TSTP Solution File: SWW470_1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SWW470_1 : TPTP v8.1.2. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% Computer : n017.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Aug 22 11:07:20 EDT 2023

% Result   : Theorem 39.89s 23.79s
% Output   : CNFRefutation 39.89s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :  197
% Syntax   : Number of formulae    :  243 (  34 unt; 183 typ;   0 def)
%            Number of atoms       :   95 (  38 equ)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :   54 (  19   ~;  24   |;   2   &)
%                                         (   3 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   3 avg)
%            Maximal term depth    :   11 (   2 avg)
%            Number of types       :   46 (  45 usr)
%            Number of type conns  :  244 ( 108   >; 136   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :  137 ( 137 usr;  30 con; 0-6 aty)
%            Number of variables   :   72 (;  68   !;   4   ?;  72   :)

% Comments : 
%------------------------------------------------------------------------------
%$ hBOOL > hoare_1652181356iple_a > finite148164294iple_a > semi > hAPP_state_bool > hAPP_s58564346l_bool > hAPP_s1806633685e_bool > hAPP_f993216280a_bool > hAPP_f963367678e_bool > hAPP_f909473944a_bool > hAPP_f817621513e_bool > hAPP_f762886889e_bool > hAPP_f749678531l_bool > hAPP_f684479953a_bool > hAPP_f644196280e_bool > hAPP_f625100287l_bool > hAPP_f490779847iple_a > hAPP_f340725611e_bool > hAPP_f2112551770a_bool > hAPP_f1824947087e_bool > hAPP_f1759915619e_bool > hAPP_f167292325e_bool > hAPP_f16502863a_bool > hAPP_f1509969235l_bool > hAPP_f1454306822l_bool > hAPP_f1261923407e_bool > hAPP_f1259673775l_bool > hAPP_f1216137953a_bool > hAPP_f1022403729a_bool > hAPP_bool_bool > hAPP_b589554111l_bool > hAPP_b540892988e_bool > hAPP_b2019457360e_bool > hAPP_a849909144l_bool > hAPP_a723219176e_bool > hAPP_a2036067514e_bool > hAPP_a1200519163e_bool > hAPP_H963118037iple_a > hAPP_H694056973l_bool > hAPP_H1975128022a_bool > hAPP_H1700437986iple_a > hAPP_H1487873860l_bool > hAPP_H1448631928a_bool > hAPP_H1027145665a_bool > finite83514413iple_a > finite2098837632iple_a > finite1511031594iple_a > #nlpp > hoare_1617968510rivs_a > finite1943414032iple_a > collec829051333iple_a > cOMBK_bool_state > cOMBK_712844119iple_a > cOMBK_1458035955bool_a > cOMBB_213049548iple_a > cOMBB_196465322iple_a > cOMBB_188601460_state > cOMBB_160679318_state > cOMBB_145932198bool_a > cOMBB_1355796797bool_a > cOMBB_1348041619bool_a > cOMBB_1083611331iple_a > the_el1997360207iple_a > the_Ho1307659873iple_a > skip > p > member127332739iple_a > insert1434104874iple_a > g > finite68738179iple_a > fimplies > fequal_state > fequal1440857775iple_a > fequal1285825639a_bool > fdisj > fconj > fTrue > fNot > fFalse > cOMBS_2061548107l_bool > cOMBS_1378840469l_bool > cOMBC_892787026e_bool > cOMBC_862840740l_bool > cOMBC_825881325a_bool > cOMBC_671859290a_bool > cOMBC_41962815e_bool > cOMBC_231445413l_bool > cOMBC_2027030106e_bool > c > bot_bot_bool > bot_bo1208640912a_bool > b > #skF_2 > #skF_11 > #skF_19 > #skF_40 > #skF_10 > #skF_35 > #skF_21 > #skF_42 > #skF_36 > #skF_5 > #skF_31 > #skF_27 > #skF_32 > #skF_39 > #skF_8 > #skF_4 > #skF_33 > #skF_38 > #skF_46 > #skF_44 > #skF_23 > #skF_29 > #skF_30 > #skF_47 > #skF_45 > #skF_28 > #skF_25 > #skF_14 > #skF_34 > #skF_18 > #skF_12 > #skF_43 > #skF_9 > #skF_15 > #skF_24 > #skF_3 > #skF_20 > #skF_41 > #skF_26 > #skF_1 > #skF_17 > #skF_6 > #skF_37 > #skF_13 > #skF_16 > #skF_7 > #skF_22

%Foreground sorts:
tff(fun_bo675861616e_bool,type,
    fun_bo675861616e_bool: $tType ).

tff(fun_fu1249172034a_bool,type,
    fun_fu1249172034a_bool: $tType ).

tff(fun_a_fun_state_bool,type,
    fun_a_fun_state_bool: $tType ).

tff(fun_Ho957066028l_bool,type,
    fun_Ho957066028l_bool: $tType ).

tff(fun_a_998512028e_bool,type,
    fun_a_998512028e_bool: $tType ).

tff(fun_fu373216837e_bool,type,
    fun_fu373216837e_bool: $tType ).

tff(fun_Ho525994229l_bool,type,
    fun_Ho525994229l_bool: $tType ).

tff(fun_bool_bool,type,
    fun_bool_bool: $tType ).

tff(fun_fu1658206819l_bool,type,
    fun_fu1658206819l_bool: $tType ).

tff(fun_a_1632297036l_bool,type,
    fun_a_1632297036l_bool: $tType ).

tff(fun_fu2008829792e_bool,type,
    fun_fu2008829792e_bool: $tType ).

tff(fun_fu269925879l_bool,type,
    fun_fu269925879l_bool: $tType ).

tff(fun_fu1192765369a_bool,type,
    fun_fu1192765369a_bool: $tType ).

tff(fun_fu2118559873l_bool,type,
    fun_fu2118559873l_bool: $tType ).

tff(fun_bo1936561970e_bool,type,
    fun_bo1936561970e_bool: $tType ).

tff(fun_fu1591723597e_bool,type,
    fun_fu1591723597e_bool: $tType ).

tff(fun_fu276214394a_bool,type,
    fun_fu276214394a_bool: $tType ).

tff(hoare_1927711152iple_a,type,
    hoare_1927711152iple_a: $tType ).

tff(state,type,
    state: $tType ).

