @ C ) )
         => ( hBOOL @ ( hAPP_pname_bool @ A @ C ) ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f759274231e_bool @ collect_pname @ B ) ) @ ( hAPP_f759274231e_bool @ collect_pname @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(391,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho784854669_state,D: fun_fu385705929_state] :
      ( ( hBOOL @ ( finite1514162941_state @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ B ) )
       => ( ( A != bot_bo1715400655e_bool )
         => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
           => ( ( hAPP_H350317809_state @ ( hAPP_H743221337_state @ C @ ( hAPP_f890249627_state @ D @ A ) ) @ ( hAPP_f890249627_state @ D @ B ) )
              = ( hAPP_f890249627_state @ D @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_468_folding__one__idem_Osubset__idem) ).

thf(2224,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho784854669_state,D: fun_fu385705929_state] :
      ( ( hBOOL @ ( finite1514162941_state @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ B ) )
       => ( ( A != bot_bo1715400655e_bool )
         => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
           => ( ( hAPP_H350317809_state @ ( hAPP_H743221337_state @ C @ ( hAPP_f890249627_state @ D @ A ) ) @ ( hAPP_f890249627_state @ D @ B ) )
              = ( hAPP_f890249627_state @ D @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(453,axiom,
    ! [A: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ bot_bo1715400655e_bool )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_458_sup__bot__right) ).

thf(2454,plain,
    ! [A: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ bot_bo1715400655e_bool )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).

thf(139,axiom,
    ! [A: fun_st1506752259e_bool,B: com,C: fun_st1506752259e_bool,D: fun_st1506752259e_bool,E: com,F: fun_st1506752259e_bool] :
      ( ( ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ A ) @ B ) @ C )
        = ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ D ) @ E ) @ F ) )
    <=> ( ( A = D )
        & ( B = E )
        & ( C = F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_triple_Oinject) ).

thf(1300,plain,
    ! [A: fun_st1506752259e_bool,B: com,C: fun_st1506752259e_bool,D: fun_st1506752259e_bool,E: com,F: fun_st1506752259e_bool] :
      ( ( ( ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ A ) @ B ) @ C )
          = ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ D ) @ E ) @ F ) )
       => ( ( A = D )
          & ( B = E )
          & ( C = F ) ) )
      & ( ( ( A = D )
          & ( B = E )
          & ( C = F ) )
       => ( ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ A ) @ B ) @ C )
          = ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ D ) @ E ) @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(789,axiom,
    ! [A: com] :
      ( ( hBOOL @ hoare_1239590103gleton )
     => ( ( hBOOL @ wT_bodies )
       => ( ( hBOOL @ ( hAPP_com_bool @ wt @ A ) )
         => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ bot_bo1715400655e_bool ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_c406083500_state @ hoare_Mirabelle_MGT @ A ) ) @ bot_bo1715400655e_bool ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_MGF) ).

thf(3691,plain,
    ! [A: com] :
      ( ( hBOOL @ hoare_1239590103gleton )
     => ( ( hBOOL @ wT_bodies )
       => ( ( hBOOL @ ( hAPP_com_bool @ wt @ A ) )
         => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ bot_bo1715400655e_bool ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_c406083500_state @ hoare_Mirabelle_MGT @ A ) ) @ bot_bo1715400655e_bool ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).

thf(104,axiom,
    ! [A: pname,B: fun_pname_bool] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_insertI1) ).

thf(1188,plain,
    ! [A: pname,B: fun_pname_bool] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(522,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_pn664418900_state,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ B ) @ C ) ) )
    <=> ? [D: fun_pname_bool] :
          ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ D ) @ C ) )
          & ( A
            = ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_subset__image__iff) ).

thf(2700,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_pn664418900_state,C: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ B ) @ C ) ) )
       => ? [D: fun_pname_bool] :
            ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ D ) @ C ) )
            & ( A
              = ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ B ) @ D ) ) ) )
      & ( ? [D: fun_pname_bool] :
            ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ D ) @ C ) )
            & ( A
              = ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ B ) @ D ) ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ B ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).

thf(128,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ A ) @ B )
      = ( hAPP_f759274231e_bool @ collect_pname @ ( hAPP_f759274231e_bool @ ( hAPP_f649174806e_bool @ cOMBS_568398431l_bool @ ( hAPP_f1402196763l_bool @ ( cOMBB_675860798_pname @ fconj ) @ ( hAPP_f759274231e_bool @ ( hAPP_f661147897e_bool @ cOMBC_1058051404l_bool @ member_pname ) @ A ) ) ) @ ( hAPP_f759274231e_bool @ ( hAPP_f661147897e_bool @ cOMBC_1058051404l_bool @ member_pname ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_572_Int__def) ).

thf(1262,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ A ) @ B )
      = ( hAPP_f759274231e_bool @ collect_pname @ ( hAPP_f759274231e_bool @ ( hAPP_f649174806e_bool @ cOMBS_568398431l_bool @ ( hAPP_f1402196763l_bool @ ( cOMBB_675860798_pname @ fconj ) @ ( hAPP_f759274231e_bool @ ( hAPP_f661147897e_bool @ cOMBC_1058051404l_bool @ member_pname ) @ A ) ) ) @ ( hAPP_f759274231e_bool @ ( hAPP_f661147897e_bool @ cOMBC_1058051404l_bool @ member_pname ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(120,axiom,
    ! [A: fun_fu2104550360e_bool,B: fun_st858662806e_bool,C: state] :
      ( ( hAPP_s1806633685e_bool @ ( hAPP_f1935169308e_bool @ ( cOMBB_1036740637_state @ A ) @ B ) @ C )
      = ( hAPP_f1012183542e_bool @ A @ ( hAPP_s336103912e_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__Com__Ostate_Mtc__) ).

thf(1235,plain,
    ! [A: fun_fu2104550360e_bool,B: fun_st858662806e_bool,C: state] :
      ( ( hAPP_s1806633685e_bool @ ( hAPP_f1935169308e_bool @ ( cOMBB_1036740637_state @ A ) @ B ) @ C )
      = ( hAPP_f1012183542e_bool @ A @ ( hAPP_s336103912e_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(405,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ C ) )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ B ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_596_Int__Un__distrib) ).

thf(2276,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ C ) )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ B ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(326,axiom,
    ! [A: fun_pn664418900_state,B: fun_Ho1996104121e_bool,C: fun_pname_bool] :
      ( ! [D: pname] :
          ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ C ) )
         => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ ( hAPP_p702226982_state @ A @ D ) ) @ B ) ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ A ) @ C ) ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_image__subsetI) ).

thf(1980,plain,
    ! [A: fun_pn664418900_state,B: fun_Ho1996104121e_bool,C: fun_pname_bool] :
      ( ! [D: pname] :
          ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ C ) )
         => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ ( hAPP_p702226982_state @ A @ D ) ) @ B ) ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ A ) @ C ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(364,axiom,
    ! [A: fun_pname_bool] :
      ( ( bot_bo844097828e_bool
        = ( hAPP_f759274231e_bool @ collect_pname @ A ) )
    <=> ! [B: pname] :
          ~ ( hBOOL @ ( hAPP_pname_bool @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_empty__Collect__eq) ).

thf(2128,plain,
    ! [A: fun_pname_bool] :
      ( ( ( bot_bo844097828e_bool
          = ( hAPP_f759274231e_bool @ collect_pname @ A ) )
       => ! [B: pname] :
            ~ ( hBOOL @ ( hAPP_pname_bool @ A @ B ) ) )
      & ( ! [B: pname] :
            ~ ( hBOOL @ ( hAPP_pname_bool @ A @ B ) )
       => ( bot_bo844097828e_bool
          = ( hAPP_f759274231e_bool @ collect_pname @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(46,axiom,
    ! [A: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ bot_bo844097828e_bool ) )
    <=> ( A = bot_bo844097828e_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_363_bot__unique) ).

thf(951,plain,
    ! [A: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ bot_bo844097828e_bool ) )
       => ( A = bot_bo844097828e_bool ) )
      & ( ( A = bot_bo844097828e_bool )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ bot_bo844097828e_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(479,axiom,
    ! [A: fun_fu689207471l_bool,B: fun_Ho1996104121e_bool] :
      ( ( ( hBOOL @ ( hAPP_f1408815105l_bool @ A @ B ) )
       => ( ( hAPP_f900945761l_bool @ collec771609166e_bool @ ( hAPP_f900945761l_bool @ ( hAPP_f2051813877l_bool @ cOMBS_1451994324l_bool @ ( hAPP_f440042033l_bool @ ( cOMBB_532710323e_bool @ fconj ) @ ( hAPP_f1873026899l_bool @ ( hAPP_f2051277573l_bool @ cOMBC_195806106l_bool @ fequal259518520e_bool ) @ B ) ) ) @ A ) )
          = ( hAPP_f900945761l_bool @ ( hAPP_f872497439l_bool @ insert504309043e_bool @ B ) @ bot_bo973479705l_bool ) ) )
      & ( ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ A @ B ) )
       => ( ( hAPP_f900945761l_bool @ collec771609166e_bool @ ( hAPP_f900945761l_bool @ ( hAPP_f2051813877l_bool @ cOMBS_1451994324l_bool @ ( hAPP_f440042033l_bool @ ( cOMBB_532710323e_bool @ fconj ) @ ( hAPP_f1873026899l_bool @ ( hAPP_f2051277573l_bool @ cOMBC_195806106l_bool @ fequal259518520e_bool ) @ B ) ) ) @ A ) )
          = bot_bo973479705l_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_Collect__conv__if) ).

thf(2545,plain,
    ! [A: fun_fu689207471l_bool,B: fun_Ho1996104121e_bool] :
      ( ( ( hBOOL @ ( hAPP_f1408815105l_bool @ A @ B ) )
       => ( ( hAPP_f900945761l_bool @ collec771609166e_bool @ ( hAPP_f900945761l_bool @ ( hAPP_f2051813877l_bool @ cOMBS_1451994324l_bool @ ( hAPP_f440042033l_bool @ ( cOMBB_532710323e_bool @ fconj ) @ ( hAPP_f1873026899l_bool @ ( hAPP_f2051277573l_bool @ cOMBC_195806106l_bool @ fequal259518520e_bool ) @ B ) ) ) @ A ) )
          = ( hAPP_f900945761l_bool @ ( hAPP_f872497439l_bool @ insert504309043e_bool @ B ) @ bot_bo973479705l_bool ) ) )
      & ( ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ A @ B ) )
       => ( ( hAPP_f900945761l_bool @ collec771609166e_bool @ ( hAPP_f900945761l_bool @ ( hAPP_f2051813877l_bool @ cOMBS_1451994324l_bool @ ( hAPP_f440042033l_bool @ ( cOMBB_532710323e_bool @ fconj ) @ ( hAPP_f1873026899l_bool @ ( hAPP_f2051277573l_bool @ cOMBC_195806106l_bool @ fequal259518520e_bool ) @ B ) ) ) @ A ) )
          = bot_bo973479705l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).

thf(699,axiom,
    ! [A: fun_Ho1653816318_pname,B: hoare_1875481847_state,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ C ) )
     => ( ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ ( hAPP_H139064010_pname @ A @ B ) ) @ ( hAPP_f1148778334e_bool @ ( image_720060442_pname @ A ) @ C ) )
        = ( hAPP_f1148778334e_bool @ ( image_720060442_pname @ A ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_insert__image) ).

thf(3359,plain,
    ! [A: fun_Ho1653816318_pname,B: hoare_1875481847_state,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ C ) )
     => ( ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ ( hAPP_H139064010_pname @ A @ B ) ) @ ( hAPP_f1148778334e_bool @ ( image_720060442_pname @ A ) @ C ) )
        = ( hAPP_f1148778334e_bool @ ( image_720060442_pname @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).

thf(691,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_340_order__trans) ).

thf(3329,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).

thf(342,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ B ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ minus_589155914e_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_691_finite__Diff) ).

thf(2044,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ B ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ minus_589155914e_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(114,axiom,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ B ) ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_insert__mono) ).

thf(1218,plain,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ B ) ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(627,axiom,
    ~ ( hBOOL @ fFalse ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).

thf(3095,plain,
    ~ ( hBOOL @ fFalse ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).

thf(458,axiom,
    ! [A: fun_state_bool,B: com] :
      ( ( hBOOL @ ( hAPP_com_bool @ wt @ B ) )
     => ( hBOOL @ ( hAPP_com_bool @ wt @ ( while @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_501_While) ).

thf(2468,plain,
    ! [A: fun_state_bool,B: com] :
      ( ( hBOOL @ ( hAPP_com_bool @ wt @ B ) )
     => ( hBOOL @ ( hAPP_com_bool @ wt @ ( while @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).

thf(115,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
     => ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ B ) @ A )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_641_inf__absorb2) ).

thf(1220,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
     => ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ B ) @ A )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(345,axiom,
    ! [A: fun_Ho1653816318_pname] :
      ( ( hAPP_f1148778334e_bool @ ( image_720060442_pname @ A ) @ bot_bo1715400655e_bool )
      = bot_bo844097828e_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_image__empty) ).

thf(2056,plain,
    ! [A: fun_Ho1653816318_pname] :
      ( ( hAPP_f1148778334e_bool @ ( image_720060442_pname @ A ) @ bot_bo1715400655e_bool )
      = bot_bo844097828e_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(735,axiom,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ B ) )
      = ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_insert__absorb2) ).

thf(3488,plain,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ B ) )
      = ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).

thf(64,axiom,
    ! [A: fun_Ho1695028467e_bool,B: fun_Ho1455141843_state,C: hoare_1875481847_state] :
      ( ( hAPP_H117293375e_bool @ ( hAPP_f474907569e_bool @ ( cOMBB_1903241981_state @ A ) @ B ) @ C )
      = ( hAPP_H117293375e_bool @ A @ ( hAPP_H350317809_state @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc__Com___237) ).

thf(1023,plain,
    ! [A: fun_Ho1695028467e_bool,B: fun_Ho1455141843_state,C: hoare_1875481847_state] :
      ( ( hAPP_H117293375e_bool @ ( hAPP_f474907569e_bool @ ( cOMBB_1903241981_state @ A ) @ B ) @ C )
      = ( hAPP_H117293375e_bool @ A @ ( hAPP_H350317809_state @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(20,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
     => ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ A ) @ B )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_639_inf__absorb1) ).

thf(864,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
     => ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ A ) @ B )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(242,axiom,
    ! [A: fun_pname_bool] :
      ( ! [B: pname] :
          ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ A ) )
    <=> ( A = bot_bo844097828e_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_all__not__in__conv) ).

thf(1670,plain,
    ! [A: fun_pname_bool] :
      ( ( ! [B: pname] :
            ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ A ) )
       => ( A = bot_bo844097828e_bool ) )
      & ( ( A = bot_bo844097828e_bool )
       => ! [B: pname] :
            ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(586,axiom,
    ! [A: fun_fu689207471l_bool,B: fun_fu947547457e_bool,C: fun_fu1163781179e_bool] :
      ( ( hBOOL @ ( finite792754358e_bool @ B @ C ) )
     => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ A ) )
       => ( ( A != bot_bo973479705l_bool )
         => ( ! [D: fun_Ho1996104121e_bool,E: fun_Ho1996104121e_bool] : ( hBOOL @ ( hAPP_f1699935247l_bool @ ( hAPP_f640685261l_bool @ member1062536460e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ B @ D ) @ E ) ) @ ( hAPP_f900945761l_bool @ ( hAPP_f872497439l_bool @ insert504309043e_bool @ D ) @ ( hAPP_f900945761l_bool @ ( hAPP_f872497439l_bool @ insert504309043e_bool @ E ) @ bot_bo973479705l_bool ) ) ) )
           => ( hBOOL @ ( hAPP_f1699935247l_bool @ ( hAPP_f640685261l_bool @ member1062536460e_bool @ ( hAPP_f962122119e_bool @ C @ A ) ) @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_518_folding__one_Oclosed) ).

thf(2949,plain,
    ! [A: fun_fu689207471l_bool,B: fun_fu947547457e_bool,C: fun_fu1163781179e_bool] :
      ( ( hBOOL @ ( finite792754358e_bool @ B @ C ) )
     => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ A ) )
       => ( ( A != bot_bo973479705l_bool )
         => ( ! [D: fun_Ho1996104121e_bool,E: fun_Ho1996104121e_bool] : ( hBOOL @ ( hAPP_f1699935247l_bool @ ( hAPP_f640685261l_bool @ member1062536460e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ B @ D ) @ E ) ) @ ( hAPP_f900945761l_bool @ ( hAPP_f872497439l_bool @ insert504309043e_bool @ D ) @ ( hAPP_f900945761l_bool @ ( hAPP_f872497439l_bool @ insert504309043e_bool @ E ) @ bot_bo973479705l_bool ) ) ) )
           => ( hBOOL @ ( hAPP_f1699935247l_bool @ ( hAPP_f640685261l_bool @ member1062536460e_bool @ ( hAPP_f962122119e_bool @ C @ A ) ) @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).

thf(710,axiom,
    ! [A: fun_pname_bool,B: hoare_1875481847_state,C: fun_pn664418900_state,D: pname] :
      ( ( B
        = ( hAPP_p702226982_state @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ A ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ C ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_image__eqI) ).

thf(3398,plain,
    ! [A: fun_pname_bool,B: hoare_1875481847_state,C: fun_pn664418900_state,D: pname] :
      ( ( B
        = ( hAPP_p702226982_state @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ A ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ C ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).

thf(291,axiom,
    ! [A: fun_pname_bool,B: pname] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ bot_bo844097828e_bool ) ) )
     => ( ( A = bot_bo844097828e_bool )
        | ( A
          = ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ bot_bo844097828e_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_subset__singletonD) ).

thf(1849,plain,
    ! [A: fun_pname_bool,B: pname] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ bot_bo844097828e_bool ) ) )
     => ( ( A = bot_bo844097828e_bool )
        | ( A
          = ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ bot_bo844097828e_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(780,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ B )
      | ~ ( hBOOL @ A )
      | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_1_1_U) ).

thf(3652,plain,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ B )
      | ~ ( hBOOL @ A )
      | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).

thf(478,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_390430481_state @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_386_hoare__sound) ).

thf(2543,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_390430481_state @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).

