%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : ITP214_1 : TPTP v8.2.0. Released v8.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n022.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 : Mon May 20 22:24:12 EDT 2024

% Result   : Theorem 19.38s 5.96s
% Output   : Refutation 20.00s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      : 1179
% Syntax   : Number of formulae    : 1288 (  74 unt;1072 typ;   0 def)
%            Number of atoms       :  596 ( 101 equ;   0 cnn)
%            Maximal formula atoms :   11 (   2 avg)
%            Number of connectives : 2391 (  59   ~;   5   |;  61   &;1952   @)
%                                         (  34 <=>; 280  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   8 avg)
%            Number of types       : 1006 (1005 usr)
%            Number of type conns  :   79 (  79   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   69 (  67 usr;  26 con; 0-4 aty)
%            Number of variables   :  541 (   0   ^ 523   !;  18   ?; 541   :)

% Comments : 
%------------------------------------------------------------------------------
thf(fun_Pr7799047134902603959l_bool_type,type,
    fun_Pr7799047134902603959l_bool: $tType ).

thf(fun_Pr3948480393858449731l_bool_type,type,
    fun_Pr3948480393858449731l_bool: $tType ).

thf(produc2280032003946194889t_bool_type,type,
    produc2280032003946194889t_bool: $tType ).

thf(produc2200565139113230972t_bool_type,type,
    produc2200565139113230972t_bool: $tType ).

thf(set_Pr6041871929502663225et_nat_type,type,
    set_Pr6041871929502663225et_nat: $tType ).

thf(fun_fu5342292996005483693t_bool_type,type,
    fun_fu5342292996005483693t_bool: $tType ).

thf(fun_Pr6803231168968006865t_bool_type,type,
    fun_Pr6803231168968006865t_bool: $tType ).

thf(produc8012095931379219673et_nat_type,type,
    produc8012095931379219673et_nat: $tType ).

thf(fun_fu6557779273964653145et_nat_type,type,
    fun_fu6557779273964653145et_nat: $tType ).

thf(fun_Pr1569400580465080109l_bool_type,type,
    fun_Pr1569400580465080109l_bool: $tType ).

thf(produc4911923886890192003t_bool_type,type,
    produc4911923886890192003t_bool: $tType ).

thf(fun_fu6062884189030247124et_nat_type,type,
    fun_fu6062884189030247124et_nat: $tType ).

thf(fun_Pr8176305432000512344et_nat_type,type,
    fun_Pr8176305432000512344et_nat: $tType ).

thf(fun_Pr80117781411144077b_bool_type,type,
    fun_Pr80117781411144077b_bool: $tType ).

thf(fun_Pr3985517622170449035a_bool_type,type,
    fun_Pr3985517622170449035a_bool: $tType ).

thf(produc2408124797091936310t_bool_type,type,
    produc2408124797091936310t_bool: $tType ).

thf(fun_op3311566623873074537at_nat_type,type,
    fun_op3311566623873074537at_nat: $tType ).

thf(fun_se6682931024248017501at_nat_type,type,
    fun_se6682931024248017501at_nat: $tType ).

thf(fun_op291006984297869545at_nat_type,type,
    fun_op291006984297869545at_nat: $tType ).

thf(set_Pr4255865656320958847et_nat_type,type,
    set_Pr4255865656320958847et_nat: $tType ).

thf(fun_fu5052605875793943143t_bool_type,type,
    fun_fu5052605875793943143t_bool: $tType ).

thf(produc586578377766392095et_nat_type,type,
    produc586578377766392095et_nat: $tType ).

thf(fun_se177437144654672861at_nat_type,type,
    fun_se177437144654672861at_nat: $tType ).

thf(fun_Pr5123258793648662203et_nat_type,type,
    fun_Pr5123258793648662203et_nat: $tType ).

thf(fun_fu8850208375822146947atural_type,type,
    fun_fu8850208375822146947atural: $tType ).

thf(fun_fu9083788306713281567et_nat_type,type,
    fun_fu9083788306713281567et_nat: $tType ).

thf(fun_op4112804339236761266it_nat_type,type,
    fun_op4112804339236761266it_nat: $tType ).

thf(fun_Pr3631287881653221602it_nat_type,type,
    fun_Pr3631287881653221602it_nat: $tType ).

thf(fun_mu1686901903498340291t_bool_type,type,
    fun_mu1686901903498340291t_bool: $tType ).

thf(fun_Pr1003294667014919570it_nat_type,type,
    fun_Pr1003294667014919570it_nat: $tType ).

thf(fun_Pr229822445725053876t_bool_type,type,
    fun_Pr229822445725053876t_bool: $tType ).

thf(fun_fu2492676192234506515it_nat_type,type,
    fun_fu2492676192234506515it_nat: $tType ).

thf(option7217372446798200844et_nat_type,type,
    option7217372446798200844et_nat: $tType ).

thf(fun_Pr2941448120420799789t_bool_type,type,
    fun_Pr2941448120420799789t_bool: $tType ).

thf(list_P2526082664410167756et_nat_type,type,
    list_P2526082664410167756et_nat: $tType ).

thf(fun_op7235540884721919880it_nat_type,type,
    fun_op7235540884721919880it_nat: $tType ).

thf(fun_op5883308099655130629it_nat_type,type,
    fun_op5883308099655130629it_nat: $tType ).

thf(set_Pr9222568342844664434et_nat_type,type,
    set_Pr9222568342844664434et_nat: $tType ).

thf(fun_fu5758690788630904038t_bool_type,type,
    fun_fu5758690788630904038t_bool: $tType ).

thf(fun_fu1965482174671583728et_nat_type,type,
    fun_fu1965482174671583728et_nat: $tType ).

thf(fun_se1253538873784568541t_bool_type,type,
    fun_se1253538873784568541t_bool: $tType ).

thf(produc1542783094787327164et_nat_type,type,
    produc1542783094787327164et_nat: $tType ).

thf(fun_se5611132204644271533t_bool_type,type,
    fun_se5611132204644271533t_bool: $tType ).

thf(fun_Pr6873217934956908984it_nat_type,type,
    fun_Pr6873217934956908984it_nat: $tType ).

thf(fun_Pr7916406164169562037it_nat_type,type,
    fun_Pr7916406164169562037it_nat: $tType ).

thf(fun_se2186744213282142921at_nat_type,type,
    fun_se2186744213282142921at_nat: $tType ).

thf(fun_fu2867219647464843235t_bool_type,type,
    fun_fu2867219647464843235t_bool: $tType ).

thf(fun_Pr1245120565860917421t_bool_type,type,
    fun_Pr1245120565860917421t_bool: $tType ).

thf(fun_fu2568544640974905491it_nat_type,type,
    fun_fu2568544640974905491it_nat: $tType ).

thf(fun_fu9056938625493858259it_nat_type,type,
    fun_fu9056938625493858259it_nat: $tType ).

thf(fun_se2714673039056557965t_bool_type,type,
    fun_se2714673039056557965t_bool: $tType ).

thf(fun_Pr4930789208686447789t_bool_type,type,
    fun_Pr4930789208686447789t_bool: $tType ).

thf(fun_Pr7633721533235036525t_bool_type,type,
    fun_Pr7633721533235036525t_bool: $tType ).

thf(fun_fu5777305227152776218et_nat_type,type,
    fun_fu5777305227152776218et_nat: $tType ).

thf(fun_Pr774283325640823912it_nat_type,type,
    fun_Pr774283325640823912it_nat: $tType ).

thf(fun_Pr7750636411365408485it_nat_type,type,
    fun_Pr7750636411365408485it_nat: $tType ).

thf(fun_se4699893527908719235at_nat_type,type,
    fun_se4699893527908719235at_nat: $tType ).

thf(fun_se4853100533979065065t_bool_type,type,
    fun_se4853100533979065065t_bool: $tType ).

thf(fun_Pr2210758139564844958et_nat_type,type,
    fun_Pr2210758139564844958et_nat: $tType ).

thf(fun_Pr761831339830696478et_nat_type,type,
    fun_Pr761831339830696478et_nat: $tType ).

thf(fun_se5010674451832123565t_bool_type,type,
    fun_se5010674451832123565t_bool: $tType ).

thf(fun_Pr4617804334418790189t_bool_type,type,
    fun_Pr4617804334418790189t_bool: $tType ).

thf(fun_se7901873761543946185at_nat_type,type,
    fun_se7901873761543946185at_nat: $tType ).

thf(produc1319942482725812455at_nat_type,type,
    produc1319942482725812455at_nat: $tType ).

thf(fun_fu224428745893945571t_bool_type,type,
    fun_fu224428745893945571t_bool: $tType ).

thf(produc833397650935741523atural_type,type,
    produc833397650935741523atural: $tType ).

thf(fun_se6392513987399461773t_bool_type,type,
    fun_se6392513987399461773t_bool: $tType ).

thf(fun_se6846035212209387651at_nat_type,type,
    fun_se6846035212209387651at_nat: $tType ).