tff(fun_bo1549164019l_bool,type,
    fun_bo1549164019l_bool: $tType ).

tff(fun_fu1585556401a_bool,type,
    fun_fu1585556401a_bool: $tType ).

tff(com,type,
    com: $tType ).

tff(fun_Ho843200573iple_a,type,
    fun_Ho843200573iple_a: $tType ).

tff(fun_fu1219323149e_bool,type,
    fun_fu1219323149e_bool: $tType ).

tff(fun_fu281355805e_bool,type,
    fun_fu281355805e_bool: $tType ).

tff(fun_Ho333840202iple_a,type,
    fun_Ho333840202iple_a: $tType ).

tff(fun_Ho440810351a_bool,type,
    fun_Ho440810351a_bool: $tType ).

tff(x_a,type,
    x_a: $tType ).

tff(fun_fu402792811e_bool,type,
    fun_fu402792811e_bool: $tType ).

tff(bool,type,
    bool: $tType ).

tff(fun_fu1033095803iple_a,type,
    fun_fu1033095803iple_a: $tType ).

tff(fun_st1506752259e_bool,type,
    fun_st1506752259e_bool: $tType ).

tff(fun_fu1905604217a_bool,type,
    fun_fu1905604217a_bool: $tType ).

tff(fun_st2063251938l_bool,type,
    fun_st2063251938l_bool: $tType ).

tff(fun_Ho1877127206a_bool,type,
    fun_Ho1877127206a_bool: $tType ).

tff(fun_Ho1630563774a_bool,type,
    fun_Ho1630563774a_bool: $tType ).

tff(fun_state_bool,type,
    fun_state_bool: $tType ).

tff(fun_fu734682033e_bool,type,
    fun_fu734682033e_bool: $tType ).

tff(fun_fu1563903738a_bool,type,
    fun_fu1563903738a_bool: $tType ).

tff(fun_fu832487784l_bool,type,
    fun_fu832487784l_bool: $tType ).

tff(fun_fu1047394976e_bool,type,
    fun_fu1047394976e_bool: $tType ).

tff(fun_fu893561155a_bool,type,
    fun_fu893561155a_bool: $tType ).

tff(fun_fu1644852787l_bool,type,
    fun_fu1644852787l_bool: $tType ).

tff(fun_fu222103665e_bool,type,
    fun_fu222103665e_bool: $tType ).

tff(fun_a_2117018159e_bool,type,
    fun_a_2117018159e_bool: $tType ).

%Background operators:

%Foreground operators:
tff(hAPP_f1261923407e_bool,type,
    hAPP_f1261923407e_bool: ( fun_fu734682033e_bool * fun_a_2117018159e_bool ) > fun_fu281355805e_bool ).

tff('#skF_2',type,
    '#skF_2': ( fun_Ho1877127206a_bool * com * fun_a_fun_state_bool * fun_a_fun_state_bool ) > state ).

tff(cOMBB_188601460_state,type,
    cOMBB_188601460_state: fun_bo1549164019l_bool > fun_fu1658206819l_bool ).

tff(hAPP_b2019457360e_bool,type,
    hAPP_b2019457360e_bool: ( fun_bo1936561970e_bool * bool ) > fun_state_bool ).

tff(cOMBB_1083611331iple_a,type,
    cOMBB_1083611331iple_a: fun_fu832487784l_bool > fun_fu1563903738a_bool ).

tff('#skF_11',type,
    '#skF_11': fun_Ho1877127206a_bool > hoare_1927711152iple_a ).

tff(cOMBB_196465322iple_a,type,
    cOMBB_196465322iple_a: fun_bo1549164019l_bool > fun_fu269925879l_bool ).

tff('#skF_19',type,
    '#skF_19': fun_Ho1877127206a_bool > hoare_1927711152iple_a ).

tff(hAPP_f1759915619e_bool,type,
    hAPP_f1759915619e_bool: ( fun_fu373216837e_bool * fun_state_bool ) > fun_state_bool ).

tff(hAPP_f1022403729a_bool,type,
    hAPP_f1022403729a_bool: ( fun_fu1905604217a_bool * fun_Ho1630563774a_bool ) > fun_fu276214394a_bool ).

tff(hoare_1652181356iple_a,type,
    hoare_1652181356iple_a: ( fun_a_fun_state_bool * com * fun_a_fun_state_bool ) > hoare_1927711152iple_a ).

tff(hAPP_f16502863a_bool,type,
    hAPP_f16502863a_bool: ( fun_fu1585556401a_bool * fun_Ho1877127206a_bool ) > fun_Ho1877127206a_bool ).

tff(cOMBC_862840740l_bool,type,
    cOMBC_862840740l_bool: fun_fu1192765369a_bool ).

tff(fTrue,type,
    fTrue: bool ).

tff(cOMBK_bool_state,type,
    cOMBK_bool_state: bool > fun_state_bool ).

tff(hoare_1617968510rivs_a,type,
    hoare_1617968510rivs_a: fun_Ho1877127206a_bool > fun_fu832487784l_bool ).

tff('#skF_40',type,
    '#skF_40': ( fun_Ho333840202iple_a * fun_Ho1877127206a_bool * hoare_1927711152iple_a ) > fun_Ho1877127206a_bool ).

tff(hAPP_f644196280e_bool,type,
    hAPP_f644196280e_bool: ( fun_fu1047394976e_bool * fun_st2063251938l_bool ) > fun_fu373216837e_bool ).

tff(cOMBC_825881325a_bool,type,
    cOMBC_825881325a_bool: fun_fu1905604217a_bool ).

tff('#skF_10',type,
    '#skF_10': fun_Ho1877127206a_bool > hoare_1927711152iple_a ).

tff('#skF_35',type,
    '#skF_35': ( fun_fu832487784l_bool * fun_Ho1877127206a_bool ) > fun_Ho1877127206a_bool ).

tff(hAPP_f340725611e_bool,type,
    hAPP_f340725611e_bool: ( fun_fu1591723597e_bool * fun_a_1632297036l_bool ) > fun_a_998512028e_bool ).

tff(skip,type,
    skip: com ).

tff(hAPP_H1700437986iple_a,type,
    hAPP_H1700437986iple_a: ( fun_Ho333840202iple_a * hoare_1927711152iple_a ) > fun_Ho843200573iple_a ).