thf(698,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_419_sup__left__idem) ).

thf(3356,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).

thf(406,axiom,
    ! [A: fun_pn664418900_state,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ A ) @ B ) ) @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_image__mono) ).

thf(2279,plain,
    ! [A: fun_pn664418900_state,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ A ) @ B ) ) @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).

thf(428,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_fu689207471l_bool] :
      ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ ( hAPP_f900945761l_bool @ ( hAPP_f872497439l_bool @ insert504309043e_bool @ A ) @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_finite__insert) ).

thf(2357,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_fu689207471l_bool] :
      ( ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ ( hAPP_f900945761l_bool @ ( hAPP_f872497439l_bool @ insert504309043e_bool @ A ) @ B ) ) )
       => ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ B ) )
       => ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ ( hAPP_f900945761l_bool @ ( hAPP_f872497439l_bool @ insert504309043e_bool @ A ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).

thf(18,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_451_sup__ge1) ).

thf(859,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(681,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1795624711e_bool @ cOMBC_1099403170l_bool @ member618553700_state ) @ A ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1795624711e_bool @ cOMBC_1099403170l_bool @ member618553700_state ) @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_396_pred__subset__eq) ).

thf(3288,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1795624711e_bool @ cOMBC_1099403170l_bool @ member618553700_state ) @ A ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1795624711e_bool @ cOMBC_1099403170l_bool @ member618553700_state ) @ B ) ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1795624711e_bool @ cOMBC_1099403170l_bool @ member618553700_state ) @ A ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1795624711e_bool @ cOMBC_1099403170l_bool @ member618553700_state ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).

thf(122,axiom,
    ! [A: fun_pn92346699_state,B: fun_pname_com,C: pname] :
      ( ( hAPP_p1985340144_state @ ( hAPP_f2116202538_state @ ( hAPP_f1339343196_state @ cOMBS_1674056844_state @ A ) @ B ) @ C )
      = ( hAPP_c681126378_state @ ( hAPP_p2012996835_state @ A @ C ) @ ( hAPP_pname_com @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__Com__Ocom_000tc__fun_Itc__fun_Itc) ).

thf(1240,plain,
    ! [A: fun_pn92346699_state,B: fun_pname_com,C: pname] :
      ( ( hAPP_p1985340144_state @ ( hAPP_f2116202538_state @ ( hAPP_f1339343196_state @ cOMBS_1674056844_state @ A ) @ B ) @ C )
      = ( hAPP_c681126378_state @ ( hAPP_p2012996835_state @ A @ C ) @ ( hAPP_pname_com @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(228,axiom,
    ! [A: fun_pname_bool] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ bot_bo844097828e_bool ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_empty__subsetI) ).

thf(1617,plain,
    ! [A: fun_pname_bool] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ bot_bo844097828e_bool ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(733,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( B = C )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_349_xt1_I3_J) ).

thf(3478,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( B = C )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).

thf(720,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( A = B )
    <=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
        & ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_356_order__eq__iff) ).

thf(3433,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( ( A = B )
       => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
          & ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
          & ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).

thf(462,axiom,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_rev__finite__subset) ).

thf(2479,plain,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).

thf(354,axiom,
    ! [A: pname,B: fun_Ho1996104121e_bool] :
      ( ( ( B = bot_bo1715400655e_bool )
       => ( ( hAPP_f1148778334e_bool @ ( image_720060442_pname @ ( cOMBK_1595564845_state @ A ) ) @ B )
          = bot_bo844097828e_bool ) )
      & ( ( B != bot_bo1715400655e_bool )
       => ( ( hAPP_f1148778334e_bool @ ( image_720060442_pname @ ( cOMBK_1595564845_state @ A ) ) @ B )
          = ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ bot_bo844097828e_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_image__constant__conv) ).

thf(2088,plain,
    ! [A: pname,B: fun_Ho1996104121e_bool] :
      ( ( ( B = bot_bo1715400655e_bool )
       => ( ( hAPP_f1148778334e_bool @ ( image_720060442_pname @ ( cOMBK_1595564845_state @ A ) ) @ B )
          = bot_bo844097828e_bool ) )
      & ( ( B != bot_bo1715400655e_bool )
       => ( ( hAPP_f1148778334e_bool @ ( image_720060442_pname @ ( cOMBK_1595564845_state @ A ) ) @ B )
          = ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ bot_bo844097828e_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(591,axiom,
    ! [A: fun_Ho1996104121e_bool,B: hoare_1875481847_state] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ bot_bo1715400655e_bool ) ) )
     => ( ( A = bot_bo1715400655e_bool )
        | ( A
          = ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ bot_bo1715400655e_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_subset__singletonD) ).

thf(2960,plain,
    ! [A: fun_Ho1996104121e_bool,B: hoare_1875481847_state] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ bot_bo1715400655e_bool ) ) )
     => ( ( A = bot_bo1715400655e_bool )
        | ( A
          = ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ bot_bo1715400655e_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).

thf(98,axiom,
    ! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ A ) )
       => ( ( ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ C )
            = ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ A ) )
        <=> ( C = A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_insert__ident) ).

thf(1157,plain,
    ! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ A ) )
       => ( ( ( ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ C )
              = ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ A ) )
           => ( C = A ) )
          & ( ( C = A )
           => ( ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ C )
              = ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(749,axiom,
    ! [A: fun_pname_option_com,B: pname,C: com] :
      ( ( ( hAPP_p799580910on_com @ A @ B )
        = ( some_com @ C ) )
     => ( ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ ( dom_pname_com @ A ) )
        = ( dom_pname_com @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_insert__dom) ).

thf(3533,plain,
    ! [A: fun_pname_option_com,B: pname,C: com] :
      ( ( ( hAPP_p799580910on_com @ A @ B )
        = ( some_com @ C ) )
     => ( ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ ( dom_pname_com @ A ) )
        = ( dom_pname_com @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).

thf(414,axiom,
    ! [A: pname,B: fun_Ho1653816318_pname,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( hAPP_f1148778334e_bool @ ( image_720060442_pname @ B ) @ C ) ) )
     => ~ ! [D: hoare_1875481847_state] :
            ( ( A
              = ( hAPP_H139064010_pname @ B @ D ) )
           => ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ D ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_imageE) ).

thf(2310,plain,
    ! [A: pname,B: fun_Ho1653816318_pname,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( hAPP_f1148778334e_bool @ ( image_720060442_pname @ B ) @ C ) ) )
     => ~ ! [D: hoare_1875481847_state] :
            ( ( A
              = ( hAPP_H139064010_pname @ B @ D ) )
           => ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ D ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).

thf(168,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ! [C: pname] : ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_pname_bool @ A @ C ) ) @ ( hAPP_pname_bool @ B @ C ) ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_400_le__funI) ).

thf(1412,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ! [C: pname] : ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_pname_bool @ A @ C ) ) @ ( hAPP_pname_bool @ B @ C ) ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(387,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ C ) )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_418_sup_Oleft__commute) ).

thf(2215,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ C ) )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(498,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_fu1604182422_state,C: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ ( hAPP_f1440968210e_bool @ ( image_1943894628_state @ B ) @ C ) ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_finite__surj) ).

thf(2611,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_fu1604182422_state,C: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ ( hAPP_f1440968210e_bool @ ( image_1943894628_state @ B ) @ C ) ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).

thf(385,axiom,
    ! [A: fun_Ho1996104121e_bool,B: hoare_1875481847_state,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ C ) )
      = ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_Un__insert__right) ).

thf(2209,plain,
    ! [A: fun_Ho1996104121e_bool,B: hoare_1875481847_state,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ C ) )
      = ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(612,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
     => ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ B )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_604_Int__absorb2) ).

thf(3039,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
     => ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ B )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).

thf(333,axiom,
    ! [A: fun_pname_bool,B: fun_fu1430349052l_bool,C: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ A ) @ ( hAPP_f559147733l_bool @ ( hAPP_f230953622l_bool @ semila1130628874l_bool @ B ) @ ( hAPP_f559147733l_bool @ collec1974731493e_bool @ C ) ) ) )
    <=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ A ) @ B ) )
        & ( hBOOL @ ( hAPP_f1664156314l_bool @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_588_Int__Collect) ).

thf(1998,plain,
    ! [A: fun_pname_bool,B: fun_fu1430349052l_bool,C: fun_fu1430349052l_bool] :
      ( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ A ) @ ( hAPP_f559147733l_bool @ ( hAPP_f230953622l_bool @ semila1130628874l_bool @ B ) @ ( hAPP_f559147733l_bool @ collec1974731493e_bool @ C ) ) ) )
       => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ A ) @ B ) )
          & ( hBOOL @ ( hAPP_f1664156314l_bool @ C @ A ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ A ) @ B ) )
          & ( hBOOL @ ( hAPP_f1664156314l_bool @ C @ A ) ) )
       => ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ A ) @ ( hAPP_f559147733l_bool @ ( hAPP_f230953622l_bool @ semila1130628874l_bool @ B ) @ ( hAPP_f559147733l_bool @ collec1974731493e_bool @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(566,axiom,
    ! [A: fun_fu689207471l_bool,B: fun_Ho1996104121e_bool] :
      ( ( ( hBOOL @ ( hAPP_f1408815105l_bool @ A @ B ) )
       => ( ( hAPP_f900945761l_bool @ collec771609166e_bool @ ( hAPP_f900945761l_bool @ ( hAPP_f2051813877l_bool @ cOMBS_1451994324l_bool @ ( hAPP_f440042033l_bool @ ( cOMBB_532710323e_bool @ fconj ) @ ( hAPP_f1873026899l_bool @ fequal259518520e_bool @ B ) ) ) @ A ) )
          = ( hAPP_f900945761l_bool @ ( hAPP_f872497439l_bool @ insert504309043e_bool @ B ) @ bot_bo973479705l_bool ) ) )
      & ( ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ A @ B ) )
       => ( ( hAPP_f900945761l_bool @ collec771609166e_bool @ ( hAPP_f900945761l_bool @ ( hAPP_f2051813877l_bool @ cOMBS_1451994324l_bool @ ( hAPP_f440042033l_bool @ ( cOMBB_532710323e_bool @ fconj ) @ ( hAPP_f1873026899l_bool @ fequal259518520e_bool @ B ) ) ) @ A ) )
          = bot_bo973479705l_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_Collect__conv__if2) ).

thf(2875,plain,
    ! [A: fun_fu689207471l_bool,B: fun_Ho1996104121e_bool] :
      ( ( ( hBOOL @ ( hAPP_f1408815105l_bool @ A @ B ) )
       => ( ( hAPP_f900945761l_bool @ collec771609166e_bool @ ( hAPP_f900945761l_bool @ ( hAPP_f2051813877l_bool @ cOMBS_1451994324l_bool @ ( hAPP_f440042033l_bool @ ( cOMBB_532710323e_bool @ fconj ) @ ( hAPP_f1873026899l_bool @ fequal259518520e_bool @ B ) ) ) @ A ) )
          = ( hAPP_f900945761l_bool @ ( hAPP_f872497439l_bool @ insert504309043e_bool @ B ) @ bot_bo973479705l_bool ) ) )
      & ( ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ A @ B ) )
       => ( ( hAPP_f900945761l_bool @ collec771609166e_bool @ ( hAPP_f900945761l_bool @ ( hAPP_f2051813877l_bool @ cOMBS_1451994324l_bool @ ( hAPP_f440042033l_bool @ ( cOMBB_532710323e_bool @ fconj ) @ ( hAPP_f1873026899l_bool @ fequal259518520e_bool @ B ) ) ) @ A ) )
          = bot_bo973479705l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).

thf(315,axiom,
    ! [A: fun_fu689207471l_bool,B: fun_fu689207471l_bool,C: fun_fu689207471l_bool,D: fun_fu689207471l_bool] :
      ( ( hBOOL @ ( hAPP_f1699935247l_bool @ ( hAPP_f1970936639l_bool @ ord_le724727525l_bool @ C ) @ D ) )
     => ( ! [E: fun_Ho1996104121e_bool] :
            ( ( hBOOL @ ( hAPP_f1699935247l_bool @ ( hAPP_f640685261l_bool @ member1062536460e_bool @ E ) @ C ) )
           => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ B @ E ) )
             => ( hBOOL @ ( hAPP_f1408815105l_bool @ A @ E ) ) ) )
       => ( hBOOL @ ( hAPP_f1699935247l_bool @ ( hAPP_f1970936639l_bool @ ord_le724727525l_bool @ ( hAPP_f900945761l_bool @ ( hAPP_f19215249l_bool @ semila1058800161l_bool @ C ) @ ( hAPP_f900945761l_bool @ collec771609166e_bool @ B ) ) ) @ ( hAPP_f900945761l_bool @ ( hAPP_f19215249l_bool @ semila1058800161l_bool @ D ) @ ( hAPP_f900945761l_bool @ collec771609166e_bool @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_673_Int__Collect__mono) ).

thf(1940,plain,
    ! [A: fun_fu689207471l_bool,B: fun_fu689207471l_bool,C: fun_fu689207471l_bool,D: fun_fu689207471l_bool] :
      ( ( hBOOL @ ( hAPP_f1699935247l_bool @ ( hAPP_f1970936639l_bool @ ord_le724727525l_bool @ C ) @ D ) )
     => ( ! [E: fun_Ho1996104121e_bool] :
            ( ( hBOOL @ ( hAPP_f1699935247l_bool @ ( hAPP_f640685261l_bool @ member1062536460e_bool @ E ) @ C ) )
           => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ B @ E ) )
             => ( hBOOL @ ( hAPP_f1408815105l_bool @ A @ E ) ) ) )
       => ( hBOOL @ ( hAPP_f1699935247l_bool @ ( hAPP_f1970936639l_bool @ ord_le724727525l_bool @ ( hAPP_f900945761l_bool @ ( hAPP_f19215249l_bool @ semila1058800161l_bool @ C ) @ ( hAPP_f900945761l_bool @ collec771609166e_bool @ B ) ) ) @ ( hAPP_f900945761l_bool @ ( hAPP_f19215249l_bool @ semila1058800161l_bool @ D ) @ ( hAPP_f900945761l_bool @ collec771609166e_bool @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(679,axiom,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_subsetD) ).

thf(3284,plain,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).

thf(13,axiom,
    ! [A: fun_pname_bool,B: fun_pname_pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( hAPP_f759274231e_bool @ ( image_pname_pname @ B ) @ C ) ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_finite__surj) ).

thf(845,plain,
    ! [A: fun_pname_bool,B: fun_pname_pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( hAPP_f759274231e_bool @ ( image_pname_pname @ B ) @ C ) ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(725,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_subset__trans) ).

thf(3457,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).

thf(426,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ A ) @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T) ).

thf(2352,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ A ) @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).

thf(183,axiom,
    ! [A: fun_option_com_com,B: fun_pname_option_com,C: pname] :
      ( ( hAPP_pname_com @ ( hAPP_f96342628me_com @ ( cOMBB_923936821_pname @ A ) @ B ) @ C )
      = ( hAPP_option_com_com @ A @ ( hAPP_p799580910on_com @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Option__Ooption_Itc__Com__Ocom_J_000tc__Com__Ocom_00) ).

thf(1459,plain,
    ! [A: fun_option_com_com,B: fun_pname_option_com,C: pname] :
      ( ( hAPP_pname_com @ ( hAPP_f96342628me_com @ ( cOMBB_923936821_pname @ A ) @ B ) @ C )
      = ( hAPP_option_com_com @ A @ ( hAPP_p799580910on_com @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(626,axiom,
    ! [A: fun_bool_bool,B: fun_fu689207471l_bool,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f1408815105l_bool @ ( hAPP_f900945761l_bool @ ( cOMBB_469839573e_bool @ A ) @ B ) @ C )
      = ( hAPP_bool_bool @ A @ ( hAPP_f1408815105l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Hoare__) ).

thf(3092,plain,
    ! [A: fun_bool_bool,B: fun_fu689207471l_bool,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f1408815105l_bool @ ( hAPP_f900945761l_bool @ ( cOMBB_469839573e_bool @ A ) @ B ) @ C )
      = ( hAPP_bool_bool @ A @ ( hAPP_f1408815105l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).

thf(620,axiom,
    ! [A: fun_Ho1996104121e_bool,B: hoare_1875481847_state,C: fun_Ho1996104121e_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ C ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ A ) ) )
      <=> ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_subset__insert) ).

thf(3067,plain,
    ! [A: fun_Ho1996104121e_bool,B: hoare_1875481847_state,C: fun_Ho1996104121e_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ C ) )
     => ( ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ C ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ A ) ) )
         => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ C ) @ A ) ) )
        & ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ C ) @ A ) )
         => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ C ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).

thf(103,axiom,
    ! [A: fun_pname_bool] :
      ( ? [B: pname] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ A ) )
    <=> ( A != bot_bo844097828e_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_ex__in__conv) ).

thf(1180,plain,
    ! [A: fun_pname_bool] :
      ( ( ? [B: pname] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ A ) )
       => ( A != bot_bo844097828e_bool ) )
      & ( ( A != bot_bo844097828e_bool )
       => ? [B: pname] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(39,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool,D: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ D ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ C ) @ A ) ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ D ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_597_Int__mono) ).

thf(931,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool,D: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ D ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ C ) @ A ) ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ D ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(246,axiom,
    ! [A: fun_pname_bool] :
      ( ( hAPP_f559147733l_bool @ collec1974731493e_bool @ ( hAPP_f434788991l_bool @ ( hAPP_f1297925993l_bool @ cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ A ) )
      = ( hAPP_f559147733l_bool @ ( hAPP_f1320879424l_bool @ insert1325755072e_bool @ A ) @ bot_bo1649642514l_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_singleton__conv) ).

thf(1685,plain,
    ! [A: fun_pname_bool] :
      ( ( hAPP_f559147733l_bool @ collec1974731493e_bool @ ( hAPP_f434788991l_bool @ ( hAPP_f1297925993l_bool @ cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ A ) )
      = ( hAPP_f559147733l_bool @ ( hAPP_f1320879424l_bool @ insert1325755072e_bool @ A ) @ bot_bo1649642514l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(568,axiom,
    ! [A: state,B: fun_state_bool] :
      ( ~ ( hBOOL @ ( hAPP_f327114704l_bool @ fAll_state @ B ) )
      | ( hBOOL @ ( hAPP_state_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fAll_1_1_fAll_000tc__Com__Ostate_U) ).