thf(fun_Pr124437560471516333t_bool_type,type,
    fun_Pr124437560471516333t_bool: $tType ).

thf(fun_se5420953908473809257t_bool_type,type,
    fun_se5420953908473809257t_bool: $tType ).

thf(fun_op7406603375158807591t_bool_type,type,
    fun_op7406603375158807591t_bool: $tType ).

thf(fun_fu2716251949043459987at_nat_type,type,
    fun_fu2716251949043459987at_nat: $tType ).

thf(produc7243647663225551966_nat_b_type,type,
    produc7243647663225551966_nat_b: $tType ).

thf(produc8033090066717023711_nat_a_type,type,
    produc8033090066717023711_nat_a: $tType ).

thf(fun_Pr509543455618818233t_bool_type,type,
    fun_Pr509543455618818233t_bool: $tType ).

thf(fun_op5969927639907011765t_bool_type,type,
    fun_op5969927639907011765t_bool: $tType ).

thf(fun_op5504856373969603958t_bool_type,type,
    fun_op5504856373969603958t_bool: $tType ).

thf(fun_Pr7644814098969791837it_nat_type,type,
    fun_Pr7644814098969791837it_nat: $tType ).

thf(produc6963950461309505482atural_type,type,
    produc6963950461309505482atural: $tType ).

thf(fun_fu695563712076452518at_nat_type,type,
    fun_fu695563712076452518at_nat: $tType ).

thf(fun_fu8161990777412754it_nat_type,type,
    fun_fu8161990777412754it_nat: $tType ).

thf(fun_fu6488529940522614227it_nat_type,type,
    fun_fu6488529940522614227it_nat: $tType ).

thf(set_Pr2055239900342597383t_bool_type,type,
    set_Pr2055239900342597383t_bool: $tType ).

thf(fun_Pr2992940411974564687it_nat_type,type,
    fun_Pr2992940411974564687it_nat: $tType ).

thf(fun_Pr8191437870481986254it_nat_type,type,
    fun_Pr8191437870481986254it_nat: $tType ).

thf(fun_Co9168753396221475450atural_type,type,
    fun_Co9168753396221475450atural: $tType ).

thf(fun_Pr1033138224055104269it_nat_type,type,
    fun_Pr1033138224055104269it_nat: $tType ).

thf(set_Pr5508209795250834101it_nat_type,type,
    set_Pr5508209795250834101it_nat: $tType ).

thf(set_Pr2819221443900773171it_nat_type,type,
    set_Pr2819221443900773171it_nat: $tType ).

thf(fun_fu2189280214036673585t_bool_type,type,
    fun_fu2189280214036673585t_bool: $tType ).

thf(fun_fu7117831083681099955t_bool_type,type,
    fun_fu7117831083681099955t_bool: $tType ).

thf(fun_Pr3073222722562426257t_bool_type,type,
    fun_Pr3073222722562426257t_bool: $tType ).

thf(produc1469476007717053223t_bool_type,type,
    produc1469476007717053223t_bool: $tType ).

thf(fun_op7507520395135695063nteger_type,type,
    fun_op7507520395135695063nteger: $tType ).

thf(option6601582610923217263et_nat_type,type,
    option6601582610923217263et_nat: $tType ).

thf(fun_b_3682875105831643059it_nat_type,type,
    fun_b_3682875105831643059it_nat: $tType ).

thf(fun_a_4942204877778174258it_nat_type,type,
    fun_a_4942204877778174258it_nat: $tType ).

thf(fun_Pr4959652356039452225it_nat_type,type,
    fun_Pr4959652356039452225it_nat: $tType ).

thf(fun_Pr7206221373966655808it_nat_type,type,
    fun_Pr7206221373966655808it_nat: $tType ).

thf(fun_Pr157300717155555520it_nat_type,type,
    fun_Pr157300717155555520it_nat: $tType ).

thf(fun_Pr2403869735082759103it_nat_type,type,
    fun_Pr2403869735082759103it_nat: $tType ).

thf(list_P5162959638400604975et_nat_type,type,
    list_P5162959638400604975et_nat: $tType ).

thf(fun_Pr7387299081059808255it_nat_type,type,
    fun_Pr7387299081059808255it_nat: $tType ).

thf(fun_Pr7227498785783423999it_nat_type,type,
    fun_Pr7227498785783423999it_nat: $tType ).

thf(set_Pr1106803562331729365et_nat_type,type,
    set_Pr1106803562331729365et_nat: $tType ).

thf(produc1273031398460193109it_nat_type,type,
    produc1273031398460193109it_nat: $tType ).

thf(produc9011797661310329043it_nat_type,type,
    produc9011797661310329043it_nat: $tType ).

thf(produc5048788716800215441_nat_b_type,type,
    produc5048788716800215441_nat_b: $tType ).

thf(produc778646029802724242_nat_a_type,type,
    produc778646029802724242_nat_a: $tType ).

thf(fun_fu400886066185544210it_nat_type,type,
    fun_fu400886066185544210it_nat: $tType ).

thf(fun_fu2643727258468172498it_nat_type,type,
    fun_fu2643727258468172498it_nat: $tType ).

thf(fun_fu2612457627315080531it_nat_type,type,
    fun_fu2612457627315080531it_nat: $tType ).

thf(fun_fu4855298819597708819it_nat_type,type,
    fun_fu4855298819597708819it_nat: $tType ).

thf(fun_fu7398481913972163267t_bool_type,type,
    fun_fu7398481913972163267t_bool: $tType ).

thf(fun_fu6675107418524772179et_nat_type,type,
    fun_fu6675107418524772179et_nat: $tType ).

thf(fun_Pr5651933991979716257it_nat_type,type,
    fun_Pr5651933991979716257it_nat: $tType ).

thf(fun_b_4161654760626720265it_nat_type,type,
    fun_b_4161654760626720265it_nat: $tType ).

thf(fun_a_6373226321756256586it_nat_type,type,
    fun_a_6373226321756256586it_nat: $tType ).

thf(produc6108883039684432031et_nat_type,type,
    produc6108883039684432031et_nat: $tType ).

thf(fun_b_7697183073795684005it_nat_type,type,
    fun_b_7697183073795684005it_nat: $tType ).

thf(fun_b_4099525269183078948it_nat_type,type,
    fun_b_4099525269183078948it_nat: $tType ).

thf(fun_a_7024012846491921188it_nat_type,type,
    fun_a_7024012846491921188it_nat: $tType ).

thf(fun_a_3426355041879316131it_nat_type,type,
    fun_a_3426355041879316131it_nat: $tType ).

thf(fun_fu3348679225844166803t_bool_type,type,
    fun_fu3348679225844166803t_bool: $tType ).

thf(fun_Co1105491363547889651atural_type,type,
    fun_Co1105491363547889651atural: $tType ).

thf(fun_Co1890133979025130057atural_type,type,
    fun_Co1890133979025130057atural: $tType ).

thf(fun_Pr2137375630576721649it_nat_type,type,
    fun_Pr2137375630576721649it_nat: $tType ).

thf(fun_Pr1634687943937911152it_nat_type,type,
    fun_Pr1634687943937911152it_nat: $tType ).

thf(fun_Pr1155457543210892272it_nat_type,type,
    fun_Pr1155457543210892272it_nat: $tType ).

thf(fun_Pr652769856572081775it_nat_type,type,
    fun_Pr652769856572081775it_nat: $tType ).

thf(fun_fu4272674133525273539t_bool_type,type,
    fun_fu4272674133525273539t_bool: $tType ).

thf(fun_fu2754956555950464963t_bool_type,type,
    fun_fu2754956555950464963t_bool: $tType ).

thf(set_Pr719794911490849221et_nat_type,type,
    set_Pr719794911490849221et_nat: $tType ).

thf(fun_ar8804793355411515200it_nat_type,type,
    fun_ar8804793355411515200it_nat: $tType ).

thf(fun_ar6592047341168336478it_nat_type,type,
    fun_ar6592047341168336478it_nat: $tType ).

thf(fun_ar554763049074313054it_nat_type,type,
    fun_ar554763049074313054it_nat: $tType ).

thf(fun_he8369595706569872389it_nat_type,type,
    fun_he8369595706569872389it_nat: $tType ).

thf(fun_Pr5026674165934347155it_nat_type,type,
    fun_Pr5026674165934347155it_nat: $tType ).

thf(fun_Pr7273243183861550738it_nat_type,type,
    fun_Pr7273243183861550738it_nat: $tType ).

thf(fun_op3037383146056310525nteger_type,type,
    fun_op3037383146056310525nteger: $tType ).

thf(fun_Pr8933696392609397829t_bool_type,type,
    fun_Pr8933696392609397829t_bool: $tType ).

thf(fun_b_7001994053037931259it_nat_type,type,
    fun_b_7001994053037931259it_nat: $tType ).

thf(fun_b_989364880692008698it_nat_type,type,
    fun_b_989364880692008698it_nat: $tType ).

thf(fun_a_9184149311047732028it_nat_type,type,
    fun_a_9184149311047732028it_nat: $tType ).