tff(cOMBK_712844119iple_a,type,
    cOMBK_712844119iple_a: bool > fun_Ho1877127206a_bool ).

tff('#skF_21',type,
    '#skF_21': ( fun_Ho1877127206a_bool * hoare_1927711152iple_a ) > hoare_1927711152iple_a ).

tff('#skF_42',type,
    '#skF_42': ( fun_Ho333840202iple_a * hoare_1927711152iple_a * fun_Ho1877127206a_bool * hoare_1927711152iple_a ) > hoare_1927711152iple_a ).

tff('#skF_36',type,
    '#skF_36': fun_Ho1877127206a_bool > fun_Ho1877127206a_bool ).

tff('#skF_5',type,
    '#skF_5': ( com * fun_Ho1877127206a_bool * fun_a_fun_state_bool * fun_a_fun_state_bool * fun_a_fun_state_bool ) > x_a ).

tff('#skF_31',type,
    '#skF_31': ( fun_Ho333840202iple_a * hoare_1927711152iple_a * fun_Ho1877127206a_bool * hoare_1927711152iple_a ) > hoare_1927711152iple_a ).

tff(fNot,type,
    fNot: fun_bool_bool ).

tff(c,type,
    c: com ).

tff('#skF_27',type,
    '#skF_27': fun_Ho1877127206a_bool > hoare_1927711152iple_a ).

tff(hAPP_bool_bool,type,
    hAPP_bool_bool: ( fun_bool_bool * bool ) > bool ).

tff('#skF_32',type,
    '#skF_32': ( fun_Ho333840202iple_a * hoare_1927711152iple_a * fun_Ho1877127206a_bool * hoare_1927711152iple_a ) > fun_Ho1877127206a_bool ).

tff(cOMBC_231445413l_bool,type,
    cOMBC_231445413l_bool: fun_fu1219323149e_bool ).

tff(finite148164294iple_a,type,
    finite148164294iple_a: ( fun_Ho333840202iple_a * hoare_1927711152iple_a * fun_Ho1877127206a_bool ) > fun_Ho1877127206a_bool ).

tff(cOMBS_2061548107l_bool,type,
    cOMBS_2061548107l_bool: fun_fu1249172034a_bool ).

tff('#skF_39',type,
    '#skF_39': ( fun_Ho333840202iple_a * fun_Ho1877127206a_bool * hoare_1927711152iple_a ) > hoare_1927711152iple_a ).

tff('#skF_8',type,
    '#skF_8': ( fun_a_fun_state_bool * fun_a_fun_state_bool * fun_a_fun_state_bool * fun_Ho1877127206a_bool * fun_a_fun_state_bool * com ) > state ).

tff('#skF_4',type,
    '#skF_4': ( fun_Ho1877127206a_bool * fun_a_fun_state_bool * fun_a_fun_state_bool * com * fun_a_fun_state_bool ) > state ).

tff(hAPP_f1509969235l_bool,type,
    hAPP_f1509969235l_bool: ( fun_fu2118559873l_bool * fun_a_fun_state_bool ) > fun_a_1632297036l_bool ).

tff('#skF_33',type,
    '#skF_33': ( fun_Ho333840202iple_a * fun_Ho1877127206a_bool ) > hoare_1927711152iple_a ).

tff(cOMBC_892787026e_bool,type,
    cOMBC_892787026e_bool: fun_fu734682033e_bool ).

tff(hAPP_f909473944a_bool,type,
    hAPP_f909473944a_bool: ( fun_fu1563903738a_bool * fun_Ho440810351a_bool ) > fun_Ho1877127206a_bool ).

tff(hAPP_f1824947087e_bool,type,
    hAPP_f1824947087e_bool: ( fun_fu222103665e_bool * fun_a_998512028e_bool ) > fun_bo675861616e_bool ).

tff(hAPP_f762886889e_bool,type,
    hAPP_f762886889e_bool: ( fun_fu281355805e_bool * fun_state_bool ) > fun_a_fun_state_bool ).

tff(hAPP_f684479953a_bool,type,
    hAPP_f684479953a_bool: ( fun_fu1192765369a_bool * fun_Ho525994229l_bool ) > fun_fu1585556401a_bool ).

tff(finite1943414032iple_a,type,
    finite1943414032iple_a: fun_Ho333840202iple_a > fun_fu1033095803iple_a ).

tff(fequal1440857775iple_a,type,
    fequal1440857775iple_a: fun_Ho440810351a_bool ).

tff(hAPP_f167292325e_bool,type,
    hAPP_f167292325e_bool: ( fun_fu1219323149e_bool * fun_st2063251938l_bool ) > fun_bo1936561970e_bool ).

tff(hAPP_s58564346l_bool,type,
    hAPP_s58564346l_bool: ( fun_st2063251938l_bool * state ) > fun_bool_bool ).

tff(b,type,
    b: fun_state_bool ).

tff(hAPP_a849909144l_bool,type,
    hAPP_a849909144l_bool: ( fun_a_1632297036l_bool * x_a ) > fun_st2063251938l_bool ).

tff(fequal_state,type,
    fequal_state: fun_st1506752259e_bool ).

tff(fimplies,type,
    fimplies: fun_bo1549164019l_bool ).

tff('#skF_38',type,
    '#skF_38': ( fun_Ho333840202iple_a * hoare_1927711152iple_a * fun_Ho1877127206a_bool ) > hoare_1927711152iple_a ).

tff(cOMBC_2027030106e_bool,type,
    cOMBC_2027030106e_bool: fun_fu402792811e_bool ).

tff('#skF_46',type,
    '#skF_46': ( fun_fu832487784l_bool * fun_Ho1877127206a_bool ) > hoare_1927711152iple_a ).

tff(hAPP_H694056973l_bool,type,
    hAPP_H694056973l_bool: ( fun_Ho525994229l_bool * hoare_1927711152iple_a ) > fun_fu832487784l_bool ).

tff('#skF_44',type,
    '#skF_44': ( fun_Ho333840202iple_a * hoare_1927711152iple_a * fun_Ho1877127206a_bool * hoare_1927711152iple_a ) > hoare_1927711152iple_a ).

tff(fequal1285825639a_bool,type,
    fequal1285825639a_bool: fun_fu1644852787l_bool ).

tff(fdisj,type,
    fdisj: fun_bo1549164019l_bool ).

