%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SWW470_1 : TPTP v8.1.2. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n024.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May 19 12:23:57 EDT 2023

% Result   : Theorem 8.86s 2.90s
% Output   : Refutation 8.99s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  271
% Syntax   : Number of formulae    :  408 ( 102 unt; 136 typ;   0 def)
%            Number of atoms       :  686 ( 270 equ;   0 cnn)
%            Maximal formula atoms :   14 (   2 avg)
%            Number of connectives : 3980 ( 130   ~;  59   |;  81   &;3436   @)
%                                         (  22 <=>; 252  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   23 (   9 avg)
%            Number of types       :   46 (  45 usr)
%            Number of type conns  :  109 ( 109   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   93 (  91 usr;  31 con; 0-3 aty)
%            Number of variables   :  756 (   0   ^; 709   !;  47   ?; 756   :)

% Comments : 
%------------------------------------------------------------------------------
thf(x_a_type,type,
    x_a: $tType ).

thf(com_type,type,
    com: $tType ).

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

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

thf(hoare_1927711152iple_a_type,type,
    hoare_1927711152iple_a: $tType ).

thf(fun_a_fun_state_bool_type,type,
    fun_a_fun_state_bool: $tType ).

thf(fun_a_1632297036l_bool_type,type,
    fun_a_1632297036l_bool: $tType ).

thf(fun_a_998512028e_bool_type,type,
    fun_a_998512028e_bool: $tType ).

thf(fun_a_2117018159e_bool_type,type,
    fun_a_2117018159e_bool: $tType ).

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

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

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

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

thf(fun_bo675861616e_bool_type,type,
    fun_bo675861616e_bool: $tType ).

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

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

thf(fun_Ho1877127206a_bool_type,type,
    fun_Ho1877127206a_bool: $tType ).

thf(fun_Ho843200573iple_a_type,type,
    fun_Ho843200573iple_a: $tType ).

thf(fun_Ho957066028l_bool_type,type,
    fun_Ho957066028l_bool: $tType ).

thf(fun_Ho440810351a_bool_type,type,
    fun_Ho440810351a_bool: $tType ).

thf(fun_Ho333840202iple_a_type,type,
    fun_Ho333840202iple_a: $tType ).

thf(fun_Ho525994229l_bool_type,type,
    fun_Ho525994229l_bool: $tType ).

thf(fun_Ho1630563774a_bool_type,type,
    fun_Ho1630563774a_bool: $tType ).

thf(fun_fu2118559873l_bool_type,type,
    fun_fu2118559873l_bool: $tType ).

thf(fun_fu1591723597e_bool_type,type,
    fun_fu1591723597e_bool: $tType ).

thf(fun_fu2008829792e_bool_type,type,
    fun_fu2008829792e_bool: $tType ).

thf(fun_fu222103665e_bool_type,type,
    fun_fu222103665e_bool: $tType ).

thf(fun_fu734682033e_bool_type,type,
    fun_fu734682033e_bool: $tType ).

thf(fun_fu281355805e_bool_type,type,
    fun_fu281355805e_bool: $tType ).

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

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

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

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

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

thf(fun_fu832487784l_bool_type,type,
    fun_fu832487784l_bool: $tType ).

thf(fun_fu1033095803iple_a_type,type,
    fun_fu1033095803iple_a: $tType ).

thf(fun_fu1585556401a_bool_type,type,
    fun_fu1585556401a_bool: $tType ).

thf(fun_fu269925879l_bool_type,type,
    fun_fu269925879l_bool: $tType ).

thf(fun_fu276214394a_bool_type,type,
    fun_fu276214394a_bool: $tType ).

thf(fun_fu1644852787l_bool_type,type,
    fun_fu1644852787l_bool: $tType ).

thf(fun_fu1249172034a_bool_type,type,
    fun_fu1249172034a_bool: $tType ).

thf(fun_fu1563903738a_bool_type,type,
    fun_fu1563903738a_bool: $tType ).

thf(fun_fu893561155a_bool_type,type,
    fun_fu893561155a_bool: $tType ).

thf(fun_fu1192765369a_bool_type,type,
    fun_fu1192765369a_bool: $tType ).

thf(fun_fu1905604217a_bool_type,type,
    fun_fu1905604217a_bool: $tType ).

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

thf(cOMBB_213049548iple_a_type,type,
    cOMBB_213049548iple_a: fun_bool_bool > fun_fu1585556401a_bool ).

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

thf(cOMBB_196465322iple_a_type,type,
    cOMBB_196465322iple_a: fun_bo1549164019l_bool > fun_fu269925879l_bool ).

thf(cOMBB_1355796797bool_a_type,type,
    cOMBB_1355796797bool_a: fun_fu1658206819l_bool > fun_fu2118559873l_bool ).

thf(cOMBB_1348041619bool_a_type,type,
    cOMBB_1348041619bool_a: fun_fu1219323149e_bool > fun_fu1591723597e_bool ).

thf(cOMBB_145932198bool_a_type,type,
    cOMBB_145932198bool_a: fun_fu1047394976e_bool > fun_fu2008829792e_bool ).

thf(cOMBB_1083611331iple_a_type,type,
    cOMBB_1083611331iple_a: fun_fu832487784l_bool > fun_fu1563903738a_bool ).

thf(cOMBC_41962815e_bool_type,type,
    cOMBC_41962815e_bool: fun_fu222103665e_bool ).

thf(cOMBC_892787026e_bool_type,type,
    cOMBC_892787026e_bool: fun_fu734682033e_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_671859290a_bool_type,type,
    cOMBC_671859290a_bool: fun_fu893561155a_bool ).

thf(cOMBC_862840740l_bool_type,type,
    cOMBC_862840740l_bool: fun_fu1192765369a_bool ).

thf(cOMBC_825881325a_bool_type,type,
    cOMBC_825881325a_bool: fun_fu1905604217a_bool ).

thf(cOMBK_bool_state_type,type,
    cOMBK_bool_state: bool > fun_state_bool ).

thf(cOMBK_712844119iple_a_type,type,
    cOMBK_712844119iple_a: bool > fun_Ho1877127206a_bool ).

thf(cOMBK_1458035955bool_a_type,type,
    cOMBK_1458035955bool_a: fun_state_bool > fun_a_fun_state_bool ).

thf(cOMBS_1378840469l_bool_type,type,
    cOMBS_1378840469l_bool: fun_fu1047394976e_bool ).

thf(cOMBS_2061548107l_bool_type,type,
    cOMBS_2061548107l_bool: fun_fu1249172034a_bool ).

thf(skip_type,type,
    skip: com ).

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

thf(finite68738179iple_a_type,type,
    finite68738179iple_a: fun_fu832487784l_bool ).

thf(finite2098837632iple_a_type,type,
    finite2098837632iple_a: fun_Ho333840202iple_a > fun_Ho1877127206a_bool > fun_Ho1877127206a_bool ).

thf(finite1943414032iple_a_type,type,
    finite1943414032iple_a: fun_Ho333840202iple_a > fun_fu1033095803iple_a ).

thf(finite148164294iple_a_type,type,
    finite148164294iple_a: fun_Ho333840202iple_a > hoare_1927711152iple_a > fun_Ho1877127206a_bool > fun_Ho1877127206a_bool ).

thf(finite83514413iple_a_type,type,
    finite83514413iple_a: fun_Ho333840202iple_a > fun_fu1033095803iple_a > bool ).

thf(finite1511031594iple_a_type,type,
    finite1511031594iple_a: fun_Ho333840202iple_a > fun_fu1033095803iple_a > bool ).

thf(the_Ho1307659873iple_a_type,type,
    the_Ho1307659873iple_a: fun_fu1033095803iple_a ).

thf(hoare_1617968510rivs_a_type,type,
    hoare_1617968510rivs_a: fun_Ho1877127206a_bool > fun_fu832487784l_bool ).

thf(hoare_1652181356iple_a_type,type,
    hoare_1652181356iple_a: fun_a_fun_state_bool > com > fun_a_fun_state_bool > hoare_1927711152iple_a ).

thf(bot_bot_bool_type,type,
    bot_bot_bool: bool ).

thf(bot_bo1208640912a_bool_type,type,
    bot_bo1208640912a_bool: fun_Ho1877127206a_bool ).

thf(collec829051333iple_a_type,type,
    collec829051333iple_a: fun_Ho1877127206a_bool > fun_Ho1877127206a_bool ).

thf(insert1434104874iple_a_type,type,
    insert1434104874iple_a: fun_Ho1630563774a_bool ).

thf(the_el1997360207iple_a_type,type,
    the_el1997360207iple_a: fun_fu1033095803iple_a ).

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_state_type,type,
    fequal_state: fun_st1506752259e_bool ).

thf(fequal1440857775iple_a_type,type,
    fequal1440857775iple_a: fun_Ho440810351a_bool ).

thf(fequal1285825639a_bool_type,type,
    fequal1285825639a_bool: fun_fu1644852787l_bool ).

thf(fimplies_type,type,
    fimplies: fun_bo1549164019l_bool ).

thf(hAPP_a2036067514e_bool_type,type,
    hAPP_a2036067514e_bool: fun_a_fun_state_bool > x_a > fun_state_bool ).

thf(hAPP_a849909144l_bool_type,type,
    hAPP_a849909144l_bool: fun_a_1632297036l_bool > x_a > fun_st2063251938l_bool ).

thf(hAPP_a723219176e_bool_type,type,
    hAPP_a723219176e_bool: fun_a_998512028e_bool > x_a > fun_bo1936561970e_bool ).

thf(hAPP_a1200519163e_bool_type,type,
    hAPP_a1200519163e_bool: fun_a_2117018159e_bool > x_a > fun_fu373216837e_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_s58564346l_bool_type,type,
    hAPP_s58564346l_bool: fun_st2063251938l_bool > state > fun_bool_bool ).

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

thf(hAPP_b540892988e_bool_type,type,
    hAPP_b540892988e_bool: fun_bo675861616e_bool > bool > fun_a_fun_state_bool ).

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

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

thf(hAPP_H1448631928a_bool_type,type,
    hAPP_H1448631928a_bool: fun_Ho1877127206a_bool > hoare_1927711152iple_a > bool ).

thf(hAPP_H963118037iple_a_type,type,
    hAPP_H963118037iple_a: fun_Ho843200573iple_a > hoare_1927711152iple_a > hoare_1927711152iple_a ).

thf(hAPP_H1487873860l_bool_type,type,
    hAPP_H1487873860l_bool: fun_Ho957066028l_bool > hoare_1927711152iple_a > fun_bool_bool ).

thf(hAPP_H1027145665a_bool_type,type,
    hAPP_H1027145665a_bool: fun_Ho440810351a_bool > hoare_1927711152iple_a > fun_Ho1877127206a_bool ).

thf(hAPP_H1700437986iple_a_type,type,
    hAPP_H1700437986iple_a: fun_Ho333840202iple_a > hoare_1927711152iple_a > fun_Ho843200573iple_a ).

thf(hAPP_H694056973l_bool_type,type,
    hAPP_H694056973l_bool: fun_Ho525994229l_bool > hoare_1927711152iple_a > fun_fu832487784l_bool ).

thf(hAPP_H1975128022a_bool_type,type,
    hAPP_H1975128022a_bool: fun_Ho1630563774a_bool > hoare_1927711152iple_a > fun_fu1585556401a_bool ).

thf(hAPP_f1509969235l_bool_type,type,
    hAPP_f1509969235l_bool: fun_fu2118559873l_bool > fun_a_fun_state_bool > fun_a_1632297036l_bool ).

thf(hAPP_f340725611e_bool_type,type,
    hAPP_f340725611e_bool: fun_fu1591723597e_bool > fun_a_1632297036l_bool > fun_a_998512028e_bool ).

thf(hAPP_f963367678e_bool_type,type,
    hAPP_f963367678e_bool: fun_fu2008829792e_bool > fun_a_1632297036l_bool > fun_a_2117018159e_bool ).

thf(hAPP_f1824947087e_bool_type,type,
    hAPP_f1824947087e_bool: fun_fu222103665e_bool > fun_a_998512028e_bool > fun_bo675861616e_bool ).

thf(hAPP_f1261923407e_bool_type,type,
    hAPP_f1261923407e_bool: fun_fu734682033e_bool > fun_a_2117018159e_bool > fun_fu281355805e_bool ).

thf(hAPP_f762886889e_bool_type,type,
    hAPP_f762886889e_bool: fun_fu281355805e_bool > fun_state_bool > fun_a_fun_state_bool ).

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

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

thf(hAPP_f817621513e_bool_type,type,
    hAPP_f817621513e_bool: fun_fu402792811e_bool > fun_st1506752259e_bool > fun_st1506752259e_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_f1454306822l_bool_type,type,
    hAPP_f1454306822l_bool: fun_fu832487784l_bool > fun_Ho1877127206a_bool > bool ).

thf(hAPP_f490779847iple_a_type,type,
    hAPP_f490779847iple_a: fun_fu1033095803iple_a > fun_Ho1877127206a_bool > hoare_1927711152iple_a ).

thf(hAPP_f16502863a_bool_type,type,
    hAPP_f16502863a_bool: fun_fu1585556401a_bool > fun_Ho1877127206a_bool > fun_Ho1877127206a_bool ).

thf(hAPP_f749678531l_bool_type,type,
    hAPP_f749678531l_bool: fun_fu269925879l_bool > fun_Ho1877127206a_bool > fun_Ho957066028l_bool ).

thf(hAPP_f993216280a_bool_type,type,
    hAPP_f993216280a_bool: fun_fu276214394a_bool > fun_Ho1877127206a_bool > fun_Ho440810351a_bool ).

thf(hAPP_f625100287l_bool_type,type,
    hAPP_f625100287l_bool: fun_fu1644852787l_bool > fun_Ho1877127206a_bool > fun_fu832487784l_bool ).

thf(hAPP_f2112551770a_bool_type,type,
    hAPP_f2112551770a_bool: fun_fu1249172034a_bool > fun_Ho957066028l_bool > fun_fu1585556401a_bool ).

thf(hAPP_f909473944a_bool_type,type,
    hAPP_f909473944a_bool: fun_fu1563903738a_bool > fun_Ho440810351a_bool > fun_Ho1877127206a_bool ).

thf(hAPP_f1216137953a_bool_type,type,
    hAPP_f1216137953a_bool: fun_fu893561155a_bool > fun_Ho440810351a_bool > fun_Ho440810351a_bool ).

thf(hAPP_f684479953a_bool_type,type,
    hAPP_f684479953a_bool: fun_fu1192765369a_bool > fun_Ho525994229l_bool > fun_fu1585556401a_bool ).

thf(hAPP_f1022403729a_bool_type,type,
    hAPP_f1022403729a_bool: fun_fu1905604217a_bool > fun_Ho1630563774a_bool > fun_fu276214394a_bool ).