thf(fun_a_3171520138701809467it_nat_type,type,
    fun_a_3171520138701809467it_nat: $tType ).

thf(fun_fu365010997111080675t_bool_type,type,
    fun_fu365010997111080675t_bool: $tType ).

thf(fun_fu4800041728187187127nteger_type,type,
    fun_fu4800041728187187127nteger: $tType ).

thf(fun_b_6809638951405183189it_nat_type,type,
    fun_b_6809638951405183189it_nat: $tType ).

thf(fun_a_576316402698418899it_nat_type,type,
    fun_a_576316402698418899it_nat: $tType ).

thf(fun_b_4666577566277263197it_nat_type,type,
    fun_b_4666577566277263197it_nat: $tType ).

thf(fun_a_728177123528609950it_nat_type,type,
    fun_a_728177123528609950it_nat: $tType ).

thf(fun_fu7950578231418614685t_bool_type,type,
    fun_fu7950578231418614685t_bool: $tType ).

thf(produc8111630337999740517et_nat_type,type,
    produc8111630337999740517et_nat: $tType ).

thf(fun_he3223939975889911031it_nat_type,type,
    fun_he3223939975889911031it_nat: $tType ).

thf(fun_he8849654208132081782it_nat_type,type,
    fun_he8849654208132081782it_nat: $tType ).

thf(fun_op4621176226433041415m_bool_type,type,
    fun_op4621176226433041415m_bool: $tType ).

thf(fun_op2573228148205091335t_bool_type,type,
    fun_op2573228148205091335t_bool: $tType ).

thf(fun_Pr3216343399241953091it_nat_type,type,
    fun_Pr3216343399241953091it_nat: $tType ).

thf(fun_Pr2713655712603142594it_nat_type,type,
    fun_Pr2713655712603142594it_nat: $tType ).

thf(fun_he5234484606919320760it_nat_type,type,
    fun_he5234484606919320760it_nat: $tType ).

thf(set_Pr4389693562480114009it_nat_type,type,
    set_Pr4389693562480114009it_nat: $tType ).

thf(fun_Pr7769407664385210434atural_type,type,
    fun_Pr7769407664385210434atural: $tType ).

thf(fun_Co5709460363461100952atural_type,type,
    fun_Co5709460363461100952atural: $tType ).

thf(produc8903623710181579841nteger_type,type,
    produc8903623710181579841nteger: $tType ).

thf(fun_Pr7091840695141096449et_nat_type,type,
    fun_Pr7091840695141096449et_nat: $tType ).

thf(fun_fu6741006549690681129nt_int_type,type,
    fun_fu6741006549690681129nt_int: $tType ).

thf(fun_se3560235952666129655at_nat_type,type,
    fun_se3560235952666129655at_nat: $tType ).

thf(fun_fu227840033125495216t_bool_type,type,
    fun_fu227840033125495216t_bool: $tType ).

thf(fun_fu3121479769846741260t_bool_type,type,
    fun_fu3121479769846741260t_bool: $tType ).

thf(fun_se8145576094667462355t_bool_type,type,
    fun_se8145576094667462355t_bool: $tType ).

thf(fun_he219029067917810067it_nat_type,type,
    fun_he219029067917810067it_nat: $tType ).

thf(fun_he986703168080474088it_nat_type,type,
    fun_he986703168080474088it_nat: $tType ).

thf(fun_he8488442066948866628it_nat_type,type,
    fun_he8488442066948866628it_nat: $tType ).

thf(produc8961450480463052793it_nat_type,type,
    produc8961450480463052793it_nat: $tType ).

thf(option2498585697089621389at_nat_type,type,
    option2498585697089621389at_nat: $tType ).

thf(fun_fu3488334964911580731er_nat_type,type,
    fun_fu3488334964911580731er_nat: $tType ).

thf(fun_fu1709340832601392443er_nat_type,type,
    fun_fu1709340832601392443er_nat: $tType ).

thf(fun_fu6449200239809977915er_int_type,type,
    fun_fu6449200239809977915er_int: $tType ).

thf(fun_fu3687342418701361539er_int_type,type,
    fun_fu3687342418701361539er_int: $tType ).

thf(fun_op2079205433508820629m_bool_type,type,
    fun_op2079205433508820629m_bool: $tType ).

thf(fun_op2372187285662272598m_bool_type,type,
    fun_op2372187285662272598m_bool: $tType ).

thf(fun_op6462303021193960085t_bool_type,type,
    fun_op6462303021193960085t_bool: $tType ).

thf(fun_op5997231755256552278t_bool_type,type,
    fun_op5997231755256552278t_bool: $tType ).

thf(fun_he8897818899970768042it_nat_type,type,
    fun_he8897818899970768042it_nat: $tType ).

thf(fun_he1921015881043195817it_nat_type,type,
    fun_he1921015881043195817it_nat: $tType ).

thf(fun_Co1561183069634336733nteger_type,type,
    fun_Co1561183069634336733nteger: $tType ).

thf(fun_he4944555133437423336it_nat_type,type,
    fun_he4944555133437423336it_nat: $tType ).

thf(fun_fu7433494735876822851at_nat_type,type,
    fun_fu7433494735876822851at_nat: $tType ).

thf(produc3911288613690379145it_nat_type,type,
    produc3911288613690379145it_nat: $tType ).

thf(fun_fu3898734532474705027nt_int_type,type,
    fun_fu3898734532474705027nt_int: $tType ).

thf(fun_Pr3976602594631769267t_bool_type,type,
    fun_Pr3976602594631769267t_bool: $tType ).

thf(fun_Pr4065951289917319378at_rat_type,type,
    fun_Pr4065951289917319378at_rat: $tType ).

thf(fun_Pr7574179848310716106at_nat_type,type,
    fun_Pr7574179848310716106at_nat: $tType ).

thf(fun_fu7832787587439741972t_bool_type,type,
    fun_fu7832787587439741972t_bool: $tType ).

thf(fun_fu5993855001459328072t_bool_type,type,
    fun_fu5993855001459328072t_bool: $tType ).

thf(fun_se8353504738346895699t_bool_type,type,
    fun_se8353504738346895699t_bool: $tType ).

thf(fun_fu1794103223568558766at_nat_type,type,
    fun_fu1794103223568558766at_nat: $tType ).

thf(fun_fu5158082794216327598at_nat_type,type,
    fun_fu5158082794216327598at_nat: $tType ).

thf(fun_fu2187553307443868334at_int_type,type,
    fun_fu2187553307443868334at_int: $tType ).

thf(fun_fu6891359585798312018nt_int_type,type,
    fun_fu6891359585798312018nt_int: $tType ).

thf(fun_fu5036059946722339607r_bool_type,type,
    fun_fu5036059946722339607r_bool: $tType ).

thf(fun_Pr6333000437718031765it_nat_type,type,
    fun_Pr6333000437718031765it_nat: $tType ).

thf(fun_se5485459612626037543t_bool_type,type,
    fun_se5485459612626037543t_bool: $tType ).

thf(fun_se2866242152837528543t_bool_type,type,
    fun_se2866242152837528543t_bool: $tType ).

thf(fun_Pr4637083014979798189l_bool_type,type,
    fun_Pr4637083014979798189l_bool: $tType ).

thf(option1583680563626158861at_nat_type,type,
    option1583680563626158861at_nat: $tType ).

thf(set_Pr8551490117392284871at_nat_type,type,
    set_Pr8551490117392284871at_nat: $tType ).

thf(option5210736251575913683nteger_type,type,
    option5210736251575913683nteger: $tType ).

thf(fun_he168995381318928090it_nat_type,type,
    fun_he168995381318928090it_nat: $tType ).

thf(fun_he8889679731534893401it_nat_type,type,
    fun_he8889679731534893401it_nat: $tType ).

thf(produc6756470014200349799atural_type,type,
    produc6756470014200349799atural: $tType ).

thf(produc7738239854019400055nt_int_type,type,
    produc7738239854019400055nt_int: $tType ).

thf(fun_fu6908345394967445887t_bool_type,type,
    fun_fu6908345394967445887t_bool: $tType ).

thf(fun_fu4755565544374692864r_assn_type,type,
    fun_fu4755565544374692864r_assn: $tType ).

thf(fun_fu9044484386125557008t_bool_type,type,
    fun_fu9044484386125557008t_bool: $tType ).

thf(fun_op5902475268499868568t_bool_type,type,
    fun_op5902475268499868568t_bool: $tType ).

thf(fun_fu8621421401018972867nt_nat_type,type,
    fun_fu8621421401018972867nt_nat: $tType ).

thf(fun_na5667031169817407269it_nat_type,type,
    fun_na5667031169817407269it_nat: $tType ).

thf(produc2207270350733924475it_nat_type,type,
    produc2207270350733924475it_nat: $tType ).

thf(produc4453839368661128058it_nat_type,type,
    produc4453839368661128058it_nat: $tType ).

thf(fun_mu3699985005841253805t_bool_type,type,
    fun_mu3699985005841253805t_bool: $tType ).