tff(finite1511031594iple_a,type,
    finite1511031594iple_a: ( fun_Ho333840202iple_a * fun_fu1033095803iple_a ) > bool ).

tff(finite68738179iple_a,type,
    finite68738179iple_a: fun_fu832487784l_bool ).

tff(cOMBK_1458035955bool_a,type,
    cOMBK_1458035955bool_a: fun_state_bool > fun_a_fun_state_bool ).

tff('#skF_23',type,
    '#skF_23': ( fun_Ho1877127206a_bool * hoare_1927711152iple_a ) > hoare_1927711152iple_a ).

tff('#skF_29',type,
    '#skF_29': ( fun_Ho1877127206a_bool * fun_Ho333840202iple_a * fun_fu1033095803iple_a ) > hoare_1927711152iple_a ).

tff(hAPP_f1454306822l_bool,type,
    hAPP_f1454306822l_bool: ( fun_fu832487784l_bool * fun_Ho1877127206a_bool ) > bool ).

tff(fconj,type,
    fconj: fun_bo1549164019l_bool ).

tff(hAPP_f749678531l_bool,type,
    hAPP_f749678531l_bool: ( fun_fu269925879l_bool * fun_Ho1877127206a_bool ) > fun_Ho957066028l_bool ).

tff(member127332739iple_a,type,
    member127332739iple_a: fun_Ho525994229l_bool ).

tff('#skF_30',type,
    '#skF_30': ( fun_Ho1877127206a_bool * fun_Ho333840202iple_a * fun_fu1033095803iple_a ) > hoare_1927711152iple_a ).

tff('#skF_47',type,
    '#skF_47': ( fun_fu832487784l_bool * fun_Ho1877127206a_bool ) > fun_Ho1877127206a_bool ).

tff('#skF_45',type,
    '#skF_45': ( fun_fu832487784l_bool * fun_Ho1877127206a_bool ) > hoare_1927711152iple_a ).

tff('#skF_28',type,
    '#skF_28': fun_Ho1877127206a_bool > fun_Ho1877127206a_bool ).

tff('#skF_25',type,
    '#skF_25': ( fun_a_fun_state_bool * fun_Ho1877127206a_bool * com * fun_a_fun_state_bool ) > state ).

tff(hAPP_a723219176e_bool,type,
    hAPP_a723219176e_bool: ( fun_a_998512028e_bool * x_a ) > fun_bo1936561970e_bool ).

tff('#skF_14',type,
    '#skF_14': hoare_1927711152iple_a > fun_a_fun_state_bool ).

tff('#skF_34',type,
    '#skF_34': ( fun_fu832487784l_bool * fun_Ho1877127206a_bool ) > hoare_1927711152iple_a ).

tff(hAPP_f993216280a_bool,type,
    hAPP_f993216280a_bool: ( fun_fu276214394a_bool * fun_Ho1877127206a_bool ) > fun_Ho440810351a_bool ).

tff('#skF_18',type,
    '#skF_18': ( hoare_1927711152iple_a * fun_Ho1877127206a_bool ) > fun_Ho1877127206a_bool ).

tff('#skF_12',type,
    '#skF_12': fun_Ho1877127206a_bool > hoare_1927711152iple_a ).

tff('#skF_43',type,
    '#skF_43': ( fun_Ho333840202iple_a * hoare_1927711152iple_a * fun_Ho1877127206a_bool * hoare_1927711152iple_a ) > fun_Ho1877127206a_bool ).

tff(cOMBS_1378840469l_bool,type,
    cOMBS_1378840469l_bool: fun_fu1047394976e_bool ).

tff(hAPP_f490779847iple_a,type,
    hAPP_f490779847iple_a: ( fun_fu1033095803iple_a * fun_Ho1877127206a_bool ) > hoare_1927711152iple_a ).

tff(hAPP_H1487873860l_bool,type,
    hAPP_H1487873860l_bool: ( fun_Ho957066028l_bool * hoare_1927711152iple_a ) > fun_bool_bool ).

tff(hAPP_H1975128022a_bool,type,
    hAPP_H1975128022a_bool: ( fun_Ho1630563774a_bool * hoare_1927711152iple_a ) > fun_fu1585556401a_bool ).

tff(hAPP_f1216137953a_bool,type,
    hAPP_f1216137953a_bool: ( fun_fu893561155a_bool * fun_Ho440810351a_bool ) > fun_Ho440810351a_bool ).

tff(the_el1997360207iple_a,type,
    the_el1997360207iple_a: fun_fu1033095803iple_a ).

tff('#skF_9',type,
    '#skF_9': ( fun_a_fun_state_bool * fun_a_fun_state_bool * fun_a_fun_state_bool * fun_Ho1877127206a_bool * fun_a_fun_state_bool * com ) > state ).

tff('#skF_15',type,
    '#skF_15': hoare_1927711152iple_a > com ).

tff('#skF_24',type,
    '#skF_24': ( fun_a_fun_state_bool * fun_Ho1877127206a_bool * com * fun_a_fun_state_bool ) > x_a ).

tff('#skF_3',type,
    '#skF_3': ( fun_Ho1877127206a_bool * fun_a_fun_state_bool * fun_a_fun_state_bool * com * fun_a_fun_state_bool ) > x_a ).

tff('#skF_20',type,
    '#skF_20': ( fun_Ho1877127206a_bool * hoare_1927711152iple_a ) > hoare_1927711152iple_a ).

tff(hAPP_a1200519163e_bool,type,
    hAPP_a1200519163e_bool: ( fun_a_2117018159e_bool * x_a ) > fun_fu373216837e_bool ).

tff(hAPP_s1806633685e_bool,type,
    hAPP_s1806633685e_bool: ( fun_st1506752259e_bool * state ) > fun_state_bool ).

tff(finite83514413iple_a,type,
    finite83514413iple_a: ( fun_Ho333840202iple_a * fun_fu1033095803iple_a ) > bool ).

tff('#skF_41',type,
    '#skF_41': ( fun_Ho333840202iple_a * fun_Ho1877127206a_bool * hoare_1927711152iple_a ) > hoare_1927711152iple_a ).

tff(cOMBB_1348041619bool_a,type,
    cOMBB_1348041619bool_a: fun_fu1219323149e_bool > fun_fu1591723597e_bool ).