thf(2885,plain,
    ! [A: state,B: fun_state_bool] :
      ( ~ ( hBOOL @ ( hAPP_f327114704l_bool @ fAll_state @ B ) )
      | ( hBOOL @ ( hAPP_state_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).

thf(600,axiom,
    ! [A: fun_pname_bool,B: fun_fu1430349052l_bool,C: fun_fu2101097872e_bool,D: fun_fu608906319e_bool] :
      ( ( hBOOL @ ( finite1268145088e_bool @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
       => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ A ) @ B ) )
         => ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ C @ A ) @ ( hAPP_f674760225e_bool @ D @ B ) )
            = ( hAPP_f674760225e_bool @ D @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_483_folding__one__idem_Oin__idem) ).

thf(2997,plain,
    ! [A: fun_pname_bool,B: fun_fu1430349052l_bool,C: fun_fu2101097872e_bool,D: fun_fu608906319e_bool] :
      ( ( hBOOL @ ( finite1268145088e_bool @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
       => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ A ) @ B ) )
         => ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ C @ A ) @ ( hAPP_f674760225e_bool @ D @ B ) )
            = ( hAPP_f674760225e_bool @ D @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).

thf(179,axiom,
    ! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_UnI1) ).

thf(1448,plain,
    ! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(378,axiom,
    ! [A: fun_fu237807729l_bool,B: fun_fu689207471l_bool,C: fun_fu689207471l_bool] :
      ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ ( hAPP_f1970936639l_bool @ ord_le724727525l_bool @ C ) @ B ) )
       => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ A @ bot_bo973479705l_bool ) )
         => ( ! [D: fun_Ho1996104121e_bool,E: fun_fu689207471l_bool] :
                ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ E ) )
               => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ ( hAPP_f640685261l_bool @ member1062536460e_bool @ D ) @ B ) )
                 => ( ~ ( hBOOL @ ( hAPP_f1699935247l_bool @ ( hAPP_f640685261l_bool @ member1062536460e_bool @ D ) @ E ) )
                   => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ A @ E ) )
                     => ( hBOOL @ ( hAPP_f1699935247l_bool @ A @ ( hAPP_f900945761l_bool @ ( hAPP_f872497439l_bool @ insert504309043e_bool @ D ) @ E ) ) ) ) ) ) )
           => ( hBOOL @ ( hAPP_f1699935247l_bool @ A @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_finite__subset__induct) ).

thf(2187,plain,
    ! [A: fun_fu237807729l_bool,B: fun_fu689207471l_bool,C: fun_fu689207471l_bool] :
      ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ ( hAPP_f1970936639l_bool @ ord_le724727525l_bool @ C ) @ B ) )
       => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ A @ bot_bo973479705l_bool ) )
         => ( ! [D: fun_Ho1996104121e_bool,E: fun_fu689207471l_bool] :
                ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ E ) )
               => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ ( hAPP_f640685261l_bool @ member1062536460e_bool @ D ) @ B ) )
                 => ( ~ ( hBOOL @ ( hAPP_f1699935247l_bool @ ( hAPP_f640685261l_bool @ member1062536460e_bool @ D ) @ E ) )
                   => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ A @ E ) )
                     => ( hBOOL @ ( hAPP_f1699935247l_bool @ A @ ( hAPP_f900945761l_bool @ ( hAPP_f872497439l_bool @ insert504309043e_bool @ D ) @ E ) ) ) ) ) ) )
           => ( hBOOL @ ( hAPP_f1699935247l_bool @ A @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

thf(60,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool,D: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ D ) )
     => ( ! [E: pname] :
            ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ E ) @ C ) )
           => ( ( hBOOL @ ( hAPP_pname_bool @ B @ E ) )
             => ( hBOOL @ ( hAPP_pname_bool @ A @ E ) ) ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ C ) @ ( hAPP_f759274231e_bool @ collect_pname @ B ) ) ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ D ) @ ( hAPP_f759274231e_bool @ collect_pname @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_670_Int__Collect__mono) ).

thf(1010,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool,D: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ D ) )
     => ( ! [E: pname] :
            ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ E ) @ C ) )
           => ( ( hBOOL @ ( hAPP_pname_bool @ B @ E ) )
             => ( hBOOL @ ( hAPP_pname_bool @ A @ E ) ) ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ C ) @ ( hAPP_f759274231e_bool @ collect_pname @ B ) ) ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ D ) @ ( hAPP_f759274231e_bool @ collect_pname @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(161,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ C ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_599_Int__greatest) ).

thf(1390,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ C ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(135,axiom,
    ! [A: pname,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_finite_OinsertI) ).

thf(1289,plain,
    ! [A: pname,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(618,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: hoare_1875481847_state] :
      ( ( hBOOL @ ( hAPP_H1173941847e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) @ C ) )
    <=> ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ semila1168014441p_bool @ ( hAPP_H1173941847e_bool @ A @ C ) ) @ ( hAPP_H1173941847e_bool @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_410_sup__apply) ).

thf(3056,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: hoare_1875481847_state] :
      ( ( ( hBOOL @ ( hAPP_H1173941847e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) @ C ) )
       => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ semila1168014441p_bool @ ( hAPP_H1173941847e_bool @ A @ C ) ) @ ( hAPP_H1173941847e_bool @ B @ C ) ) ) )
      & ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ semila1168014441p_bool @ ( hAPP_H1173941847e_bool @ A @ C ) ) @ ( hAPP_H1173941847e_bool @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_H1173941847e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).

thf(181,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pn1208287926_pname,D: fun_fu1499449723_pname] :
      ( ( hBOOL @ ( finite89670078_pname @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
       => ( ( B != bot_bo844097828e_bool )
         => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
           => ( ( A != bot_bo844097828e_bool )
             => ( ( hAPP_f1297739591_pname @ D @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ B ) @ A ) )
                = ( hAPP_pname_pname @ ( hAPP_p1170154830_pname @ C @ ( hAPP_f1297739591_pname @ D @ B ) ) @ ( hAPP_f1297739591_pname @ D @ A ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_463_folding__one__idem_Ounion__idem) ).

thf(1453,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pn1208287926_pname,D: fun_fu1499449723_pname] :
      ( ( hBOOL @ ( finite89670078_pname @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
       => ( ( B != bot_bo844097828e_bool )
         => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
           => ( ( A != bot_bo844097828e_bool )
             => ( ( hAPP_f1297739591_pname @ D @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ B ) @ A ) )
                = ( hAPP_pname_pname @ ( hAPP_p1170154830_pname @ C @ ( hAPP_f1297739591_pname @ D @ B ) ) @ ( hAPP_f1297739591_pname @ D @ A ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(258,axiom,
    ! [A: fun_fu1430349052l_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( ( B != bot_bo844097828e_bool )
       => ( ! [C: pname] : ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ C ) @ bot_bo844097828e_bool ) ) )
         => ( ! [C: pname,D: fun_pname_bool] :
                ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ D ) )
               => ( ( D != bot_bo844097828e_bool )
                 => ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ D ) )
                   => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ D ) )
                     => ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ C ) @ D ) ) ) ) ) ) )
           => ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_474_finite__ne__induct) ).

thf(1734,plain,
    ! [A: fun_fu1430349052l_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( ( B != bot_bo844097828e_bool )
       => ( ! [C: pname] : ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ C ) @ bot_bo844097828e_bool ) ) )
         => ( ! [C: pname,D: fun_pname_bool] :
                ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ D ) )
               => ( ( D != bot_bo844097828e_bool )
                 => ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ D ) )
                   => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ D ) )
                     => ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ C ) @ D ) ) ) ) ) ) )
           => ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(575,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( ( B = A )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_344_xt1_I4_J) ).

thf(2907,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( ( B = A )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).

thf(729,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_weaken) ).

thf(3465,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).

thf(797,axiom,
    hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ bot_bo973479705l_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_finite_OemptyI) ).

thf(3729,plain,
    hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ bot_bo973479705l_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).

thf(48,axiom,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_pname_bool @ B @ A ) ) @ ( hAPP_pname_bool @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_367_le__funE) ).

thf(961,plain,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_pname_bool @ B @ A ) ) @ ( hAPP_pname_bool @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(236,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ A ) @ B )
        = bot_bo844097828e_bool )
    <=> ! [C: pname] :
          ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ A ) )
         => ! [D: pname] :
              ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ B ) )
             => ( C != D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_566_disjoint__iff__not__equal) ).

thf(1639,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ A ) @ B )
          = bot_bo844097828e_bool )
       => ! [C: pname] :
            ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ A ) )
           => ! [D: pname] :
                ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ B ) )
               => ( C != D ) ) ) )
      & ( ! [C: pname] :
            ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ A ) )
           => ! [D: pname] :
                ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ B ) )
               => ( C != D ) ) )
       => ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ A ) @ B )
          = bot_bo844097828e_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(409,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( B = C )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_350_ord__eq__le__trans) ).

thf(2290,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( B = C )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(259,axiom,
    ! [A: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ bot_bo844097828e_bool ) @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_Un__empty__left) ).

thf(1745,plain,
    ! [A: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ bot_bo844097828e_bool ) @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(338,axiom,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ B ) )
     => ( ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ B )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_insert__absorb) ).

thf(2026,plain,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ B ) )
     => ( ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(594,axiom,
    ! [A: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ collec1735317154_state @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_Collect__def) ).

thf(2971,plain,
    ! [A: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ collec1735317154_state @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).

thf(744,axiom,
    ! [A: fun_Ho1996104121e_bool] : ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_order__refl) ).

thf(3516,plain,
    ! [A: fun_Ho1996104121e_bool] : ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).

thf(670,axiom,
    ! [A: hoare_1875481847_state] :
      ( ( set_Ho691846255_state @ ( some_H2141159592_state @ A ) )
      = ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ bot_bo1715400655e_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_403_Option_Oset_Osimps_I2_J) ).

thf(3252,plain,
    ! [A: hoare_1875481847_state] :
      ( ( set_Ho691846255_state @ ( some_H2141159592_state @ A ) )
      = ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ bot_bo1715400655e_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).

thf(473,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_Un__commute) ).

thf(2526,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).

thf(55,axiom,
    ! [A: fun_fu1219323149e_bool,B: fun_st2116860965l_bool,C: state] :
      ( ( hAPP_s1874344717e_bool @ ( hAPP_f873506917e_bool @ ( cOMBB_1757942702_state @ A ) @ B ) @ C )
      = ( hAPP_f167292325e_bool @ A @ ( hAPP_s2001034685l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__HOL__Obool_Mtc__H) ).

thf(995,plain,
    ! [A: fun_fu1219323149e_bool,B: fun_st2116860965l_bool,C: state] :
      ( ( hAPP_s1874344717e_bool @ ( hAPP_f873506917e_bool @ ( cOMBB_1757942702_state @ A ) @ B ) @ C )
      = ( hAPP_f167292325e_bool @ A @ ( hAPP_s2001034685l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(438,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_342_order__antisym) ).

thf(2394,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).

thf(49,axiom,
    ! [A: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ A ) @ bot_bo844097828e_bool )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_Un__empty__right) ).

thf(963,plain,
    ! [A: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ A ) @ bot_bo844097828e_bool )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(375,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: hoare_1875481847_state] :
      ( ( hBOOL @ ( hAPP_H1173941847e_bool @ B @ C ) )
     => ( hBOOL @ ( hAPP_H1173941847e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_394_sup1I1) ).

thf(2167,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: hoare_1875481847_state] :
      ( ( hBOOL @ ( hAPP_H1173941847e_bool @ B @ C ) )
     => ( hBOOL @ ( hAPP_H1173941847e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(404,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
     => ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ B ) @ A )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_602_Int__absorb1) ).

thf(2273,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
     => ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ B ) @ A )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(29,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ B ) @ A ) ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_635_le__infI1) ).

thf(896,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ B ) @ A ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(356,axiom,
    ! [A: hoare_1875481847_state,B: hoare_1875481847_state,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ C ) ) )
     => ( ( A != B )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_insertE) ).

thf(2098,plain,
    ! [A: hoare_1875481847_state,B: hoare_1875481847_state,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ C ) ) )
     => ( ( A != B )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(306,axiom,
    ! [A: fun_Ho1455141843_state,B: fun_Ho1996104121e_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ B ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ ( hAPP_f121055253e_bool @ ( image_436941729_state @ A ) @ B ) ) )
       => ? [C: hoare_1875481847_state] :
            ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ ( hAPP_f121055253e_bool @ collec1735317154_state @ ( hAPP_f121055253e_bool @ ( hAPP_f1300953505e_bool @ cOMBS_896408300l_bool @ ( hAPP_f932622461l_bool @ ( cOMBB_242064253_state @ fconj ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1795624711e_bool @ cOMBC_1099403170l_bool @ member618553700_state ) @ B ) ) ) @ ( hAPP_H117293375e_bool @ ( hAPP_f2101312745e_bool @ cOMBC_1972244470e_bool @ ( hAPP_f474907569e_bool @ ( cOMBB_1903241981_state @ fequal391417144_state ) @ A ) ) @ ( hAPP_H350317809_state @ A @ C ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_pigeonhole__infinite) ).

thf(1903,plain,
    ! [A: fun_Ho1455141843_state,B: fun_Ho1996104121e_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ B ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ ( hAPP_f121055253e_bool @ ( image_436941729_state @ A ) @ B ) ) )
       => ? [C: hoare_1875481847_state] :
            ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ ( hAPP_f121055253e_bool @ collec1735317154_state @ ( hAPP_f121055253e_bool @ ( hAPP_f1300953505e_bool @ cOMBS_896408300l_bool @ ( hAPP_f932622461l_bool @ ( cOMBB_242064253_state @ fconj ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1795624711e_bool @ cOMBC_1099403170l_bool @ member618553700_state ) @ B ) ) ) @ ( hAPP_H117293375e_bool @ ( hAPP_f2101312745e_bool @ cOMBC_1972244470e_bool @ ( hAPP_f474907569e_bool @ ( cOMBB_1903241981_state @ fequal391417144_state ) @ A ) ) @ ( hAPP_H350317809_state @ A @ C ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(365,axiom,
    ! [A: fun_fu689207471l_bool] :
      ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ A ) )
     => ( hBOOL @ ( hAPP_f755416249l_bool @ finite1234242204l_bool @ ( hAPP_f57684501l_bool @ collec925828570l_bool @ ( hAPP_f1970936639l_bool @ ( hAPP_f1475014121l_bool @ cOMBC_686159718l_bool @ ord_le724727525l_bool ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_finite__Collect__subsets) ).

thf(2135,plain,
    ! [A: fun_fu689207471l_bool] :
      ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ A ) )
     => ( hBOOL @ ( hAPP_f755416249l_bool @ finite1234242204l_bool @ ( hAPP_f57684501l_bool @ collec925828570l_bool @ ( hAPP_f1970936639l_bool @ ( hAPP_f1475014121l_bool @ cOMBC_686159718l_bool @ ord_le724727525l_bool ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(441,axiom,
    ! [A: fun_fu399576434l_bool,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
     => ( ( B != bot_bo1649642514l_bool )
       => ( ! [C: fun_pname_bool] : ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ ( hAPP_f559147733l_bool @ ( hAPP_f1320879424l_bool @ insert1325755072e_bool @ C ) @ bot_bo1649642514l_bool ) ) )
         => ( ! [C: fun_pname_bool,D: fun_fu1430349052l_bool] :
                ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ D ) )
               => ( ( D != bot_bo1649642514l_bool )
                 => ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ C ) @ D ) )
                   => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ D ) )
                     => ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ ( hAPP_f559147733l_bool @ ( hAPP_f1320879424l_bool @ insert1325755072e_bool @ C ) @ D ) ) ) ) ) ) )
           => ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_476_finite__ne__induct) ).

thf(2406,plain,
    ! [A: fun_fu399576434l_bool,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
     => ( ( B != bot_bo1649642514l_bool )
       => ( ! [C: fun_pname_bool] : ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ ( hAPP_f559147733l_bool @ ( hAPP_f1320879424l_bool @ insert1325755072e_bool @ C ) @ bot_bo1649642514l_bool ) ) )
         => ( ! [C: fun_pname_bool,D: fun_fu1430349052l_bool] :
                ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ D ) )
               => ( ( D != bot_bo1649642514l_bool )
                 => ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ C ) @ D ) )
                   => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ D ) )
                     => ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ ( hAPP_f559147733l_bool @ ( hAPP_f1320879424l_bool @ insert1325755072e_bool @ C ) @ D ) ) ) ) ) ) )
           => ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).

thf(703,axiom,
    ! [A: fun_pn760644914e_bool,B: fun_pname_bool,C: fun_fu689207471l_bool] :
      ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ ( hAPP_f1970936639l_bool @ ord_le724727525l_bool @ C ) @ ( hAPP_f1522632684l_bool @ ( image_1165561978e_bool @ A ) @ B ) ) )
       => ? [D: fun_pname_bool] :
            ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ D ) )
            & ( C
              = ( hAPP_f1522632684l_bool @ ( image_1165561978e_bool @ A ) @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_finite__subset__image) ).

thf(3369,plain,
    ! [A: fun_pn760644914e_bool,B: fun_pname_bool,C: fun_fu689207471l_bool] :
      ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ ( hAPP_f1970936639l_bool @ ord_le724727525l_bool @ C ) @ ( hAPP_f1522632684l_bool @ ( image_1165561978e_bool @ A ) @ B ) ) )
       => ? [D: fun_pname_bool] :
            ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ D ) )
            & ( C
              = ( hAPP_f1522632684l_bool @ ( image_1165561978e_bool @ A ) @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).

thf(552,axiom,
    ! [A: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ bot_bo1715400655e_bool ) )
    <=> ( A = bot_bo1715400655e_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_364_bot__unique) ).

thf(2823,plain,
    ! [A: fun_Ho1996104121e_bool] :
      ( ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ bot_bo1715400655e_bool ) )
       => ( A = bot_bo1715400655e_bool ) )
      & ( ( A = bot_bo1715400655e_bool )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ bot_bo1715400655e_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).