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

thf(member127332739iple_a_type,type,
    member127332739iple_a: fun_Ho525994229l_bool ).

thf(g_type,type,
    g: fun_Ho1877127206a_bool ).

thf(p_type,type,
    p: fun_a_fun_state_bool ).

thf(b_type,type,
    b: fun_state_bool ).

thf(c_type,type,
    c: com ).

thf(127,axiom,
    ! [A: hoare_1927711152iple_a,B: hoare_1927711152iple_a] :
      ( ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ A ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ B ) @ bot_bo1208640912a_bool ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_singletonE) ).

thf(640,plain,
    ! [A: hoare_1927711152iple_a,B: hoare_1927711152iple_a] :
      ( ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ A ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ B ) @ bot_bo1208640912a_bool ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(3,axiom,
    ! [A: com,B: com] :
      ( skip
     != ( semi @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_com_Osimps_I12_J) ).

thf(138,plain,
    ! [A: com,B: com] :
      ( skip
     != ( semi @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(124,axiom,
    ! [A: hoare_1927711152iple_a,B: fun_Ho1877127206a_bool] :
      ( ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ A ) @ B )
     != bot_bo1208640912a_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_insert__not__empty) ).

thf(628,plain,
    ! [A: hoare_1927711152iple_a,B: fun_Ho1877127206a_bool] :
      ( ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ A ) @ B )
     != bot_bo1208640912a_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(92,axiom,
    ! [A: fun_Ho1877127206a_bool] :
      ( ( hBOOL @ ( hAPP_f1454306822l_bool @ finite68738179iple_a @ A ) )
    <=> ( ( A = bot_bo1208640912a_bool )
        | ? [B: fun_Ho1877127206a_bool,C: hoare_1927711152iple_a] :
            ( ( A
              = ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ C ) @ B ) )
            & ( hBOOL @ ( hAPP_f1454306822l_bool @ finite68738179iple_a @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_finite_Osimps) ).

thf(468,plain,
    ! [A: fun_Ho1877127206a_bool] :
      ( ( ( hBOOL @ ( hAPP_f1454306822l_bool @ finite68738179iple_a @ A ) )
       => ( ( A = bot_bo1208640912a_bool )
          | ? [B: fun_Ho1877127206a_bool,C: hoare_1927711152iple_a] :
              ( ( A
                = ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ C ) @ B ) )
              & ( hBOOL @ ( hAPP_f1454306822l_bool @ finite68738179iple_a @ B ) ) ) ) )
      & ( ( ( A = bot_bo1208640912a_bool )
          | ? [B: fun_Ho1877127206a_bool,C: hoare_1927711152iple_a] :
              ( ( A
                = ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ C ) @ B ) )
              & ( hBOOL @ ( hAPP_f1454306822l_bool @ finite68738179iple_a @ B ) ) ) )
       => ( hBOOL @ ( hAPP_f1454306822l_bool @ finite68738179iple_a @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(132,axiom,
    ! [A: hoare_1927711152iple_a] :
      ~ ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ A ) @ bot_bo1208640912a_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_empty__iff) ).

thf(666,plain,
    ! [A: hoare_1927711152iple_a] :
      ~ ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ A ) @ bot_bo1208640912a_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(85,axiom,
    ! [A: hoare_1927711152iple_a,B: fun_Ho1877127206a_bool,C: fun_Ho333840202iple_a,D: fun_fu1033095803iple_a] :
      ( ( hBOOL @ ( finite83514413iple_a @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1454306822l_bool @ finite68738179iple_a @ B ) )
       => ( ~ ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ A ) @ B ) )
         => ( ( B != bot_bo1208640912a_bool )
           => ( ( hAPP_f490779847iple_a @ D @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ A ) @ B ) )
              = ( hAPP_H963118037iple_a @ ( hAPP_H1700437986iple_a @ C @ A ) @ ( hAPP_f490779847iple_a @ D @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_folding__one_Oinsert) ).

thf(449,plain,
    ! [A: hoare_1927711152iple_a,B: fun_Ho1877127206a_bool,C: fun_Ho333840202iple_a,D: fun_fu1033095803iple_a] :
      ( ( hBOOL @ ( finite83514413iple_a @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1454306822l_bool @ finite68738179iple_a @ B ) )
       => ( ~ ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ A ) @ B ) )
         => ( ( B != bot_bo1208640912a_bool )
           => ( ( hAPP_f490779847iple_a @ D @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ A ) @ B ) )
              = ( hAPP_H963118037iple_a @ ( hAPP_H1700437986iple_a @ C @ A ) @ ( hAPP_f490779847iple_a @ D @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(32,axiom,
    ! [A: hoare_1927711152iple_a] :
      ( ( collec829051333iple_a @ ( hAPP_H1027145665a_bool @ ( hAPP_f1216137953a_bool @ cOMBC_671859290a_bool @ fequal1440857775iple_a ) @ A ) )
      = ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ A ) @ bot_bo1208640912a_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_singleton__conv) ).

thf(247,plain,
    ! [A: hoare_1927711152iple_a] :
      ( ( collec829051333iple_a @ ( hAPP_H1027145665a_bool @ ( hAPP_f1216137953a_bool @ cOMBC_671859290a_bool @ fequal1440857775iple_a ) @ A ) )
      = ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ A ) @ bot_bo1208640912a_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(100,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ B )
      | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_2_1_U) ).

thf(511,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)],[100]) ).

thf(69,axiom,
    ! [A: fun_Ho1877127206a_bool,B: fun_Ho1877127206a_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_f625100287l_bool @ fequal1285825639a_bool @ A ) @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple) ).

thf(384,plain,
    ! [A: fun_Ho1877127206a_bool,B: fun_Ho1877127206a_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_f625100287l_bool @ fequal1285825639a_bool @ A ) @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(4,axiom,
    ! [A: fun_Ho1877127206a_bool] :
      ( ( collec829051333iple_a @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_Collect__def) ).

thf(142,plain,
    ! [A: fun_Ho1877127206a_bool] :
      ( ( collec829051333iple_a @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(74,axiom,
    ! [A: fun_Ho333840202iple_a,B: hoare_1927711152iple_a,C: fun_Ho1877127206a_bool,D: hoare_1927711152iple_a] :
      ( ( hBOOL @ ( hAPP_H1448631928a_bool @ ( finite148164294iple_a @ A @ B @ C ) @ D ) )
     => ( ~ ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ B ) @ C ) )
       => ( hBOOL @ ( hAPP_H1448631928a_bool @ ( finite2098837632iple_a @ A @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ B ) @ C ) ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_fold1Set_Ointros) ).

thf(404,plain,
    ! [A: fun_Ho333840202iple_a,B: hoare_1927711152iple_a,C: fun_Ho1877127206a_bool,D: hoare_1927711152iple_a] :
      ( ( hBOOL @ ( hAPP_H1448631928a_bool @ ( finite148164294iple_a @ A @ B @ C ) @ D ) )
     => ( ~ ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ B ) @ C ) )
       => ( hBOOL @ ( hAPP_H1448631928a_bool @ ( finite2098837632iple_a @ A @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ B ) @ C ) ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(43,axiom,
    ! [A: hoare_1927711152iple_a,B: fun_Ho1877127206a_bool] :
      ( ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ A ) @ B )
      = ( collec829051333iple_a @ ( hAPP_f16502863a_bool @ ( hAPP_f2112551770a_bool @ cOMBS_2061548107l_bool @ ( hAPP_f749678531l_bool @ ( cOMBB_196465322iple_a @ fdisj ) @ ( hAPP_H1027145665a_bool @ ( hAPP_f1216137953a_bool @ cOMBC_671859290a_bool @ fequal1440857775iple_a ) @ A ) ) ) @ ( hAPP_f16502863a_bool @ ( hAPP_f684479953a_bool @ cOMBC_862840740l_bool @ member127332739iple_a ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_insert__compr) ).

thf(288,plain,
    ! [A: hoare_1927711152iple_a,B: fun_Ho1877127206a_bool] :
      ( ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ A ) @ B )
      = ( collec829051333iple_a @ ( hAPP_f16502863a_bool @ ( hAPP_f2112551770a_bool @ cOMBS_2061548107l_bool @ ( hAPP_f749678531l_bool @ ( cOMBB_196465322iple_a @ fdisj ) @ ( hAPP_H1027145665a_bool @ ( hAPP_f1216137953a_bool @ cOMBC_671859290a_bool @ fequal1440857775iple_a ) @ A ) ) ) @ ( hAPP_f16502863a_bool @ ( hAPP_f684479953a_bool @ cOMBC_862840740l_bool @ member127332739iple_a ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(81,axiom,
    ! [A: fun_Ho1877127206a_bool,B: hoare_1927711152iple_a] :
      ( ( hBOOL @ ( hAPP_H1448631928a_bool @ A @ B ) )
     => ( ! [C: hoare_1927711152iple_a] :
            ( ( hBOOL @ ( hAPP_H1448631928a_bool @ A @ C ) )
           => ( C = B ) )
       => ( ( hAPP_f490779847iple_a @ the_Ho1307659873iple_a @ A )
          = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_the__equality) ).

thf(436,plain,
    ! [A: fun_Ho1877127206a_bool,B: hoare_1927711152iple_a] :
      ( ( hBOOL @ ( hAPP_H1448631928a_bool @ A @ B ) )
     => ( ! [C: hoare_1927711152iple_a] :
            ( ( hBOOL @ ( hAPP_H1448631928a_bool @ A @ C ) )
           => ( C = B ) )
       => ( ( hAPP_f490779847iple_a @ the_Ho1307659873iple_a @ A )
          = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(130,axiom,
    ! [A: fun_Ho1877127206a_bool] :
      ( ( ( collec829051333iple_a @ A )
        = bot_bo1208640912a_bool )
    <=> ! [B: hoare_1927711152iple_a] :
          ~ ( hBOOL @ ( hAPP_H1448631928a_bool @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_Collect__empty__eq) ).

thf(651,plain,
    ! [A: fun_Ho1877127206a_bool] :
      ( ( ( ( collec829051333iple_a @ A )
          = bot_bo1208640912a_bool )
       => ! [B: hoare_1927711152iple_a] :
            ~ ( hBOOL @ ( hAPP_H1448631928a_bool @ A @ B ) ) )
      & ( ! [B: hoare_1927711152iple_a] :
            ~ ( hBOOL @ ( hAPP_H1448631928a_bool @ A @ B ) )
       => ( ( collec829051333iple_a @ A )
          = bot_bo1208640912a_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(49,axiom,
    ! [A: hoare_1927711152iple_a,B: hoare_1927711152iple_a] :
      ( ( ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ A ) @ bot_bo1208640912a_bool )
        = ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ B ) @ bot_bo1208640912a_bool ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_singleton__inject) ).

thf(320,plain,
    ! [A: hoare_1927711152iple_a,B: hoare_1927711152iple_a] :
      ( ( ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ A ) @ bot_bo1208640912a_bool )
        = ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ B ) @ bot_bo1208640912a_bool ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(115,axiom,
    ! [A: fun_Ho1877127206a_bool] :
      ( ! [B: hoare_1927711152iple_a] :
          ~ ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ B ) @ A ) )
    <=> ( A = bot_bo1208640912a_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_all__not__in__conv) ).

thf(565,plain,
    ! [A: fun_Ho1877127206a_bool] :
      ( ( ! [B: hoare_1927711152iple_a] :
            ~ ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ B ) @ A ) )
       => ( A = bot_bo1208640912a_bool ) )
      & ( ( A = bot_bo1208640912a_bool )
       => ! [B: hoare_1927711152iple_a] :
            ~ ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(15,axiom,
    ! [A: bool,B: hoare_1927711152iple_a] :
      ( ( hAPP_H1448631928a_bool @ ( cOMBK_712844119iple_a @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Hoare____Mirabelle____yiemogtkbg__) ).

thf(184,plain,
    ! [A: bool,B: hoare_1927711152iple_a] :
      ( ( hAPP_H1448631928a_bool @ ( cOMBK_712844119iple_a @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(89,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ B )
      | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_1_1_U) ).

thf(460,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)],[89]) ).

thf(113,axiom,
    ! [A: fun_fu1047394976e_bool,B: fun_a_1632297036l_bool,C: x_a] :
      ( ( hAPP_a1200519163e_bool @ ( hAPP_f963367678e_bool @ ( cOMBB_145932198bool_a @ A ) @ B ) @ C )
      = ( hAPP_f644196280e_bool @ A @ ( hAPP_a849909144l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__HOL__Obool_Mtc__H_040) ).

thf(559,plain,
    ! [A: fun_fu1047394976e_bool,B: fun_a_1632297036l_bool,C: x_a] :
      ( ( hAPP_a1200519163e_bool @ ( hAPP_f963367678e_bool @ ( cOMBB_145932198bool_a @ A ) @ B ) @ C )
      = ( hAPP_f644196280e_bool @ A @ ( hAPP_a849909144l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(78,axiom,
    ! [A: state,B: state] :
      ( ( A != B )
      | ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ fequal_state @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Com__Ostate_T) ).

thf(421,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)],[78]) ).

thf(121,axiom,
    ! [A: fun_Ho1877127206a_bool,B: hoare_1927711152iple_a,C: fun_Ho1877127206a_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ B ) @ C ) )
     => ( ~ ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ B ) @ A ) )
       => ( ( ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ B ) @ C )
            = ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ B ) @ A ) )
        <=> ( C = A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_insert__ident) ).

thf(606,plain,
    ! [A: fun_Ho1877127206a_bool,B: hoare_1927711152iple_a,C: fun_Ho1877127206a_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ B ) @ C ) )
     => ( ~ ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ B ) @ A ) )
       => ( ( ( ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ B ) @ C )
              = ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ B ) @ A ) )
           => ( C = A ) )
          & ( ( C = A )
           => ( ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ B ) @ C )
              = ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ B ) @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(77,axiom,
    ! [A: hoare_1927711152iple_a,B: fun_Ho1877127206a_bool] :
      ( ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ A ) @ B ) )
    <=> ( hBOOL @ ( hAPP_H1448631928a_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_mem__def) ).

thf(416,plain,
    ! [A: hoare_1927711152iple_a,B: fun_Ho1877127206a_bool] :
      ( ( ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_H1448631928a_bool @ B @ A ) ) )
      & ( ( hBOOL @ ( hAPP_H1448631928a_bool @ B @ A ) )
       => ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(48,axiom,
    ! [A: hoare_1927711152iple_a,B: hoare_1927711152iple_a] :
      ( ( A != B )
      | ( hBOOL @ ( hAPP_H1448631928a_bool @ ( hAPP_H1027145665a_bool @ fequal1440857775iple_a @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_) ).

thf(316,plain,
    ! [A: hoare_1927711152iple_a,B: hoare_1927711152iple_a] :
      ( ( A != B )
      | ( hBOOL @ ( hAPP_H1448631928a_bool @ ( hAPP_H1027145665a_bool @ fequal1440857775iple_a @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(35,axiom,
    ! [A: fun_Ho957066028l_bool,B: fun_Ho1877127206a_bool,C: hoare_1927711152iple_a] :
      ( ( hAPP_H1448631928a_bool @ ( hAPP_f16502863a_bool @ ( hAPP_f2112551770a_bool @ cOMBS_2061548107l_bool @ A ) @ B ) @ C )
      = ( hAPP_bool_bool @ ( hAPP_H1487873860l_bool @ A @ C ) @ ( hAPP_H1448631928a_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_00) ).

thf(261,plain,
    ! [A: fun_Ho957066028l_bool,B: fun_Ho1877127206a_bool,C: hoare_1927711152iple_a] :
      ( ( hAPP_H1448631928a_bool @ ( hAPP_f16502863a_bool @ ( hAPP_f2112551770a_bool @ cOMBS_2061548107l_bool @ A ) @ B ) @ C )
      = ( hAPP_bool_bool @ ( hAPP_H1487873860l_bool @ A @ C ) @ ( hAPP_H1448631928a_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(83,axiom,
    ! [A: hoare_1927711152iple_a,B: fun_Ho1877127206a_bool] :
      ( ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ A ) @ B ) )
     => ( ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ A ) @ B )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_insert__absorb) ).

thf(443,plain,
    ! [A: hoare_1927711152iple_a,B: fun_Ho1877127206a_bool] :
      ( ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ A ) @ B ) )
     => ( ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ A ) @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(23,axiom,
    ! [A: fun_Ho333840202iple_a,B: hoare_1927711152iple_a,C: hoare_1927711152iple_a,D: hoare_1927711152iple_a,E: fun_Ho1877127206a_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ D ) @ E ) )
     => ( ( hBOOL @ ( hAPP_H1448631928a_bool @ ( finite148164294iple_a @ A @ B @ E ) @ C ) )
       => ( hBOOL @ ( hAPP_H1448631928a_bool @ ( finite148164294iple_a @ A @ B @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ D ) @ E ) ) @ ( hAPP_H963118037iple_a @ ( hAPP_H1700437986iple_a @ A @ D ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_fold__graph_OinsertI) ).

thf(211,plain,
    ! [A: fun_Ho333840202iple_a,B: hoare_1927711152iple_a,C: hoare_1927711152iple_a,D: hoare_1927711152iple_a,E: fun_Ho1877127206a_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ D ) @ E ) )
     => ( ( hBOOL @ ( hAPP_H1448631928a_bool @ ( finite148164294iple_a @ A @ B @ E ) @ C ) )
       => ( hBOOL @ ( hAPP_H1448631928a_bool @ ( finite148164294iple_a @ A @ B @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ D ) @ E ) ) @ ( hAPP_H963118037iple_a @ ( hAPP_H1700437986iple_a @ A @ D ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(93,axiom,
    ! [A: hoare_1927711152iple_a,B: fun_Ho1877127206a_bool,C: hoare_1927711152iple_a] :
      ( ( hBOOL @ ( hAPP_H1448631928a_bool @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ A ) @ B ) @ C ) )
    <=> ( ( A = C )
        | ( hBOOL @ ( hAPP_H1448631928a_bool @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_insert__code) ).

thf(480,plain,
    ! [A: hoare_1927711152iple_a,B: fun_Ho1877127206a_bool,C: hoare_1927711152iple_a] :
      ( ( ( hBOOL @ ( hAPP_H1448631928a_bool @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ A ) @ B ) @ C ) )
       => ( ( A = C )
          | ( hBOOL @ ( hAPP_H1448631928a_bool @ B @ C ) ) ) )
      & ( ( ( A = C )
          | ( hBOOL @ ( hAPP_H1448631928a_bool @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_H1448631928a_bool @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ A ) @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(57,axiom,
    ! [A: fun_Ho333840202iple_a,B: fun_Ho1877127206a_bool] :
      ( ( hBOOL @ ( hAPP_f1454306822l_bool @ finite68738179iple_a @ B ) )
     => ( ( B != bot_bo1208640912a_bool )
       => ? [C: hoare_1927711152iple_a] : ( hBOOL @ ( hAPP_H1448631928a_bool @ ( finite2098837632iple_a @ A @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_finite__nonempty__imp__fold1Set) ).