tff('#skF_26',type,
    '#skF_26': ( fun_Ho1877127206a_bool * fun_a_fun_state_bool * com * fun_a_fun_state_bool * fun_a_fun_state_bool * fun_a_fun_state_bool ) > state ).

tff('#skF_1',type,
    '#skF_1': ( fun_Ho1877127206a_bool * com * fun_a_fun_state_bool * fun_a_fun_state_bool ) > x_a ).

tff('#skF_17',type,
    '#skF_17': ( hoare_1927711152iple_a * fun_Ho1877127206a_bool ) > fun_Ho1877127206a_bool ).

tff(hAPP_b540892988e_bool,type,
    hAPP_b540892988e_bool: ( fun_bo675861616e_bool * bool ) > fun_a_fun_state_bool ).

tff(finite2098837632iple_a,type,
    finite2098837632iple_a: ( fun_Ho333840202iple_a * fun_Ho1877127206a_bool ) > fun_Ho1877127206a_bool ).

tff(cOMBB_1355796797bool_a,type,
    cOMBB_1355796797bool_a: fun_fu1658206819l_bool > fun_fu2118559873l_bool ).

tff(hAPP_state_bool,type,
    hAPP_state_bool: ( fun_state_bool * state ) > bool ).

tff(hAPP_f817621513e_bool,type,
    hAPP_f817621513e_bool: ( fun_fu402792811e_bool * fun_st1506752259e_bool ) > fun_st1506752259e_bool ).

tff(cOMBC_671859290a_bool,type,
    cOMBC_671859290a_bool: fun_fu893561155a_bool ).

tff(fFalse,type,
    fFalse: bool ).

tff(bot_bo1208640912a_bool,type,
    bot_bo1208640912a_bool: fun_Ho1877127206a_bool ).

tff(p,type,
    p: fun_a_fun_state_bool ).

tff('#skF_6',type,
    '#skF_6': ( com * fun_Ho1877127206a_bool * fun_a_fun_state_bool * fun_a_fun_state_bool * fun_a_fun_state_bool ) > state ).

tff(g,type,
    g: fun_Ho1877127206a_bool ).

tff(hBOOL,type,
    hBOOL: bool > $o ).

tff(bot_bot_bool,type,
    bot_bot_bool: bool ).

tff(hAPP_b589554111l_bool,type,
    hAPP_b589554111l_bool: ( fun_bo1549164019l_bool * bool ) > fun_bool_bool ).

tff('#skF_37',type,
    '#skF_37': fun_Ho1877127206a_bool > hoare_1927711152iple_a ).

tff(the_Ho1307659873iple_a,type,
    the_Ho1307659873iple_a: fun_fu1033095803iple_a ).

tff(collec829051333iple_a,type,
    collec829051333iple_a: fun_Ho1877127206a_bool > fun_Ho1877127206a_bool ).

tff('#skF_13',type,
    '#skF_13': fun_Ho1877127206a_bool > hoare_1927711152iple_a ).

tff(insert1434104874iple_a,type,
    insert1434104874iple_a: fun_Ho1630563774a_bool ).

tff(hAPP_H1448631928a_bool,type,
    hAPP_H1448631928a_bool: ( fun_Ho1877127206a_bool * hoare_1927711152iple_a ) > bool ).

tff(cOMBB_213049548iple_a,type,
    cOMBB_213049548iple_a: fun_bool_bool > fun_fu1585556401a_bool ).

tff('#skF_16',type,
    '#skF_16': hoare_1927711152iple_a > fun_a_fun_state_bool ).

tff(hAPP_a2036067514e_bool,type,
    hAPP_a2036067514e_bool: ( fun_a_fun_state_bool * x_a ) > fun_state_bool ).

tff(semi,type,
    semi: ( com * com ) > com ).

tff(cOMBC_41962815e_bool,type,
    cOMBC_41962815e_bool: fun_fu222103665e_bool ).

tff(cOMBB_145932198bool_a,type,
    cOMBB_145932198bool_a: fun_fu1047394976e_bool > fun_fu2008829792e_bool ).

tff('#skF_7',type,
    '#skF_7': ( fun_a_fun_state_bool * fun_a_fun_state_bool * fun_a_fun_state_bool * fun_Ho1877127206a_bool * fun_a_fun_state_bool * com ) > x_a ).

tff(cOMBB_160679318_state,type,
    cOMBB_160679318_state: fun_bool_bool > fun_fu373216837e_bool ).

tff(hAPP_f1259673775l_bool,type,
    hAPP_f1259673775l_bool: ( fun_fu1658206819l_bool * fun_state_bool ) > fun_st2063251938l_bool ).

tff(hAPP_f963367678e_bool,type,
    hAPP_f963367678e_bool: ( fun_fu2008829792e_bool * fun_a_1632297036l_bool ) > fun_a_2117018159e_bool ).

tff(hAPP_H1027145665a_bool,type,
    hAPP_H1027145665a_bool: ( fun_Ho440810351a_bool * hoare_1927711152iple_a ) > fun_Ho1877127206a_bool ).

tff(hAPP_f2112551770a_bool,type,
    hAPP_f2112551770a_bool: ( fun_fu1249172034a_bool * fun_Ho957066028l_bool ) > fun_fu1585556401a_bool ).

tff('#skF_22',type,
    '#skF_22': ( hoare_1927711152iple_a * fun_Ho1877127206a_bool * hoare_1927711152iple_a ) > hoare_1927711152iple_a ).

tff(hAPP_H963118037iple_a,type,
    hAPP_H963118037iple_a: ( fun_Ho843200573iple_a * hoare_1927711152iple_a ) > hoare_1927711152iple_a ).

tff(hAPP_f625100287l_bool,type,
    hAPP_f625100287l_bool: ( fun_fu1644852787l_bool * fun_Ho1877127206a_bool ) > fun_fu832487784l_bool ).

tff(f_436,axiom,
    ! [Pa: fun_Ho1877127206a_bool] : ( collec829051333iple_a(Pa) = Pa ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_Collect__def) ).

tff(f_158,axiom,
    ! [Pa: fun_Ho1877127206a_bool] :
      ( ( bot_bo1208640912a_bool = collec829051333iple_a(Pa) )
    <=> ! [X_2: hoare_1927711152iple_a] : ~ hBOOL(hAPP_H1448631928a_bool(Pa,X_2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_empty__Collect__eq) ).