thf(233,axiom,
    ! [A: fun_fu802393907l_bool,B: fun_pn800050071e_bool,C: pname] :
      ( ( hAPP_p338031245l_bool @ ( hAPP_f567934427l_bool @ ( cOMBB_408569982_pname @ A ) @ B ) @ C )
      = ( hAPP_f434788991l_bool @ A @ ( hAPP_p61793385e_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It) ).

thf(1629,plain,
    ! [A: fun_fu802393907l_bool,B: fun_pn800050071e_bool,C: pname] :
      ( ( hAPP_p338031245l_bool @ ( hAPP_f567934427l_bool @ ( cOMBB_408569982_pname @ A ) @ B ) @ C )
      = ( hAPP_f434788991l_bool @ A @ ( hAPP_p61793385e_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(334,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
     => ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_Un__absorb2) ).

thf(2004,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
     => ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(667,axiom,
    ! [A: hoare_1875481847_state] :
      ( ( hBOOL @ ( hAPP_H1173941847e_bool @ bot_bo1715400655e_bool @ A ) )
    <=> ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ bot_bo1715400655e_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_388_bot__empty__eq) ).

thf(3235,plain,
    ! [A: hoare_1875481847_state] :
      ( ( ( hBOOL @ ( hAPP_H1173941847e_bool @ bot_bo1715400655e_bool @ A ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ bot_bo1715400655e_bool ) ) )
      & ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ bot_bo1715400655e_bool ) )
       => ( hBOOL @ ( hAPP_H1173941847e_bool @ bot_bo1715400655e_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).

thf(446,axiom,
    ! [A: fun_fu1604182422_state,B: fun_fu1430349052l_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ ( hAPP_f1440968210e_bool @ ( image_1943894628_state @ A ) @ B ) ) )
       => ? [C: fun_pname_bool] :
            ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( hAPP_f559147733l_bool @ collec1974731493e_bool @ ( hAPP_f559147733l_bool @ ( hAPP_f624840228l_bool @ cOMBS_350070575l_bool @ ( hAPP_f143162813l_bool @ ( cOMBB_2095475776e_bool @ fconj ) @ ( hAPP_f559147733l_bool @ ( hAPP_f1145991873l_bool @ cOMBC_1988546018l_bool @ member799430823e_bool ) @ B ) ) ) @ ( hAPP_H434980226l_bool @ ( hAPP_f492176169l_bool @ cOMBC_620146361e_bool @ ( hAPP_f1703905905e_bool @ ( cOMBB_93797312e_bool @ fequal391417144_state ) @ A ) ) @ ( hAPP_f168815540_state @ A @ C ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_pigeonhole__infinite) ).

thf(2431,plain,
    ! [A: fun_fu1604182422_state,B: fun_fu1430349052l_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ ( hAPP_f1440968210e_bool @ ( image_1943894628_state @ A ) @ B ) ) )
       => ? [C: fun_pname_bool] :
            ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( hAPP_f559147733l_bool @ collec1974731493e_bool @ ( hAPP_f559147733l_bool @ ( hAPP_f624840228l_bool @ cOMBS_350070575l_bool @ ( hAPP_f143162813l_bool @ ( cOMBB_2095475776e_bool @ fconj ) @ ( hAPP_f559147733l_bool @ ( hAPP_f1145991873l_bool @ cOMBC_1988546018l_bool @ member799430823e_bool ) @ B ) ) ) @ ( hAPP_H434980226l_bool @ ( hAPP_f492176169l_bool @ cOMBC_620146361e_bool @ ( hAPP_f1703905905e_bool @ ( cOMBB_93797312e_bool @ fequal391417144_state ) @ A ) ) @ ( hAPP_f168815540_state @ A @ C ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(739,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( A != B )
      | ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ fequal259518520e_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Otriple) ).

thf(3501,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( A != B )
      | ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ fequal259518520e_bool @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).

thf(602,axiom,
    hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( dom_pname_com @ body ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_finite__dom__body) ).

thf(3003,plain,
    hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( dom_pname_com @ body ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).

thf(692,axiom,
    ! [A: fun_fu689207471l_bool,B: fun_Ho1695028467e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ C ) )
     => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ ( hAPP_f1970936639l_bool @ ord_le724727525l_bool @ A ) @ ( hAPP_f1873026899l_bool @ ( image_896278159e_bool @ B ) @ C ) ) )
       => ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_finite__surj) ).

thf(3331,plain,
    ! [A: fun_fu689207471l_bool,B: fun_Ho1695028467e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ C ) )
     => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ ( hAPP_f1970936639l_bool @ ord_le724727525l_bool @ A ) @ ( hAPP_f1873026899l_bool @ ( image_896278159e_bool @ B ) @ C ) ) )
       => ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).

thf(639,axiom,
    ! [A: fun_pn760644914e_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ ( hAPP_f1522632684l_bool @ ( image_1165561978e_bool @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_finite__imageI) ).

thf(3136,plain,
    ! [A: fun_pn760644914e_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ ( hAPP_f1522632684l_bool @ ( image_1165561978e_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).

thf(294,axiom,
    ! [A: fun_fu410713561e_bool,B: fun_pname_bool,C: fun_pname_bool,D: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ D ) )
     => ( ( ( hAPP_f759274231e_bool @ A @ C )
          = B )
       => ( ! [E: fun_pname_bool,F: fun_pname_bool] :
              ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ F ) @ E ) )
             => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f759274231e_bool @ A @ F ) ) @ ( hAPP_f759274231e_bool @ A @ E ) ) ) )
         => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ ( hAPP_f759274231e_bool @ A @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_548_xt1_I16_J) ).

thf(1861,plain,
    ! [A: fun_fu410713561e_bool,B: fun_pname_bool,C: fun_pname_bool,D: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ D ) )
     => ( ( ( hAPP_f759274231e_bool @ A @ C )
          = B )
       => ( ! [E: fun_pname_bool,F: fun_pname_bool] :
              ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ F ) @ E ) )
             => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f759274231e_bool @ A @ F ) ) @ ( hAPP_f759274231e_bool @ A @ E ) ) ) )
         => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ ( hAPP_f759274231e_bool @ A @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(194,axiom,
    ! [A: fun_fu1430349052l_bool,B: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ B ) )
       => ( ( hAPP_f559147733l_bool @ collec1974731493e_bool @ ( hAPP_f559147733l_bool @ ( hAPP_f624840228l_bool @ cOMBS_350070575l_bool @ ( hAPP_f143162813l_bool @ ( cOMBB_2095475776e_bool @ fconj ) @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ B ) ) ) @ A ) )
          = ( hAPP_f559147733l_bool @ ( hAPP_f1320879424l_bool @ insert1325755072e_bool @ B ) @ bot_bo1649642514l_bool ) ) )
      & ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ B ) )
       => ( ( hAPP_f559147733l_bool @ collec1974731493e_bool @ ( hAPP_f559147733l_bool @ ( hAPP_f624840228l_bool @ cOMBS_350070575l_bool @ ( hAPP_f143162813l_bool @ ( cOMBB_2095475776e_bool @ fconj ) @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ B ) ) ) @ A ) )
          = bot_bo1649642514l_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_Collect__conv__if2) ).

thf(1491,plain,
    ! [A: fun_fu1430349052l_bool,B: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ B ) )
       => ( ( hAPP_f559147733l_bool @ collec1974731493e_bool @ ( hAPP_f559147733l_bool @ ( hAPP_f624840228l_bool @ cOMBS_350070575l_bool @ ( hAPP_f143162813l_bool @ ( cOMBB_2095475776e_bool @ fconj ) @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ B ) ) ) @ A ) )
          = ( hAPP_f559147733l_bool @ ( hAPP_f1320879424l_bool @ insert1325755072e_bool @ B ) @ bot_bo1649642514l_bool ) ) )
      & ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ B ) )
       => ( ( hAPP_f559147733l_bool @ collec1974731493e_bool @ ( hAPP_f559147733l_bool @ ( hAPP_f624840228l_bool @ cOMBS_350070575l_bool @ ( hAPP_f143162813l_bool @ ( cOMBB_2095475776e_bool @ fconj ) @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ B ) ) ) @ A ) )
          = bot_bo1649642514l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(690,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_fu689207471l_bool,C: fun_fu947547457e_bool,D: fun_fu1163781179e_bool] :
      ( ( hBOOL @ ( finite792754358e_bool @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ B ) )
       => ( ( ( ( hAPP_f900945761l_bool @ ( hAPP_f19215249l_bool @ minus_1959767774l_bool @ B ) @ ( hAPP_f900945761l_bool @ ( hAPP_f872497439l_bool @ insert504309043e_bool @ A ) @ bot_bo973479705l_bool ) )
              = bot_bo973479705l_bool )
           => ( ( hAPP_f962122119e_bool @ D @ ( hAPP_f900945761l_bool @ ( hAPP_f872497439l_bool @ insert504309043e_bool @ A ) @ B ) )
              = A ) )
          & ( ( ( hAPP_f900945761l_bool @ ( hAPP_f19215249l_bool @ minus_1959767774l_bool @ B ) @ ( hAPP_f900945761l_bool @ ( hAPP_f872497439l_bool @ insert504309043e_bool @ A ) @ bot_bo973479705l_bool ) )
             != bot_bo973479705l_bool )
           => ( ( hAPP_f962122119e_bool @ D @ ( hAPP_f900945761l_bool @ ( hAPP_f872497439l_bool @ insert504309043e_bool @ A ) @ B ) )
              = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ C @ A ) @ ( hAPP_f962122119e_bool @ D @ ( hAPP_f900945761l_bool @ ( hAPP_f19215249l_bool @ minus_1959767774l_bool @ B ) @ ( hAPP_f900945761l_bool @ ( hAPP_f872497439l_bool @ insert504309043e_bool @ A ) @ bot_bo973479705l_bool ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_683_folding__one_Oinsert__remove) ).

thf(3324,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_fu689207471l_bool,C: fun_fu947547457e_bool,D: fun_fu1163781179e_bool] :
      ( ( hBOOL @ ( finite792754358e_bool @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ B ) )
       => ( ( ( ( hAPP_f900945761l_bool @ ( hAPP_f19215249l_bool @ minus_1959767774l_bool @ B ) @ ( hAPP_f900945761l_bool @ ( hAPP_f872497439l_bool @ insert504309043e_bool @ A ) @ bot_bo973479705l_bool ) )
              = bot_bo973479705l_bool )
           => ( ( hAPP_f962122119e_bool @ D @ ( hAPP_f900945761l_bool @ ( hAPP_f872497439l_bool @ insert504309043e_bool @ A ) @ B ) )
              = A ) )
          & ( ( ( hAPP_f900945761l_bool @ ( hAPP_f19215249l_bool @ minus_1959767774l_bool @ B ) @ ( hAPP_f900945761l_bool @ ( hAPP_f872497439l_bool @ insert504309043e_bool @ A ) @ bot_bo973479705l_bool ) )
             != bot_bo973479705l_bool )
           => ( ( hAPP_f962122119e_bool @ D @ ( hAPP_f900945761l_bool @ ( hAPP_f872497439l_bool @ insert504309043e_bool @ A ) @ B ) )
              = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ C @ A ) @ ( hAPP_f962122119e_bool @ D @ ( hAPP_f900945761l_bool @ ( hAPP_f19215249l_bool @ minus_1959767774l_bool @ B ) @ ( hAPP_f900945761l_bool @ ( hAPP_f872497439l_bool @ insert504309043e_bool @ A ) @ bot_bo973479705l_bool ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).

thf(719,axiom,
    ! [A: hoare_1875481847_state,B: hoare_1875481847_state] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ bot_bo1715400655e_bool ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_singletonE) ).

thf(3430,plain,
    ! [A: hoare_1875481847_state,B: hoare_1875481847_state] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ bot_bo1715400655e_bool ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).

thf(420,axiom,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool,C: fun_fu2101097872e_bool,D: fun_fu608906319e_bool] :
      ( ( hBOOL @ ( finite1626890877e_bool @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
       => ( ( B != bot_bo1649642514l_bool )
         => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) )
           => ( ( A != bot_bo1649642514l_bool )
             => ( ( ( hAPP_f559147733l_bool @ ( hAPP_f230953622l_bool @ semila1130628874l_bool @ B ) @ A )
                  = bot_bo1649642514l_bool )
               => ( ( hAPP_f674760225e_bool @ D @ ( hAPP_f559147733l_bool @ ( hAPP_f230953622l_bool @ semila1782091504l_bool @ B ) @ A ) )
                  = ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ C @ ( hAPP_f674760225e_bool @ D @ B ) ) @ ( hAPP_f674760225e_bool @ D @ A ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_554_folding__one_Ounion__disjoint) ).

thf(2330,plain,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool,C: fun_fu2101097872e_bool,D: fun_fu608906319e_bool] :
      ( ( hBOOL @ ( finite1626890877e_bool @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
       => ( ( B != bot_bo1649642514l_bool )
         => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) )
           => ( ( A != bot_bo1649642514l_bool )
             => ( ( ( hAPP_f559147733l_bool @ ( hAPP_f230953622l_bool @ semila1130628874l_bool @ B ) @ A )
                  = bot_bo1649642514l_bool )
               => ( ( hAPP_f674760225e_bool @ D @ ( hAPP_f559147733l_bool @ ( hAPP_f230953622l_bool @ semila1782091504l_bool @ B ) @ A ) )
                  = ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ C @ ( hAPP_f674760225e_bool @ D @ B ) ) @ ( hAPP_f674760225e_bool @ D @ A ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).

thf(380,axiom,
    ! [A: fun_pn664418900_state,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_finite__imageI) ).

thf(2198,plain,
    ! [A: fun_pn664418900_state,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

thf(250,axiom,
    ! [A: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ bot_bo844097828e_bool ) )
    <=> ( A = bot_bo844097828e_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_subset__empty) ).

thf(1706,plain,
    ! [A: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ bot_bo844097828e_bool ) )
       => ( A = bot_bo844097828e_bool ) )
      & ( ( A = bot_bo844097828e_bool )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ bot_bo844097828e_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(429,axiom,
    ! [A: fun_fu1430349052l_bool,B: fun_fu410713561e_bool,C: fun_fu2101097872e_bool,D: fun_fu608906319e_bool] :
      ( ( hBOOL @ ( finite1268145088e_bool @ C @ D ) )
     => ( ! [E: fun_pname_bool,F: fun_pname_bool] :
            ( ( hAPP_f759274231e_bool @ B @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ C @ E ) @ F ) )
            = ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ C @ ( hAPP_f759274231e_bool @ B @ E ) ) @ ( hAPP_f759274231e_bool @ B @ F ) ) )
       => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) )
         => ( ( A != bot_bo1649642514l_bool )
           => ( ( hAPP_f759274231e_bool @ B @ ( hAPP_f674760225e_bool @ D @ A ) )
              = ( hAPP_f674760225e_bool @ D @ ( hAPP_f559147733l_bool @ ( image_2063528359e_bool @ B ) @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_485_folding__one__idem_Ohom__commute) ).

thf(2362,plain,
    ! [A: fun_fu1430349052l_bool,B: fun_fu410713561e_bool,C: fun_fu2101097872e_bool,D: fun_fu608906319e_bool] :
      ( ( hBOOL @ ( finite1268145088e_bool @ C @ D ) )
     => ( ! [E: fun_pname_bool,F: fun_pname_bool] :
            ( ( hAPP_f759274231e_bool @ B @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ C @ E ) @ F ) )
            = ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ C @ ( hAPP_f759274231e_bool @ B @ E ) ) @ ( hAPP_f759274231e_bool @ B @ F ) ) )
       => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) )
         => ( ( A != bot_bo1649642514l_bool )
           => ( ( hAPP_f759274231e_bool @ B @ ( hAPP_f674760225e_bool @ D @ A ) )
              = ( hAPP_f674760225e_bool @ D @ ( hAPP_f559147733l_bool @ ( image_2063528359e_bool @ B ) @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).

thf(224,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool,D: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ D ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ C ) @ A ) ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ D ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_647_inf__mono) ).

thf(1607,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool,D: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ D ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ C ) @ A ) ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ D ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(331,axiom,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) )
       => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( hAPP_f559147733l_bool @ ( hAPP_f230953622l_bool @ semila1782091504l_bool @ B ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_finite__UnI) ).

thf(1994,plain,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) )
       => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( hAPP_f559147733l_bool @ ( hAPP_f230953622l_bool @ semila1782091504l_bool @ B ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(69,axiom,
    ! [A: pname,B: pname,C: pname,D: pname] :
      ( ( ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ bot_bo844097828e_bool ) )
        = ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ C ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ D ) @ bot_bo844097828e_bool ) ) )
    <=> ( ( ( A = C )
          & ( B = D ) )
        | ( ( A = D )
          & ( B = C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_doubleton__eq__iff) ).

thf(1045,plain,
    ! [A: pname,B: pname,C: pname,D: pname] :
      ( ( ( ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ bot_bo844097828e_bool ) )
          = ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ C ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ D ) @ bot_bo844097828e_bool ) ) )
       => ( ( ( A = C )
            & ( B = D ) )
          | ( ( A = D )
            & ( B = C ) ) ) )
      & ( ( ( ( A = C )
            & ( B = D ) )
          | ( ( A = D )
            & ( B = C ) ) )
       => ( ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ bot_bo844097828e_bool ) )
          = ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ C ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ D ) @ bot_bo844097828e_bool ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(436,axiom,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ B ) @ ( hAPP_f121055253e_bool @ collec1735317154_state @ C ) ) ) )
    <=> ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ B ) )
        & ( hBOOL @ ( hAPP_H1173941847e_bool @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_587_Int__Collect) ).

thf(2384,plain,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ B ) @ ( hAPP_f121055253e_bool @ collec1735317154_state @ C ) ) ) )
       => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ B ) )
          & ( hBOOL @ ( hAPP_H1173941847e_bool @ C @ A ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ B ) )
          & ( hBOOL @ ( hAPP_H1173941847e_bool @ C @ A ) ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ B ) @ ( hAPP_f121055253e_bool @ collec1735317154_state @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).

thf(790,axiom,
    ! [A: fun_fu385705929_state,B: fun_fu689207471l_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ C ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ C ) @ ( hAPP_f962122119e_bool @ ( image_1669234411_state @ A ) @ B ) ) )
       => ? [D: fun_fu689207471l_bool] :
            ( ( hBOOL @ ( hAPP_f1699935247l_bool @ ( hAPP_f1970936639l_bool @ ord_le724727525l_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ D ) )
            & ( C
              = ( hAPP_f962122119e_bool @ ( image_1669234411_state @ A ) @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_finite__subset__image) ).