thf(348,plain,
    ! [A: fun_Ho333840202iple_a,B: fun_Ho1877127206a_bool] :
      ( ( hBOOL @ ( hAPP_f1454306822l_bool @ finite68738179iple_a @ B ) )
     => ( ( B != bot_bo1208640912a_bool )
       => ? [C: hoare_1927711152iple_a] : ( hBOOL @ ( hAPP_H1448631928a_bool @ ( finite2098837632iple_a @ A @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(117,axiom,
    ! [A: fun_Ho1877127206a_bool] :
      ( ? [B: hoare_1927711152iple_a] :
          ( ( hBOOL @ ( hAPP_H1448631928a_bool @ A @ B ) )
          & ! [C: hoare_1927711152iple_a] :
              ( ( hBOOL @ ( hAPP_H1448631928a_bool @ A @ C ) )
             => ( C = B ) ) )
     => ( hBOOL @ ( hAPP_H1448631928a_bool @ A @ ( hAPP_f490779847iple_a @ the_Ho1307659873iple_a @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_theI_H) ).

thf(574,plain,
    ! [A: fun_Ho1877127206a_bool] :
      ( ? [B: hoare_1927711152iple_a] :
          ( ( hBOOL @ ( hAPP_H1448631928a_bool @ A @ B ) )
          & ! [C: hoare_1927711152iple_a] :
              ( ( hBOOL @ ( hAPP_H1448631928a_bool @ A @ C ) )
             => ( C = B ) ) )
     => ( hBOOL @ ( hAPP_H1448631928a_bool @ A @ ( hAPP_f490779847iple_a @ the_Ho1307659873iple_a @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(72,axiom,
    ! [A: fun_Ho1877127206a_bool,B: fun_Ho1877127206a_bool] :
      ( ( A != B )
      | ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_f625100287l_bool @ fequal1285825639a_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple) ).

thf(397,plain,
    ! [A: fun_Ho1877127206a_bool,B: fun_Ho1877127206a_bool] :
      ( ( A != B )
      | ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_f625100287l_bool @ fequal1285825639a_bool @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(41,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/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo) ).

thf(280,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)],[41]) ).

thf(104,axiom,
    ! [A: hoare_1927711152iple_a,B: fun_Ho1877127206a_bool] :
      ( ( hBOOL @ ( hAPP_f1454306822l_bool @ finite68738179iple_a @ B ) )
     => ( hBOOL @ ( hAPP_f1454306822l_bool @ finite68738179iple_a @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_finite_OinsertI) ).

thf(527,plain,
    ! [A: hoare_1927711152iple_a,B: fun_Ho1877127206a_bool] :
      ( ( hBOOL @ ( hAPP_f1454306822l_bool @ finite68738179iple_a @ B ) )
     => ( hBOOL @ ( hAPP_f1454306822l_bool @ finite68738179iple_a @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(86,axiom,
    ! [A: fun_Ho1877127206a_bool,B: fun_Ho1877127206a_bool,C: hoare_1927711152iple_a] :
      ( ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hoare_1617968510rivs_a @ B ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ C ) @ bot_bo1208640912a_bool ) ) )
     => ( ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hoare_1617968510rivs_a @ B ) @ A ) )
       => ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hoare_1617968510rivs_a @ B ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ C ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_hoare__derivs_Oinsert) ).

thf(452,plain,
    ! [A: fun_Ho1877127206a_bool,B: fun_Ho1877127206a_bool,C: hoare_1927711152iple_a] :
      ( ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hoare_1617968510rivs_a @ B ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ C ) @ bot_bo1208640912a_bool ) ) )
     => ( ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hoare_1617968510rivs_a @ B ) @ A ) )
       => ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hoare_1617968510rivs_a @ B ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ C ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(68,axiom,
    ! [A: hoare_1927711152iple_a,B: fun_Ho1877127206a_bool] :
      ( bot_bo1208640912a_bool
     != ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_empty__not__insert) ).

thf(380,plain,
    ! [A: hoare_1927711152iple_a,B: fun_Ho1877127206a_bool] :
      ( bot_bo1208640912a_bool
     != ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(109,axiom,
    ! [A: fun_Ho333840202iple_a,B: hoare_1927711152iple_a] :
      ~ ( hBOOL @ ( hAPP_H1448631928a_bool @ ( finite2098837632iple_a @ A @ bot_bo1208640912a_bool ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_empty__fold1SetE) ).

thf(546,plain,
    ! [A: fun_Ho333840202iple_a,B: hoare_1927711152iple_a] :
      ~ ( hBOOL @ ( hAPP_H1448631928a_bool @ ( finite2098837632iple_a @ A @ bot_bo1208640912a_bool ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(21,axiom,
    ! [A: fun_Ho1877127206a_bool,B: hoare_1927711152iple_a] :
      ( ( ( hBOOL @ ( hAPP_H1448631928a_bool @ A @ B ) )
       => ( ( collec829051333iple_a @ ( hAPP_f16502863a_bool @ ( hAPP_f2112551770a_bool @ cOMBS_2061548107l_bool @ ( hAPP_f749678531l_bool @ ( cOMBB_196465322iple_a @ fconj ) @ ( hAPP_H1027145665a_bool @ ( hAPP_f1216137953a_bool @ cOMBC_671859290a_bool @ fequal1440857775iple_a ) @ B ) ) ) @ A ) )
          = ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ B ) @ bot_bo1208640912a_bool ) ) )
      & ( ~ ( hBOOL @ ( hAPP_H1448631928a_bool @ A @ B ) )
       => ( ( collec829051333iple_a @ ( hAPP_f16502863a_bool @ ( hAPP_f2112551770a_bool @ cOMBS_2061548107l_bool @ ( hAPP_f749678531l_bool @ ( cOMBB_196465322iple_a @ fconj ) @ ( hAPP_H1027145665a_bool @ ( hAPP_f1216137953a_bool @ cOMBC_671859290a_bool @ fequal1440857775iple_a ) @ B ) ) ) @ A ) )
          = bot_bo1208640912a_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_Collect__conv__if) ).

thf(201,plain,
    ! [A: fun_Ho1877127206a_bool,B: hoare_1927711152iple_a] :
      ( ( ( hBOOL @ ( hAPP_H1448631928a_bool @ A @ B ) )
       => ( ( collec829051333iple_a @ ( hAPP_f16502863a_bool @ ( hAPP_f2112551770a_bool @ cOMBS_2061548107l_bool @ ( hAPP_f749678531l_bool @ ( cOMBB_196465322iple_a @ fconj ) @ ( hAPP_H1027145665a_bool @ ( hAPP_f1216137953a_bool @ cOMBC_671859290a_bool @ fequal1440857775iple_a ) @ B ) ) ) @ A ) )
          = ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ B ) @ bot_bo1208640912a_bool ) ) )
      & ( ~ ( hBOOL @ ( hAPP_H1448631928a_bool @ A @ B ) )
       => ( ( collec829051333iple_a @ ( hAPP_f16502863a_bool @ ( hAPP_f2112551770a_bool @ cOMBS_2061548107l_bool @ ( hAPP_f749678531l_bool @ ( cOMBB_196465322iple_a @ fconj ) @ ( hAPP_H1027145665a_bool @ ( hAPP_f1216137953a_bool @ cOMBC_671859290a_bool @ fequal1440857775iple_a ) @ B ) ) ) @ A ) )
          = bot_bo1208640912a_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(25,axiom,
    ! [A: hoare_1927711152iple_a] :
      ( ( collec829051333iple_a @ ( hAPP_H1027145665a_bool @ fequal1440857775iple_a @ A ) )
      = ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ A ) @ bot_bo1208640912a_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_singleton__conv2) ).

thf(220,plain,
    ! [A: hoare_1927711152iple_a] :
      ( ( collec829051333iple_a @ ( hAPP_H1027145665a_bool @ fequal1440857775iple_a @ A ) )
      = ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ A ) @ bot_bo1208640912a_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(38,axiom,
    ! [A: fun_Ho333840202iple_a,B: hoare_1927711152iple_a,C: fun_Ho1877127206a_bool] :
      ( ( hBOOL @ ( hAPP_f1454306822l_bool @ finite68738179iple_a @ C ) )
     => ? [D: hoare_1927711152iple_a] : ( hBOOL @ ( hAPP_H1448631928a_bool @ ( finite148164294iple_a @ A @ B @ C ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_finite__imp__fold__graph) ).

thf(270,plain,
    ! [A: fun_Ho333840202iple_a,B: hoare_1927711152iple_a,C: fun_Ho1877127206a_bool] :
      ( ( hBOOL @ ( hAPP_f1454306822l_bool @ finite68738179iple_a @ C ) )
     => ? [D: hoare_1927711152iple_a] : ( hBOOL @ ( hAPP_H1448631928a_bool @ ( finite148164294iple_a @ A @ B @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(105,axiom,
    ! [A: fun_a_fun_state_bool,B: fun_Ho1877127206a_bool,C: fun_a_fun_state_bool,D: com,E: fun_a_fun_state_bool] :
      ( ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hoare_1617968510rivs_a @ B ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ ( hoare_1652181356iple_a @ C @ D @ E ) ) @ bot_bo1208640912a_bool ) ) )
     => ( ! [F: x_a,G: state] :
            ( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_a2036067514e_bool @ E @ F ) @ G ) )
           => ( hBOOL @ ( hAPP_state_bool @ ( hAPP_a2036067514e_bool @ A @ F ) @ G ) ) )
       => ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hoare_1617968510rivs_a @ B ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ ( hoare_1652181356iple_a @ C @ D @ A ) ) @ bot_bo1208640912a_bool ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_conseq2) ).

thf(529,plain,
    ! [A: fun_a_fun_state_bool,B: fun_Ho1877127206a_bool,C: fun_a_fun_state_bool,D: com,E: fun_a_fun_state_bool] :
      ( ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hoare_1617968510rivs_a @ B ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ ( hoare_1652181356iple_a @ C @ D @ E ) ) @ bot_bo1208640912a_bool ) ) )
     => ( ! [F: x_a,G: state] :
            ( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_a2036067514e_bool @ E @ F ) @ G ) )
           => ( hBOOL @ ( hAPP_state_bool @ ( hAPP_a2036067514e_bool @ A @ F ) @ G ) ) )
       => ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hoare_1617968510rivs_a @ B ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ ( hoare_1652181356iple_a @ C @ D @ A ) ) @ bot_bo1208640912a_bool ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(53,axiom,
    ! [A: fun_Ho1877127206a_bool] :
      ( ! [B: hoare_1927711152iple_a] :
          ~ ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ B ) @ A ) )
     => ( A = bot_bo1208640912a_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_equals0I) ).

thf(334,plain,
    ! [A: fun_Ho1877127206a_bool] :
      ( ! [B: hoare_1927711152iple_a] :
          ~ ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ B ) @ A ) )
     => ( A = bot_bo1208640912a_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(46,axiom,
    ! [A: fun_Ho1877127206a_bool,B: fun_a_fun_state_bool,C: com,D: fun_a_fun_state_bool,E: bool] :
      ( ( ( hBOOL @ E )
       => ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hoare_1617968510rivs_a @ A ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ ( hoare_1652181356iple_a @ B @ C @ D ) ) @ bot_bo1208640912a_bool ) ) ) )
     => ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hoare_1617968510rivs_a @ A ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ ( hoare_1652181356iple_a @ ( hAPP_b540892988e_bool @ ( hAPP_f1824947087e_bool @ cOMBC_41962815e_bool @ ( hAPP_f340725611e_bool @ ( cOMBB_1348041619bool_a @ cOMBC_231445413l_bool ) @ ( hAPP_f1509969235l_bool @ ( cOMBB_1355796797bool_a @ ( cOMBB_188601460_state @ fconj ) ) @ B ) ) ) @ E ) @ C @ D ) ) @ bot_bo1208640912a_bool ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_constant) ).

thf(297,plain,
    ! [A: fun_Ho1877127206a_bool,B: fun_a_fun_state_bool,C: com,D: fun_a_fun_state_bool,E: bool] :
      ( ( ( hBOOL @ E )
       => ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hoare_1617968510rivs_a @ A ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ ( hoare_1652181356iple_a @ B @ C @ D ) ) @ bot_bo1208640912a_bool ) ) ) )
     => ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hoare_1617968510rivs_a @ A ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ ( hoare_1652181356iple_a @ ( hAPP_b540892988e_bool @ ( hAPP_f1824947087e_bool @ cOMBC_41962815e_bool @ ( hAPP_f340725611e_bool @ ( cOMBB_1348041619bool_a @ cOMBC_231445413l_bool ) @ ( hAPP_f1509969235l_bool @ ( cOMBB_1355796797bool_a @ ( cOMBB_188601460_state @ fconj ) ) @ B ) ) ) @ E ) @ C @ D ) ) @ bot_bo1208640912a_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(18,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/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Com__Ostate_000tc__HOL__Obool_000tc__HOL__Obool_U) ).

thf(192,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)],[18]) ).

thf(76,axiom,
    ! [A: fun_Ho1877127206a_bool] :
      ( ( A != bot_bo1208640912a_bool )
    <=> ? [B: hoare_1927711152iple_a,C: fun_Ho1877127206a_bool] :
          ( ( A
            = ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ B ) @ C ) )
          & ~ ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_nonempty__iff) ).

thf(407,plain,
    ! [A: fun_Ho1877127206a_bool] :
      ( ( ( A != bot_bo1208640912a_bool )
       => ? [B: hoare_1927711152iple_a,C: fun_Ho1877127206a_bool] :
            ( ( A
              = ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ B ) @ C ) )
            & ~ ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ B ) @ C ) ) ) )
      & ( ? [B: hoare_1927711152iple_a,C: fun_Ho1877127206a_bool] :
            ( ( A
              = ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ B ) @ C ) )
            & ~ ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ B ) @ C ) ) )
       => ( A != bot_bo1208640912a_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(40,axiom,
    ! [A: fun_fu832487784l_bool,B: fun_Ho1877127206a_bool] :
      ( ( hBOOL @ ( hAPP_f1454306822l_bool @ finite68738179iple_a @ B ) )
     => ( ( hBOOL @ ( hAPP_f1454306822l_bool @ A @ bot_bo1208640912a_bool ) )
       => ( ! [C: hoare_1927711152iple_a,D: fun_Ho1877127206a_bool] :
              ( ( hBOOL @ ( hAPP_f1454306822l_bool @ finite68738179iple_a @ D ) )
             => ( ~ ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ C ) @ D ) )
               => ( ( hBOOL @ ( hAPP_f1454306822l_bool @ A @ D ) )
                 => ( hBOOL @ ( hAPP_f1454306822l_bool @ A @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ C ) @ D ) ) ) ) ) )
         => ( hBOOL @ ( hAPP_f1454306822l_bool @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_finite__induct) ).

thf(275,plain,
    ! [A: fun_fu832487784l_bool,B: fun_Ho1877127206a_bool] :
      ( ( hBOOL @ ( hAPP_f1454306822l_bool @ finite68738179iple_a @ B ) )
     => ( ( hBOOL @ ( hAPP_f1454306822l_bool @ A @ bot_bo1208640912a_bool ) )
       => ( ! [C: hoare_1927711152iple_a,D: fun_Ho1877127206a_bool] :
              ( ( hBOOL @ ( hAPP_f1454306822l_bool @ finite68738179iple_a @ D ) )
             => ( ~ ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ C ) @ D ) )
               => ( ( hBOOL @ ( hAPP_f1454306822l_bool @ A @ D ) )
                 => ( hBOOL @ ( hAPP_f1454306822l_bool @ A @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ C ) @ D ) ) ) ) ) )
         => ( hBOOL @ ( hAPP_f1454306822l_bool @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(1,conjecture,
    hBOOL @ ( hAPP_f1454306822l_bool @ ( hoare_1617968510rivs_a @ g ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ ( hoare_1652181356iple_a @ ( cOMBK_1458035955bool_a @ ( cOMBK_bool_state @ fFalse ) ) @ c @ ( hAPP_f762886889e_bool @ ( hAPP_f1261923407e_bool @ cOMBC_892787026e_bool @ ( hAPP_f963367678e_bool @ ( cOMBB_145932198bool_a @ cOMBS_1378840469l_bool ) @ ( hAPP_f1509969235l_bool @ ( cOMBB_1355796797bool_a @ ( cOMBB_188601460_state @ fconj ) ) @ p ) ) ) @ ( hAPP_f1759915619e_bool @ ( cOMBB_160679318_state @ fNot ) @ b ) ) ) ) @ bot_bo1208640912a_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

thf(2,negated_conjecture,
    ~ ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hoare_1617968510rivs_a @ g ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ ( hoare_1652181356iple_a @ ( cOMBK_1458035955bool_a @ ( cOMBK_bool_state @ fFalse ) ) @ c @ ( hAPP_f762886889e_bool @ ( hAPP_f1261923407e_bool @ cOMBC_892787026e_bool @ ( hAPP_f963367678e_bool @ ( cOMBB_145932198bool_a @ cOMBS_1378840469l_bool ) @ ( hAPP_f1509969235l_bool @ ( cOMBB_1355796797bool_a @ ( cOMBB_188601460_state @ fconj ) ) @ p ) ) ) @ ( hAPP_f1759915619e_bool @ ( cOMBB_160679318_state @ fNot ) @ b ) ) ) ) @ bot_bo1208640912a_bool ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(137,plain,
    ~ ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hoare_1617968510rivs_a @ g ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ ( hoare_1652181356iple_a @ ( cOMBK_1458035955bool_a @ ( cOMBK_bool_state @ fFalse ) ) @ c @ ( hAPP_f762886889e_bool @ ( hAPP_f1261923407e_bool @ cOMBC_892787026e_bool @ ( hAPP_f963367678e_bool @ ( cOMBB_145932198bool_a @ cOMBS_1378840469l_bool ) @ ( hAPP_f1509969235l_bool @ ( cOMBB_1355796797bool_a @ ( cOMBB_188601460_state @ fconj ) ) @ p ) ) ) @ ( hAPP_f1759915619e_bool @ ( cOMBB_160679318_state @ fNot ) @ b ) ) ) ) @ bot_bo1208640912a_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(28,axiom,
    ( bot_bo1208640912a_bool
    = ( collec829051333iple_a @ ( cOMBK_712844119iple_a @ fFalse ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_empty__def) ).