tff(f_251,axiom,
    ! [X_2: hoare_1927711152iple_a] :
      ( hBOOL(hAPP_H1448631928a_bool(bot_bo1208640912a_bool,X_2))
    <=> hBOOL(bot_bot_bool) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_bot__fun__def) ).

tff(f_684,axiom,
    ! [P: bool,Q: state] : ( hAPP_state_bool(cOMBK_bool_state(P),Q) = P ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Com__Ostate_U) ).

tff(f_655,axiom,
    ! [P: bool] :
      ( ( P = fTrue )
      | ( P = fFalse ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).

tff(f_651,axiom,
    ~ hBOOL(fFalse),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).

tff(f_526,axiom,
    ! [A_3: fun_Ho1877127206a_bool] :
      ( hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,A_3))
    <=> ( ( A_3 = bot_bo1208640912a_bool )
        | ? [A_1: fun_Ho1877127206a_bool,A_2: hoare_1927711152iple_a] :
            ( ( A_3 = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,A_2),A_1) )
            & hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,A_1)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_finite_Osimps) ).

tff(f_118,axiom,
    ! [A_3: hoare_1927711152iple_a] : ( collec829051333iple_a(hAPP_H1027145665a_bool(fequal1440857775iple_a,A_3)) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,A_3),bot_bo1208640912a_bool) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_singleton__conv2) ).

tff(f_120,axiom,
    ! [A_3: hoare_1927711152iple_a] : ( collec829051333iple_a(hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,fequal1440857775iple_a),A_3)) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,A_3),bot_bo1208640912a_bool) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_singleton__conv) ).

tff(f_745,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))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

tff(f_33,axiom,
    ! [Ga: fun_Ho1877127206a_bool] : hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(Ga),bot_bo1208640912a_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_empty) ).

tff(f_47,axiom,
    ! [Ga: fun_Ho1877127206a_bool,G_1: fun_Ho1877127206a_bool,Ts: fun_Ho1877127206a_bool] :
      ( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(G_1),Ts))
     => ( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(Ga),G_1))
       => hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(Ga),Ts)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_cut) ).

tff(f_686,axiom,
    ! [P: fun_state_bool,Q: x_a] : ( hAPP_a2036067514e_bool(cOMBK_1458035955bool_a(P),Q) = P ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000t__a_U) ).

tff(f_369,axiom,
    ! [Q_1: fun_a_fun_state_bool,Ga: fun_Ho1877127206a_bool,Ca: com,Pa: fun_a_fun_state_bool] :
      ( ! [Z_1: x_a,S: state] :
          ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_1),S))
         => ? [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
              ( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(Ga),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(P_1,Ca,Q_2)),bot_bo1208640912a_bool)))
              & ! [S_1: state] :
                  ( ! [Z_2: x_a] :
                      ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),S))
                     => hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),S_1)) )
                 => hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_1),S_1)) ) ) )
     => hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(Ga),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(Pa,Ca,Q_1)),bot_bo1208640912a_bool))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_conseq) ).

tff(c_246,plain,
    ! [Pa_259: fun_Ho1877127206a_bool] : ( collec829051333iple_a(Pa_259) = Pa_259 ),
    inference(cnfTransformation,[status(thm)],[f_436]) ).

tff(c_67,plain,
    ! [Pa_78: fun_Ho1877127206a_bool,X_2_81: hoare_1927711152iple_a] :
      ( ~ hBOOL(hAPP_H1448631928a_bool(Pa_78,X_2_81))
      | ( collec829051333iple_a(Pa_78) != bot_bo1208640912a_bool ) ),
    inference(cnfTransformation,[status(thm)],[f_158]) ).

tff(c_439,plain,
    ! [X_2_81: hoare_1927711152iple_a] : ~ hBOOL(hAPP_H1448631928a_bool(bot_bo1208640912a_bool,X_2_81)),
    inference(demodulation,[status(thm),theory(equality)],[c_246,c_67]) ).

tff(c_147,plain,
    ! [X_2_133: hoare_1927711152iple_a] :
      ( hBOOL(hAPP_H1448631928a_bool(bot_bo1208640912a_bool,X_2_133))
      | ~ hBOOL(bot_bot_bool) ),
    inference(cnfTransformation,[status(thm)],[f_251]) ).

tff(c_440,plain,
    ~ hBOOL(bot_bot_bool),
    inference(negUnitSimplification,[status(thm)],[c_439,c_147]) ).

tff(c_374,plain,
    ! [P_377: bool,Q_378: state] : ( hAPP_state_bool(cOMBK_bool_state(P_377),Q_378) = P_377 ),
    inference(cnfTransformation,[status(thm)],[f_684]) ).

tff(c_656,plain,
    ( ( fFalse = bot_bot_bool )
    | ( fTrue = bot_bot_bool ) ),
    inference(cnfTransformation,[status(thm)],[f_655]) ).

tff(c_360,plain,
    ~ hBOOL(fFalse),
    inference(cnfTransformation,[status(thm)],[f_651]) ).

tff(c_294,plain,
    hBOOL(hAPP_f1454306822l_bool(finite68738179iple_a,bot_bo1208640912a_bool)),
    inference(cnfTransformation,[status(thm)],[f_526]) ).

tff(c_362,plain,
    ! [P_366: bool] :
      ( ( fFalse = P_366 )
      | ( fTrue = P_366 ) ),
    inference(cnfTransformation,[status(thm)],[f_655]) ).

tff(c_551,plain,
    ! [P_446: bool] :
      ( ( fFalse = P_446 )
      | ( fTrue = P_446 ) ),
    inference(cnfTransformation,[status(thm)],[f_655]) ).

tff(c_47,plain,
    ! [A_3_65: hoare_1927711152iple_a] : ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,A_3_65),bot_bo1208640912a_bool) = collec829051333iple_a(hAPP_H1027145665a_bool(fequal1440857775iple_a,A_3_65)) ),
    inference(cnfTransformation,[status(thm)],[f_118]) ).

tff(c_472,plain,
    ! [A_3_65: hoare_1927711152iple_a] : ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,A_3_65),bot_bo1208640912a_bool) = hAPP_H1027145665a_bool(fequal1440857775iple_a,A_3_65) ),
    inference(demodulation,[status(thm),theory(equality)],[c_246,c_47]) ).