thf(fun_fu8798293629092361859r_bool_type,type,
    fun_fu8798293629092361859r_bool: $tType ).

thf(fun_Pr1607443439640623155t_bool_type,type,
    fun_Pr1607443439640623155t_bool: $tType ).

thf(fun_na1945018436707187408at_nat_type,type,
    fun_na1945018436707187408at_nat: $tType ).

thf(fun_fu8778301040783821591l_bool_type,type,
    fun_fu8778301040783821591l_bool: $tType ).

thf(fun_fu3970489814086470791l_bool_type,type,
    fun_fu3970489814086470791l_bool: $tType ).

thf(fun_fu4086510383517613953r_bool_type,type,
    fun_fu4086510383517613953r_bool: $tType ).

thf(fun_Pr6968369006614801746at_rat_type,type,
    fun_Pr6968369006614801746at_rat: $tType ).

thf(fun_Pr1253225528153422666at_nat_type,type,
    fun_Pr1253225528153422666at_nat: $tType ).

thf(fun_fu4671764723984660721t_bool_type,type,
    fun_fu4671764723984660721t_bool: $tType ).

thf(fun_fu2749353902725170073t_bool_type,type,
    fun_fu2749353902725170073t_bool: $tType ).

thf(fun_fu2194082084716825453t_bool_type,type,
    fun_fu2194082084716825453t_bool: $tType ).

thf(fun_se6964483239604720653t_bool_type,type,
    fun_se6964483239604720653t_bool: $tType ).

thf(fun_fu324568207353485199t_bool_type,type,
    fun_fu324568207353485199t_bool: $tType ).

thf(produc4166570645942440679at_nat_type,type,
    produc4166570645942440679at_nat: $tType ).

thf(fun_se2235623607936449885t_bool_type,type,
    fun_se2235623607936449885t_bool: $tType ).

thf(fun_se7324996035117135669t_bool_type,type,
    fun_se7324996035117135669t_bool: $tType ).

thf(fun_Pr2477239776880934807at_nat_type,type,
    fun_Pr2477239776880934807at_nat: $tType ).

thf(fun_Pr1308109350235310159nt_int_type,type,
    fun_Pr1308109350235310159nt_int: $tType ).

thf(set_Pr4329608150637261639at_nat_type,type,
    set_Pr4329608150637261639at_nat: $tType ).

thf(produc9217583074051984497at_nat_type,type,
    produc9217583074051984497at_nat: $tType ).

thf(fun_fu1597678101255499801at_rat_type,type,
    fun_fu1597678101255499801at_rat: $tType ).

thf(fun_Pr5876161306168176259nteger_type,type,
    fun_Pr5876161306168176259nteger: $tType ).

thf(option5602014572997026083it_nat_type,type,
    option5602014572997026083it_nat: $tType ).

thf(fun_fu577696735405313155ol_nat_type,type,
    fun_fu577696735405313155ol_nat: $tType ).

thf(fun_fu8646012520862679939ol_nat_type,type,
    fun_fu8646012520862679939ol_nat: $tType ).

thf(fun_fu6440258525219039875ol_int_type,type,
    fun_fu6440258525219039875ol_int: $tType ).

thf(fun_fu1485461732534078339ol_int_type,type,
    fun_fu1485461732534078339ol_int: $tType ).

thf(option4277301481530639448it_nat_type,type,
    option4277301481530639448it_nat: $tType ).

thf(option2555668343544256180it_nat_type,type,
    option2555668343544256180it_nat: $tType ).

thf(fun_fu1166741194689021184at_nat_type,type,
    fun_fu1166741194689021184at_nat: $tType ).

thf(fun_fu1759362394388581888at_nat_type,type,
    fun_fu1759362394388581888at_nat: $tType ).

thf(fun_fu4572545742693709496at_int_type,type,
    fun_fu4572545742693709496at_int: $tType ).

thf(fun_fu1233762487186198548nt_int_type,type,
    fun_fu1233762487186198548nt_int: $tType ).

thf(fun_op8365621174827171622t_bool_type,type,
    fun_op8365621174827171622t_bool: $tType ).

thf(fun_op2491542651970850919t_bool_type,type,
    fun_op2491542651970850919t_bool: $tType ).

thf(fun_na3679441993588394007it_nat_type,type,
    fun_na3679441993588394007it_nat: $tType ).

thf(fun_na5926011011515597590it_nat_type,type,
    fun_na5926011011515597590it_nat: $tType ).

thf(fun_fu4246887593415901128at_nat_type,type,
    fun_fu4246887593415901128at_nat: $tType ).

thf(fun_fu2448115762823361296at_nat_type,type,
    fun_fu2448115762823361296at_nat: $tType ).

thf(fun_fu5666819356987731308nt_nat_type,type,
    fun_fu5666819356987731308nt_nat: $tType ).

thf(fun_fu2946920718754786320at_int_type,type,
    fun_fu2946920718754786320at_int: $tType ).

thf(fun_fu6165624312919156332nt_int_type,type,
    fun_fu6165624312919156332nt_int: $tType ).

thf(fun_fu5002972218919249680at_nat_type,type,
    fun_fu5002972218919249680at_nat: $tType ).

thf(fun_fu8221675813083619692nt_nat_type,type,
    fun_fu8221675813083619692nt_nat: $tType ).

thf(fun_fu1204527555220168225r_bool_type,type,
    fun_fu1204527555220168225r_bool: $tType ).

thf(fun_Pr7669129556548838760t_bool_type,type,
    fun_Pr7669129556548838760t_bool: $tType ).

thf(fun_fu6327154928193479288nteger_type,type,
    fun_fu6327154928193479288nteger: $tType ).

thf(fun_fu8767785434844327952er_rat_type,type,
    fun_fu8767785434844327952er_rat: $tType ).

thf(fun_fu2498091903632033272er_nat_type,type,
    fun_fu2498091903632033272er_nat: $tType ).

thf(fun_fu1007793439646807308er_int_type,type,
    fun_fu1007793439646807308er_int: $tType ).

thf(fun_Pr1075626608990047775at_num_type,type,
    fun_Pr1075626608990047775at_num: $tType ).

thf(fun_Pr367382672041210069at_nat_type,type,
    fun_Pr367382672041210069at_nat: $tType ).

thf(fun_nu5234077238548837151it_nat_type,type,
    fun_nu5234077238548837151it_nat: $tType ).

thf(fun_se1534075524646452397t_bool_type,type,
    fun_se1534075524646452397t_bool: $tType ).

thf(fun_se6520218648942456493t_bool_type,type,
    fun_se6520218648942456493t_bool: $tType ).

thf(option8956607266484857688it_nat_type,type,
    option8956607266484857688it_nat: $tType ).

thf(fun_fu5241435528817219169t_bool_type,type,
    fun_fu5241435528817219169t_bool: $tType ).

thf(fun_fu2983679652716955429nt_int_type,type,
    fun_fu2983679652716955429nt_int: $tType ).

thf(fun_se5244420045238757833at_nat_type,type,
    fun_se5244420045238757833at_nat: $tType ).

thf(fun_fu717549361983437348nt_int_type,type,
    fun_fu717549361983437348nt_int: $tType ).

thf(fun_fu918106826131887214nt_int_type,type,
    fun_fu918106826131887214nt_int: $tType ).

thf(fun_mu2328110650637990531at_nat_type,type,
    fun_mu2328110650637990531at_nat: $tType ).

thf(list_P626663023886443800it_nat_type,type,
    list_P626663023886443800it_nat: $tType ).

thf(fun_as4100195077546555551t_bool_type,type,
    fun_as4100195077546555551t_bool: $tType ).

thf(produc3843707927480180839at_nat_type,type,
    produc3843707927480180839at_nat: $tType ).

thf(fun_fu6897202038601531823t_bool_type,type,
    fun_fu6897202038601531823t_bool: $tType ).

thf(fun_fu7672510408924296255t_bool_type,type,
    fun_fu7672510408924296255t_bool: $tType ).

thf(fun_fu5703663724705206032t_bool_type,type,
    fun_fu5703663724705206032t_bool: $tType ).

thf(fun_fu3997796857297124035at_rat_type,type,
    fun_fu3997796857297124035at_rat: $tType ).

thf(fun_fu3064074204415222357nt_int_type,type,
    fun_fu3064074204415222357nt_int: $tType ).

thf(fun_fu1098312133097393581at_rat_type,type,
    fun_fu1098312133097393581at_rat: $tType ).

thf(fun_Pr557098546508347797at_nat_type,type,
    fun_Pr557098546508347797at_nat: $tType ).

thf(fun_na1668100129766719005at_nat_type,type,
    fun_na1668100129766719005at_nat: $tType ).

thf(fun_fu8051085961303112187r_bool_type,type,
    fun_fu8051085961303112187r_bool: $tType ).

thf(fun_fu1696078252837777177l_bool_type,type,
    fun_fu1696078252837777177l_bool: $tType ).

thf(fun_fu4087525139388848025l_bool_type,type,
    fun_fu4087525139388848025l_bool: $tType ).