thf(3694,plain,
    ! [A: fun_fu385705929_state,B: fun_fu689207471l_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ C ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ C ) @ ( hAPP_f962122119e_bool @ ( image_1669234411_state @ A ) @ B ) ) )
       => ? [D: fun_fu689207471l_bool] :
            ( ( hBOOL @ ( hAPP_f1699935247l_bool @ ( hAPP_f1970936639l_bool @ ord_le724727525l_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ D ) )
            & ( C
              = ( hAPP_f962122119e_bool @ ( image_1669234411_state @ A ) @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).

thf(545,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_fu1296727421e_bool,D: fun_Ho1996104121e_bool] :
      ( ( B
        = ( hAPP_f121055253e_bool @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ D ) )
       => ( ! [E: fun_Ho1996104121e_bool,F: fun_Ho1996104121e_bool] :
              ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ F ) @ E ) )
             => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f121055253e_bool @ C @ F ) ) @ ( hAPP_f121055253e_bool @ C @ E ) ) ) )
         => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f121055253e_bool @ C @ A ) ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_547_xt1_I15_J) ).

thf(2796,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_fu1296727421e_bool,D: fun_Ho1996104121e_bool] :
      ( ( B
        = ( hAPP_f121055253e_bool @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ D ) )
       => ( ! [E: fun_Ho1996104121e_bool,F: fun_Ho1996104121e_bool] :
              ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ F ) @ E ) )
             => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f121055253e_bool @ C @ F ) ) @ ( hAPP_f121055253e_bool @ C @ E ) ) ) )
         => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f121055253e_bool @ C @ A ) ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).

thf(34,axiom,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
      ( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( hAPP_f559147733l_bool @ collec1974731493e_bool @ B ) ) )
        | ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( hAPP_f559147733l_bool @ collec1974731493e_bool @ A ) ) ) )
     => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( hAPP_f559147733l_bool @ collec1974731493e_bool @ ( hAPP_f559147733l_bool @ ( hAPP_f624840228l_bool @ cOMBS_350070575l_bool @ ( hAPP_f143162813l_bool @ ( cOMBB_2095475776e_bool @ fconj ) @ B ) ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_finite__Collect__conjI) ).

thf(914,plain,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
      ( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( hAPP_f559147733l_bool @ collec1974731493e_bool @ B ) ) )
        | ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( hAPP_f559147733l_bool @ collec1974731493e_bool @ A ) ) ) )
     => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( hAPP_f559147733l_bool @ collec1974731493e_bool @ ( hAPP_f559147733l_bool @ ( hAPP_f624840228l_bool @ cOMBS_350070575l_bool @ ( hAPP_f143162813l_bool @ ( cOMBB_2095475776e_bool @ fconj ) @ B ) ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(440,axiom,
    ! [A: hoare_1875481847_state,B: option1681283416_state] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ ( set_Ho691846255_state @ B ) ) )
    <=> ( B
        = ( some_H2141159592_state @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_406_elem__set) ).

thf(2399,plain,
    ! [A: hoare_1875481847_state,B: option1681283416_state] :
      ( ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ ( set_Ho691846255_state @ B ) ) )
       => ( B
          = ( some_H2141159592_state @ A ) ) )
      & ( ( B
          = ( some_H2141159592_state @ A ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ ( set_Ho691846255_state @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).

thf(341,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
     => ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_Un__absorb1) ).

thf(2041,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
     => ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(674,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_fu689207471l_bool,C: fun_fu947547457e_bool,D: fun_fu1163781179e_bool] :
      ( ( hBOOL @ ( finite1619424307e_bool @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ B ) )
       => ( ( B != bot_bo973479705l_bool )
         => ( ( hAPP_f962122119e_bool @ D @ ( hAPP_f900945761l_bool @ ( hAPP_f872497439l_bool @ insert504309043e_bool @ A ) @ B ) )
            = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ C @ A ) @ ( hAPP_f962122119e_bool @ D @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_473_folding__one__idem_Oinsert__idem) ).

thf(3267,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_fu689207471l_bool,C: fun_fu947547457e_bool,D: fun_fu1163781179e_bool] :
      ( ( hBOOL @ ( finite1619424307e_bool @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ B ) )
       => ( ( B != bot_bo973479705l_bool )
         => ( ( hAPP_f962122119e_bool @ D @ ( hAPP_f900945761l_bool @ ( hAPP_f872497439l_bool @ insert504309043e_bool @ A ) @ B ) )
            = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ C @ A ) @ ( hAPP_f962122119e_bool @ D @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).

thf(137,axiom,
    ! [A: pname,B: pname] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ bot_bo844097828e_bool ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_singletonE) ).

thf(1294,plain,
    ! [A: pname,B: pname] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ bot_bo844097828e_bool ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(456,axiom,
    ! [A: pname] :
      ( ( hAPP_pname_com @ body_1 @ A )
     != skip ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_478_com_Osimps_I19_J) ).

thf(2462,plain,
    ! [A: pname] :
      ( ( hAPP_pname_com @ body_1 @ A )
     != skip ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).

thf(518,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( A = B )
    <=> ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
        & ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_357_order__eq__iff) ).

thf(2680,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( ( A = B )
       => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
          & ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ A ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
          & ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ A ) ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).

thf(112,axiom,
    ! [A: fun_pn800050071e_bool,B: fun_Ho1653816318_pname,C: hoare_1875481847_state] :
      ( ( hAPP_H785152948e_bool @ ( hAPP_f190028117e_bool @ ( cOMBB_315976743_state @ A ) @ B ) @ C )
      = ( hAPP_p61793385e_bool @ A @ ( hAPP_H139064010_pname @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_224) ).

thf(1212,plain,
    ! [A: fun_pn800050071e_bool,B: fun_Ho1653816318_pname,C: hoare_1875481847_state] :
      ( ( hAPP_H785152948e_bool @ ( hAPP_f190028117e_bool @ ( cOMBB_315976743_state @ A ) @ B ) @ C )
      = ( hAPP_p61793385e_bool @ A @ ( hAPP_H139064010_pname @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(393,axiom,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_set__mp) ).

thf(2230,plain,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(303,axiom,
    ! [A: fun_Ho1653816318_pname,B: fun_Ho1996104121e_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ B ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( hAPP_f1148778334e_bool @ ( image_720060442_pname @ A ) @ B ) ) )
       => ? [C: hoare_1875481847_state] :
            ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ ( hAPP_f121055253e_bool @ collec1735317154_state @ ( hAPP_f121055253e_bool @ ( hAPP_f1300953505e_bool @ cOMBS_896408300l_bool @ ( hAPP_f932622461l_bool @ ( cOMBB_242064253_state @ fconj ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1795624711e_bool @ cOMBC_1099403170l_bool @ member618553700_state ) @ B ) ) ) @ ( hAPP_p1537966538e_bool @ ( hAPP_f1188413809e_bool @ cOMBC_1259060397e_bool @ ( hAPP_f190028117e_bool @ ( cOMBB_315976743_state @ fequal_pname ) @ A ) ) @ ( hAPP_H139064010_pname @ A @ C ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_pigeonhole__infinite) ).

thf(1893,plain,
    ! [A: fun_Ho1653816318_pname,B: fun_Ho1996104121e_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ B ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( hAPP_f1148778334e_bool @ ( image_720060442_pname @ A ) @ B ) ) )
       => ? [C: hoare_1875481847_state] :
            ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ ( hAPP_f121055253e_bool @ collec1735317154_state @ ( hAPP_f121055253e_bool @ ( hAPP_f1300953505e_bool @ cOMBS_896408300l_bool @ ( hAPP_f932622461l_bool @ ( cOMBB_242064253_state @ fconj ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1795624711e_bool @ cOMBC_1099403170l_bool @ member618553700_state ) @ B ) ) ) @ ( hAPP_p1537966538e_bool @ ( hAPP_f1188413809e_bool @ cOMBC_1259060397e_bool @ ( hAPP_f190028117e_bool @ ( cOMBB_315976743_state @ fequal_pname ) @ A ) ) @ ( hAPP_H139064010_pname @ A @ C ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(410,axiom,
    ! [A: fun_fu689207471l_bool,B: fun_fu689207471l_bool] :
      ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ B ) )
     => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ ( hAPP_f1970936639l_bool @ ord_le724727525l_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_rev__finite__subset) ).

thf(2294,plain,
    ! [A: fun_fu689207471l_bool,B: fun_fu689207471l_bool] :
      ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ B ) )
     => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ ( hAPP_f1970936639l_bool @ ord_le724727525l_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

thf(716,axiom,
    ! [A: fun_Ho1996104121e_bool,B: hoare_1875481847_state,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_UnI2) ).

thf(3420,plain,
    ! [A: fun_Ho1996104121e_bool,B: hoare_1875481847_state,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).

thf(227,axiom,
    ! [A: fun_Ho1695028467e_bool,B: hoare_1875481847_state,C: hoare_1875481847_state] :
      ( ( hAPP_H1173941847e_bool @ ( hAPP_H117293375e_bool @ ( hAPP_f2101312745e_bool @ cOMBC_1972244470e_bool @ A ) @ B ) @ C )
      = ( hAPP_H1173941847e_bool @ ( hAPP_H117293375e_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc__Com___228) ).

thf(1614,plain,
    ! [A: fun_Ho1695028467e_bool,B: hoare_1875481847_state,C: hoare_1875481847_state] :
      ( ( hAPP_H1173941847e_bool @ ( hAPP_H117293375e_bool @ ( hAPP_f2101312745e_bool @ cOMBC_1972244470e_bool @ A ) @ B ) @ C )
      = ( hAPP_H1173941847e_bool @ ( hAPP_H117293375e_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(308,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( A = B )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_equalityD1) ).

thf(1908,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( A = B )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(149,axiom,
    ! [A: pname,B: fun_pname_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
     => ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ minus_1015773161e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ B ) ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ bot_bo844097828e_bool ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_694_Diff__insert__absorb) ).

thf(1348,plain,
    ! [A: pname,B: fun_pname_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
     => ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ minus_1015773161e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ B ) ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ bot_bo844097828e_bool ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(408,axiom,
    ! [A: fun_fu2083718837l_bool,B: fun_fu689207471l_bool,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f1408815105l_bool @ ( hAPP_f900945761l_bool @ ( hAPP_f1846363427l_bool @ cOMBC_1909905718l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1699935247l_bool @ ( hAPP_f640685261l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____xlrqixeqwe__Otriple_I_239) ).

thf(2287,plain,
    ! [A: fun_fu2083718837l_bool,B: fun_fu689207471l_bool,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f1408815105l_bool @ ( hAPP_f900945761l_bool @ ( hAPP_f1846363427l_bool @ cOMBC_1909905718l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1699935247l_bool @ ( hAPP_f640685261l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(199,axiom,
    ! [A: fun_fu689207471l_bool,B: fun_fu689207471l_bool] :
      ( ( hAPP_f900945761l_bool @ ( hAPP_f19215249l_bool @ semila1058800161l_bool @ A ) @ B )
      = ( hAPP_f900945761l_bool @ collec771609166e_bool @ ( hAPP_f900945761l_bool @ ( hAPP_f2051813877l_bool @ cOMBS_1451994324l_bool @ ( hAPP_f440042033l_bool @ ( cOMBB_532710323e_bool @ fconj ) @ ( hAPP_f900945761l_bool @ ( hAPP_f1846363427l_bool @ cOMBC_1909905718l_bool @ member1062536460e_bool ) @ A ) ) ) @ ( hAPP_f900945761l_bool @ ( hAPP_f1846363427l_bool @ cOMBC_1909905718l_bool @ member1062536460e_bool ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_575_Int__def) ).

thf(1512,plain,
    ! [A: fun_fu689207471l_bool,B: fun_fu689207471l_bool] :
      ( ( hAPP_f900945761l_bool @ ( hAPP_f19215249l_bool @ semila1058800161l_bool @ A ) @ B )
      = ( hAPP_f900945761l_bool @ collec771609166e_bool @ ( hAPP_f900945761l_bool @ ( hAPP_f2051813877l_bool @ cOMBS_1451994324l_bool @ ( hAPP_f440042033l_bool @ ( cOMBB_532710323e_bool @ fconj ) @ ( hAPP_f900945761l_bool @ ( hAPP_f1846363427l_bool @ cOMBC_1909905718l_bool @ member1062536460e_bool ) @ A ) ) ) @ ( hAPP_f900945761l_bool @ ( hAPP_f1846363427l_bool @ cOMBC_1909905718l_bool @ member1062536460e_bool ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(255,axiom,
    ! [A: fun_pn800050071e_bool,B: fun_fu1499449723_pname,C: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool @ ( hAPP_f1385420507e_bool @ ( cOMBB_598082538e_bool @ A ) @ B ) @ C )
      = ( hAPP_p61793385e_bool @ A @ ( hAPP_f1297739591_pname @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_220) ).

thf(1725,plain,
    ! [A: fun_pn800050071e_bool,B: fun_fu1499449723_pname,C: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool @ ( hAPP_f1385420507e_bool @ ( cOMBB_598082538e_bool @ A ) @ B ) @ C )
      = ( hAPP_p61793385e_bool @ A @ ( hAPP_f1297739591_pname @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(526,axiom,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_H1173941847e_bool @ B @ A ) ) @ ( hAPP_H1173941847e_bool @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_368_le__funE) ).

thf(2719,plain,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_H1173941847e_bool @ B @ A ) ) @ ( hAPP_H1173941847e_bool @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).

thf(766,axiom,
    ! [A: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ bot_bo1715400655e_bool ) @ A )
      = bot_bo1715400655e_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_571_Int__empty__left) ).

thf(3601,plain,
    ! [A: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ bot_bo1715400655e_bool ) @ A )
      = bot_bo1715400655e_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).

thf(673,axiom,
    ! [A: fun_pn664418900_state,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ B ) @ C ) )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ A ) @ B ) ) @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ A ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_image__Un) ).

thf(3264,plain,
    ! [A: fun_pn664418900_state,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ B ) @ C ) )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ A ) @ B ) ) @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).

thf(159,axiom,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_578_IntD1) ).

thf(1380,plain,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(746,axiom,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ B )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ ( hAPP_f121055253e_bool @ collec1735317154_state @ ( hAPP_H117293375e_bool @ ( hAPP_f2101312745e_bool @ cOMBC_1972244470e_bool @ fequal391417144_state ) @ A ) ) ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_insert__def) ).

thf(3521,plain,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ B )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ ( hAPP_f121055253e_bool @ collec1735317154_state @ ( hAPP_H117293375e_bool @ ( hAPP_f2101312745e_bool @ cOMBC_1972244470e_bool @ fequal391417144_state ) @ A ) ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).

thf(328,axiom,
    ! [A: fun_Ho1996104121e_bool,B: hoare_1875481847_state,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ A ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ C ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_559_IntI) ).

thf(1986,plain,
    ! [A: fun_Ho1996104121e_bool,B: hoare_1875481847_state,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ A ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ C ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(21,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
    <=> ! [C: pname] : ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_pname_bool @ A @ C ) ) @ ( hAPP_pname_bool @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_371_le__fun__def) ).

thf(867,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
       => ! [C: pname] : ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_pname_bool @ A @ C ) ) @ ( hAPP_pname_bool @ B @ C ) ) ) )
      & ( ! [C: pname] : ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_pname_bool @ A @ C ) ) @ ( hAPP_pname_bool @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(191,axiom,
    ! [A: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ A ) @ bot_bo844097828e_bool )
      = bot_bo844097828e_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_657_inf__bot__right) ).

thf(1480,plain,
    ! [A: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ A ) @ bot_bo844097828e_bool )
      = bot_bo844097828e_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(388,axiom,
    ! [A: pname,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_c406083500_state @ hoare_Mirabelle_MGT @ ( hAPP_pname_com @ body_1 @ A ) ) ) @ B ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_c406083500_state @ hoare_Mirabelle_MGT @ ( hAPP_option_com_com @ the_com @ ( hAPP_p799580910on_com @ body @ A ) ) ) ) @ bot_bo1715400655e_bool ) ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_c406083500_state @ hoare_Mirabelle_MGT @ ( hAPP_pname_com @ body_1 @ A ) ) ) @ bot_bo1715400655e_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_MGT__BodyN) ).

thf(2218,plain,
    ! [A: pname,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_c406083500_state @ hoare_Mirabelle_MGT @ ( hAPP_pname_com @ body_1 @ A ) ) ) @ B ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_c406083500_state @ hoare_Mirabelle_MGT @ ( hAPP_option_com_com @ the_com @ ( hAPP_p799580910on_com @ body @ A ) ) ) ) @ bot_bo1715400655e_bool ) ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_c406083500_state @ hoare_Mirabelle_MGT @ ( hAPP_pname_com @ body_1 @ A ) ) ) @ bot_bo1715400655e_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(400,axiom,
    ! [A: fun_Ho1996104121e_bool] :
      ( ( ( hAPP_f121055253e_bool @ collec1735317154_state @ A )
        = bot_bo1715400655e_bool )
    <=> ! [B: hoare_1875481847_state] :
          ~ ( hBOOL @ ( hAPP_H1173941847e_bool @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_Collect__empty__eq) ).

thf(2258,plain,
    ! [A: fun_Ho1996104121e_bool] :
      ( ( ( ( hAPP_f121055253e_bool @ collec1735317154_state @ A )
          = bot_bo1715400655e_bool )
       => ! [B: hoare_1875481847_state] :
            ~ ( hBOOL @ ( hAPP_H1173941847e_bool @ A @ B ) ) )
      & ( ! [B: hoare_1875481847_state] :
            ~ ( hBOOL @ ( hAPP_H1173941847e_bool @ A @ B ) )
       => ( ( hAPP_f121055253e_bool @ collec1735317154_state @ A )
          = bot_bo1715400655e_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).

thf(578,axiom,
    ! [A: fun_Ho1996104121e_bool,B: hoare_1875481847_state,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ minus_589155914e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ C ) )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ minus_589155914e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ minus_589155914e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ bot_bo1715400655e_bool ) ) ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_698_Diff__insert2) ).