thf(229,plain,
    ( bot_bo1208640912a_bool
    = ( collec829051333iple_a @ ( cOMBK_712844119iple_a @ fFalse ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(62,axiom,
    ! [A: hoare_1927711152iple_a,B: hoare_1927711152iple_a] :
      ( ~ ( hBOOL @ ( hAPP_H1448631928a_bool @ ( hAPP_H1027145665a_bool @ fequal1440857775iple_a @ A ) @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_) ).

thf(361,plain,
    ! [A: hoare_1927711152iple_a,B: hoare_1927711152iple_a] :
      ( ~ ( hBOOL @ ( hAPP_H1448631928a_bool @ ( hAPP_H1027145665a_bool @ fequal1440857775iple_a @ A ) @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(52,axiom,
    ! [A: hoare_1927711152iple_a,B: fun_fu1033095803iple_a,C: fun_Ho333840202iple_a] :
      ( ( B
        = ( finite1943414032iple_a @ C ) )
     => ( ( hAPP_f490779847iple_a @ B @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ A ) @ bot_bo1208640912a_bool ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_fold1__singleton__def) ).

thf(329,plain,
    ! [A: hoare_1927711152iple_a,B: fun_fu1033095803iple_a,C: fun_Ho333840202iple_a] :
      ( ( B
        = ( finite1943414032iple_a @ C ) )
     => ( ( hAPP_f490779847iple_a @ B @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ A ) @ bot_bo1208640912a_bool ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(96,axiom,
    ! [A: hoare_1927711152iple_a] :
      ( ( hBOOL @ ( hAPP_H1448631928a_bool @ bot_bo1208640912a_bool @ A ) )
    <=> ( hBOOL @ bot_bot_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_bot__apply) ).

thf(493,plain,
    ! [A: hoare_1927711152iple_a] :
      ( ( ( hBOOL @ ( hAPP_H1448631928a_bool @ bot_bo1208640912a_bool @ A ) )
       => ( hBOOL @ bot_bot_bool ) )
      & ( ( hBOOL @ bot_bot_bool )
       => ( hBOOL @ ( hAPP_H1448631928a_bool @ bot_bo1208640912a_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(119,axiom,
    ! [A: hoare_1927711152iple_a] :
      ( ( hBOOL @ ( hAPP_H1448631928a_bool @ bot_bo1208640912a_bool @ A ) )
    <=> ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ A ) @ bot_bo1208640912a_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_bot__empty__eq) ).

thf(583,plain,
    ! [A: hoare_1927711152iple_a] :
      ( ( ( hBOOL @ ( hAPP_H1448631928a_bool @ bot_bo1208640912a_bool @ A ) )
       => ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ A ) @ bot_bo1208640912a_bool ) ) )
      & ( ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ A ) @ bot_bo1208640912a_bool ) )
       => ( hBOOL @ ( hAPP_H1448631928a_bool @ bot_bo1208640912a_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(103,axiom,
    ! [A: hoare_1927711152iple_a] :
      ( ( hBOOL @ ( hAPP_H1448631928a_bool @ bot_bo1208640912a_bool @ A ) )
    <=> ( hBOOL @ bot_bot_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_bot__fun__def) ).

thf(522,plain,
    ! [A: hoare_1927711152iple_a] :
      ( ( ( hBOOL @ ( hAPP_H1448631928a_bool @ bot_bo1208640912a_bool @ A ) )
       => ( hBOOL @ bot_bot_bool ) )
      & ( ( hBOOL @ bot_bot_bool )
       => ( hBOOL @ ( hAPP_H1448631928a_bool @ bot_bo1208640912a_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(118,axiom,
    ! [A: hoare_1927711152iple_a,B: fun_Ho1877127206a_bool] :
      ( ( hBOOL @ ( hAPP_f1454306822l_bool @ finite68738179iple_a @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ A ) @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f1454306822l_bool @ finite68738179iple_a @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_finite__insert) ).

thf(578,plain,
    ! [A: hoare_1927711152iple_a,B: fun_Ho1877127206a_bool] :
      ( ( ( hBOOL @ ( hAPP_f1454306822l_bool @ finite68738179iple_a @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ A ) @ B ) ) )
       => ( hBOOL @ ( hAPP_f1454306822l_bool @ finite68738179iple_a @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f1454306822l_bool @ finite68738179iple_a @ B ) )
       => ( hBOOL @ ( hAPP_f1454306822l_bool @ finite68738179iple_a @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ A ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(60,axiom,
    ! [A: bool] :
      ( ( hBOOL @ A )
      | ( hBOOL @ ( hAPP_bool_bool @ fNot @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_2_1_U) ).

thf(356,plain,
    ! [A: bool] :
      ( ( hBOOL @ A )
      | ( hBOOL @ ( hAPP_bool_bool @ fNot @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(10,axiom,
    ! [A: fun_Ho333840202iple_a,B: fun_Ho1877127206a_bool] :
      ( ( hAPP_f490779847iple_a @ ( finite1943414032iple_a @ A ) @ B )
      = ( hAPP_f490779847iple_a @ the_Ho1307659873iple_a @ ( finite2098837632iple_a @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_fold1__def) ).

thf(169,plain,
    ! [A: fun_Ho333840202iple_a,B: fun_Ho1877127206a_bool] :
      ( ( hAPP_f490779847iple_a @ ( finite1943414032iple_a @ A ) @ B )
      = ( hAPP_f490779847iple_a @ the_Ho1307659873iple_a @ ( finite2098837632iple_a @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(133,axiom,
    ! [A: bool,B: bool] :
      ( ( hBOOL @ B )
      | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_1_1_U) ).

thf(669,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)],[133]) ).

thf(136,axiom,
    ! [A: bool] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ fNot @ A ) )
      | ~ ( hBOOL @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_1_1_U) ).

thf(686,plain,
    ! [A: bool] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ fNot @ A ) )
      | ~ ( hBOOL @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(126,axiom,
    ! [A: hoare_1927711152iple_a,B: hoare_1927711152iple_a,C: fun_Ho1877127206a_bool] :
      ( ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ A ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ B ) @ C ) ) )
     => ( ( A != B )
       => ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_insertE) ).

thf(637,plain,
    ! [A: hoare_1927711152iple_a,B: hoare_1927711152iple_a,C: fun_Ho1877127206a_bool] :
      ( ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ A ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ B ) @ C ) ) )
     => ( ( A != B )
       => ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(94,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ A ) @ B ) )
      | ~ ( hBOOL @ A )
      | ( hBOOL @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_3_1_U) ).

thf(489,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)],[94]) ).

thf(88,axiom,
    ! [A: fun_a_fun_state_bool,B: fun_Ho1877127206a_bool,C: fun_a_fun_state_bool,D: com,E: fun_a_fun_state_bool] :
      ( ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hoare_1617968510rivs_a @ B ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ ( hoare_1652181356iple_a @ C @ D @ E ) ) @ bot_bo1208640912a_bool ) ) )
     => ( ! [F: x_a,G: state] :
            ( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_a2036067514e_bool @ A @ F ) @ G ) )
           => ( hBOOL @ ( hAPP_state_bool @ ( hAPP_a2036067514e_bool @ C @ F ) @ G ) ) )
       => ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hoare_1617968510rivs_a @ B ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ ( hoare_1652181356iple_a @ A @ D @ E ) ) @ bot_bo1208640912a_bool ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_conseq1) ).

thf(457,plain,
    ! [A: fun_a_fun_state_bool,B: fun_Ho1877127206a_bool,C: fun_a_fun_state_bool,D: com,E: fun_a_fun_state_bool] :
      ( ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hoare_1617968510rivs_a @ B ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ ( hoare_1652181356iple_a @ C @ D @ E ) ) @ bot_bo1208640912a_bool ) ) )
     => ( ! [F: x_a,G: state] :
            ( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_a2036067514e_bool @ A @ F ) @ G ) )
           => ( hBOOL @ ( hAPP_state_bool @ ( hAPP_a2036067514e_bool @ C @ F ) @ G ) ) )
       => ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hoare_1617968510rivs_a @ B ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ ( hoare_1652181356iple_a @ A @ D @ E ) ) @ bot_bo1208640912a_bool ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(98,axiom,
    ! [A: fun_Ho333840202iple_a,B: fun_Ho1877127206a_bool,C: hoare_1927711152iple_a] :
      ( ( hBOOL @ ( hAPP_H1448631928a_bool @ ( finite2098837632iple_a @ A @ B ) @ C ) )
     => ( B != bot_bo1208640912a_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_fold1Set__nonempty) ).

thf(503,plain,
    ! [A: fun_Ho333840202iple_a,B: fun_Ho1877127206a_bool,C: hoare_1927711152iple_a] :
      ( ( hBOOL @ ( hAPP_H1448631928a_bool @ ( finite2098837632iple_a @ A @ B ) @ C ) )
     => ( B != bot_bo1208640912a_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(31,axiom,
    ! [A: fun_Ho1877127206a_bool] :
      ( ( hAPP_f490779847iple_a @ the_el1997360207iple_a @ A )
      = ( hAPP_f490779847iple_a @ the_Ho1307659873iple_a @ ( hAPP_f909473944a_bool @ ( cOMBB_1083611331iple_a @ ( hAPP_f625100287l_bool @ fequal1285825639a_bool @ A ) ) @ ( hAPP_f993216280a_bool @ ( hAPP_f1022403729a_bool @ cOMBC_825881325a_bool @ insert1434104874iple_a ) @ bot_bo1208640912a_bool ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_the__elem__def) ).

thf(244,plain,
    ! [A: fun_Ho1877127206a_bool] :
      ( ( hAPP_f490779847iple_a @ the_el1997360207iple_a @ A )
      = ( hAPP_f490779847iple_a @ the_Ho1307659873iple_a @ ( hAPP_f909473944a_bool @ ( cOMBB_1083611331iple_a @ ( hAPP_f625100287l_bool @ fequal1285825639a_bool @ A ) ) @ ( hAPP_f993216280a_bool @ ( hAPP_f1022403729a_bool @ cOMBC_825881325a_bool @ insert1434104874iple_a ) @ bot_bo1208640912a_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(99,axiom,
    ! [A: state,B: state] :
      ( ~ ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ fequal_state @ A ) @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Com__Ostate_T) ).

thf(508,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)],[99]) ).

thf(79,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ B )
      | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_2_1_U) ).

thf(425,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)],[79]) ).

thf(101,axiom,
    ! [A: fun_Ho1877127206a_bool] :
      ( ( bot_bo1208640912a_bool
        = ( collec829051333iple_a @ A ) )
    <=> ! [B: hoare_1927711152iple_a] :
          ~ ( hBOOL @ ( hAPP_H1448631928a_bool @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_empty__Collect__eq) ).

thf(513,plain,
    ! [A: fun_Ho1877127206a_bool] :
      ( ( ( bot_bo1208640912a_bool
          = ( collec829051333iple_a @ A ) )
       => ! [B: hoare_1927711152iple_a] :
            ~ ( hBOOL @ ( hAPP_H1448631928a_bool @ A @ B ) ) )
      & ( ! [B: hoare_1927711152iple_a] :
            ~ ( hBOOL @ ( hAPP_H1448631928a_bool @ A @ B ) )
       => ( bot_bo1208640912a_bool
          = ( collec829051333iple_a @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(9,axiom,
    ! [A: fun_Ho440810351a_bool,B: hoare_1927711152iple_a,C: hoare_1927711152iple_a] :
      ( ( hAPP_H1448631928a_bool @ ( hAPP_H1027145665a_bool @ ( hAPP_f1216137953a_bool @ cOMBC_671859290a_bool @ A ) @ B ) @ C )
      = ( hAPP_H1448631928a_bool @ ( hAPP_H1027145665a_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_00) ).

thf(166,plain,
    ! [A: fun_Ho440810351a_bool,B: hoare_1927711152iple_a,C: hoare_1927711152iple_a] :
      ( ( hAPP_H1448631928a_bool @ ( hAPP_H1027145665a_bool @ ( hAPP_f1216137953a_bool @ cOMBC_671859290a_bool @ A ) @ B ) @ C )
      = ( hAPP_H1448631928a_bool @ ( hAPP_H1027145665a_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(6,axiom,
    ! [A: com,B: com,C: com,D: com] :
      ( ( ( semi @ A @ B )
        = ( semi @ C @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_com_Osimps_I3_J) ).

thf(148,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)],[6]) ).

thf(36,axiom,
    ! [A: fun_Ho1877127206a_bool,B: com,C: fun_a_fun_state_bool,D: fun_a_fun_state_bool] :
      ( ! [E: x_a,F: state] :
          ( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_a2036067514e_bool @ D @ E ) @ F ) )
         => ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hoare_1617968510rivs_a @ A ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ ( hoare_1652181356iple_a @ ( cOMBK_1458035955bool_a @ ( hAPP_s1806633685e_bool @ ( hAPP_f817621513e_bool @ cOMBC_2027030106e_bool @ fequal_state ) @ F ) ) @ B @ ( cOMBK_1458035955bool_a @ ( hAPP_a2036067514e_bool @ C @ E ) ) ) ) @ bot_bo1208640912a_bool ) ) ) )
     => ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hoare_1617968510rivs_a @ A ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ ( hoare_1652181356iple_a @ D @ B @ C ) ) @ bot_bo1208640912a_bool ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_escape) ).

thf(264,plain,
    ! [A: fun_Ho1877127206a_bool,B: com,C: fun_a_fun_state_bool,D: fun_a_fun_state_bool] :
      ( ! [E: x_a,F: state] :
          ( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_a2036067514e_bool @ D @ E ) @ F ) )
         => ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hoare_1617968510rivs_a @ A ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ ( hoare_1652181356iple_a @ ( cOMBK_1458035955bool_a @ ( hAPP_s1806633685e_bool @ ( hAPP_f817621513e_bool @ cOMBC_2027030106e_bool @ fequal_state ) @ F ) ) @ B @ ( cOMBK_1458035955bool_a @ ( hAPP_a2036067514e_bool @ C @ E ) ) ) ) @ bot_bo1208640912a_bool ) ) ) )
     => ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hoare_1617968510rivs_a @ A ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ ( hoare_1652181356iple_a @ D @ B @ C ) ) @ bot_bo1208640912a_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(114,axiom,
    ! [A: fun_a_2117018159e_bool,B: fun_state_bool,C: x_a] :
      ( ( hAPP_a2036067514e_bool @ ( hAPP_f762886889e_bool @ ( hAPP_f1261923407e_bool @ cOMBC_892787026e_bool @ A ) @ B ) @ C )
      = ( hAPP_f1759915619e_bool @ ( hAPP_a1200519163e_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000t__a_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc) ).

thf(562,plain,
    ! [A: fun_a_2117018159e_bool,B: fun_state_bool,C: x_a] :
      ( ( hAPP_a2036067514e_bool @ ( hAPP_f762886889e_bool @ ( hAPP_f1261923407e_bool @ cOMBC_892787026e_bool @ A ) @ B ) @ C )
      = ( hAPP_f1759915619e_bool @ ( hAPP_a1200519163e_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(44,axiom,
    ! [A: hoare_1927711152iple_a,B: fun_Ho1877127206a_bool] :
      ( ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ A ) @ ( collec829051333iple_a @ B ) )
      = ( collec829051333iple_a @ ( hAPP_f16502863a_bool @ ( hAPP_f2112551770a_bool @ cOMBS_2061548107l_bool @ ( hAPP_f749678531l_bool @ ( cOMBB_196465322iple_a @ fimplies ) @ ( hAPP_f16502863a_bool @ ( cOMBB_213049548iple_a @ fNot ) @ ( hAPP_H1027145665a_bool @ ( hAPP_f1216137953a_bool @ cOMBC_671859290a_bool @ fequal1440857775iple_a ) @ A ) ) ) ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_insert__Collect) ).