thf(fun_fu8571960779141011225r_bool_type,type,
    fun_fu8571960779141011225r_bool: $tType ).

thf(fun_fu2216953070675676215l_bool_type,type,
    fun_fu2216953070675676215l_bool: $tType ).

thf(fun_na2419096353205528t_bool_type,type,
    fun_na2419096353205528t_bool: $tType ).

thf(fun_li124330075790197867t_assn_type,type,
    fun_li124330075790197867t_assn: $tType ).

thf(fun_in8031269491544239620t_bool_type,type,
    fun_in8031269491544239620t_bool: $tType ).

thf(fun_Co2470855966376689427nteger_type,type,
    fun_Co2470855966376689427nteger: $tType ).

thf(fun_fu9160419385450930796l_bool_type,type,
    fun_fu9160419385450930796l_bool: $tType ).

thf(fun_fu1788334712973291331r_bool_type,type,
    fun_fu1788334712973291331r_bool: $tType ).

thf(fun_fu7410765799605690051t_bool_type,type,
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thf(fun_fu939660078065702467r_bool_type,type,
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thf(fun_fu5828654989214587843t_bool_type,type,
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thf(fun_fu4694495798485950403r_bool_type,type,
    fun_fu4694495798485950403r_bool: $tType ).

thf(fun_fu1093554848263573315t_bool_type,type,
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thf(fun_fu5417119095707709635r_bool_type,type,
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thf(fun_fu1082741970001819203t_bool_type,type,
    fun_fu1082741970001819203t_bool: $tType ).

thf(fun_Pr446604468264085555t_bool_type,type,
    fun_Pr446604468264085555t_bool: $tType ).

thf(fun_Pr6553600481296542259t_bool_type,type,
    fun_Pr6553600481296542259t_bool: $tType ).

thf(fun_fu8715438531829836670t_bool_type,type,
    fun_fu8715438531829836670t_bool: $tType ).

thf(fun_fu5963139849246984042t_bool_type,type,
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thf(fun_se3305628495172992525t_bool_type,type,
    fun_se3305628495172992525t_bool: $tType ).

thf(produc5008756268773954781it_nat_type,type,
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thf(produc6751673265320737416it_nat_type,type,
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thf(produc7196121022310644452it_nat_type,type,
    produc7196121022310644452it_nat: $tType ).

thf(fun_Pr4515439997229668598t_bool_type,type,
    fun_Pr4515439997229668598t_bool: $tType ).

thf(fun_Pr2906233850362575543t_bool_type,type,
    fun_Pr2906233850362575543t_bool: $tType ).

thf(fun_Pr6180708418112149265at_num_type,type,
    fun_Pr6180708418112149265at_num: $tType ).

thf(fun_Pr5472464481163311559at_nat_type,type,
    fun_Pr5472464481163311559at_nat: $tType ).

thf(fun_Pr5112106203349071120at_num_type,type,
    fun_Pr5112106203349071120at_num: $tType ).

thf(fun_Pr4403862266400233414at_nat_type,type,
    fun_Pr4403862266400233414at_nat: $tType ).

thf(fun_nu147038076112158225it_nat_type,type,
    fun_nu147038076112158225it_nat: $tType ).

thf(fun_nu8867722426328123536it_nat_type,type,
    fun_nu8867722426328123536it_nat: $tType ).

thf(produc4428605777065428680et_nat_type,type,
    produc4428605777065428680et_nat: $tType ).

thf(fun_fu6605489587527791784l_assn_type,type,
    fun_fu6605489587527791784l_assn: $tType ).

thf(list_f5857023252961307252t_bool_type,type,
    list_f5857023252961307252t_bool: $tType ).

thf(fun_b_4190609728018899208t_bool_type,type,
    fun_b_4190609728018899208t_bool: $tType ).

thf(fun_a_3884643061924904137t_bool_type,type,
    fun_a_3884643061924904137t_bool: $tType ).

thf(option4065278094766928714it_nat_type,type,
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thf(option3562590408128118217it_nat_type,type,
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thf(fun_b_7146180689985673569et_nat_type,type,
    fun_b_7146180689985673569et_nat: $tType ).

thf(fun_b_2332632271197754813et_int_type,type,
    fun_b_2332632271197754813et_int: $tType ).

thf(fun_a_8173838432492502368et_nat_type,type,
    fun_a_8173838432492502368et_nat: $tType ).

thf(fun_fu1851216944655731660er_nat_type,type,
    fun_fu1851216944655731660er_nat: $tType ).

thf(set_Pr8693737435421807431at_nat_type,type,
    set_Pr8693737435421807431at_nat: $tType ).

thf(set_Pr2560585780119916871nt_int_type,type,
    set_Pr2560585780119916871nt_int: $tType ).

thf(fun_fu3959123160307459545t_assn_type,type,
    fun_fu3959123160307459545t_assn: $tType ).

thf(fun_fu5832215286117076717t_assn_type,type,
    fun_fu5832215286117076717t_assn: $tType ).

thf(produc8664842809031399944it_nat_type,type,
    produc8664842809031399944it_nat: $tType ).

thf(fun_fu813382667476268716l_bool_type,type,
    fun_fu813382667476268716l_bool: $tType ).

thf(fun_se320340636488258563at_nat_type,type,
    fun_se320340636488258563at_nat: $tType ).

thf(list_P7438302566501821706it_nat_type,type,
    list_P7438302566501821706it_nat: $tType ).

thf(list_P6935614879863011209it_nat_type,type,
    list_P6935614879863011209it_nat: $tType ).

thf(fun_fu5933960805034414761t_bool_type,type,
    fun_fu5933960805034414761t_bool: $tType ).

thf(fun_fu5372840394358096997t_bool_type,type,
    fun_fu5372840394358096997t_bool: $tType ).

thf(fun_fu8159772421396582028t_bool_type,type,
    fun_fu8159772421396582028t_bool: $tType ).

thf(fun_fu7888190625410830553l_bool_type,type,
    fun_fu7888190625410830553l_bool: $tType ).

thf(fun_op386870758422531628et_nat_type,type,
    fun_op386870758422531628et_nat: $tType ).

thf(fun_op8756596739451609009nteger_type,type,
    fun_op8756596739451609009nteger: $tType ).

thf(fun_Co3025358997185726883r_bool_type,type,
    fun_Co3025358997185726883r_bool: $tType ).

thf(set_Pr7600907837789447088it_nat_type,type,
    set_Pr7600907837789447088it_nat: $tType ).

thf(set_Pr7098220151150636591it_nat_type,type,
    set_Pr7098220151150636591it_nat: $tType ).

thf(fun_fu5207212825597307859nt_int_type,type,
    fun_fu5207212825597307859nt_int: $tType ).

thf(fun_fu3910677444521609704t_bool_type,type,
    fun_fu3910677444521609704t_bool: $tType ).

thf(fun_fu656925638523502036t_bool_type,type,
    fun_fu656925638523502036t_bool: $tType ).

thf(fun_fu5510336631606277565nteger_type,type,
    fun_fu5510336631606277565nteger: $tType ).

thf(fun_fu1763652423599918571nteger_type,type,
    fun_fu1763652423599918571nteger: $tType ).

thf(fun_Pr1029825253981700553at_nat_type,type,
    fun_Pr1029825253981700553at_nat: $tType ).

thf(fun_fu7919257609373989805t_bool_type,type,
    fun_fu7919257609373989805t_bool: $tType ).

thf(fun_fu4802881585551670701t_bool_type,type,
    fun_fu4802881585551670701t_bool: $tType ).

thf(fun_Pr5837708615769641901m_bool_type,type,
    fun_Pr5837708615769641901m_bool: $tType ).

thf(fun_Pr248683899324676269t_bool_type,type,
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thf(fun_Pr3099820731930151597t_bool_type,type,
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thf(fun_na8713714802964096592at_nat_type,type,
    fun_na8713714802964096592at_nat: $tType ).

thf(produc5504626439533210094nt_int_type,type,
    produc5504626439533210094nt_int: $tType ).

thf(produc5835291356934675326atural_type,type,
    produc5835291356934675326atural: $tType ).

thf(fun_se2759736925585322443t_bool_type,type,
    fun_se2759736925585322443t_bool: $tType ).

thf(fun_se1071123033157107803t_bool_type,type,
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thf(fun_Pr4895395666488778003r_bool_type,type,
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thf(fun_b_6437489657800174120t_bool_type,type,
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thf(fun_a_4602865052023851497t_bool_type,type,
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thf(fun_fu6387919364058294660er_nat_type,type,
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thf(fun_fu7205652234716754201er_nat_type,type,
    fun_fu7205652234716754201er_nat: $tType ).

thf(fun_fu440692136686903449er_nat_type,type,
    fun_fu440692136686903449er_nat: $tType ).

thf(fun_fu7173981028609952501er_int_type,type,
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thf(fun_fu2200728800440014653er_nat_type,type,
    fun_fu2200728800440014653er_nat: $tType ).