thf(2930,plain,
    ! [A: fun_Ho1996104121e_bool,B: hoare_1875481847_state,C: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ minus_589155914e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ C ) )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ minus_589155914e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ minus_589155914e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ bot_bo1715400655e_bool ) ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).

thf(363,axiom,
    ! [A: fun_pname_bool,B: fun_fu1430349052l_bool,C: fun_fu2101097872e_bool,D: fun_fu608906319e_bool] :
      ( ( hBOOL @ ( finite1626890877e_bool @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
       => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ A ) @ B ) )
         => ( ( ( ( hAPP_f559147733l_bool @ ( hAPP_f230953622l_bool @ minus_1290075917l_bool @ B ) @ ( hAPP_f559147733l_bool @ ( hAPP_f1320879424l_bool @ insert1325755072e_bool @ A ) @ bot_bo1649642514l_bool ) )
                = bot_bo1649642514l_bool )
             => ( ( hAPP_f674760225e_bool @ D @ B )
                = A ) )
            & ( ( ( hAPP_f559147733l_bool @ ( hAPP_f230953622l_bool @ minus_1290075917l_bool @ B ) @ ( hAPP_f559147733l_bool @ ( hAPP_f1320879424l_bool @ insert1325755072e_bool @ A ) @ bot_bo1649642514l_bool ) )
               != bot_bo1649642514l_bool )
             => ( ( hAPP_f674760225e_bool @ D @ B )
                = ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ C @ A ) @ ( hAPP_f674760225e_bool @ D @ ( hAPP_f559147733l_bool @ ( hAPP_f230953622l_bool @ minus_1290075917l_bool @ B ) @ ( hAPP_f559147733l_bool @ ( hAPP_f1320879424l_bool @ insert1325755072e_bool @ A ) @ bot_bo1649642514l_bool ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_678_folding__one_Oremove) ).

thf(2123,plain,
    ! [A: fun_pname_bool,B: fun_fu1430349052l_bool,C: fun_fu2101097872e_bool,D: fun_fu608906319e_bool] :
      ( ( hBOOL @ ( finite1626890877e_bool @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
       => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ A ) @ B ) )
         => ( ( ( ( hAPP_f559147733l_bool @ ( hAPP_f230953622l_bool @ minus_1290075917l_bool @ B ) @ ( hAPP_f559147733l_bool @ ( hAPP_f1320879424l_bool @ insert1325755072e_bool @ A ) @ bot_bo1649642514l_bool ) )
                = bot_bo1649642514l_bool )
             => ( ( hAPP_f674760225e_bool @ D @ B )
                = A ) )
            & ( ( ( hAPP_f559147733l_bool @ ( hAPP_f230953622l_bool @ minus_1290075917l_bool @ B ) @ ( hAPP_f559147733l_bool @ ( hAPP_f1320879424l_bool @ insert1325755072e_bool @ A ) @ bot_bo1649642514l_bool ) )
               != bot_bo1649642514l_bool )
             => ( ( hAPP_f674760225e_bool @ D @ B )
                = ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ C @ A ) @ ( hAPP_f674760225e_bool @ D @ ( hAPP_f559147733l_bool @ ( hAPP_f230953622l_bool @ minus_1290075917l_bool @ B ) @ ( hAPP_f559147733l_bool @ ( hAPP_f1320879424l_bool @ insert1325755072e_bool @ A ) @ bot_bo1649642514l_bool ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(475,axiom,
    ! [A: fun_Ho1695028467e_bool,B: fun_Ho1996104121e_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ B ) )
     => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ ( hAPP_f1873026899l_bool @ ( image_896278159e_bool @ A ) @ B ) ) )
       => ? [C: hoare_1875481847_state] :
            ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ ( hAPP_f121055253e_bool @ collec1735317154_state @ ( hAPP_f121055253e_bool @ ( hAPP_f1300953505e_bool @ cOMBS_896408300l_bool @ ( hAPP_f932622461l_bool @ ( cOMBB_242064253_state @ fconj ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1795624711e_bool @ cOMBC_1099403170l_bool @ member618553700_state ) @ B ) ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1795624711e_bool @ cOMBC_1099403170l_bool @ ( hAPP_f2059405973l_bool @ ( cOMBB_2063006993_state @ fequal259518520e_bool ) @ A ) ) @ ( hAPP_H117293375e_bool @ A @ C ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_pigeonhole__infinite) ).

thf(2534,plain,
    ! [A: fun_Ho1695028467e_bool,B: fun_Ho1996104121e_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ B ) )
     => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ ( hAPP_f1873026899l_bool @ ( image_896278159e_bool @ A ) @ B ) ) )
       => ? [C: hoare_1875481847_state] :
            ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ ( hAPP_f121055253e_bool @ collec1735317154_state @ ( hAPP_f121055253e_bool @ ( hAPP_f1300953505e_bool @ cOMBS_896408300l_bool @ ( hAPP_f932622461l_bool @ ( cOMBB_242064253_state @ fconj ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1795624711e_bool @ cOMBC_1099403170l_bool @ member618553700_state ) @ B ) ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1795624711e_bool @ cOMBC_1099403170l_bool @ ( hAPP_f2059405973l_bool @ ( cOMBB_2063006993_state @ fequal259518520e_bool ) @ A ) ) @ ( hAPP_H117293375e_bool @ A @ C ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).

thf(666,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_421_sup_Oleft__idem) ).

thf(3232,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).

thf(472,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ C ) )
     => ( ( B = A )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_xt1_I4_J) ).

thf(2522,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ C ) )
     => ( ( B = A )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).

thf(629,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_Un__left__absorb) ).

thf(3100,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).

thf(293,axiom,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_in__mono) ).

thf(1859,plain,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(141,axiom,
    ! [A: pname,B: fun_pname_bool,C: fun_pn1208287926_pname,D: fun_fu1499449723_pname] :
      ( ( hBOOL @ ( finite1282449217_pname @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
       => ( ( ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ minus_1015773161e_bool @ B ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ bot_bo844097828e_bool ) )
              = bot_bo844097828e_bool )
           => ( ( hAPP_f1297739591_pname @ D @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ B ) )
              = A ) )
          & ( ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ minus_1015773161e_bool @ B ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ bot_bo844097828e_bool ) )
             != bot_bo844097828e_bool )
           => ( ( hAPP_f1297739591_pname @ D @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ B ) )
              = ( hAPP_pname_pname @ ( hAPP_p1170154830_pname @ C @ A ) @ ( hAPP_f1297739591_pname @ D @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ minus_1015773161e_bool @ B ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ bot_bo844097828e_bool ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_680_folding__one_Oinsert__remove) ).

thf(1314,plain,
    ! [A: pname,B: fun_pname_bool,C: fun_pn1208287926_pname,D: fun_fu1499449723_pname] :
      ( ( hBOOL @ ( finite1282449217_pname @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
       => ( ( ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ minus_1015773161e_bool @ B ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ bot_bo844097828e_bool ) )
              = bot_bo844097828e_bool )
           => ( ( hAPP_f1297739591_pname @ D @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ B ) )
              = A ) )
          & ( ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ minus_1015773161e_bool @ B ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ bot_bo844097828e_bool ) )
             != bot_bo844097828e_bool )
           => ( ( hAPP_f1297739591_pname @ D @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ B ) )
              = ( hAPP_pname_pname @ ( hAPP_p1170154830_pname @ C @ A ) @ ( hAPP_f1297739591_pname @ D @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ minus_1015773161e_bool @ B ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ bot_bo844097828e_bool ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(756,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
    <=> ! [C: hoare_1875481847_state] : ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_H1173941847e_bool @ A @ C ) ) @ ( hAPP_H1173941847e_bool @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_372_le__fun__def) ).

thf(3558,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
       => ! [C: hoare_1875481847_state] : ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_H1173941847e_bool @ A @ C ) ) @ ( hAPP_H1173941847e_bool @ B @ C ) ) ) )
      & ( ! [C: hoare_1875481847_state] : ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_H1173941847e_bool @ A @ C ) ) @ ( hAPP_H1173941847e_bool @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).

thf(348,axiom,
    ! [A: pname,B: fun_pname_bool,C: fun_pn1208287926_pname,D: fun_fu1499449723_pname] :
      ( ( hBOOL @ ( finite89670078_pname @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
       => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
         => ( ( hAPP_pname_pname @ ( hAPP_p1170154830_pname @ C @ A ) @ ( hAPP_f1297739591_pname @ D @ B ) )
            = ( hAPP_f1297739591_pname @ D @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_481_folding__one__idem_Oin__idem) ).

thf(2070,plain,
    ! [A: pname,B: fun_pname_bool,C: fun_pn1208287926_pname,D: fun_fu1499449723_pname] :
      ( ( hBOOL @ ( finite89670078_pname @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
       => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
         => ( ( hAPP_pname_pname @ ( hAPP_p1170154830_pname @ C @ A ) @ ( hAPP_f1297739591_pname @ D @ B ) )
            = ( hAPP_f1297739591_pname @ D @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(214,axiom,
    ! [A: fun_pname_bool,B: fun_fu1430349052l_bool,C: fun_fu2101097872e_bool,D: fun_fu608906319e_bool] :
      ( ( hBOOL @ ( finite1626890877e_bool @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
       => ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ A ) @ B ) )
         => ( ( B != bot_bo1649642514l_bool )
           => ( ( hAPP_f674760225e_bool @ D @ ( hAPP_f559147733l_bool @ ( hAPP_f1320879424l_bool @ insert1325755072e_bool @ A ) @ B ) )
              = ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ C @ A ) @ ( hAPP_f674760225e_bool @ D @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_511_folding__one_Oinsert) ).

thf(1561,plain,
    ! [A: fun_pname_bool,B: fun_fu1430349052l_bool,C: fun_fu2101097872e_bool,D: fun_fu608906319e_bool] :
      ( ( hBOOL @ ( finite1626890877e_bool @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
       => ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ A ) @ B ) )
         => ( ( B != bot_bo1649642514l_bool )
           => ( ( hAPP_f674760225e_bool @ D @ ( hAPP_f559147733l_bool @ ( hAPP_f1320879424l_bool @ insert1325755072e_bool @ A ) @ B ) )
              = ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ C @ A ) @ ( hAPP_f674760225e_bool @ D @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(7,axiom,
    ! [A: fun_st2063251938l_bool,B: fun_state_bool,C: state] :
      ( ( hAPP_state_bool @ ( hAPP_f1759915619e_bool @ ( hAPP_f644196280e_bool @ cOMBS_1378840469l_bool @ A ) @ B ) @ C )
      = ( hAPP_bool_bool @ ( hAPP_s58564346l_bool @ A @ C ) @ ( hAPP_state_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Com__Ostate_000tc__HOL__Obool_000tc__HOL__Obool_U) ).

thf(828,plain,
    ! [A: fun_st2063251938l_bool,B: fun_state_bool,C: state] :
      ( ( hAPP_state_bool @ ( hAPP_f1759915619e_bool @ ( hAPP_f644196280e_bool @ cOMBS_1378840469l_bool @ A ) @ B ) @ C )
      = ( hAPP_bool_bool @ ( hAPP_s58564346l_bool @ A @ C ) @ ( hAPP_state_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(777,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( A = B )
    <=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
        & ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_set__eq__subset) ).

thf(3633,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( ( A = B )
       => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
          & ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
          & ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).

thf(688,axiom,
    ! [A: fun_fu385705929_state,B: fun_fu689207471l_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ B ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ ( hAPP_f962122119e_bool @ ( image_1669234411_state @ A ) @ B ) ) )
       => ? [C: fun_Ho1996104121e_bool] :
            ( ( hBOOL @ ( hAPP_f1699935247l_bool @ ( hAPP_f640685261l_bool @ member1062536460e_bool @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ ( hAPP_f900945761l_bool @ collec771609166e_bool @ ( hAPP_f900945761l_bool @ ( hAPP_f2051813877l_bool @ cOMBS_1451994324l_bool @ ( hAPP_f440042033l_bool @ ( cOMBB_532710323e_bool @ fconj ) @ ( hAPP_f900945761l_bool @ ( hAPP_f1846363427l_bool @ cOMBC_1909905718l_bool @ member1062536460e_bool ) @ B ) ) ) @ ( hAPP_H810811817l_bool @ ( hAPP_f309954467l_bool @ cOMBC_685773310e_bool @ ( hAPP_f1185879473e_bool @ ( cOMBB_1094554675e_bool @ fequal391417144_state ) @ A ) ) @ ( hAPP_f890249627_state @ A @ C ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_pigeonhole__infinite) ).

thf(3309,plain,
    ! [A: fun_fu385705929_state,B: fun_fu689207471l_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ B ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ ( hAPP_f962122119e_bool @ ( image_1669234411_state @ A ) @ B ) ) )
       => ? [C: fun_Ho1996104121e_bool] :
            ( ( hBOOL @ ( hAPP_f1699935247l_bool @ ( hAPP_f640685261l_bool @ member1062536460e_bool @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ ( hAPP_f900945761l_bool @ collec771609166e_bool @ ( hAPP_f900945761l_bool @ ( hAPP_f2051813877l_bool @ cOMBS_1451994324l_bool @ ( hAPP_f440042033l_bool @ ( cOMBB_532710323e_bool @ fconj ) @ ( hAPP_f900945761l_bool @ ( hAPP_f1846363427l_bool @ cOMBC_1909905718l_bool @ member1062536460e_bool ) @ B ) ) ) @ ( hAPP_H810811817l_bool @ ( hAPP_f309954467l_bool @ cOMBC_685773310e_bool @ ( hAPP_f1185879473e_bool @ ( cOMBB_1094554675e_bool @ fequal391417144_state ) @ A ) ) @ ( hAPP_f890249627_state @ A @ C ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).

thf(643,axiom,
    ! [A: fun_Ho1996104121e_bool,B: hoare_1875481847_state,C: fun_Ho1996104121e_bool] :
      ( ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ C ) )
       => ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ A ) ) @ C )
          = ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ C ) ) ) )
      & ( ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ C ) )
       => ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ A ) ) @ C )
          = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_620_Int__insert__left) ).

thf(3145,plain,
    ! [A: fun_Ho1996104121e_bool,B: hoare_1875481847_state,C: fun_Ho1996104121e_bool] :
      ( ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ C ) )
       => ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ A ) ) @ C )
          = ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ C ) ) ) )
      & ( ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ C ) )
       => ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ A ) ) @ C )
          = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).

thf(167,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool,D: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ D ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ C ) @ A ) ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ D ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_429_sup__mono) ).

thf(1410,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool,D: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ D ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ C ) @ A ) ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ D ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(442,axiom,
    ! [A: hoare_1875481847_state,B: hoare_1875481847_state] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ bot_bo1715400655e_bool ) ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_singleton__iff) ).

thf(2417,plain,
    ! [A: hoare_1875481847_state,B: hoare_1875481847_state] :
      ( ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ bot_bo1715400655e_bool ) ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ bot_bo1715400655e_bool ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).

thf(655,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_fu689207471l_bool] :
      ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ B ) )
     => ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ ( hAPP_f900945761l_bool @ ( hAPP_f872497439l_bool @ insert504309043e_bool @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_finite_OinsertI) ).

thf(3196,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_fu689207471l_bool] :
      ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ B ) )
     => ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ ( hAPP_f900945761l_bool @ ( hAPP_f872497439l_bool @ insert504309043e_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).

thf(718,axiom,
    ! [A: hoare_1875481847_state,B: hoare_1875481847_state] :
      ( ( A != B )
      | ( hBOOL @ ( hAPP_H1173941847e_bool @ ( hAPP_H117293375e_bool @ fequal391417144_state @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____xlrqixeqwe__Otriple_Itc__Com) ).

thf(3426,plain,
    ! [A: hoare_1875481847_state,B: hoare_1875481847_state] :
      ( ( A != B )
      | ( hBOOL @ ( hAPP_H1173941847e_bool @ ( hAPP_H117293375e_bool @ fequal391417144_state @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).

thf(423,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_fu689207471l_bool,C: fun_fu689207471l_bool] :
      ( ( hBOOL @ ( hAPP_f1699935247l_bool @ ( hAPP_f640685261l_bool @ member1062536460e_bool @ A ) @ ( hAPP_f900945761l_bool @ ( hAPP_f19215249l_bool @ semila1058800161l_bool @ B ) @ ( hAPP_f900945761l_bool @ collec771609166e_bool @ C ) ) ) )
    <=> ( ( hBOOL @ ( hAPP_f1699935247l_bool @ ( hAPP_f640685261l_bool @ member1062536460e_bool @ A ) @ B ) )
        & ( hBOOL @ ( hAPP_f1408815105l_bool @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_589_Int__Collect) ).

thf(2340,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_fu689207471l_bool,C: fun_fu689207471l_bool] :
      ( ( ( hBOOL @ ( hAPP_f1699935247l_bool @ ( hAPP_f640685261l_bool @ member1062536460e_bool @ A ) @ ( hAPP_f900945761l_bool @ ( hAPP_f19215249l_bool @ semila1058800161l_bool @ B ) @ ( hAPP_f900945761l_bool @ collec771609166e_bool @ C ) ) ) )
       => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ ( hAPP_f640685261l_bool @ member1062536460e_bool @ A ) @ B ) )
          & ( hBOOL @ ( hAPP_f1408815105l_bool @ C @ A ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f1699935247l_bool @ ( hAPP_f640685261l_bool @ member1062536460e_bool @ A ) @ B ) )
          & ( hBOOL @ ( hAPP_f1408815105l_bool @ C @ A ) ) )
       => ( hBOOL @ ( hAPP_f1699935247l_bool @ ( hAPP_f640685261l_bool @ member1062536460e_bool @ A ) @ ( hAPP_f900945761l_bool @ ( hAPP_f19215249l_bool @ semila1058800161l_bool @ B ) @ ( hAPP_f900945761l_bool @ collec771609166e_bool @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).

thf(100,axiom,
    ! [A: fun_fu1911931399l_bool,B: fun_fu1430349052l_bool,C: fun_fu1430349052l_bool] :
      ( ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ( hAPP_f1879335953l_bool @ cOMBC_7971162l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_) ).