thf(291,plain,
    ! [A: hoare_1927711152iple_a,B: fun_Ho1877127206a_bool] :
      ( ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ A ) @ ( collec829051333iple_a @ B ) )
      = ( collec829051333iple_a @ ( hAPP_f16502863a_bool @ ( hAPP_f2112551770a_bool @ cOMBS_2061548107l_bool @ ( hAPP_f749678531l_bool @ ( cOMBB_196465322iple_a @ fimplies ) @ ( hAPP_f16502863a_bool @ ( cOMBB_213049548iple_a @ fNot ) @ ( hAPP_H1027145665a_bool @ ( hAPP_f1216137953a_bool @ cOMBC_671859290a_bool @ fequal1440857775iple_a ) @ A ) ) ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(116,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ A ) @ B ) )
      | ( hBOOL @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_3_1_U) ).

thf(572,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)],[116]) ).

thf(97,axiom,
    ! [A: hoare_1927711152iple_a,B: fun_Ho1877127206a_bool] :
      ( ? [C: hoare_1927711152iple_a] :
          ( ( hBOOL @ ( hAPP_H1448631928a_bool @ B @ C ) )
          & ! [D: hoare_1927711152iple_a] :
              ( ( hBOOL @ ( hAPP_H1448631928a_bool @ B @ D ) )
             => ( D = C ) ) )
     => ( ( hBOOL @ ( hAPP_H1448631928a_bool @ B @ A ) )
       => ( ( hAPP_f490779847iple_a @ the_Ho1307659873iple_a @ B )
          = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_the1__equality) ).

thf(498,plain,
    ! [A: hoare_1927711152iple_a,B: fun_Ho1877127206a_bool] :
      ( ? [C: hoare_1927711152iple_a] :
          ( ( hBOOL @ ( hAPP_H1448631928a_bool @ B @ C ) )
          & ! [D: hoare_1927711152iple_a] :
              ( ( hBOOL @ ( hAPP_H1448631928a_bool @ B @ D ) )
             => ( D = C ) ) )
     => ( ( hBOOL @ ( hAPP_H1448631928a_bool @ B @ A ) )
       => ( ( hAPP_f490779847iple_a @ the_Ho1307659873iple_a @ B )
          = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(14,axiom,
    ! [A: hoare_1927711152iple_a] :
      ( ( hAPP_f490779847iple_a @ the_Ho1307659873iple_a @ ( hAPP_H1027145665a_bool @ fequal1440857775iple_a @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_the__sym__eq__trivial) ).

thf(181,plain,
    ! [A: hoare_1927711152iple_a] :
      ( ( hAPP_f490779847iple_a @ the_Ho1307659873iple_a @ ( hAPP_H1027145665a_bool @ fequal1440857775iple_a @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(7,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/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Ostate_000tc__HOL__Obool_000tc__HOL__Obool_U) ).

thf(159,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)],[7]) ).

thf(16,axiom,
    ! [A: fun_fu1219323149e_bool,B: fun_a_1632297036l_bool,C: x_a] :
      ( ( hAPP_a723219176e_bool @ ( hAPP_f340725611e_bool @ ( cOMBB_1348041619bool_a @ A ) @ B ) @ C )
      = ( hAPP_f167292325e_bool @ A @ ( hAPP_a849909144l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__HOL__Obool_Mtc__H) ).

thf(187,plain,
    ! [A: fun_fu1219323149e_bool,B: fun_a_1632297036l_bool,C: x_a] :
      ( ( hAPP_a723219176e_bool @ ( hAPP_f340725611e_bool @ ( cOMBB_1348041619bool_a @ A ) @ B ) @ C )
      = ( hAPP_f167292325e_bool @ A @ ( hAPP_a849909144l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(75,axiom,
    hBOOL @ ( hAPP_f1454306822l_bool @ finite68738179iple_a @ bot_bo1208640912a_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_finite_OemptyI) ).

thf(406,plain,
    hBOOL @ ( hAPP_f1454306822l_bool @ finite68738179iple_a @ bot_bo1208640912a_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(11,axiom,
    ! [A: hoare_1927711152iple_a] :
      ( ( hAPP_f490779847iple_a @ the_Ho1307659873iple_a @ ( hAPP_H1027145665a_bool @ ( hAPP_f1216137953a_bool @ cOMBC_671859290a_bool @ fequal1440857775iple_a ) @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_the__eq__trivial) ).

thf(172,plain,
    ! [A: hoare_1927711152iple_a] :
      ( ( hAPP_f490779847iple_a @ the_Ho1307659873iple_a @ ( hAPP_H1027145665a_bool @ ( hAPP_f1216137953a_bool @ cOMBC_671859290a_bool @ fequal1440857775iple_a ) @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(67,axiom,
    ! [A: fun_fu1658206819l_bool,B: fun_a_fun_state_bool,C: x_a] :
      ( ( hAPP_a849909144l_bool @ ( hAPP_f1509969235l_bool @ ( cOMBB_1355796797bool_a @ A ) @ B ) @ C )
      = ( hAPP_f1259673775l_bool @ A @ ( hAPP_a2036067514e_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc__fun_It) ).

thf(377,plain,
    ! [A: fun_fu1658206819l_bool,B: fun_a_fun_state_bool,C: x_a] :
      ( ( hAPP_a849909144l_bool @ ( hAPP_f1509969235l_bool @ ( cOMBB_1355796797bool_a @ A ) @ B ) @ C )
      = ( hAPP_f1259673775l_bool @ A @ ( hAPP_a2036067514e_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(129,axiom,
    ! [A: fun_Ho1877127206a_bool,B: fun_a_fun_state_bool] : ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hoare_1617968510rivs_a @ A ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ ( hoare_1652181356iple_a @ B @ skip @ B ) ) @ bot_bo1208640912a_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_hoare__derivs_OSkip) ).

thf(649,plain,
    ! [A: fun_Ho1877127206a_bool,B: fun_a_fun_state_bool] : ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hoare_1617968510rivs_a @ A ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ ( hoare_1652181356iple_a @ B @ skip @ B ) ) @ bot_bo1208640912a_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(22,axiom,
    ! [A: fun_Ho333840202iple_a,B: hoare_1927711152iple_a,C: hoare_1927711152iple_a] :
      ( ( hBOOL @ ( hAPP_H1448631928a_bool @ ( finite148164294iple_a @ A @ B @ bot_bo1208640912a_bool ) @ C ) )
     => ( C = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_empty__fold__graphE) ).

thf(208,plain,
    ! [A: fun_Ho333840202iple_a,B: hoare_1927711152iple_a,C: hoare_1927711152iple_a] :
      ( ( hBOOL @ ( hAPP_H1448631928a_bool @ ( finite148164294iple_a @ A @ B @ bot_bo1208640912a_bool ) @ C ) )
     => ( C = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(70,axiom,
    ! [A: fun_Ho1877127206a_bool,B: fun_Ho1877127206a_bool] :
      ( ( ( hBOOL @ ( hAPP_f1454306822l_bool @ finite68738179iple_a @ ( collec829051333iple_a @ B ) ) )
        | ( hBOOL @ ( hAPP_f1454306822l_bool @ finite68738179iple_a @ ( collec829051333iple_a @ A ) ) ) )
     => ( hBOOL @ ( hAPP_f1454306822l_bool @ finite68738179iple_a @ ( collec829051333iple_a @ ( hAPP_f16502863a_bool @ ( hAPP_f2112551770a_bool @ cOMBS_2061548107l_bool @ ( hAPP_f749678531l_bool @ ( cOMBB_196465322iple_a @ fconj ) @ B ) ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_finite__Collect__conjI) ).

thf(387,plain,
    ! [A: fun_Ho1877127206a_bool,B: fun_Ho1877127206a_bool] :
      ( ( ( hBOOL @ ( hAPP_f1454306822l_bool @ finite68738179iple_a @ ( collec829051333iple_a @ B ) ) )
        | ( hBOOL @ ( hAPP_f1454306822l_bool @ finite68738179iple_a @ ( collec829051333iple_a @ A ) ) ) )
     => ( hBOOL @ ( hAPP_f1454306822l_bool @ finite68738179iple_a @ ( collec829051333iple_a @ ( hAPP_f16502863a_bool @ ( hAPP_f2112551770a_bool @ cOMBS_2061548107l_bool @ ( hAPP_f749678531l_bool @ ( cOMBB_196465322iple_a @ fconj ) @ B ) ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(107,axiom,
    ! [A: hoare_1927711152iple_a,B: fun_Ho1877127206a_bool] :
      ( ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ A ) @ B ) )
     => ? [C: fun_Ho1877127206a_bool] :
          ( ( B
            = ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ A ) @ C ) )
          & ~ ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_mk__disjoint__insert) ).

thf(535,plain,
    ! [A: hoare_1927711152iple_a,B: fun_Ho1877127206a_bool] :
      ( ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ A ) @ B ) )
     => ? [C: fun_Ho1877127206a_bool] :
          ( ( B
            = ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ A ) @ C ) )
          & ~ ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(50,axiom,
    ! [A: hoare_1927711152iple_a,B: fun_Ho333840202iple_a,C: fun_fu1033095803iple_a] :
      ( ( hBOOL @ ( finite83514413iple_a @ B @ C ) )
     => ( ( hAPP_f490779847iple_a @ C @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ A ) @ bot_bo1208640912a_bool ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_folding__one_Osingleton) ).

thf(323,plain,
    ! [A: hoare_1927711152iple_a,B: fun_Ho333840202iple_a,C: fun_fu1033095803iple_a] :
      ( ( hBOOL @ ( finite83514413iple_a @ B @ C ) )
     => ( ( hAPP_f490779847iple_a @ C @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ A ) @ bot_bo1208640912a_bool ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(24,axiom,
    ! [A: fun_Ho333840202iple_a,B: hoare_1927711152iple_a,C: hoare_1927711152iple_a] :
      ( ( hBOOL @ ( hAPP_H1448631928a_bool @ ( finite2098837632iple_a @ A @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ B ) @ bot_bo1208640912a_bool ) ) @ C ) )
    <=> ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_fold1Set__sing) ).

thf(213,plain,
    ! [A: fun_Ho333840202iple_a,B: hoare_1927711152iple_a,C: hoare_1927711152iple_a] :
      ( ( ( hBOOL @ ( hAPP_H1448631928a_bool @ ( finite2098837632iple_a @ A @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ B ) @ bot_bo1208640912a_bool ) ) @ C ) )
       => ( B = C ) )
      & ( ( B = C )
       => ( hBOOL @ ( hAPP_H1448631928a_bool @ ( finite2098837632iple_a @ A @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ B ) @ bot_bo1208640912a_bool ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(102,axiom,
    ! [A: com,B: fun_a_fun_state_bool,C: fun_Ho1877127206a_bool,D: fun_a_fun_state_bool,E: com,F: fun_a_fun_state_bool] :
      ( ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hoare_1617968510rivs_a @ C ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ ( hoare_1652181356iple_a @ D @ E @ F ) ) @ bot_bo1208640912a_bool ) ) )
     => ( ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hoare_1617968510rivs_a @ C ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ ( hoare_1652181356iple_a @ F @ A @ B ) ) @ bot_bo1208640912a_bool ) ) )
       => ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hoare_1617968510rivs_a @ C ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ ( hoare_1652181356iple_a @ D @ ( semi @ E @ A ) @ B ) ) @ bot_bo1208640912a_bool ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_Comp) ).

thf(520,plain,
    ! [A: com,B: fun_a_fun_state_bool,C: fun_Ho1877127206a_bool,D: fun_a_fun_state_bool,E: com,F: fun_a_fun_state_bool] :
      ( ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hoare_1617968510rivs_a @ C ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ ( hoare_1652181356iple_a @ D @ E @ F ) ) @ bot_bo1208640912a_bool ) ) )
     => ( ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hoare_1617968510rivs_a @ C ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ ( hoare_1652181356iple_a @ F @ A @ B ) ) @ bot_bo1208640912a_bool ) ) )
       => ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hoare_1617968510rivs_a @ C ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ ( hoare_1652181356iple_a @ D @ ( semi @ E @ A ) @ B ) ) @ bot_bo1208640912a_bool ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(123,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ B )
      | ~ ( hBOOL @ A )
      | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_1_1_U) ).

thf(626,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)],[123]) ).

thf(20,axiom,
    ! [A: hoare_1927711152iple_a] :
      ~ ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ A ) @ bot_bo1208640912a_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_emptyE) ).

thf(198,plain,
    ! [A: hoare_1927711152iple_a] :
      ~ ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ A ) @ bot_bo1208640912a_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(90,axiom,
    ~ ( hBOOL @ fFalse ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).

thf(462,plain,
    ~ ( hBOOL @ fFalse ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(56,axiom,
    ! [A: bool] :
      ( ( A = fTrue )
      | ( A = fFalse ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).

thf(345,plain,
    ! [A: bool] :
      ( ( A = fTrue )
      | ( A = fFalse ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(64,axiom,
    ! [A: fun_Ho1877127206a_bool,B: fun_Ho333840202iple_a,C: fun_fu1033095803iple_a] :
      ( ( hBOOL @ ( finite83514413iple_a @ B @ C ) )
     => ( ( hBOOL @ ( hAPP_f1454306822l_bool @ finite68738179iple_a @ A ) )
       => ( ( hAPP_f490779847iple_a @ C @ A )
          = ( hAPP_f490779847iple_a @ ( finite1943414032iple_a @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_folding__one_Oeq__fold) ).

thf(367,plain,
    ! [A: fun_Ho1877127206a_bool,B: fun_Ho333840202iple_a,C: fun_fu1033095803iple_a] :
      ( ( hBOOL @ ( finite83514413iple_a @ B @ C ) )
     => ( ( hBOOL @ ( hAPP_f1454306822l_bool @ finite68738179iple_a @ A ) )
       => ( ( hAPP_f490779847iple_a @ C @ A )
          = ( hAPP_f490779847iple_a @ ( finite1943414032iple_a @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(26,axiom,
    ! [A: fun_Ho1877127206a_bool,B: hoare_1927711152iple_a] :
      ( ( hBOOL @ ( hAPP_H1448631928a_bool @ A @ B ) )
     => ( ! [C: hoare_1927711152iple_a] :
            ( ( hBOOL @ ( hAPP_H1448631928a_bool @ A @ C ) )
           => ( C = B ) )
       => ( hBOOL @ ( hAPP_H1448631928a_bool @ A @ ( hAPP_f490779847iple_a @ the_Ho1307659873iple_a @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_theI) ).

thf(223,plain,
    ! [A: fun_Ho1877127206a_bool,B: hoare_1927711152iple_a] :
      ( ( hBOOL @ ( hAPP_H1448631928a_bool @ A @ B ) )
     => ( ! [C: hoare_1927711152iple_a] :
            ( ( hBOOL @ ( hAPP_H1448631928a_bool @ A @ C ) )
           => ( C = B ) )
       => ( hBOOL @ ( hAPP_H1448631928a_bool @ A @ ( hAPP_f490779847iple_a @ the_Ho1307659873iple_a @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(37,axiom,
    ! [A: hoare_1927711152iple_a,B: hoare_1927711152iple_a,C: fun_Ho1877127206a_bool] :
      ( ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ A ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ B ) @ C ) )
      = ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ B ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_insert__commute) ).

thf(267,plain,
    ! [A: hoare_1927711152iple_a,B: hoare_1927711152iple_a,C: fun_Ho1877127206a_bool] :
      ( ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ A ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ B ) @ C ) )
      = ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ B ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(131,axiom,
    ! [A: fun_Ho1877127206a_bool] :
      ( ? [B: hoare_1927711152iple_a] : ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ B ) @ A ) )
    <=> ( A != bot_bo1208640912a_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_ex__in__conv) ).