thf(fun_fu8934017692363063705er_int_type,type,
    fun_fu8934017692363063705er_int: $tType ).

thf(fun_Pr6001797050664311790t_bool_type,type,
    fun_Pr6001797050664311790t_bool: $tType ).

thf(fun_Pr554477149536188932t_bool_type,type,
    fun_Pr554477149536188932t_bool: $tType ).

thf(produc859450856879609959at_nat_type,type,
    produc859450856879609959at_nat: $tType ).

thf(produc1219242969750017639nt_int_type,type,
    produc1219242969750017639nt_int: $tType ).

thf(fun_Pr4335030045194121423et_nat_type,type,
    fun_Pr4335030045194121423et_nat: $tType ).

thf(fun_Pr1844946900262394667et_int_type,type,
    fun_Pr1844946900262394667et_int: $tType ).

thf(fun_b_7832390750199427630it_nat_type,type,
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thf(fun_a_1313742400928293293it_nat_type,type,
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thf(fun_fu8539566175054216963l_bool_type,type,
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thf(option936205604648967762et_nat_type,type,
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thf(fun_fu3137670002121144605l_bool_type,type,
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thf(fun_fu213826762832963033t_bool_type,type,
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thf(fun_fu4429343779803225557l_bool_type,type,
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thf(fun_fu796599533827200217t_bool_type,type,
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thf(fun_fu5912831971618039257l_bool_type,type,
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thf(fun_fu2988988732329857685t_bool_type,type,
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thf(fun_fu6847067296440702169l_bool_type,type,
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thf(fun_fu3214323050464676829t_bool_type,type,
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thf(fun_fu8303122171908583641l_bool_type,type,
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thf(fun_fu6470717055334781657l_bool_type,type,
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thf(produc7388388658123137530it_nat_type,type,
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thf(produc3260487557148687353it_nat_type,type,
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thf(fun_fu6757280373297557336ol_rat_type,type,
    fun_fu6757280373297557336ol_rat: $tType ).

thf(fun_fu6077215957461099344ol_nat_type,type,
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thf(fun_fu2549468117332453036ol_int_type,type,
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thf(fun_in217785400498748499nt_int_type,type,
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thf(set_Pr7577011563204128103nteger_type,type,
    set_Pr7577011563204128103nteger: $tType ).

thf(fun_fu4970875099359191043t_bool_type,type,
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thf(fun_fu3078129256884107011t_bool_type,type,
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thf(fun_fu7165551060251750659t_bool_type,type,
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thf(fun_fu7719728765329718531t_bool_type,type,
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thf(fun_fu2583778531842586371t_bool_type,type,
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thf(fun_fu691032689367502339t_bool_type,type,
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thf(list_P9062070895058802706et_nat_type,type,
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thf(fun_fu2971308621445215880t_bool_type,type,
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thf(fun_fu9131882981303784088t_bool_type,type,
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thf(fun_fu122198335894243788t_bool_type,type,
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thf(fun_fu5340484500765211138nt_int_type,type,
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thf(fun_fu163127709195666036t_bool_type,type,
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thf(fun_fu3332619399063632157nteger_type,type,
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thf(fun_fu513838225013818538r_bool_type,type,
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thf(fun_fu4454055256145563701r_bool_type,type,
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thf(fun_fu6579618355643354601at_rat_type,type,
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thf(fun_fu5935951186182374353at_nat_type,type,
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thf(fun_fu960360787657196261at_int_type,type,
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thf(fun_fu6092417073193843705nt_int_type,type,
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thf(fun_fu1617438229336688381nt_rat_type,type,
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thf(fun_fu973771059875708133nt_nat_type,type,
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thf(fun_fu5221552698205305849nt_int_type,type,
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thf(fun_fu5082522747898945281r_assn_type,type,
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thf(fun_li8221786654549472865l_assn_type,type,
    fun_li8221786654549472865l_assn: $tType ).