tff(c_49,plain,
    ! [A_3_66: hoare_1927711152iple_a] : ( collec829051333iple_a(hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,fequal1440857775iple_a),A_3_66)) = hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,A_3_66),bot_bo1208640912a_bool) ),
    inference(cnfTransformation,[status(thm)],[f_120]) ).

tff(c_448,plain,
    ! [A_3_66: hoare_1927711152iple_a] : ( hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,A_3_66),bot_bo1208640912a_bool) = hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,fequal1440857775iple_a),A_3_66) ),
    inference(demodulation,[status(thm),theory(equality)],[c_246,c_49]) ).

tff(c_473,plain,
    ! [A_3_66: hoare_1927711152iple_a] : ( hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,fequal1440857775iple_a),A_3_66) = hAPP_H1027145665a_bool(fequal1440857775iple_a,A_3_66) ),
    inference(demodulation,[status(thm),theory(equality)],[c_472,c_448]) ).

tff(c_422,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(cnfTransformation,[status(thm)],[f_745]) ).

tff(c_465,plain,
    ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(g),hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,fequal1440857775iple_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)))))),
    inference(demodulation,[status(thm),theory(equality)],[c_448,c_422]) ).

tff(c_497,plain,
    ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(g),hAPP_H1027145665a_bool(fequal1440857775iple_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)))))),
    inference(demodulation,[status(thm),theory(equality)],[c_473,c_465]) ).

tff(c_560,plain,
    ( ~ hBOOL(fTrue)
    | ( hAPP_f1454306822l_bool(hoare_1617968510rivs_a(g),hAPP_H1027145665a_bool(fequal1440857775iple_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))))) = fFalse ) ),
    inference(superposition,[status(thm),theory(equality)],[c_551,c_497]) ).

tff(c_636,plain,
    ~ hBOOL(fTrue),
    inference(splitLeft,[status(thm)],[c_560]) ).

tff(c_638,plain,
    ! [P_925: bool] :
      ( ~ hBOOL(P_925)
      | ( fFalse = P_925 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_362,c_636]) ).

tff(c_650,plain,
    hAPP_f1454306822l_bool(finite68738179iple_a,bot_bo1208640912a_bool) = fFalse,
    inference(resolution,[status(thm)],[c_294,c_638]) ).

tff(c_651,plain,
    hBOOL(fFalse),
    inference(demodulation,[status(thm),theory(equality)],[c_650,c_294]) ).

tff(c_653,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_360,c_651]) ).

tff(c_655,plain,
    hBOOL(fTrue),
    inference(splitRight,[status(thm)],[c_560]) ).

tff(c_657,plain,
    ( hBOOL(bot_bot_bool)
    | ( fFalse = bot_bot_bool ) ),
    inference(superposition,[status(thm),theory(equality)],[c_656,c_655]) ).

tff(c_662,plain,
    fFalse = bot_bot_bool,
    inference(negUnitSimplification,[status(thm)],[c_440,c_657]) ).

tff(c_654,plain,
    hAPP_f1454306822l_bool(hoare_1617968510rivs_a(g),hAPP_H1027145665a_bool(fequal1440857775iple_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))))) = fFalse,
    inference(splitRight,[status(thm)],[c_560]) ).

tff(c_800,plain,
    hAPP_f1454306822l_bool(hoare_1617968510rivs_a(g),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(bot_bot_bool)),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_bot_bool,
    inference(demodulation,[status(thm),theory(equality)],[c_662,c_662,c_654]) ).

tff(c_667,plain,
    ! [P_366: bool] :
      ( ( bot_bot_bool = P_366 )
      | ( fTrue = P_366 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_662,c_362]) ).

tff(c_2,plain,
    ! [Ga_1: fun_Ho1877127206a_bool] : hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(Ga_1),bot_bo1208640912a_bool)),
    inference(cnfTransformation,[status(thm)],[f_33]) ).

tff(c_11110,plain,
    ! [Ga_5052: fun_Ho1877127206a_bool,Ts_5053: fun_Ho1877127206a_bool,G_1_5054: fun_Ho1877127206a_bool] :
      ( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(Ga_5052),Ts_5053))
      | ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(Ga_5052),G_1_5054))
      | ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(G_1_5054),Ts_5053)) ),
    inference(cnfTransformation,[status(thm)],[f_47]) ).

tff(c_11132,plain,
    ! [Ga_5067: fun_Ho1877127206a_bool,Ts_5068: fun_Ho1877127206a_bool] :
      ( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(Ga_5067),Ts_5068))
      | ~ hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(bot_bo1208640912a_bool),Ts_5068)) ),
    inference(resolution,[status(thm)],[c_2,c_11110]) ).

tff(c_11144,plain,
    ! [Ga_5067: fun_Ho1877127206a_bool,Ts_5068: fun_Ho1877127206a_bool] :
      ( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(Ga_5067),Ts_5068))
      | ~ hBOOL(fTrue)
      | ( hAPP_f1454306822l_bool(hoare_1617968510rivs_a(bot_bo1208640912a_bool),Ts_5068) = bot_bot_bool ) ),
    inference(superposition,[status(thm),theory(equality)],[c_667,c_11132]) ).

tff(c_11156,plain,
    ! [Ga_5081: fun_Ho1877127206a_bool,Ts_5082: fun_Ho1877127206a_bool] :
      ( hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(Ga_5081),Ts_5082))
      | ( hAPP_f1454306822l_bool(hoare_1617968510rivs_a(bot_bo1208640912a_bool),Ts_5082) = bot_bot_bool ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_655,c_11144]) ).

tff(c_11174,plain,
    ( hBOOL(bot_bot_bool)
    | ( hAPP_f1454306822l_bool(hoare_1617968510rivs_a(bot_bo1208640912a_bool),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(bot_bot_bool)),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_bot_bool ) ),
    inference(superposition,[status(thm),theory(equality)],[c_800,c_11156]) ).

tff(c_11183,plain,
    hAPP_f1454306822l_bool(hoare_1617968510rivs_a(bot_bo1208640912a_bool),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(bot_bot_bool)),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_bot_bool,
    inference(negUnitSimplification,[status(thm)],[c_440,c_11174]) ).