thf(658,plain,
    ! [A: fun_Ho1877127206a_bool] :
      ( ( ? [B: hoare_1927711152iple_a] : ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ B ) @ A ) )
       => ( A != bot_bo1208640912a_bool ) )
      & ( ( A != bot_bo1208640912a_bool )
       => ? [B: hoare_1927711152iple_a] : ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(135,axiom,
    ! [A: fun_fu832487784l_bool,B: fun_Ho1877127206a_bool] :
      ( ( hBOOL @ ( hAPP_f1454306822l_bool @ finite68738179iple_a @ B ) )
     => ( ( B != bot_bo1208640912a_bool )
       => ( ! [C: hoare_1927711152iple_a] : ( hBOOL @ ( hAPP_f1454306822l_bool @ A @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ C ) @ bot_bo1208640912a_bool ) ) )
         => ( ! [C: hoare_1927711152iple_a,D: fun_Ho1877127206a_bool] :
                ( ( hBOOL @ ( hAPP_f1454306822l_bool @ finite68738179iple_a @ D ) )
               => ( ( D != bot_bo1208640912a_bool )
                 => ( ~ ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ C ) @ D ) )
                   => ( ( hBOOL @ ( hAPP_f1454306822l_bool @ A @ D ) )
                     => ( hBOOL @ ( hAPP_f1454306822l_bool @ A @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ C ) @ D ) ) ) ) ) ) )
           => ( hBOOL @ ( hAPP_f1454306822l_bool @ A @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_finite__ne__induct) ).

thf(675,plain,
    ! [A: fun_fu832487784l_bool,B: fun_Ho1877127206a_bool] :
      ( ( hBOOL @ ( hAPP_f1454306822l_bool @ finite68738179iple_a @ B ) )
     => ( ( B != bot_bo1208640912a_bool )
       => ( ! [C: hoare_1927711152iple_a] : ( hBOOL @ ( hAPP_f1454306822l_bool @ A @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ C ) @ bot_bo1208640912a_bool ) ) )
         => ( ! [C: hoare_1927711152iple_a,D: fun_Ho1877127206a_bool] :
                ( ( hBOOL @ ( hAPP_f1454306822l_bool @ finite68738179iple_a @ D ) )
               => ( ( D != bot_bo1208640912a_bool )
                 => ( ~ ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ C ) @ D ) )
                   => ( ( hBOOL @ ( hAPP_f1454306822l_bool @ A @ D ) )
                     => ( hBOOL @ ( hAPP_f1454306822l_bool @ A @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ C ) @ D ) ) ) ) ) ) )
           => ( hBOOL @ ( hAPP_f1454306822l_bool @ A @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(8,axiom,
    ! [A: com,B: com] :
      ( ( semi @ A @ B )
     != skip ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_com_Osimps_I13_J) ).

thf(162,plain,
    ! [A: com,B: com] :
      ( ( semi @ A @ B )
     != skip ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(55,axiom,
    ! [A: fun_bool_bool,B: fun_Ho1877127206a_bool,C: hoare_1927711152iple_a] :
      ( ( hAPP_H1448631928a_bool @ ( hAPP_f16502863a_bool @ ( cOMBB_213049548iple_a @ A ) @ B ) @ C )
      = ( hAPP_bool_bool @ A @ ( hAPP_H1448631928a_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Hoare____Mirabel) ).

thf(342,plain,
    ! [A: fun_bool_bool,B: fun_Ho1877127206a_bool,C: hoare_1927711152iple_a] :
      ( ( hAPP_H1448631928a_bool @ ( hAPP_f16502863a_bool @ ( cOMBB_213049548iple_a @ A ) @ B ) @ C )
      = ( hAPP_bool_bool @ A @ ( hAPP_H1448631928a_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(111,axiom,
    ! [A: fun_Ho333840202iple_a,B: hoare_1927711152iple_a] :
      ( ( hAPP_f490779847iple_a @ ( finite1943414032iple_a @ A ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ B ) @ bot_bo1208640912a_bool ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_fold1__singleton) ).

thf(553,plain,
    ! [A: fun_Ho333840202iple_a,B: hoare_1927711152iple_a] :
      ( ( hAPP_f490779847iple_a @ ( finite1943414032iple_a @ A ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ B ) @ bot_bo1208640912a_bool ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(5,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/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Ostate_000tc__Com__Ostate_000tc__HOL__Obool_U) ).

thf(145,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)],[5]) ).

thf(82,axiom,
    ! [A: fun_Ho1877127206a_bool] : ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hoare_1617968510rivs_a @ A ) @ bot_bo1208640912a_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_empty) ).

thf(441,plain,
    ! [A: fun_Ho1877127206a_bool] : ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hoare_1617968510rivs_a @ A ) @ bot_bo1208640912a_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(65,axiom,
    ! [A: hoare_1927711152iple_a,B: fun_Ho1877127206a_bool] :
      ( ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ A ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ A ) @ B ) )
      = ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_insert__absorb2) ).

thf(370,plain,
    ! [A: hoare_1927711152iple_a,B: fun_Ho1877127206a_bool] :
      ( ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ A ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ A ) @ B ) )
      = ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(54,axiom,
    ! [A: hoare_1927711152iple_a,B: fun_Ho333840202iple_a,C: fun_fu1033095803iple_a] :
      ( ( hBOOL @ ( finite1511031594iple_a @ B @ C ) )
     => ( ( hAPP_H963118037iple_a @ ( hAPP_H1700437986iple_a @ B @ A ) @ A )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_folding__one__idem_Oidem) ).

thf(338,plain,
    ! [A: hoare_1927711152iple_a,B: fun_Ho333840202iple_a,C: fun_fu1033095803iple_a] :
      ( ( hBOOL @ ( finite1511031594iple_a @ B @ C ) )
     => ( ( hAPP_H963118037iple_a @ ( hAPP_H1700437986iple_a @ B @ A ) @ A )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(128,axiom,
    ! [A: fun_Ho1877127206a_bool,B: fun_Ho1877127206a_bool] :
      ( ( hBOOL @ ( hAPP_f1454306822l_bool @ finite68738179iple_a @ ( collec829051333iple_a @ ( hAPP_f16502863a_bool @ ( hAPP_f2112551770a_bool @ cOMBS_2061548107l_bool @ ( hAPP_f749678531l_bool @ ( cOMBB_196465322iple_a @ fdisj ) @ A ) ) @ B ) ) ) )
    <=> ( ( hBOOL @ ( hAPP_f1454306822l_bool @ finite68738179iple_a @ ( collec829051333iple_a @ A ) ) )
        & ( hBOOL @ ( hAPP_f1454306822l_bool @ finite68738179iple_a @ ( collec829051333iple_a @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_finite__Collect__disjI) ).

thf(643,plain,
    ! [A: fun_Ho1877127206a_bool,B: fun_Ho1877127206a_bool] :
      ( ( ( hBOOL @ ( hAPP_f1454306822l_bool @ finite68738179iple_a @ ( collec829051333iple_a @ ( hAPP_f16502863a_bool @ ( hAPP_f2112551770a_bool @ cOMBS_2061548107l_bool @ ( hAPP_f749678531l_bool @ ( cOMBB_196465322iple_a @ fdisj ) @ A ) ) @ B ) ) ) )
       => ( ( hBOOL @ ( hAPP_f1454306822l_bool @ finite68738179iple_a @ ( collec829051333iple_a @ A ) ) )
          & ( hBOOL @ ( hAPP_f1454306822l_bool @ finite68738179iple_a @ ( collec829051333iple_a @ B ) ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f1454306822l_bool @ finite68738179iple_a @ ( collec829051333iple_a @ A ) ) )
          & ( hBOOL @ ( hAPP_f1454306822l_bool @ finite68738179iple_a @ ( collec829051333iple_a @ B ) ) ) )
       => ( hBOOL @ ( hAPP_f1454306822l_bool @ finite68738179iple_a @ ( collec829051333iple_a @ ( hAPP_f16502863a_bool @ ( hAPP_f2112551770a_bool @ cOMBS_2061548107l_bool @ ( hAPP_f749678531l_bool @ ( cOMBB_196465322iple_a @ fdisj ) @ A ) ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(12,axiom,
    ! [A: fun_bo1549164019l_bool,B: fun_Ho1877127206a_bool,C: hoare_1927711152iple_a] :
      ( ( hAPP_H1487873860l_bool @ ( hAPP_f749678531l_bool @ ( cOMBB_196465322iple_a @ A ) @ B ) @ C )
      = ( hAPP_b589554111l_bool @ A @ ( hAPP_H1448631928a_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_038) ).

thf(175,plain,
    ! [A: fun_bo1549164019l_bool,B: fun_Ho1877127206a_bool,C: hoare_1927711152iple_a] :
      ( ( hAPP_H1487873860l_bool @ ( hAPP_f749678531l_bool @ ( cOMBB_196465322iple_a @ A ) @ B ) @ C )
      = ( hAPP_b589554111l_bool @ A @ ( hAPP_H1448631928a_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(84,axiom,
    ! [A: hoare_1927711152iple_a,B: fun_Ho1877127206a_bool,C: fun_Ho333840202iple_a,D: fun_fu1033095803iple_a] :
      ( ( hBOOL @ ( finite1511031594iple_a @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1454306822l_bool @ finite68738179iple_a @ B ) )
       => ( ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ A ) @ B ) )
         => ( ( hAPP_H963118037iple_a @ ( hAPP_H1700437986iple_a @ C @ A ) @ ( hAPP_f490779847iple_a @ D @ B ) )
            = ( hAPP_f490779847iple_a @ D @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_folding__one__idem_Oin__idem) ).

thf(446,plain,
    ! [A: hoare_1927711152iple_a,B: fun_Ho1877127206a_bool,C: fun_Ho333840202iple_a,D: fun_fu1033095803iple_a] :
      ( ( hBOOL @ ( finite1511031594iple_a @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1454306822l_bool @ finite68738179iple_a @ B ) )
       => ( ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ A ) @ B ) )
         => ( ( hAPP_H963118037iple_a @ ( hAPP_H1700437986iple_a @ C @ A ) @ ( hAPP_f490779847iple_a @ D @ B ) )
            = ( hAPP_f490779847iple_a @ D @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(122,axiom,
    ! [A: fun_a_fun_state_bool,B: com,C: fun_a_fun_state_bool,D: fun_a_fun_state_bool,E: com,F: fun_a_fun_state_bool] :
      ( ( ( hoare_1652181356iple_a @ A @ B @ C )
        = ( hoare_1652181356iple_a @ D @ E @ F ) )
    <=> ( ( A = D )
        & ( B = E )
        & ( C = F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_triple_Oinject) ).

thf(612,plain,
    ! [A: fun_a_fun_state_bool,B: com,C: fun_a_fun_state_bool,D: fun_a_fun_state_bool,E: com,F: fun_a_fun_state_bool] :
      ( ( ( ( hoare_1652181356iple_a @ A @ B @ C )
          = ( hoare_1652181356iple_a @ D @ E @ F ) )
       => ( ( A = D )
          & ( B = E )
          & ( C = F ) ) )
      & ( ( ( A = D )
          & ( B = E )
          & ( C = F ) )
       => ( ( hoare_1652181356iple_a @ A @ B @ C )
          = ( hoare_1652181356iple_a @ D @ E @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(112,axiom,
    ! [A: fun_Ho1630563774a_bool,B: fun_Ho1877127206a_bool,C: hoare_1927711152iple_a] :
      ( ( hAPP_H1027145665a_bool @ ( hAPP_f993216280a_bool @ ( hAPP_f1022403729a_bool @ cOMBC_825881325a_bool @ A ) @ B ) @ C )
      = ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_00_041) ).

thf(556,plain,
    ! [A: fun_Ho1630563774a_bool,B: fun_Ho1877127206a_bool,C: hoare_1927711152iple_a] :
      ( ( hAPP_H1027145665a_bool @ ( hAPP_f993216280a_bool @ ( hAPP_f1022403729a_bool @ cOMBC_825881325a_bool @ A ) @ B ) @ C )
      = ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(108,axiom,
    ! [A: hoare_1927711152iple_a,B: hoare_1927711152iple_a] :
      ( ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ A ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ B ) @ bot_bo1208640912a_bool ) ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_singleton__iff) ).

thf(539,plain,
    ! [A: hoare_1927711152iple_a,B: hoare_1927711152iple_a] :
      ( ( ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ A ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ B ) @ bot_bo1208640912a_bool ) ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ A ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ B ) @ bot_bo1208640912a_bool ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(134,axiom,
    ! [A: hoare_1927711152iple_a,B: fun_Ho1877127206a_bool] :
      ( ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ A ) @ B ) )
     => ~ ! [C: fun_Ho1877127206a_bool] :
            ( ( B
              = ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ A ) @ C ) )
           => ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_Set_Oset__insert) ).

thf(671,plain,
    ! [A: hoare_1927711152iple_a,B: fun_Ho1877127206a_bool] :
      ( ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ A ) @ B ) )
     => ~ ! [C: fun_Ho1877127206a_bool] :
            ( ( B
              = ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ A ) @ C ) )
           => ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(33,axiom,
    ! [A: fun_a_fun_state_bool,B: fun_a_fun_state_bool,C: fun_Ho1877127206a_bool,D: fun_a_fun_state_bool,E: com,F: fun_a_fun_state_bool] :
      ( ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hoare_1617968510rivs_a @ C ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ ( hoare_1652181356iple_a @ D @ E @ F ) ) @ bot_bo1208640912a_bool ) ) )
     => ( ! [G: x_a,H: state] :
            ( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_a2036067514e_bool @ B @ G ) @ H ) )
           => ! [I: state] :
                ( ! [J: x_a] :
                    ( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_a2036067514e_bool @ D @ J ) @ H ) )
                   => ( hBOOL @ ( hAPP_state_bool @ ( hAPP_a2036067514e_bool @ F @ J ) @ I ) ) )
               => ( hBOOL @ ( hAPP_state_bool @ ( hAPP_a2036067514e_bool @ A @ G ) @ I ) ) ) )
       => ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hoare_1617968510rivs_a @ C ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ ( hoare_1652181356iple_a @ B @ E @ A ) ) @ bot_bo1208640912a_bool ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_conseq12) ).

thf(250,plain,
    ! [A: fun_a_fun_state_bool,B: fun_a_fun_state_bool,C: fun_Ho1877127206a_bool,D: fun_a_fun_state_bool,E: com,F: fun_a_fun_state_bool] :
      ( ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hoare_1617968510rivs_a @ C ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ ( hoare_1652181356iple_a @ D @ E @ F ) ) @ bot_bo1208640912a_bool ) ) )
     => ( ! [G: x_a,H: state] :
            ( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_a2036067514e_bool @ B @ G ) @ H ) )
           => ! [I: state] :
                ( ! [J: x_a] :
                    ( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_a2036067514e_bool @ D @ J ) @ H ) )
                   => ( hBOOL @ ( hAPP_state_bool @ ( hAPP_a2036067514e_bool @ F @ J ) @ I ) ) )
               => ( hBOOL @ ( hAPP_state_bool @ ( hAPP_a2036067514e_bool @ A @ G ) @ I ) ) ) )
       => ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hoare_1617968510rivs_a @ C ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ ( hoare_1652181356iple_a @ B @ E @ A ) ) @ bot_bo1208640912a_bool ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(29,axiom,
    ! [A: fun_Ho333840202iple_a,B: fun_Ho1877127206a_bool,C: hoare_1927711152iple_a] :
      ( ( hBOOL @ ( hAPP_H1448631928a_bool @ ( finite2098837632iple_a @ A @ B ) @ C ) )
    <=> ? [D: hoare_1927711152iple_a,E: fun_Ho1877127206a_bool,F: hoare_1927711152iple_a] :
          ( ( B
            = ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ D ) @ E ) )
          & ( C = F )
          & ( hBOOL @ ( hAPP_H1448631928a_bool @ ( finite148164294iple_a @ A @ D @ E ) @ F ) )
          & ~ ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ D ) @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_fold1Set_Osimps) ).

thf(231,plain,
    ! [A: fun_Ho333840202iple_a,B: fun_Ho1877127206a_bool,C: hoare_1927711152iple_a] :
      ( ( ( hBOOL @ ( hAPP_H1448631928a_bool @ ( finite2098837632iple_a @ A @ B ) @ C ) )
       => ? [D: hoare_1927711152iple_a,E: fun_Ho1877127206a_bool,F: hoare_1927711152iple_a] :
            ( ( B
              = ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ D ) @ E ) )
            & ( C = F )
            & ( hBOOL @ ( hAPP_H1448631928a_bool @ ( finite148164294iple_a @ A @ D @ E ) @ F ) )
            & ~ ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ D ) @ E ) ) ) )
      & ( ? [D: hoare_1927711152iple_a,E: fun_Ho1877127206a_bool,F: hoare_1927711152iple_a] :
            ( ( B
              = ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ D ) @ E ) )
            & ( C = F )
            & ( hBOOL @ ( hAPP_H1448631928a_bool @ ( finite148164294iple_a @ A @ D @ E ) @ F ) )
            & ~ ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ D ) @ E ) ) )
       => ( hBOOL @ ( hAPP_H1448631928a_bool @ ( finite2098837632iple_a @ A @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(120,axiom,
    ! [A: fun_Ho333840202iple_a,B: hoare_1927711152iple_a,C: fun_Ho1877127206a_bool,D: hoare_1927711152iple_a] :
      ( ( hBOOL @ ( hAPP_H1448631928a_bool @ ( finite148164294iple_a @ A @ B @ C ) @ D ) )
    <=> ( ( ( C = bot_bo1208640912a_bool )
          & ( D = B ) )
        | ? [E: hoare_1927711152iple_a,F: fun_Ho1877127206a_bool,G: hoare_1927711152iple_a] :
            ( ( C
              = ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ E ) @ F ) )
            & ( D
              = ( hAPP_H963118037iple_a @ ( hAPP_H1700437986iple_a @ A @ E ) @ G ) )
            & ~ ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ E ) @ F ) )
            & ( hBOOL @ ( hAPP_H1448631928a_bool @ ( finite148164294iple_a @ A @ B @ F ) @ G ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_fold__graph_Osimps) ).