thf(fun_fu2868497722653781188t_bool_type,type,
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thf(fun_li6911922195568332558t_assn_type,type,
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thf(fun_li8672845860709154922t_assn_type,type,
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thf(fun_fu2987389051837124479on_num_type,type,
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thf(fun_fu1574286537503582443on_num_type,type,
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thf(fun_Pr5765855711896469291t_bool_type,type,
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thf(fun_na4786964484885125043t_bool_type,type,
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thf(fun_in4759738464598724019t_bool_type,type,
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thf(fun_fu7460908759652350970nt_rat_type,type,
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thf(fun_fu499174143044172372ol_nat_type,type,
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thf(fun_na4143055713577223196at_nat_type,type,
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thf(fun_in2204242111582549184nt_int_type,type,
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thf(fun_Co6597186368970283863nteger_type,type,
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thf(fun_fu71443909538865932at_nat_type,type,
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thf(fun_fu8556815104317537292nt_nat_type,type,
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thf(fun_fu8141884252878344844at_nat_type,type,
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thf(fun_fu5651801107946618088at_int_type,type,
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thf(fun_fu1653192730248997864nt_int_type,type,
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thf(fun_fu5114706524692223720r_assn_type,type,
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thf(fun_fu2342990897131189674r_bool_type,type,
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thf(fun_se4340818509347730467r_bool_type,type,
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thf(fun_Pr5068263890658062116t_bool_type,type,
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thf(fun_fu2454420574033104442at_nat_type,type,
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thf(fun_fu3739269683040691718nt_int_type,type,
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thf(fun_se5087743179055239239nteger_type,type,
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thf(fun_fu8303687057036190147t_bool_type,type,
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thf(fun_Pr2118491707810114563at_nat_type,type,
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thf(fun_Pr2478283820680522243nt_int_type,type,
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thf(option233860712434008220it_nat_type,type,
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thf(fun_fu2359051559149003772t_bool_type,type,
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thf(fun_fu551331151826482407at_rat_type,type,
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thf(fun_na2866682563581395078t_bool_type,type,
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thf(fun_na3576068603431507918t_bool_type,type,
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thf(produc4329699000281053074t_unit_type,type,
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thf(produc6491284506569428743nteger_type,type,
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thf(produc1730305018825802663t_unit_type,type,
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thf(produc3407818250607552075t_unit_type,type,
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thf(fun_fu7495562154832025027t_bool_type,type,
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thf(fun_fu624093908337759363nteger_type,type,
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thf(fun_fu9052069482527730051r_bool_type,type,
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thf(list_P131111800688179804it_nat_type,type,
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thf(fun_fu8021297703010766256t_bool_type,type,
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thf(fun_fu1107212216887061754r_bool_type,type,
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thf(fun_fu7000754783045315842r_bool_type,type,
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thf(fun_fu815224830654673830r_bool_type,type,
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thf(fun_fu8008802022867541912er_rat_type,type,
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thf(fun_fu5165416323490443664er_nat_type,type,
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thf(fun_fu2675333178558716908er_int_type,type,
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thf(fun_fu1590586450949517859at_nat_type,type,
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thf(fun_fu6924846375782198887atural_type,type,
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thf(fun_fu2499394402704830801nteger_type,type,
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thf(fun_fu6921880696561781257nteger_type,type,
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thf(fun_fu3628599891403802633nteger_type,type,
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thf(fun_fu722387130092441185er_rat_type,type,
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thf(fun_fu7724909810345500241er_nat_type,type,
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thf(fun_fu403917627589892361er_int_type,type,
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thf(fun_se7799640332748030482r_assn_type,type,
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thf(fun_Co5080488584548667985nteger_type,type,
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thf(produc3658429121746597890et_nat_type,type,
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thf(fun_se7035039998181355731t_bool_type,type,
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thf(fun_ar7139816496917982587t_assn_type,type,
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thf(fun_fu7353774216694237776ol_nat_type,type,
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thf(fun_se5089947911621939745t_bool_type,type,
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thf(fun_Pr5591635095200564269t_bool_type,type,
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thf(fun_Pr8133618145831759733t_bool_type,type,
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thf(fun_op1637087682669155543nteger_type,type,
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thf(fun_Co7333321365496032713r_bool_type,type,
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thf(fun_fu953397851080917123ol_nat_type,type,
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thf(fun_fu5827305053654988013l_bool_type,type,
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thf(fun_fu7925731147167280621l_bool_type,type,
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thf(fun_fu9217928336980114631ol_nat_type,type,
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thf(fun_fu6727845192048387875ol_int_type,type,
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thf(fun_fu8444598815406890787ol_nat_type,type,
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thf(fun_fu5954515670475164031ol_int_type,type,
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thf(fun_se3394281818192328589t_bool_type,type,
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thf(fun_in3304247434473118374nt_int_type,type,
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thf(fun_fu5926195154906828138at_nat_type,type,
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thf(fun_fu98928519719771682nt_nat_type,type,
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thf(fun_fu6875386846537121830at_nat_type,type,
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thf(fun_fu4385303701605395074at_int_type,type,
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thf(fun_fu386695323907774850nt_int_type,type,
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thf(fun_fu9051297857939674819t_bool_type,type,
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thf(fun_fu740641253506916313at_nat_type,type,
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thf(fun_fu3778483337971050109at_nat_type,type,
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thf(fun_fu1288400193039323353at_int_type,type,
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thf(fun_fu5965404912664071897nt_nat_type,type,
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thf(fun_fu3475321767732345141nt_int_type,type,
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thf(fun_fu5970656269460422159t_bool_type,type,
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thf(fun_fu228726614528254077at_nat_type,type,
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thf(fun_fu2415648189221275865nt_nat_type,type,
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thf(fun_fu5453490273685409661nt_nat_type,type,
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thf(fun_fu8467804991414204575t_bool_type,type,
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thf(fun_se1925730536474940935t_bool_type,type,
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thf(fun_na5642534631560016699t_bool_type,type,
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thf(fun_in8964175134550391243t_bool_type,type,
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thf(fun_fu4413992040155564420at_nat_type,type,
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thf(fun_fu923337204662071120nt_int_type,type,
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thf(fun_fu5689865433563736081nteger_type,type,
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thf(fun_se1909708154429037836et_nat_type,type,
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thf(fun_se6573205548028396576et_int_type,type,
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thf(fun_se8983711159220854466er_rat_type,type,
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thf(fun_se6140325459843756218er_nat_type,type,
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thf(fun_ra8505079968215247908at_rat_type,type,
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thf(fun_Co6813818151677833714atural_type,type,
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thf(fun_Co8514937155073724839atural_type,type,
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thf(fun_Co1981900195452921617nteger_type,type,
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thf(fun_fu1757461920858180226t_bool_type,type,
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thf(fun_fu7572710155198003306on_num_type,type,
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thf(fun_fu152868422178311599um_num_type,type,
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thf(fun_fu1947565687807238081um_int_type,type,
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thf(fun_fu4719417816141531311on_num_type,type,
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thf(fun_fu7964671872712412353on_num_type,type,
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thf(fun_fu1502755112258691281at_nat_type,type,
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thf(fun_fu5130958774822480081on_num_type,type,
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thf(fun_mu2814435412087153747t_bool_type,type,
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thf(fun_he5875662316245821270t_bool_type,type,
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thf(fun_fu5641360819561228055l_bool_type,type,
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thf(fun_fu4264586804747991503l_bool_type,type,
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thf(fun_op1962577433978643573m_bool_type,type,
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thf(fun_na2338080690716861136at_nat_type,type,
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thf(fun_in259009099871059828at_nat_type,type,
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thf(fun_Pr5932607294251420486t_bool_type,type,
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thf(fun_Pr3145601080792579042t_bool_type,type,
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thf(fun_op3323321805596408808on_num_type,type,
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thf(fun_op7680796716376270858on_nat_type,type,
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thf(fun_op7417050415941327134on_int_type,type,
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thf(fun_na4827981024643048934t_bool_type,type,
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thf(fun_in4812163815185324938t_bool_type,type,
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thf(fun_fu1925869420691536157nteger_type,type,
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thf(fun_fu490033871300650088l_bool_type,type,
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thf(fun_fu3953527911151619997l_bool_type,type,
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thf(fun_ra6264997190470632278at_rat_type,type,
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thf(fun_na4138050610385705875at_nat_type,type,
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thf(fun_na2750682433154738518at_nat_type,type,
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thf(fun_in7410854813335147606at_int_type,type,
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thf(fun_in1696471567231710611nt_int_type,type,
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thf(set_Pr5488025237498180813et_nat_type,type,
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thf(set_Pr2522554150109002629et_int_type,type,
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thf(fun_fu4708731997093370859l_bool_type,type,
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thf(fun_fu3561611792623449554r_bool_type,type,
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thf(fun_fu574094095068873155l_assn_type,type,
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thf(fun_ra7317100687414072407at_rat_type,type,
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thf(fun_ra1107035566227760819at_rat_type,type,
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thf(fun_na6244580715232974919at_nat_type,type,
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thf(fun_na34515594046663331at_nat_type,type,
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thf(fun_in2640216123419753727at_int_type,type,
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thf(fun_in5653523039088217947at_int_type,type,
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thf(option495425031756530865t_bool_type,type,
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thf(fun_fu3002462811980898909nteger_type,type,
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thf(fun_fu1699057998260582084t_bool_type,type,
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thf(fun_fu9135849066224463439t_bool_type,type,
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thf(fun_fu4771103787859698525nteger_type,type,
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thf(fun_fu6221978408351936012t_bool_type,type,
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thf(fun_fu4435397439461041559t_bool_type,type,
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thf(fun_fu3380082687118895412nteger_type,type,
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thf(fun_fu2995346897264222311t_assn_type,type,
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thf(fun_fu6568868615275847455t_assn_type,type,
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thf(produc6653097349344004940it_nat_type,type,
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thf(produc7248412053542808358at_nat_type,type,
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thf(fun_li8598321315282354825t_bool_type,type,
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thf(fun_se3032438776331272065t_bool_type,type,
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thf(fun_fu2358325754833327848l_assn_type,type,
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thf(fun_fu8340641457845911400l_bool_type,type,
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thf(fun_se593059424582005380nt_rat_type,type,
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thf(fun_se7834784120450421933l_bool_type,type,
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thf(fun_ra7314870381713115802nt_int_type,type,
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thf(fun_Pr6026251430685297nteger_type,type,
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thf(fun_na1463218212465827171t_bool_type,type,
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thf(fun_na7044673412300895210at_nat_type,type,
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thf(fun_in7209865251430457670nt_int_type,type,
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thf(fun_se5639388791307298963nteger_type,type,
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thf(fun_Pr2477578491906815678t_assn_type,type,
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thf(fun_he5123621388056232515t_unit_type,type,
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thf(fun_fu6395640590628241448t_assn_type,type,
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thf(fun_fu6838017323210031556t_bool_type,type,
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thf(fun_fu4854284890850328872t_assn_type,type,
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thf(fun_fu420584378438320396t_bool_type,type,
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thf(fun_se707272970763642173t_bool_type,type,
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thf(fun_se6049520964208396421t_bool_type,type,
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thf(fun_na5377294648341738301t_bool_type,type,
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thf(fun_na4145236241668639526r_bool_type,type,
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thf(fun_Co9170264581657726457l_bool_type,type,
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thf(fun_Co394175896199268228r_bool_type,type,
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thf(fun_Co8310303586393106575r_bool_type,type,
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thf(fun_na7078387940644931716nteger_type,type,
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thf(fun_Co740390889742897050atural_type,type,
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thf(fun_Co6749200540738471926atural_type,type,
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thf(fun_Co6226381647958292740nteger_type,type,
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thf(fun_Co8521658056209057742er_num_type,type,
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thf(fun_as4019953064511417593t_assn_type,type,
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thf(fun_fu6678276313180071960l_bool_type,type,
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thf(fun_fu913567913430682128l_bool_type,type,
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thf(fun_fu3926874829099146348l_bool_type,type,
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thf(fun_fu7923017422675304344ol_rat_type,type,
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thf(fun_ar8560675821539856405t_assn_type,type,
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thf(fun_ar528246731820255437t_assn_type,type,
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thf(set_se7855581050983116737at_nat_type,type,
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thf(fun_li4928566814967809234t_assn_type,type,
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thf(fun_li1703715468755832110t_assn_type,type,
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thf(fun_fu3052598110916186900t_bool_type,type,
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thf(fun_fu8422113094057456412t_bool_type,type,
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thf(fun_fu5590568769550944704t_bool_type,type,
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thf(fun_bo7720638723722887333nt_int_type,type,
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thf(fun_ra4503298312962071866nt_int_type,type,
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thf(fun_a_6164325696594227994Heap_b_type,type,
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thf(fun_a_6093291656547882009Heap_a_type,type,
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    fun_nat_Code_integer: $tType ).

thf(fun_int_set_nat_type,type,
    fun_int_set_nat: $tType ).

thf(fun_int_set_int_type,type,
    fun_int_set_int: $tType ).

thf(fun_int_Code_natural_type,type,
    fun_int_Code_natural: $tType ).

thf(fun_int_Code_integer_type,type,
    fun_int_Code_integer: $tType ).

thf(fun_Code_natural_nat_type,type,
    fun_Code_natural_nat: $tType ).

thf(fun_Code_integer_rat_type,type,
    fun_Code_integer_rat: $tType ).

thf(fun_Code_integer_num_type,type,
    fun_Code_integer_num: $tType ).

thf(fun_Code_integer_nat_type,type,
    fun_Code_integer_nat: $tType ).

thf(fun_Code_integer_int_type,type,
    fun_Code_integer_int: $tType ).

thf(fun_assn_assn_type,type,
    fun_assn_assn: $tType ).

thf(list_option_num_type,type,
    list_option_num: $tType ).

thf(option_set_bool_type,type,
    option_set_bool: $tType ).

thf(fun_Pr1572506220757514509t_bool_type,type,
    fun_Pr1572506220757514509t_bool: $tType ).