tff(c_376,plain,
    ! [P_379: fun_state_bool,Q_380: x_a] : ( hAPP_a2036067514e_bool(cOMBK_1458035955bool_a(P_379),Q_380) = P_379 ),
    inference(cnfTransformation,[status(thm)],[f_686]) ).

tff(c_202,plain,
    ! [Pa_190: fun_a_fun_state_bool,Q_1_187: fun_a_fun_state_bool,Ga_188: fun_Ho1877127206a_bool,Ca_189: com] :
      ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa_190,'#skF_24'(Q_1_187,Ga_188,Ca_189,Pa_190)),'#skF_25'(Q_1_187,Ga_188,Ca_189,Pa_190)))
      | hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(Ga_188),hAPP_f16502863a_bool(hAPP_H1975128022a_bool(insert1434104874iple_a,hoare_1652181356iple_a(Pa_190,Ca_189,Q_1_187)),bot_bo1208640912a_bool))) ),
    inference(cnfTransformation,[status(thm)],[f_369]) ).

tff(c_462,plain,
    ! [Pa_190: fun_a_fun_state_bool,Q_1_187: fun_a_fun_state_bool,Ga_188: fun_Ho1877127206a_bool,Ca_189: com] :
      ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa_190,'#skF_24'(Q_1_187,Ga_188,Ca_189,Pa_190)),'#skF_25'(Q_1_187,Ga_188,Ca_189,Pa_190)))
      | hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(Ga_188),hAPP_H1027145665a_bool(hAPP_f1216137953a_bool(cOMBC_671859290a_bool,fequal1440857775iple_a),hoare_1652181356iple_a(Pa_190,Ca_189,Q_1_187)))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_448,c_202]) ).

tff(c_22410,plain,
    ! [Pa_7040: fun_a_fun_state_bool,Q_1_7041: fun_a_fun_state_bool,Ga_7042: fun_Ho1877127206a_bool,Ca_7043: com] :
      ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa_7040,'#skF_24'(Q_1_7041,Ga_7042,Ca_7043,Pa_7040)),'#skF_25'(Q_1_7041,Ga_7042,Ca_7043,Pa_7040)))
      | hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(Ga_7042),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(Pa_7040,Ca_7043,Q_1_7041)))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_473,c_462]) ).

tff(c_116547,plain,
    ! [P_71333: fun_state_bool,Q_1_71334: fun_a_fun_state_bool,Ga_71335: fun_Ho1877127206a_bool,Ca_71336: com] :
      ( hBOOL(hAPP_state_bool(P_71333,'#skF_25'(Q_1_71334,Ga_71335,Ca_71336,cOMBK_1458035955bool_a(P_71333))))
      | hBOOL(hAPP_f1454306822l_bool(hoare_1617968510rivs_a(Ga_71335),hAPP_H1027145665a_bool(fequal1440857775iple_a,hoare_1652181356iple_a(cOMBK_1458035955bool_a(P_71333),Ca_71336,Q_1_71334)))) ),
    inference(superposition,[status(thm),theory(equality)],[c_376,c_22410]) ).

tff(c_116589,plain,
    ( hBOOL(hAPP_state_bool(cOMBK_bool_state(bot_bot_bool),'#skF_25'(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,c,cOMBK_1458035955bool_a(cOMBK_bool_state(bot_bot_bool)))))
    | hBOOL(bot_bot_bool) ),
    inference(superposition,[status(thm),theory(equality)],[c_11183,c_116547]) ).

tff(c_116630,plain,
    ( hBOOL(bot_bot_bool)
    | hBOOL(bot_bot_bool) ),
    inference(demodulation,[status(thm),theory(equality)],[c_374,c_116589]) ).

tff(c_116632,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_440,c_440,c_116630]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SWW470_1 : TPTP v8.1.2. Released v5.3.0.
% 0.00/0.14  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.36  % Computer : n017.cluster.edu
% 0.13/0.36  % Model    : x86_64 x86_64
% 0.13/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36  % Memory   : 8042.1875MB
% 0.13/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36  % CPULimit : 300
% 0.13/0.36  % WCLimit  : 300
% 0.13/0.36  % DateTime : Thu Aug  3 19:11:51 EDT 2023
% 0.13/0.36  % CPUTime  : 
% 39.89/23.79  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 39.89/23.80  
% 39.89/23.80  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 39.89/23.84  
% 39.89/23.84  Inference rules
% 39.89/23.84  ----------------------
% 39.89/23.84  #Ref     : 12
% 39.89/23.84  #Sup     : 28571
% 39.89/23.84  #Fact    : 5
% 39.89/23.84  #Define  : 0
% 39.89/23.84  #Split   : 3
% 39.89/23.84  #Chain   : 0
% 39.89/23.84  #Close   : 0
% 39.89/23.84  
% 39.89/23.84  Ordering : KBO
% 39.89/23.84  
% 39.89/23.84  Simplification rules
% 39.89/23.84  ----------------------
% 39.89/23.84  #Subsume      : 10375
% 39.89/23.84  #Demod        : 9592
% 39.89/23.84  #Tautology    : 8517
% 39.89/23.84  #SimpNegUnit  : 4814
% 39.89/23.84  #BackRed      : 43
% 39.89/23.84  
% 39.89/23.84  #Partial instantiations: 27294
% 39.89/23.84  #Strategies tried      : 1
% 39.89/23.84  
% 39.89/23.84  Timing (in seconds)
% 39.89/23.84  ----------------------
% 39.89/23.84  Preprocessing        : 1.12
% 39.89/23.84  Parsing              : 0.64
% 39.89/23.85  CNF conversion       : 0.09
% 39.89/23.85  Main loop            : 21.67
% 39.89/23.85  Inferencing          : 3.62
% 39.89/23.85  Reduction            : 10.85
% 39.89/23.85  Demodulation         : 8.79
% 39.89/23.85  BG Simplification    : 0.32
% 39.89/23.85  Subsumption          : 5.92
% 39.89/23.85  Abstraction          : 0.49
% 39.89/23.85  MUC search           : 0.00
% 39.89/23.85  Cooper               : 0.00
% 39.89/23.85  Total                : 22.85
% 39.89/23.85  Index Insertion      : 0.00
% 39.89/23.85  Index Deletion       : 0.00
% 39.89/23.85  Index Matching       : 0.00
% 39.89/23.85  BG Taut test         : 0.00
%------------------------------------------------------------------------------