thf(1165,plain,
    ! [A: fun_fu1911931399l_bool,B: fun_fu1430349052l_bool,C: fun_fu1430349052l_bool] :
      ( ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ( hAPP_f1879335953l_bool @ cOMBC_7971162l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(11,axiom,
    ! [A: fun_bo1549164019l_bool,B: fun_fu1430349052l_bool,C: fun_pname_bool] :
      ( ( hAPP_f1476298914l_bool @ ( hAPP_f143162813l_bool @ ( cOMBB_2095475776e_bool @ A ) @ B ) @ C )
      = ( hAPP_b589554111l_bool @ A @ ( hAPP_f1664156314l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_219) ).

thf(839,plain,
    ! [A: fun_bo1549164019l_bool,B: fun_fu1430349052l_bool,C: fun_pname_bool] :
      ( ( hAPP_f1476298914l_bool @ ( hAPP_f143162813l_bool @ ( cOMBB_2095475776e_bool @ A ) @ B ) @ C )
      = ( hAPP_b589554111l_bool @ A @ ( hAPP_f1664156314l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(468,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_st1506752259e_bool,C: com,D: fun_st1506752259e_bool,E: bool] :
      ( ( ( hBOOL @ E )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ B ) @ C ) @ D ) ) @ bot_bo1715400655e_bool ) ) ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ ( hAPP_b1095269219e_bool @ ( hAPP_f701449317e_bool @ cOMBC_471052088e_bool @ ( hAPP_f873506917e_bool @ ( cOMBB_1757942702_state @ cOMBC_231445413l_bool ) @ ( hAPP_f1283379615l_bool @ ( cOMBB_1759179140_state @ ( cOMBB_188601460_state @ fconj ) ) @ B ) ) ) @ E ) ) @ C ) @ D ) ) @ bot_bo1715400655e_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_359_constant) ).

thf(2502,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_st1506752259e_bool,C: com,D: fun_st1506752259e_bool,E: bool] :
      ( ( ( hBOOL @ E )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ B ) @ C ) @ D ) ) @ bot_bo1715400655e_bool ) ) ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ ( hAPP_b1095269219e_bool @ ( hAPP_f701449317e_bool @ cOMBC_471052088e_bool @ ( hAPP_f873506917e_bool @ ( cOMBB_1757942702_state @ cOMBC_231445413l_bool ) @ ( hAPP_f1283379615l_bool @ ( cOMBB_1759179140_state @ ( cOMBB_188601460_state @ fconj ) ) @ B ) ) ) @ E ) ) @ C ) @ D ) ) @ bot_bo1715400655e_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).

thf(285,axiom,
    ! [A: pname] :
      ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ bot_bo844097828e_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_emptyE) ).

thf(1827,plain,
    ! [A: pname] :
      ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ bot_bo844097828e_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(130,axiom,
    ! [A: fun_st1506752259e_bool,B: state,C: state] :
      ( ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ ( hAPP_f817621513e_bool @ cOMBC_2027030106e_bool @ A ) @ B ) @ C )
      = ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Ostate_000tc__Com__Ostate_000tc__HOL__Obool_U) ).

thf(1268,plain,
    ! [A: fun_st1506752259e_bool,B: state,C: state] :
      ( ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ ( hAPP_f817621513e_bool @ cOMBC_2027030106e_bool @ A ) @ B ) @ C )
      = ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(158,axiom,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_subset__insertI2) ).

thf(1378,plain,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(196,axiom,
    ! [A: fun_pname_bool] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ bot_bo844097828e_bool ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_365_bot__least) ).

thf(1500,plain,
    ! [A: fun_pname_bool] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ bot_bo844097828e_bool ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(251,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
     => ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ B ) @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_Un__absorb2) ).

thf(1713,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
     => ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ B ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(700,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_asm) ).

thf(3362,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).

thf(548,axiom,
    ! [A: fun_pn664418900_state] :
      ( ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ A ) @ bot_bo844097828e_bool )
      = bot_bo1715400655e_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_image__empty) ).

thf(2810,plain,
    ! [A: fun_pn664418900_state] :
      ( ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ A ) @ bot_bo844097828e_bool )
      = bot_bo1715400655e_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).

thf(637,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ B ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_finite__subset) ).

thf(3128,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ B ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).

thf(324,axiom,
    ! [A: fun_fu689207471l_bool,B: fun_pn760644914e_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
     => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ ( hAPP_f1970936639l_bool @ ord_le724727525l_bool @ A ) @ ( hAPP_f1522632684l_bool @ ( image_1165561978e_bool @ B ) @ C ) ) )
       => ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_finite__surj) ).

thf(1977,plain,
    ! [A: fun_fu689207471l_bool,B: fun_pn760644914e_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
     => ( ( hBOOL @ ( hAPP_f1699935247l_bool @ ( hAPP_f1970936639l_bool @ ord_le724727525l_bool @ A ) @ ( hAPP_f1522632684l_bool @ ( image_1165561978e_bool @ B ) @ C ) ) )
       => ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(93,axiom,
    ! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ A ) ) @ C )
        = ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_609_Int__insert__left__if1) ).

thf(1129,plain,
    ! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ A ) ) @ C )
        = ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(546,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: hoare_1875481847_state] :
      ( ( hBOOL @ ( hAPP_H1173941847e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1795624711e_bool @ cOMBC_1099403170l_bool @ member618553700_state ) @ A ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1795624711e_bool @ cOMBC_1099403170l_bool @ member618553700_state ) @ B ) ) @ C ) )
    <=> ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ C ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_591_inf__Int__eq) ).

thf(2803,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: hoare_1875481847_state] :
      ( ( ( hBOOL @ ( hAPP_H1173941847e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1795624711e_bool @ cOMBC_1099403170l_bool @ member618553700_state ) @ A ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1795624711e_bool @ cOMBC_1099403170l_bool @ member618553700_state ) @ B ) ) @ C ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ C ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ B ) ) ) )
      & ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ C ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ B ) ) )
       => ( hBOOL @ ( hAPP_H1173941847e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1795624711e_bool @ cOMBC_1099403170l_bool @ member618553700_state ) @ A ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1795624711e_bool @ cOMBC_1099403170l_bool @ member618553700_state ) @ B ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).

thf(206,axiom,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
      ( ( hAPP_f559147733l_bool @ ( hAPP_f230953622l_bool @ semila1782091504l_bool @ A ) @ B )
      = ( hAPP_f559147733l_bool @ collec1974731493e_bool @ ( hAPP_f559147733l_bool @ ( hAPP_f624840228l_bool @ cOMBS_350070575l_bool @ ( hAPP_f143162813l_bool @ ( cOMBB_2095475776e_bool @ fdisj ) @ ( hAPP_f559147733l_bool @ ( hAPP_f1145991873l_bool @ cOMBC_1988546018l_bool @ member799430823e_bool ) @ A ) ) ) @ ( hAPP_f559147733l_bool @ ( hAPP_f1145991873l_bool @ cOMBC_1988546018l_bool @ member799430823e_bool ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_Un__def) ).

thf(1532,plain,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
      ( ( hAPP_f559147733l_bool @ ( hAPP_f230953622l_bool @ semila1782091504l_bool @ A ) @ B )
      = ( hAPP_f559147733l_bool @ collec1974731493e_bool @ ( hAPP_f559147733l_bool @ ( hAPP_f624840228l_bool @ cOMBS_350070575l_bool @ ( hAPP_f143162813l_bool @ ( cOMBB_2095475776e_bool @ fdisj ) @ ( hAPP_f559147733l_bool @ ( hAPP_f1145991873l_bool @ cOMBC_1988546018l_bool @ member799430823e_bool ) @ A ) ) ) @ ( hAPP_f559147733l_bool @ ( hAPP_f1145991873l_bool @ cOMBC_1988546018l_bool @ member799430823e_bool ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(557,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ A ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_Un__least) ).

thf(2847,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ A ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).

thf(495,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) )
      <=> ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_352_order__antisym__conv) ).

thf(2600,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
     => ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) )
         => ( B = A ) )
        & ( ( B = A )
         => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).

thf(572,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ B ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_652_sup__inf__absorb) ).

thf(2898,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ A ) @ B ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).

thf(218,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ A ) @ B )
        = bot_bo844097828e_bool )
    <=> ( ( A = bot_bo844097828e_bool )
        & ( B = bot_bo844097828e_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_Un__empty) ).

thf(1582,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ A ) @ B )
          = bot_bo844097828e_bool )
       => ( ( A = bot_bo844097828e_bool )
          & ( B = bot_bo844097828e_bool ) ) )
      & ( ( ( A = bot_bo844097828e_bool )
          & ( B = bot_bo844097828e_bool ) )
       => ( ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ A ) @ B )
          = bot_bo844097828e_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(401,axiom,
    ! [A: fun_Ho14659478e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ B ) )
     => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( hAPP_f1628972376l_bool @ ( image_412748388e_bool @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_finite__imageI) ).

thf(2265,plain,
    ! [A: fun_Ho14659478e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ B ) )
     => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( hAPP_f1628972376l_bool @ ( image_412748388e_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

thf(152,axiom,
    ! [A: fun_pn1776597836_state,B: fun_pn664418900_state,C: pname] :
      ( ( hAPP_p702226982_state @ ( hAPP_f1981552043_state @ ( hAPP_f1875279510_state @ cOMBS_629630867_state @ A ) @ B ) @ C )
      = ( hAPP_H350317809_state @ ( hAPP_p1279250276_state @ A @ C ) @ ( hAPP_p702226982_state @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__Hoare____Mirabelle____xlrqixeqwe_) ).

thf(1357,plain,
    ! [A: fun_pn1776597836_state,B: fun_pn664418900_state,C: pname] :
      ( ( hAPP_p702226982_state @ ( hAPP_f1981552043_state @ ( hAPP_f1875279510_state @ cOMBS_629630867_state @ A ) @ B ) @ C )
      = ( hAPP_H350317809_state @ ( hAPP_p1279250276_state @ A @ C ) @ ( hAPP_p702226982_state @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(672,axiom,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ B ) )
    <=> ( hBOOL @ ( hAPP_H1173941847e_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_mem__def) ).

thf(3259,plain,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool] :
      ( ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_H1173941847e_bool @ B @ A ) ) )
      & ( ( hBOOL @ ( hAPP_H1173941847e_bool @ B @ A ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).

thf(221,axiom,
    ! [A: fun_state_bool,B: com] :
      ( skip
     != ( while @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_502_com_Osimps_I16_J) ).

thf(1597,plain,
    ! [A: fun_state_bool,B: com] :
      ( skip
     != ( while @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(802,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_xt1_I6_J) ).

thf(3740,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).

thf(464,axiom,
    ! [A: fun_Ho1996104121e_bool,B: hoare_1875481847_state,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ C ) )
     => ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ C ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ A ) )
        = ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_612_Int__insert__right__if1) ).

thf(2484,plain,
    ! [A: fun_Ho1996104121e_bool,B: hoare_1875481847_state,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ C ) )
     => ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ C ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ A ) )
        = ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila657954503e_bool @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).

thf(300,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_cut) ).

thf(1885,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(737,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ C ) )
     => ( ( C = A )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_ord__le__eq__trans) ).

thf(3494,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ C ) )
     => ( ( C = A )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).

thf(198,axiom,
    ! [A: pname,B: pname] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ bot_bo844097828e_bool ) ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_singleton__iff) ).

thf(1505,plain,
    ! [A: pname,B: pname] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ bot_bo844097828e_bool ) ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ B ) @ bot_bo844097828e_bool ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(163,axiom,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_subsetD) ).

thf(1399,plain,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(403,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_422_sup__commute) ).

thf(2270,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B )
      = ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(230,axiom,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
      ( ( hAPP_f559147733l_bool @ collec1974731493e_bool @ ( hAPP_f559147733l_bool @ ( hAPP_f624840228l_bool @ cOMBS_350070575l_bool @ ( hAPP_f143162813l_bool @ ( cOMBB_2095475776e_bool @ fconj ) @ A ) ) @ B ) )
      = ( hAPP_f559147733l_bool @ ( hAPP_f230953622l_bool @ semila1130628874l_bool @ ( hAPP_f559147733l_bool @ collec1974731493e_bool @ A ) ) @ ( hAPP_f559147733l_bool @ collec1974731493e_bool @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_584_Collect__conj__eq) ).

thf(1621,plain,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
      ( ( hAPP_f559147733l_bool @ collec1974731493e_bool @ ( hAPP_f559147733l_bool @ ( hAPP_f624840228l_bool @ cOMBS_350070575l_bool @ ( hAPP_f143162813l_bool @ ( cOMBB_2095475776e_bool @ fconj ) @ A ) ) @ B ) )
      = ( hAPP_f559147733l_bool @ ( hAPP_f230953622l_bool @ semila1130628874l_bool @ ( hAPP_f559147733l_bool @ collec1974731493e_bool @ A ) ) @ ( hAPP_f559147733l_bool @ collec1974731493e_bool @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(748,axiom,
    ! [A: fun_pn664418900_state,B: fun_pname_bool] :
      ( ( bot_bo1715400655e_bool
        = ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ A ) @ B ) )
    <=> ( B = bot_bo844097828e_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_empty__is__image) ).

thf(3526,plain,
    ! [A: fun_pn664418900_state,B: fun_pname_bool] :
      ( ( ( bot_bo1715400655e_bool
          = ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ A ) @ B ) )
       => ( B = bot_bo844097828e_bool ) )
      & ( ( B = bot_bo844097828e_bool )
       => ( bot_bo1715400655e_bool
          = ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).

thf(515,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: hoare_1875481847_state] :
      ( ( hBOOL @ ( hAPP_H1173941847e_bool @ B @ C ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ A ) )
       => ( hBOOL @ ( hAPP_H1173941847e_bool @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_390_rev__predicate1D) ).

thf(2672,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: hoare_1875481847_state] :
      ( ( hBOOL @ ( hAPP_H1173941847e_bool @ B @ C ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ B ) @ A ) )
       => ( hBOOL @ ( hAPP_H1173941847e_bool @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).

thf(727,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: hoare_1875481847_state] :
      ( ( hBOOL @ ( hAPP_H1173941847e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) @ C ) )
     => ( ~ ( hBOOL @ ( hAPP_H1173941847e_bool @ A @ C ) )
       => ( hBOOL @ ( hAPP_H1173941847e_bool @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_384_sup1E) ).

thf(3461,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool,C: hoare_1875481847_state] :
      ( ( hBOOL @ ( hAPP_H1173941847e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B ) @ C ) )
     => ( ~ ( hBOOL @ ( hAPP_H1173941847e_bool @ A @ C ) )
       => ( hBOOL @ ( hAPP_H1173941847e_bool @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).

thf(661,axiom,
    ! [A: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_Un__absorb) ).

thf(3212,plain,
    ! [A: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).

thf(448,axiom,
    ! [A: fun_pname_bool,B: fun_Ho1653816318_pname,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( hAPP_f1148778334e_bool @ ( image_720060442_pname @ B ) @ C ) ) )
    <=> ? [D: fun_Ho1996104121e_bool] :
          ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ D ) @ C ) )
          & ( A
            = ( hAPP_f1148778334e_bool @ ( image_720060442_pname @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_subset__image__iff) ).

thf(2436,plain,
    ! [A: fun_pname_bool,B: fun_Ho1653816318_pname,C: fun_Ho1996104121e_bool] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( hAPP_f1148778334e_bool @ ( image_720060442_pname @ B ) @ C ) ) )
       => ? [D: fun_Ho1996104121e_bool] :
            ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ D ) @ C ) )
            & ( A
              = ( hAPP_f1148778334e_bool @ ( image_720060442_pname @ B ) @ D ) ) ) )
      & ( ? [D: fun_Ho1996104121e_bool] :
            ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ D ) @ C ) )
            & ( A
              = ( hAPP_f1148778334e_bool @ ( image_720060442_pname @ B ) @ D ) ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( hAPP_f1148778334e_bool @ ( image_720060442_pname @ B ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).

thf(346,axiom,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool,C: hoare_1875481847_state] :
      ( ( hBOOL @ ( hAPP_H1173941847e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ B ) @ C ) )
    <=> ( ( A = C )
        | ( hBOOL @ ( hAPP_H1173941847e_bool @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_insert__code) ).

thf(2059,plain,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool,C: hoare_1875481847_state] :
      ( ( ( hBOOL @ ( hAPP_H1173941847e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ B ) @ C ) )
       => ( ( A = C )
          | ( hBOOL @ ( hAPP_H1173941847e_bool @ B @ C ) ) ) )
      & ( ( ( A = C )
          | ( hBOOL @ ( hAPP_H1173941847e_bool @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_H1173941847e_bool @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(309,axiom,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool] :
      ( bot_bo1715400655e_bool
     != ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_empty__not__insert) ).

thf(1912,plain,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool] :
      ( bot_bo1715400655e_bool
     != ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(25,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ C ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_643_le__infI) ).

thf(882,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ C ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(237,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ B ) @ C ) ) ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ A ) @ B ) ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_661_distrib__sup__le) ).

thf(1653,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ A ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ B ) @ C ) ) ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila1635148844e_bool @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ A ) @ B ) ) @ ( hAPP_f759274231e_bool @ ( hAPP_f1388330588e_bool @ semila278973382e_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(316,axiom,
    ! [A: fun_fu689207471l_bool] :
      ( ( ( hAPP_f900945761l_bool @ collec771609166e_bool @ A )
        = bot_bo973479705l_bool )
    <=> ! [B: fun_Ho1996104121e_bool] :
          ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_Collect__empty__eq) ).

thf(1944,plain,
    ! [A: fun_fu689207471l_bool] :
      ( ( ( ( hAPP_f900945761l_bool @ collec771609166e_bool @ A )
          = bot_bo973479705l_bool )
       => ! [B: fun_Ho1996104121e_bool] :
            ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ A @ B ) ) )
      & ( ! [B: fun_Ho1996104121e_bool] :
            ~ ( hBOOL @ ( hAPP_f1408815105l_bool @ A @ B ) )
       => ( ( hAPP_f900945761l_bool @ collec771609166e_bool @ A )
          = bot_bo973479705l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(484,axiom,
    ! [A: fun_Ho1653816318_pname,B: hoare_1875481847_state,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( hAPP_H139064010_pname @ A @ B ) ) @ ( hAPP_f1148778334e_bool @ ( image_720060442_pname @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_imageI) ).