thf(588,plain,
    ! [A: fun_Ho333840202iple_a,B: hoare_1927711152iple_a,C: fun_Ho1877127206a_bool,D: hoare_1927711152iple_a] :
      ( ( ( hBOOL @ ( hAPP_H1448631928a_bool @ ( finite148164294iple_a @ A @ B @ C ) @ D ) )
       => ( ( ( C = bot_bo1208640912a_bool )
            & ( D = B ) )
          | ? [E: hoare_1927711152iple_a,F: fun_Ho1877127206a_bool,G: hoare_1927711152iple_a] :
              ( ( C
                = ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ E ) @ F ) )
              & ( D
                = ( hAPP_H963118037iple_a @ ( hAPP_H1700437986iple_a @ A @ E ) @ G ) )
              & ~ ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ E ) @ F ) )
              & ( hBOOL @ ( hAPP_H1448631928a_bool @ ( finite148164294iple_a @ A @ B @ F ) @ G ) ) ) ) )
      & ( ( ( ( C = bot_bo1208640912a_bool )
            & ( D = B ) )
          | ? [E: hoare_1927711152iple_a,F: fun_Ho1877127206a_bool,G: hoare_1927711152iple_a] :
              ( ( C
                = ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ E ) @ F ) )
              & ( D
                = ( hAPP_H963118037iple_a @ ( hAPP_H1700437986iple_a @ A @ E ) @ G ) )
              & ~ ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ E ) @ F ) )
              & ( hBOOL @ ( hAPP_H1448631928a_bool @ ( finite148164294iple_a @ A @ B @ F ) @ G ) ) ) )
       => ( hBOOL @ ( hAPP_H1448631928a_bool @ ( finite148164294iple_a @ A @ B @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(58,axiom,
    ! [A: fun_Ho525994229l_bool,B: fun_Ho1877127206a_bool,C: hoare_1927711152iple_a] :
      ( ( hAPP_H1448631928a_bool @ ( hAPP_f16502863a_bool @ ( hAPP_f684479953a_bool @ cOMBC_862840740l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_00_039) ).

thf(351,plain,
    ! [A: fun_Ho525994229l_bool,B: fun_Ho1877127206a_bool,C: hoare_1927711152iple_a] :
      ( ( hAPP_H1448631928a_bool @ ( hAPP_f16502863a_bool @ ( hAPP_f684479953a_bool @ cOMBC_862840740l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(71,axiom,
    ! [A: fun_Ho1877127206a_bool,B: hoare_1927711152iple_a] :
      ( ( ( hBOOL @ ( hAPP_H1448631928a_bool @ A @ B ) )
       => ( ( collec829051333iple_a @ ( hAPP_f16502863a_bool @ ( hAPP_f2112551770a_bool @ cOMBS_2061548107l_bool @ ( hAPP_f749678531l_bool @ ( cOMBB_196465322iple_a @ fconj ) @ ( hAPP_H1027145665a_bool @ fequal1440857775iple_a @ B ) ) ) @ A ) )
          = ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ B ) @ bot_bo1208640912a_bool ) ) )
      & ( ~ ( hBOOL @ ( hAPP_H1448631928a_bool @ A @ B ) )
       => ( ( collec829051333iple_a @ ( hAPP_f16502863a_bool @ ( hAPP_f2112551770a_bool @ cOMBS_2061548107l_bool @ ( hAPP_f749678531l_bool @ ( cOMBB_196465322iple_a @ fconj ) @ ( hAPP_H1027145665a_bool @ fequal1440857775iple_a @ B ) ) ) @ A ) )
          = bot_bo1208640912a_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_Collect__conv__if2) ).

thf(390,plain,
    ! [A: fun_Ho1877127206a_bool,B: hoare_1927711152iple_a] :
      ( ( ( hBOOL @ ( hAPP_H1448631928a_bool @ A @ B ) )
       => ( ( collec829051333iple_a @ ( hAPP_f16502863a_bool @ ( hAPP_f2112551770a_bool @ cOMBS_2061548107l_bool @ ( hAPP_f749678531l_bool @ ( cOMBB_196465322iple_a @ fconj ) @ ( hAPP_H1027145665a_bool @ fequal1440857775iple_a @ B ) ) ) @ A ) )
          = ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ B ) @ bot_bo1208640912a_bool ) ) )
      & ( ~ ( hBOOL @ ( hAPP_H1448631928a_bool @ A @ B ) )
       => ( ( collec829051333iple_a @ ( hAPP_f16502863a_bool @ ( hAPP_f2112551770a_bool @ cOMBS_2061548107l_bool @ ( hAPP_f749678531l_bool @ ( cOMBB_196465322iple_a @ fconj ) @ ( hAPP_H1027145665a_bool @ fequal1440857775iple_a @ B ) ) ) @ A ) )
          = bot_bo1208640912a_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(125,axiom,
    ! [A: fun_Ho333840202iple_a,B: hoare_1927711152iple_a,C: fun_Ho1877127206a_bool,D: hoare_1927711152iple_a] :
      ( ( hBOOL @ ( hAPP_H1448631928a_bool @ ( finite2098837632iple_a @ A @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ B ) @ C ) ) @ D ) )
     => ~ ! [E: hoare_1927711152iple_a,F: fun_Ho1877127206a_bool] :
            ( ( ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ B ) @ C )
              = ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ E ) @ F ) )
           => ( ( hBOOL @ ( hAPP_H1448631928a_bool @ ( finite148164294iple_a @ A @ E @ F ) @ D ) )
             => ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ E ) @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_insert__fold1SetE) ).

thf(632,plain,
    ! [A: fun_Ho333840202iple_a,B: hoare_1927711152iple_a,C: fun_Ho1877127206a_bool,D: hoare_1927711152iple_a] :
      ( ( hBOOL @ ( hAPP_H1448631928a_bool @ ( finite2098837632iple_a @ A @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ B ) @ C ) ) @ D ) )
     => ~ ! [E: hoare_1927711152iple_a,F: fun_Ho1877127206a_bool] :
            ( ( ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ B ) @ C )
              = ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ E ) @ F ) )
           => ( ( hBOOL @ ( hAPP_H1448631928a_bool @ ( finite148164294iple_a @ A @ E @ F ) @ D ) )
             => ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ E ) @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(73,axiom,
    ! [A: fun_state_bool,B: x_a] :
      ( ( hAPP_a2036067514e_bool @ ( cOMBK_1458035955bool_a @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000t__a_U) ).

thf(401,plain,
    ! [A: fun_state_bool,B: x_a] :
      ( ( hAPP_a2036067514e_bool @ ( cOMBK_1458035955bool_a @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(39,axiom,
    ! [A: fun_fu832487784l_bool,B: fun_Ho440810351a_bool,C: hoare_1927711152iple_a] :
      ( ( hAPP_H1448631928a_bool @ ( hAPP_f909473944a_bool @ ( cOMBB_1083611331iple_a @ A ) @ B ) @ C )
      = ( hAPP_f1454306822l_bool @ A @ ( hAPP_H1027145665a_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_I) ).

thf(272,plain,
    ! [A: fun_fu832487784l_bool,B: fun_Ho440810351a_bool,C: hoare_1927711152iple_a] :
      ( ( hAPP_H1448631928a_bool @ ( hAPP_f909473944a_bool @ ( cOMBB_1083611331iple_a @ A ) @ B ) @ C )
      = ( hAPP_f1454306822l_bool @ A @ ( hAPP_H1027145665a_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(110,axiom,
    ! [A: hoare_1927711152iple_a,B: fun_Ho1877127206a_bool] :
      ( ( B = bot_bo1208640912a_bool )
     => ~ ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_equals0D) ).

thf(549,plain,
    ! [A: hoare_1927711152iple_a,B: fun_Ho1877127206a_bool] :
      ( ( B = bot_bo1208640912a_bool )
     => ~ ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(47,axiom,
    ! [A: hoare_1927711152iple_a,B: hoare_1927711152iple_a,C: hoare_1927711152iple_a,D: hoare_1927711152iple_a] :
      ( ( ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ A ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ B ) @ bot_bo1208640912a_bool ) )
        = ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ C ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ D ) @ bot_bo1208640912a_bool ) ) )
    <=> ( ( ( A = C )
          & ( B = D ) )
        | ( ( A = D )
          & ( B = C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_doubleton__eq__iff) ).

thf(300,plain,
    ! [A: hoare_1927711152iple_a,B: hoare_1927711152iple_a,C: hoare_1927711152iple_a,D: hoare_1927711152iple_a] :
      ( ( ( ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ A ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ B ) @ bot_bo1208640912a_bool ) )
          = ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ C ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ D ) @ bot_bo1208640912a_bool ) ) )
       => ( ( ( A = C )
            & ( B = D ) )
          | ( ( A = D )
            & ( B = C ) ) ) )
      & ( ( ( ( A = C )
            & ( B = D ) )
          | ( ( A = D )
            & ( B = C ) ) )
       => ( ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ A ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ B ) @ bot_bo1208640912a_bool ) )
          = ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ C ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ D ) @ bot_bo1208640912a_bool ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(17,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ A ) @ B ) )
      | ( hBOOL @ A )
      | ( hBOOL @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_3_1_U) ).

thf(190,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)],[17]) ).

thf(66,axiom,
    ! [A: fun_a_fun_state_bool,B: fun_Ho1877127206a_bool,C: com,D: fun_a_fun_state_bool] :
      ( ! [E: x_a,F: state] :
          ( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_a2036067514e_bool @ D @ E ) @ F ) )
         => ? [G: fun_a_fun_state_bool,H: fun_a_fun_state_bool] :
              ( ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hoare_1617968510rivs_a @ B ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ ( hoare_1652181356iple_a @ G @ C @ H ) ) @ bot_bo1208640912a_bool ) ) )
              & ! [I: state] :
                  ( ! [J: x_a] :
                      ( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_a2036067514e_bool @ G @ J ) @ F ) )
                     => ( hBOOL @ ( hAPP_state_bool @ ( hAPP_a2036067514e_bool @ H @ J ) @ I ) ) )
                 => ( hBOOL @ ( hAPP_state_bool @ ( hAPP_a2036067514e_bool @ A @ E ) @ I ) ) ) ) )
     => ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hoare_1617968510rivs_a @ B ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ ( hoare_1652181356iple_a @ D @ C @ A ) ) @ bot_bo1208640912a_bool ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_conseq) ).

thf(373,plain,
    ! [A: fun_a_fun_state_bool,B: fun_Ho1877127206a_bool,C: com,D: fun_a_fun_state_bool] :
      ( ! [E: x_a,F: state] :
          ( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_a2036067514e_bool @ D @ E ) @ F ) )
         => ? [G: fun_a_fun_state_bool,H: fun_a_fun_state_bool] :
              ( ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hoare_1617968510rivs_a @ B ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ ( hoare_1652181356iple_a @ G @ C @ H ) ) @ bot_bo1208640912a_bool ) ) )
              & ! [I: state] :
                  ( ! [J: x_a] :
                      ( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_a2036067514e_bool @ G @ J ) @ F ) )
                     => ( hBOOL @ ( hAPP_state_bool @ ( hAPP_a2036067514e_bool @ H @ J ) @ I ) ) )
                 => ( hBOOL @ ( hAPP_state_bool @ ( hAPP_a2036067514e_bool @ A @ E ) @ I ) ) ) ) )
     => ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hoare_1617968510rivs_a @ B ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ ( hoare_1652181356iple_a @ D @ C @ A ) ) @ bot_bo1208640912a_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(51,axiom,
    ! [A: bool,B: state] :
      ( ( hAPP_state_bool @ ( cOMBK_bool_state @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Com__Ostate_U) ).

thf(326,plain,
    ! [A: bool,B: state] :
      ( ( hAPP_state_bool @ ( cOMBK_bool_state @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(30,axiom,
    ! [A: fun_Ho333840202iple_a,B: hoare_1927711152iple_a] : ( hBOOL @ ( hAPP_H1448631928a_bool @ ( finite148164294iple_a @ A @ B @ bot_bo1208640912a_bool ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_fold__graph_OemptyI) ).

thf(242,plain,
    ! [A: fun_Ho333840202iple_a,B: hoare_1927711152iple_a] : ( hBOOL @ ( hAPP_H1448631928a_bool @ ( finite148164294iple_a @ A @ B @ bot_bo1208640912a_bool ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(45,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/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Ostate_U) ).

thf(294,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)],[45]) ).

thf(61,axiom,
    ! [A: hoare_1927711152iple_a] :
      ( ( hAPP_f490779847iple_a @ the_el1997360207iple_a @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ A ) @ bot_bo1208640912a_bool ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_the__elem__eq) ).

thf(358,plain,
    ! [A: hoare_1927711152iple_a] :
      ( ( hAPP_f490779847iple_a @ the_el1997360207iple_a @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ A ) @ bot_bo1208640912a_bool ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(19,axiom,
    ! [A: hoare_1927711152iple_a,B: fun_Ho1877127206a_bool,C: fun_Ho333840202iple_a,D: fun_fu1033095803iple_a] :
      ( ( hBOOL @ ( finite1511031594iple_a @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1454306822l_bool @ finite68738179iple_a @ B ) )
       => ( ( B != bot_bo1208640912a_bool )
         => ( ( hAPP_f490779847iple_a @ D @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ A ) @ B ) )
            = ( hAPP_H963118037iple_a @ ( hAPP_H1700437986iple_a @ C @ A ) @ ( hAPP_f490779847iple_a @ D @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_folding__one__idem_Oinsert__idem) ).

thf(195,plain,
    ! [A: hoare_1927711152iple_a,B: fun_Ho1877127206a_bool,C: fun_Ho333840202iple_a,D: fun_fu1033095803iple_a] :
      ( ( hBOOL @ ( finite1511031594iple_a @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1454306822l_bool @ finite68738179iple_a @ B ) )
       => ( ( B != bot_bo1208640912a_bool )
         => ( ( hAPP_f490779847iple_a @ D @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ A ) @ B ) )
            = ( hAPP_H963118037iple_a @ ( hAPP_H1700437986iple_a @ C @ A ) @ ( hAPP_f490779847iple_a @ D @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(106,axiom,
    ! [A: fun_Ho1877127206a_bool,B: fun_Ho333840202iple_a,C: fun_fu1033095803iple_a] :
      ( ( hBOOL @ ( finite83514413iple_a @ B @ C ) )
     => ( ( hBOOL @ ( hAPP_f1454306822l_bool @ finite68738179iple_a @ A ) )
       => ( ( A != bot_bo1208640912a_bool )
         => ( ! [D: hoare_1927711152iple_a,E: hoare_1927711152iple_a] : ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ ( hAPP_H963118037iple_a @ ( hAPP_H1700437986iple_a @ B @ D ) @ E ) ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ D ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ E ) @ bot_bo1208640912a_bool ) ) ) )
           => ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ ( hAPP_f490779847iple_a @ C @ A ) ) @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_folding__one_Oclosed) ).

thf(532,plain,
    ! [A: fun_Ho1877127206a_bool,B: fun_Ho333840202iple_a,C: fun_fu1033095803iple_a] :
      ( ( hBOOL @ ( finite83514413iple_a @ B @ C ) )
     => ( ( hBOOL @ ( hAPP_f1454306822l_bool @ finite68738179iple_a @ A ) )
       => ( ( A != bot_bo1208640912a_bool )
         => ( ! [D: hoare_1927711152iple_a,E: hoare_1927711152iple_a] : ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ ( hAPP_H963118037iple_a @ ( hAPP_H1700437986iple_a @ B @ D ) @ E ) ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ D ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ E ) @ bot_bo1208640912a_bool ) ) ) )
           => ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ ( hAPP_f490779847iple_a @ C @ A ) ) @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(42,axiom,
    ! [A: hoare_1927711152iple_a,B: hoare_1927711152iple_a,C: fun_Ho1877127206a_bool] :
      ( ( ~ ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ B ) @ C ) )
       => ( B = A ) )
     => ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ B ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_insertCI) ).

thf(283,plain,
    ! [A: hoare_1927711152iple_a,B: hoare_1927711152iple_a,C: fun_Ho1877127206a_bool] :
      ( ( ~ ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ B ) @ C ) )
       => ( B = A ) )
     => ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ B ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(91,axiom,
    ! [A: hoare_1927711152iple_a] :
      ~ ! [B: fun_a_fun_state_bool,C: com,D: fun_a_fun_state_bool] :
          ( A
         != ( hoare_1652181356iple_a @ B @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_triple_Oexhaust) ).

thf(464,plain,
    ! [A: hoare_1927711152iple_a] :
      ~ ! [B: fun_a_fun_state_bool,C: com,D: fun_a_fun_state_bool] :
          ( A
         != ( hoare_1652181356iple_a @ B @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(80,axiom,
    ! [A: hoare_1927711152iple_a,B: hoare_1927711152iple_a,C: fun_Ho1877127206a_bool] :
      ( ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ A ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ B ) @ C ) ) )
    <=> ( ( A = B )
        | ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_insert__iff) ).

thf(427,plain,
    ! [A: hoare_1927711152iple_a,B: hoare_1927711152iple_a,C: fun_Ho1877127206a_bool] :
      ( ( ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ A ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ B ) @ C ) ) )
       => ( ( A = B )
          | ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ A ) @ C ) ) ) )
      & ( ( ( A = B )
          | ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ A ) @ C ) ) )
       => ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ A ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ B ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(13,axiom,
    ! [A: fun_a_998512028e_bool,B: bool,C: x_a] :
      ( ( hAPP_a2036067514e_bool @ ( hAPP_b540892988e_bool @ ( hAPP_f1824947087e_bool @ cOMBC_41962815e_bool @ A ) @ B ) @ C )
      = ( hAPP_b2019457360e_bool @ ( hAPP_a723219176e_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000t__a_000tc__HOL__Obool_000tc__fun_Itc__Com__Ostate_Mtc__) ).

thf(178,plain,
    ! [A: fun_a_998512028e_bool,B: bool,C: x_a] :
      ( ( hAPP_a2036067514e_bool @ ( hAPP_b540892988e_bool @ ( hAPP_f1824947087e_bool @ cOMBC_41962815e_bool @ A ) @ B ) @ C )
      = ( hAPP_b2019457360e_bool @ ( hAPP_a723219176e_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(59,axiom,
    ! [A: hoare_1927711152iple_a,B: fun_Ho1877127206a_bool] : ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ A ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_insertI1) ).

thf(354,plain,
    ! [A: hoare_1927711152iple_a,B: fun_Ho1877127206a_bool] : ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ A ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(95,axiom,
    ! [A: fun_Ho1877127206a_bool,B: fun_Ho1877127206a_bool,C: fun_Ho1877127206a_bool] :
      ( ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hoare_1617968510rivs_a @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hoare_1617968510rivs_a @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hoare_1617968510rivs_a @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_cut) ).

thf(491,plain,
    ! [A: fun_Ho1877127206a_bool,B: fun_Ho1877127206a_bool,C: fun_Ho1877127206a_bool] :
      ( ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hoare_1617968510rivs_a @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hoare_1617968510rivs_a @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hoare_1617968510rivs_a @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(87,axiom,
    ! [A: hoare_1927711152iple_a,B: fun_Ho1877127206a_bool] :
      ( ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ A ) @ B )
      = ( collec829051333iple_a @ ( hAPP_f16502863a_bool @ ( hAPP_f2112551770a_bool @ cOMBS_2061548107l_bool @ ( hAPP_f749678531l_bool @ ( cOMBB_196465322iple_a @ fdisj ) @ ( hAPP_H1027145665a_bool @ ( hAPP_f1216137953a_bool @ cOMBC_671859290a_bool @ fequal1440857775iple_a ) @ A ) ) ) @ ( hAPP_f16502863a_bool @ ( hAPP_f684479953a_bool @ cOMBC_862840740l_bool @ member127332739iple_a ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_insert__compr__raw) ).

thf(454,plain,
    ! [A: hoare_1927711152iple_a,B: fun_Ho1877127206a_bool] :
      ( ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ A ) @ B )
      = ( collec829051333iple_a @ ( hAPP_f16502863a_bool @ ( hAPP_f2112551770a_bool @ cOMBS_2061548107l_bool @ ( hAPP_f749678531l_bool @ ( cOMBB_196465322iple_a @ fdisj ) @ ( hAPP_H1027145665a_bool @ ( hAPP_f1216137953a_bool @ cOMBC_671859290a_bool @ fequal1440857775iple_a ) @ A ) ) ) @ ( hAPP_f16502863a_bool @ ( hAPP_f684479953a_bool @ cOMBC_862840740l_bool @ member127332739iple_a ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(63,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ A ) @ B ) )
      | ( hBOOL @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_2_1_U) ).

thf(364,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)],[63]) ).

thf(34,axiom,
    ! [A: hoare_1927711152iple_a,B: hoare_1927711152iple_a,C: bool] :
      ( ( ( hBOOL @ C )
       => ( A
          = ( hAPP_f490779847iple_a @ the_Ho1307659873iple_a @ ( hAPP_f16502863a_bool @ ( hAPP_f2112551770a_bool @ cOMBS_2061548107l_bool @ ( hAPP_f749678531l_bool @ ( cOMBB_196465322iple_a @ fconj ) @ ( hAPP_f16502863a_bool @ ( cOMBB_213049548iple_a @ ( hAPP_b589554111l_bool @ fimplies @ C ) ) @ ( hAPP_H1027145665a_bool @ ( hAPP_f1216137953a_bool @ cOMBC_671859290a_bool @ fequal1440857775iple_a ) @ A ) ) ) ) @ ( hAPP_f16502863a_bool @ ( cOMBB_213049548iple_a @ ( hAPP_b589554111l_bool @ fimplies @ ( hAPP_bool_bool @ fNot @ C ) ) ) @ ( hAPP_H1027145665a_bool @ ( hAPP_f1216137953a_bool @ cOMBC_671859290a_bool @ fequal1440857775iple_a ) @ B ) ) ) ) ) )
      & ( ~ ( hBOOL @ C )
       => ( B
          = ( hAPP_f490779847iple_a @ the_Ho1307659873iple_a @ ( hAPP_f16502863a_bool @ ( hAPP_f2112551770a_bool @ cOMBS_2061548107l_bool @ ( hAPP_f749678531l_bool @ ( cOMBB_196465322iple_a @ fconj ) @ ( hAPP_f16502863a_bool @ ( cOMBB_213049548iple_a @ ( hAPP_b589554111l_bool @ fimplies @ C ) ) @ ( hAPP_H1027145665a_bool @ ( hAPP_f1216137953a_bool @ cOMBC_671859290a_bool @ fequal1440857775iple_a ) @ A ) ) ) ) @ ( hAPP_f16502863a_bool @ ( cOMBB_213049548iple_a @ ( hAPP_b589554111l_bool @ fimplies @ ( hAPP_bool_bool @ fNot @ C ) ) ) @ ( hAPP_H1027145665a_bool @ ( hAPP_f1216137953a_bool @ cOMBC_671859290a_bool @ fequal1440857775iple_a ) @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_If__def) ).

thf(254,plain,
    ! [A: hoare_1927711152iple_a,B: hoare_1927711152iple_a,C: bool] :
      ( ( ( hBOOL @ C )
       => ( A
          = ( hAPP_f490779847iple_a @ the_Ho1307659873iple_a @ ( hAPP_f16502863a_bool @ ( hAPP_f2112551770a_bool @ cOMBS_2061548107l_bool @ ( hAPP_f749678531l_bool @ ( cOMBB_196465322iple_a @ fconj ) @ ( hAPP_f16502863a_bool @ ( cOMBB_213049548iple_a @ ( hAPP_b589554111l_bool @ fimplies @ C ) ) @ ( hAPP_H1027145665a_bool @ ( hAPP_f1216137953a_bool @ cOMBC_671859290a_bool @ fequal1440857775iple_a ) @ A ) ) ) ) @ ( hAPP_f16502863a_bool @ ( cOMBB_213049548iple_a @ ( hAPP_b589554111l_bool @ fimplies @ ( hAPP_bool_bool @ fNot @ C ) ) ) @ ( hAPP_H1027145665a_bool @ ( hAPP_f1216137953a_bool @ cOMBC_671859290a_bool @ fequal1440857775iple_a ) @ B ) ) ) ) ) )
      & ( ~ ( hBOOL @ C )
       => ( B
          = ( hAPP_f490779847iple_a @ the_Ho1307659873iple_a @ ( hAPP_f16502863a_bool @ ( hAPP_f2112551770a_bool @ cOMBS_2061548107l_bool @ ( hAPP_f749678531l_bool @ ( cOMBB_196465322iple_a @ fconj ) @ ( hAPP_f16502863a_bool @ ( cOMBB_213049548iple_a @ ( hAPP_b589554111l_bool @ fimplies @ C ) ) @ ( hAPP_H1027145665a_bool @ ( hAPP_f1216137953a_bool @ cOMBC_671859290a_bool @ fequal1440857775iple_a ) @ A ) ) ) ) @ ( hAPP_f16502863a_bool @ ( cOMBB_213049548iple_a @ ( hAPP_b589554111l_bool @ fimplies @ ( hAPP_bool_bool @ fNot @ C ) ) ) @ ( hAPP_H1027145665a_bool @ ( hAPP_f1216137953a_bool @ cOMBC_671859290a_bool @ fequal1440857775iple_a ) @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(27,axiom,
    ! [A: hoare_1927711152iple_a,B: hoare_1927711152iple_a,C: fun_Ho1877127206a_bool] :
      ( ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ B ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_insertI2) ).

thf(227,plain,
    ! [A: hoare_1927711152iple_a,B: hoare_1927711152iple_a,C: fun_Ho1877127206a_bool] :
      ( ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1454306822l_bool @ ( hAPP_H694056973l_bool @ member127332739iple_a @ B ) @ ( hAPP_f16502863a_bool @ ( hAPP_H1975128022a_bool @ insert1434104874iple_a @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(702,plain,
    $false,
    inference(cvc4,[status(thm)],[640,138,628,468,666,449,247,511,384,142,404,288,436,651,320,565,184,460,559,421,606,416,316,261,443,211,480,348,574,397,280,527,452,380,546,201,220,270,529,334,297,192,407,275,137,229,361,329,493,583,522,578,356,169,669,686,637,489,457,503,244,508,425,513,166,148,264,562,291,572,498,181,159,187,406,172,377,649,208,387,535,323,213,520,626,198,462,345,367,223,267,658,675,162,342,553,145,441,370,338,643,175,446,612,556,539,671,250,231,588,351,390,632,401,272,549,300,190,373,326,242,294,358,195,532,283,464,427,178,354,491,454,364,254,227]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWW470_1 : TPTP v8.1.2. Released v5.3.0.
% 0.07/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n024.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 : Thu May 18 22:46:22 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 0.97/0.84  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.42/1.05  % [INFO] 	 Parsing done (200ms). 
% 1.75/1.05  % [INFO] 	 Running in sequential loop mode. 
% 2.22/1.25  % [INFO] 	 eprover registered as external prover. 
% 2.22/1.26  % [INFO] 	 cvc4 registered as external prover. 
% 2.22/1.26  % [INFO] 	 Scanning for conjecture ... 
% 2.66/1.38  % [INFO] 	 Found a conjecture and 134 axioms. Running axiom selection ... 
% 3.01/1.47  % [INFO] 	 Axiom selection finished. Selected 134 axioms (removed 0 axioms). 
% 3.40/1.60  % [INFO] 	 Problem is typed first-order (TPTP TFF). 
% 3.40/1.61  % [INFO] 	 Type checking passed. 
% 3.40/1.62  % [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 ... 
% 5.04/2.10  % [INFO] 	 [Domain constraints] Detected constraint on bool 
% 5.04/2.10  % [INFO] 	 [Domain constraints] dom(bool) ⊆ {fTrue,fFalse} 
% 8.83/2.90  % External prover 'cvc4' found a proof!
% 8.83/2.90  % [INFO] 	 Killing All external provers ... 
% 8.83/2.90  % Time passed: 2381ms (effective reasoning time: 1839ms)
% 8.83/2.90  % 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)>
% 8.86/2.90  % Axioms used in derivation (134): fact_10_insertCI, help_fdisj_1_1_U, fact_4_constant, fact_20_ex__in__conv, fact_42_bot__fun__def, fact_23_insert__absorb, help_fimplies_2_1_U, fact_54_If__def, fact_60_conseq, fact_67_fold1Set_Ointros, fact_53_the__eq__trivial, fact_65_empty__fold1SetE, help_fconj_3_1_U, fact_75_folding__one_Oeq__fold, help_COMBC_1_1_COMBC_000tc__Com__Ostate_000tc__HOL__Obool_000tc__HOL__Obool_U, fact_6_conseq2, fact_56_the__equality, fact_46_Set_Oset__insert, help_COMBB_1_1_COMBB_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_I, help_fequal_1_1_fequal_000tc__Com__Ostate_T, fact_55_equals0I, fact_3_hoare__derivs_Oinsert, fact_34_singleton__inject, fact_5_escape, fact_80_finite__insert, fact_0_empty, fact_92_finite__ne__induct, fact_27_insert__iff, help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_, fact_52_the__sym__eq__trivial, fact_16_equals0D, fact_44_Comp, fact_15_Collect__conv__if, help_fNot_2_1_U, fact_90_fold__graph_Osimps, help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Com__Ostate_U, fact_25_insert__ident, help_COMBC_1_1_COMBC_000t__a_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc, help_fNot_1_1_U, help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Hoare____Mirabelle____yiemogtkbg__, fact_87_finite_Osimps, fact_73_mem__def, help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_00_039, fact_74_Collect__def, help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_00, help_fFalse_1_1_T, fact_8_conseq12, fact_2_cut, fact_37_singleton__iff, help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_00_041, fact_85_finite__nonempty__imp__fold1Set, help_fequal_1_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple, fact_41_bot__apply, fact_50_mk__disjoint__insert, fact_78_fold__graph_OinsertI, fact_38_insert__not__empty, help_fconj_2_1_U, fact_12_singleton__conv2, fact_29_insert__absorb2, help_COMBS_1_1_COMBS_000tc__Com__Ostate_000tc__HOL__Obool_000tc__HOL__Obool_U, fact_48_com_Osimps_I12_J, fact_77_empty__fold__graphE, fact_69_fold1__def, help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc__fun_It, fact_93_folding__one__idem_Oidem, fact_79_finite__Collect__disjI, fact_51_com_Osimps_I3_J, fact_36_doubleton__eq__iff, fact_47_com_Osimps_I13_J, fact_58_the1__equality, fact_91_folding__one__idem_Oinsert__idem, fact_14_Collect__conv__if2, fact_49_the__elem__def, fact_62_fold1Set__sing, fact_18_empty__iff, fact_22_empty__def, fact_68_folding__one_Oinsert, help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_, fact_17_Collect__empty__eq, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Ostate_U, help_fdisj_2_1_U, fact_64_bot__empty__eq, fact_70_finite__Collect__conjI, fact_1_triple_Oinject, fact_59_theI_H, fact_35_singletonE, help_COMBC_1_1_COMBC_000tc__Com__Ostate_000tc__Com__Ostate_000tc__HOL__Obool_U, fact_28_insert__commute, fact_19_empty__Collect__eq, fact_31_insert__compr, fact_76_fold__graph_OemptyI, help_COMBS_1_1_COMBS_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_It__a_J_00, fact_13_singleton__conv, fact_33_insert__compr__raw, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo, fact_24_insertI2, fact_86_finite__induct, help_fconj_1_1_U, help_fdisj_3_1_U, fact_63_folding__one_Osingleton, fact_21_all__not__in__conv, fact_89_fold1Set_Osimps, fact_39_empty__not__insert, help_fFalse_1_1_U, fact_11_emptyE, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_038, fact_30_insert__Collect, fact_84_insert__fold1SetE, help_fequal_2_1_fequal_000tc__Com__Ostate_T, fact_26_insert__code, fact_83_folding__one_Oclosed, fact_45_triple_Oexhaust, fact_40_the__elem__eq, fact_72_finite_OinsertI, fact_43_hoare__derivs_OSkip, help_fimplies_1_1_U, help_COMBK_1_1_COMBK_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000t__a_U, fact_57_theI, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Hoare____Mirabel, fact_66_fold1Set__nonempty, help_fimplies_3_1_U, help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__HOL__Obool_Mtc__H_040, fact_81_fold1__singleton__def, fact_9_insertE, help_COMBC_1_1_COMBC_000t__a_000tc__HOL__Obool_000tc__fun_Itc__Com__Ostate_Mtc__, fact_71_finite_OemptyI, fact_32_insertI1, fact_94_folding__one__idem_Oin__idem, fact_88_finite__imp__fold__graph, help_fequal_2_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple, help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__HOL__Obool_Mtc__H, fact_61_nonempty__iff, fact_82_fold1__singleton, fact_7_conseq1
% 8.86/2.90  % No. of inferences in proof: 272
% 8.86/2.90  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2381 ms resp. 1839 ms w/o parsing
% 8.99/3.00  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.99/3.00  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------