thf(2563,plain,
    ! [A: fun_Ho1653816318_pname,B: hoare_1875481847_state,C: fun_Ho1996104121e_bool] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( hAPP_H139064010_pname @ A @ B ) ) @ ( hAPP_f1148778334e_bool @ ( image_720060442_pname @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).

thf(775,axiom,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool,C: fun_Ho784854669_state,D: fun_fu385705929_state] :
      ( ( hBOOL @ ( finite1782051386_state @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ B ) )
       => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ B ) )
         => ( ( ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ minus_589155914e_bool @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ bot_bo1715400655e_bool ) )
                = bot_bo1715400655e_bool )
             => ( ( hAPP_f890249627_state @ D @ B )
                = A ) )
            & ( ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ minus_589155914e_bool @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ bot_bo1715400655e_bool ) )
               != bot_bo1715400655e_bool )
             => ( ( hAPP_f890249627_state @ D @ B )
                = ( hAPP_H350317809_state @ ( hAPP_H743221337_state @ C @ A ) @ ( hAPP_f890249627_state @ D @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ minus_589155914e_bool @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ bot_bo1715400655e_bool ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_677_folding__one_Oremove) ).

thf(3626,plain,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool,C: fun_Ho784854669_state,D: fun_fu385705929_state] :
      ( ( hBOOL @ ( finite1782051386_state @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ B ) )
       => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ B ) )
         => ( ( ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ minus_589155914e_bool @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ bot_bo1715400655e_bool ) )
                = bot_bo1715400655e_bool )
             => ( ( hAPP_f890249627_state @ D @ B )
                = A ) )
            & ( ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ minus_589155914e_bool @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ bot_bo1715400655e_bool ) )
               != bot_bo1715400655e_bool )
             => ( ( hAPP_f890249627_state @ D @ B )
                = ( hAPP_H350317809_state @ ( hAPP_H743221337_state @ C @ A ) @ ( hAPP_f890249627_state @ D @ ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ minus_589155914e_bool @ B ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ bot_bo1715400655e_bool ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).

thf(569,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_fu385705929_state,C: fun_fu689207471l_bool] :
      ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ ( hAPP_f962122119e_bool @ ( image_1669234411_state @ B ) @ C ) ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_finite__surj) ).

thf(2887,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_fu385705929_state,C: fun_fu689207471l_bool] :
      ( ( hBOOL @ ( hAPP_f1699935247l_bool @ finite1559130124e_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_f1873026899l_bool @ ord_le233469699e_bool @ A ) @ ( hAPP_f962122119e_bool @ ( image_1669234411_state @ B ) @ C ) ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ finite1792194148_state @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).

thf(712,axiom,
    ! [A: fun_Ho1996104121e_bool,B: com] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_c406083500_state @ hoare_Mirabelle_MGT @ B ) ) @ bot_bo1715400655e_bool ) ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ ( hAPP_f1935169308e_bool @ ( cOMBB_1036740637_state @ ( cOMBB_1911358915_state @ fAll_state ) ) @ ( hAPP_f249262236e_bool @ ( cOMBB_1476898461_state @ ( hAPP_f915354021e_bool @ cOMBC_952831051e_bool @ ( hAPP_f1138284024e_bool @ ( cOMBB_20296667_state @ cOMBS_1378840469l_bool ) @ ( hAPP_f1283379615l_bool @ ( cOMBB_1759179140_state @ ( cOMBB_188601460_state @ fimplies ) ) @ ( evalc @ B ) ) ) ) ) @ fequal_state ) ) ) @ B ) @ fequal_state ) ) @ bot_bo1715400655e_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_534_MGT__alternI) ).

thf(3405,plain,
    ! [A: fun_Ho1996104121e_bool,B: com] :
      ( ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_c406083500_state @ hoare_Mirabelle_MGT @ B ) ) @ bot_bo1715400655e_bool ) ) )
     => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hoare_2131502867_state @ A ) @ ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ ( hAPP_f1595846909_state @ ( hAPP_c681126378_state @ ( hAPP_f1930074316_state @ hoare_13225861_state @ ( hAPP_f1935169308e_bool @ ( cOMBB_1036740637_state @ ( cOMBB_1911358915_state @ fAll_state ) ) @ ( hAPP_f249262236e_bool @ ( cOMBB_1476898461_state @ ( hAPP_f915354021e_bool @ cOMBC_952831051e_bool @ ( hAPP_f1138284024e_bool @ ( cOMBB_20296667_state @ cOMBS_1378840469l_bool ) @ ( hAPP_f1283379615l_bool @ ( cOMBB_1759179140_state @ ( cOMBB_188601460_state @ fimplies ) ) @ ( evalc @ B ) ) ) ) ) @ fequal_state ) ) ) @ B ) @ fequal_state ) ) @ bot_bo1715400655e_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).

thf(657,axiom,
    ! [A: hoare_1875481847_state] :
      ( ( hBOOL @ ( hAPP_H1173941847e_bool @ bot_bo1715400655e_bool @ A ) )
    <=> ( hBOOL @ bot_bot_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_374_bot__apply) ).

thf(3200,plain,
    ! [A: hoare_1875481847_state] :
      ( ( ( hBOOL @ ( hAPP_H1173941847e_bool @ bot_bo1715400655e_bool @ A ) )
       => ( hBOOL @ bot_bot_bool ) )
      & ( ( hBOOL @ bot_bot_bool )
       => ( hBOOL @ ( hAPP_H1173941847e_bool @ bot_bo1715400655e_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).

thf(280,axiom,
    ! [A: fun_fu931343505l_bool,B: fun_fu1430349052l_bool,C: fun_pname_bool] :
      ( ( hAPP_f1664156314l_bool @ ( hAPP_f559147733l_bool @ ( hAPP_f1145991873l_bool @ cOMBC_1988546018l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_225) ).

thf(1812,plain,
    ! [A: fun_fu931343505l_bool,B: fun_fu1430349052l_bool,C: fun_pname_bool] :
      ( ( hAPP_f1664156314l_bool @ ( hAPP_f559147733l_bool @ ( hAPP_f1145991873l_bool @ cOMBC_1988546018l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(615,axiom,
    ! [A: hoare_1875481847_state,B: fun_pn664418900_state,C: pname,D: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ D ) )
     => ( ( A
          = ( hAPP_p702226982_state @ B @ C ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ B ) @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_rev__image__eqI) ).

thf(3047,plain,
    ! [A: hoare_1875481847_state,B: fun_pn664418900_state,C: pname,D: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ D ) )
     => ( ( A
          = ( hAPP_p702226982_state @ B @ C ) )
       => ( hBOOL @ ( hAPP_f1408815105l_bool @ ( hAPP_H810811817l_bool @ member618553700_state @ A ) @ ( hAPP_f1291720380e_bool @ ( image_1283223414_state @ B ) @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).

thf(459,axiom,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ B )
     != bot_bo1715400655e_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_insert__not__empty) ).

thf(2470,plain,
    ! [A: hoare_1875481847_state,B: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_H1625489667e_bool @ insert694999549_state @ A ) @ B )
     != bot_bo1715400655e_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).

thf(61,axiom,
    ! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
      ( ( hAPP_f559147733l_bool @ ( hAPP_f1320879424l_bool @ insert1325755072e_bool @ A ) @ ( hAPP_f559147733l_bool @ collec1974731493e_bool @ B ) )
      = ( hAPP_f559147733l_bool @ collec1974731493e_bool @ ( hAPP_f559147733l_bool @ ( hAPP_f624840228l_bool @ cOMBS_350070575l_bool @ ( hAPP_f143162813l_bool @ ( cOMBB_2095475776e_bool @ fimplies ) @ ( hAPP_f559147733l_bool @ ( cOMBB_307249310e_bool @ fNot ) @ ( hAPP_f434788991l_bool @ ( hAPP_f1297925993l_bool @ cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ A ) ) ) ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_insert__Collect) ).

thf(1014,plain,
    ! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
      ( ( hAPP_f559147733l_bool @ ( hAPP_f1320879424l_bool @ insert1325755072e_bool @ A ) @ ( hAPP_f559147733l_bool @ collec1974731493e_bool @ B ) )
      = ( hAPP_f559147733l_bool @ collec1974731493e_bool @ ( hAPP_f559147733l_bool @ ( hAPP_f624840228l_bool @ cOMBS_350070575l_bool @ ( hAPP_f143162813l_bool @ ( cOMBB_2095475776e_bool @ fimplies ) @ ( hAPP_f559147733l_bool @ ( cOMBB_307249310e_bool @ fNot ) @ ( hAPP_f434788991l_bool @ ( hAPP_f1297925993l_bool @ cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ A ) ) ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(170,axiom,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B )
      = ( hAPP_f121055253e_bool @ collec1735317154_state @ ( hAPP_f121055253e_bool @ ( hAPP_f1300953505e_bool @ cOMBS_896408300l_bool @ ( hAPP_f932622461l_bool @ ( cOMBB_242064253_state @ fdisj ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1795624711e_bool @ cOMBC_1099403170l_bool @ member618553700_state ) @ A ) ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1795624711e_bool @ cOMBC_1099403170l_bool @ member618553700_state ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_Un__def) ).

thf(1417,plain,
    ! [A: fun_Ho1996104121e_bool,B: fun_Ho1996104121e_bool] :
      ( ( hAPP_f121055253e_bool @ ( hAPP_f1204759513e_bool @ semila1107643821e_bool @ A ) @ B )
      = ( hAPP_f121055253e_bool @ collec1735317154_state @ ( hAPP_f121055253e_bool @ ( hAPP_f1300953505e_bool @ cOMBS_896408300l_bool @ ( hAPP_f932622461l_bool @ ( cOMBB_242064253_state @ fdisj ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1795624711e_bool @ cOMBC_1099403170l_bool @ member618553700_state ) @ A ) ) ) @ ( hAPP_f121055253e_bool @ ( hAPP_f1795624711e_bool @ cOMBC_1099403170l_bool @ member618553700_state ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(296,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ A ) @ B ) )
      | ( hBOOL @ A )
      | ( hBOOL @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fdisj_3_1_U) ).

thf(1870,plain,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ A ) @ B ) )
      | ( hBOOL @ A )
      | ( hBOOL @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(29422,plain,
    $false,
    inference(cvc4,[status(thm)],[2630,2452,1469,1168,2336,2778,3666,2427,2559,941,3566,1818,1554,1322,1665,2889,1190,909,1031,893,1840,2077,2622,3549,3377,1401,2947,1073,1205,1591,3498,861,1486,1924,1005,2940,1406,2808,3762,2644,1443,3417,1728,3108,1971,1793,3402,2854,3017,1655,1756,3649,3044,3446,2933,1233,2580,2901,1354,1078,1426,3217,3004,3367,2434,1872,2476,2627,1988,2459,1342,3121,1954,2844,1095,2046,2227,3513,3730,1601,2082,2173,1529,1803,1887,2957,3335,1196,3103,898,1001,2723,1127,2491,1243,1518,1265,1703,2328,3029,3644,2667,3342,2755,3061,2708,2444,3612,917,3542,3280,3744,3353,2466,2571,3749,3089,1462,1132,1800,2169,1147,2552,1319,2767,1609,2373,3734,2158,1773,1362,1875,2852,817,2691,902,3463,3374,1115,3470,3312,3657,1931,2301,1815,2007,2222,924,2616,3524,3393,3295,3621,1677,2555,966,3152,2105,3075,1450,1109,1632,1682,834,1383,1020,2254,1283,2073,2508,1896,3505,2424,2772,1351,998,2750,3226,2965,3184,2367,3537,2618,2833,2281,2861,1215,1526,2137,1345,2639,1104,849,3606,1521,3510,1564,2954,1604,3097,3011,1067,3450,3459,3301,2204,2574,1438,1199,2164,1311,3767,2232,2296,3054,2660,1768,1868,3037,1163,1274,1900,1223,2428,825,2249,2541,2596,1570,2147,3742,2606,3286,3022,1502,1751,820,1824,1619,3207,3682,3778,1238,2015,3166,847,3618,1365,852,3349,1951,3718,1210,2741,1392,1291,842,3595,1106,3282,1423,3307,1968,2565,3198,2068,1624,2200,2609,1836,1787,1983,2115,1259,1017,1121,1111,1498,2694,3704,3518,1878,3746,3078,1118,3205,3176,1360,1936,3467,3699,1089,3615,3482,1762,2515,3413,2577,1064,1719,2537,884,1659,3000,933,2830,3714,2868,1075,2349,2085,2317,2781,3775,3141,3407,2561,3210,1414,2053,1700,2613,3032,2108,2038,1889,3555,1612,2649,970,837,1776,3654,1249,2487,2153,2355,3247,3333,1979,3364,1759,1297,3126,3787,1539,1456,3770,1668,1974,2505,3390,1852,2813,2697,1246,1627,2370,3215,3476,1991,1202,3592,2963,1515,1026,3422,2529,1086,938,3563,2761,1779,3624,2793,3190,1996,3675,1906,3660,3707,3130,2677,3042,2717,1548,856,3111,2376,3158,2235,2144,2936,2729,2904,1680,3491,1483,1154,1833,3070,1916,3240,2981,2489,875,1795,3604,1965,1124,3599,975,3387,3187,2859,2938,1784,3255,3609,2849,3758,1929,2674,2568,1535,2991,958,1403,1256,1226,2161,1139,2193,2220,3051,3663,3594,1332,1092,1765,3304,3568,2573,3773,936,2029,2326,1271,2308,1371,1635,2935,2759,2753,2457,919,1464,2474,947,2346,2079,831,3631,3551,1806,1524,3270,3732,2955,1722,2839,2943,880,2871,2721,2119,2151,2642,3155,3106,1542,2856,3138,2378,3182,2896,890,3219,2632,1339,816,2267,2446,1325,3298,2252,1177,2974,1061,1688,2314,3668,2625,2111,3073,1821,1731,2593,1029,1556,2647,2710,2911,912,2365,1474,2212,3759,1445,986,1435,2101,2390,1102,2156,2207,922,2984,3380,3539,2770,2725,1594,2765,2481,1477,3142,3009,2096,3193,1208,1467,3293,1277,2449,1081,2202,1472,1551,3571,3444,1034,2914,2816,1809,2952,3576,944,3161,1420,2333,2256,3278,1958,968,823,1845,1748,2977,2012,2588,1368,2821,1230,1098,2882,1003,3737,1770,2397,3507,1070,3112,872,3448,1432,3722,1830,2322,1579,2656,3019,2747,1790,1716,2224,2454,1300,3691,1188,2700,1262,1235,2276,1980,2128,951,2545,3359,3329,2044,1218,3095,2468,1220,2056,3488,1023,864,1670,2949,3398,1849,3652,2543,3356,2279,2357,859,3288,1240,1617,3478,3433,2479,2088,2960,1157,3533,2310,1412,2215,2611,2209,3039,1998,2875,1940,3284,845,3457,2352,1459,3092,3067,1180,931,1685,2885,2997,1448,2187,1010,1390,1289,3056,1453,1734,2907,3465,3729,961,1639,2290,1745,2026,2971,3516,3252,2526,995,2394,963,2167,2273,896,2098,1903,2135,2406,3369,2823,1629,2004,3235,2431,3501,3003,3331,3136,1861,1491,3324,3430,2330,2198,1706,2362,1607,1994,1045,2384,3694,2796,914,2399,2041,3267,1294,2462,2680,1212,2230,1893,2294,3420,1614,1908,1348,2287,1512,1725,2719,3601,3264,1380,3521,1986,867,1480,2218,2258,2930,2123,2534,3232,2522,3100,1859,1314,3558,2070,1561,828,3633,3309,3145,1410,2417,3196,3426,2340,1165,839,2502,1827,1268,1378,1500,1713,3362,2810,3128,1977,1129,2803,1532,2847,2600,2898,1582,2265,1357,3259,1597,3740,2484,1885,3494,1505,1399,2270,1621,3526,2672,3461,3212,2436,2059,1912,882,1653,1944,2563,3626,2887,3405,3200,1812,3047,2470,1014,1417,1870]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SWW474_2 : TPTP v8.2.0. Released v5.3.0.
% 0.14/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n008.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Sat May 18 20:53:24 EDT 2024
% 0.15/0.36  % CPUTime  : 
% 0.95/0.85  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.88/1.14  % [INFO] 	 Parsing done (293ms). 
% 1.88/1.15  % [INFO] 	 Running in sequential loop mode. 
% 2.76/1.36  % [INFO] 	 eprover registered as external prover. 
% 2.76/1.37  % [INFO] 	 cvc4 registered as external prover. 
% 2.76/1.37  % [INFO] 	 Scanning for conjecture ... 
% 3.28/1.57  % [INFO] 	 Found a conjecture (or negated_conjecture) and 813 axioms. Running axiom selection ... 
% 4.31/1.79  % [INFO] 	 Axiom selection finished. Selected 813 axioms (removed 0 axioms). 
% 5.53/2.14  % [INFO] 	 Problem is typed first-order (TPTP TFF). 
% 5.53/2.16  % [INFO] 	 Type checking passed. 
% 5.53/2.16  % [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 ... 
% 9.50/3.21  % [INFO] 	 [Domain constraints] Detected constraint on bool 
% 9.50/3.21  % [INFO] 	 [Domain constraints] dom(bool) ⊆ {fTrue,fFalse} 
% 10.37/3.46  % [INFO] 	 [Domain constraints] Detected constraint on bool 
% 10.37/3.46  % [INFO] 	 [Domain constraints] dom(bool) ⊆ {fTrue,fFalse} 
% 10.99/3.52  % [INFO] 	 [Domain constraints] Detected constraint on bool 
% 10.99/3.52  % [INFO] 	 [Domain constraints] dom(bool) ⊆ {fTrue,fFalse} 
% 95.62/23.53  % External prover 'cvc4' found a proof!
% 95.62/23.53  % [INFO] 	 Killing All external provers ... 
% 95.62/23.54  % Time passed: 23020ms (effective reasoning time: 22381ms)
% 95.62/23.54  % 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)>
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% 95.62/23.55  % No. of inferences in proof: 1630
% 95.62/23.55  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 23020 ms resp. 22381 ms w/o parsing
% 97.19/24.23  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 97.19/24.25  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------