thf(fun_bo1891391082718140537t_unit_type,type,
    fun_bo1891391082718140537t_unit: $tType ).

thf(option_set_nat_type,type,
    option_set_nat: $tType ).

thf(option_set_int_type,type,
    option_set_int: $tType ).

thf(option_Code_integer_type,type,
    option_Code_integer: $tType ).

thf(filter_set_nat_type,type,
    filter_set_nat: $tType ).

thf(fun_Product_unit_nat_type,type,
    fun_Product_unit_nat: $tType ).

thf(heap_Time_Heap_bool_type,type,
    heap_Time_Heap_bool: $tType ).

thf(set_list_bool_type,type,
    set_list_bool: $tType ).

thf(heap_Time_Heap_nat_type,type,
    heap_Time_Heap_nat: $tType ).

thf(heap_Time_Heap_int_type,type,
    heap_Time_Heap_int: $tType ).

thf(set_list_nat_type,type,
    set_list_nat: $tType ).

thf(set_list_int_type,type,
    set_list_int: $tType ).

thf(fun_bool_assn_type,type,
    fun_bool_assn: $tType ).

thf(fun_assn_bool_type,type,
    fun_assn_bool: $tType ).

thf(fun_rat_assn_type,type,
    fun_rat_assn: $tType ).

thf(fun_num_assn_type,type,
    fun_num_assn: $tType ).

thf(fun_nat_assn_type,type,
    fun_nat_assn: $tType ).

thf(fun_int_assn_type,type,
    fun_int_assn: $tType ).

thf(fun_assn_rat_type,type,
    fun_assn_rat: $tType ).

thf(fun_assn_num_type,type,
    fun_assn_num: $tType ).

thf(fun_assn_nat_type,type,
    fun_assn_nat: $tType ).

thf(fun_assn_int_type,type,
    fun_assn_int: $tType ).

thf(set_set_nat_type,type,
    set_set_nat: $tType ).

thf(set_set_int_type,type,
    set_set_int: $tType ).

thf(set_Code_integer_type,type,
    set_Code_integer: $tType ).

thf(array_Product_unit_type,type,
    array_Product_unit: $tType ).

thf(list_Product_unit_type,type,
    list_Product_unit: $tType ).

thf(option_assn_type,type,
    option_assn: $tType ).

thf(ref_Product_unit_type,type,
    ref_Product_unit: $tType ).

thf(set_Product_unit_type,type,
    set_Product_unit: $tType ).

thf(product_prod_b_b_type,type,
    product_prod_b_b: $tType ).

thf(product_prod_a_a_type,type,
    product_prod_a_a: $tType ).

thf(heap_Time_Heap_b_type,type,
    heap_Time_Heap_b: $tType ).

thf(heap_Time_Heap_a_type,type,
    heap_Time_Heap_a: $tType ).

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

thf(fun_b_assn_type,type,
    fun_b_assn: $tType ).

thf(fun_a_assn_type,type,
    fun_a_assn: $tType ).

thf(fun_rat_bool_type,type,
    fun_rat_bool: $tType ).

thf(fun_num_bool_type,type,
    fun_num_bool: $tType ).

thf(fun_nat_bool_type,type,
    fun_nat_bool: $tType ).

thf(fun_int_bool_type,type,
    fun_int_bool: $tType ).

thf(fun_bool_rat_type,type,
    fun_bool_rat: $tType ).

thf(fun_bool_num_type,type,
    fun_bool_num: $tType ).

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

thf(fun_bool_int_type,type,
    fun_bool_int: $tType ).

thf(fun_rat_rat_type,type,
    fun_rat_rat: $tType ).

thf(fun_rat_num_type,type,
    fun_rat_num: $tType ).

thf(fun_rat_nat_type,type,
    fun_rat_nat: $tType ).

thf(fun_rat_int_type,type,
    fun_rat_int: $tType ).

thf(fun_num_rat_type,type,
    fun_num_rat: $tType ).

thf(fun_num_num_type,type,
    fun_num_num: $tType ).

thf(fun_num_nat_type,type,
    fun_num_nat: $tType ).

thf(fun_num_int_type,type,
    fun_num_int: $tType ).

thf(fun_nat_rat_type,type,
    fun_nat_rat: $tType ).

thf(fun_nat_num_type,type,
    fun_nat_num: $tType ).

thf(fun_nat_nat_type,type,
    fun_nat_nat: $tType ).

thf(fun_nat_int_type,type,
    fun_nat_int: $tType ).

thf(fun_int_rat_type,type,
    fun_int_rat: $tType ).

thf(fun_int_num_type,type,
    fun_int_num: $tType ).

thf(fun_int_nat_type,type,
    fun_int_nat: $tType ).

thf(fun_int_int_type,type,
    fun_int_int: $tType ).

thf(set_assn_type,type,
    set_assn: $tType ).

thf(option_bool_type,type,
    option_bool: $tType ).

thf(option_rat_type,type,
    option_rat: $tType ).

thf(option_num_type,type,
    option_num: $tType ).

thf(option_nat_type,type,
    option_nat: $tType ).

thf(option_int_type,type,
    option_int: $tType ).

thf(list_char_type,type,
    list_char: $tType ).

thf(filter_nat_type,type,
    filter_nat: $tType ).

thf(array_bool_type,type,
    array_bool: $tType ).

thf(list_bool_type,type,
    list_bool: $tType ).

thf(array_nat_type,type,
    array_nat: $tType ).

thf(array_int_type,type,
    array_int: $tType ).

thf(fun_b_bool_type,type,
    fun_b_bool: $tType ).

thf(fun_a_bool_type,type,
    fun_a_bool: $tType ).

thf(list_rat_type,type,
    list_rat: $tType ).

thf(list_num_type,type,
    list_num: $tType ).

thf(list_nat_type,type,
    list_nat: $tType ).

thf(list_int_type,type,
    list_int: $tType ).

thf(set_bool_type,type,
    set_bool: $tType ).

thf(set_rat_type,type,
    set_rat: $tType ).

thf(set_num_type,type,
    set_num: $tType ).

thf(set_nat_type,type,
    set_nat: $tType ).

thf(set_int_type,type,
    set_int: $tType ).

thf(code_natural_type,type,
    code_natural: $tType ).

thf(code_integer_type,type,
    code_integer: $tType ).

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

thf(list_b_type,type,
    list_b: $tType ).

thf(list_a_type,type,
    list_a: $tType ).

thf(assn_type,type,
    assn: $tType ).

thf(char_type,type,
    char: $tType ).

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

thf(rat_type,type,
    rat: $tType ).

thf(num_type,type,
    num: $tType ).

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

thf(int_type,type,
    int: $tType ).

thf(b_type,type,
    b: $tType ).

thf(a_type,type,
    a: $tType ).

thf(aTP_Lamm_af_type,type,
    aTP_Lamm_af: fun_nat_bool ).

thf(aTP_Lamm_ag_type,type,
    aTP_Lamm_ag: fun_nat_bool ).

thf(aTP_Lamm_eo_type,type,
    aTP_Lamm_eo: fun_nat_bool ).

thf(aTP_Lamm_ey_type,type,
    aTP_Lamm_ey: fun_Pr6626665806141890376t_assn ).

thf(aTP_Lamm_gt_type,type,
    aTP_Lamm_gt: fun_Pr6001797050664311790t_bool ).

thf(aTP_Lamm_gu_type,type,
    aTP_Lamm_gu: assn > fun_as4100195077546555551t_bool ).

thf(aTP_Lamm_gv_type,type,
    aTP_Lamm_gv: assn > fun_as4100195077546555551t_bool ).

thf(aTP_Lamm_ho_type,type,
    aTP_Lamm_ho: assn > fun_Pr6001797050664311790t_bool ).

thf(abs_assn_type,type,
    abs_assn: fun_Pr6001797050664311790t_bool > assn ).

thf(rep_assn_type,type,
    rep_assn: assn > fun_Pr6001797050664311790t_bool ).

thf(entails_type,type,
    entails: assn > assn > $o ).

thf(in_range_type,type,
    in_range: fun_Pr6001797050664311790t_bool ).

thf(one_assn_raw_type,type,
    one_assn_raw: fun_Pr6001797050664311790t_bool ).

thf(pure_assn_type,type,
    pure_assn: fun_bool_assn ).

thf(pure_a825153325127701367it_nat_type,type,
    pure_a825153325127701367it_nat: bool > fun_Pr6001797050664311790t_bool ).

thf(relH_type,type,
    relH: set_nat > heap_e7401611519738050253t_unit > fun_he6201055237484778573t_bool ).

thf(one_one_assn_type,type,
    one_one_assn: assn ).

thf(heap_T6553295506729943825t_unit_type,type,
    heap_T6553295506729943825t_unit: heap_T5738788834812785303t_unit > heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit > product_unit > fun_nat_bool ).

thf(heap_Time_effect_a_type,type,
    heap_Time_effect_a: heap_Time_Heap_a > heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit > a > fun_nat_bool ).

thf(heap_Time_effect_b_type,type,
    heap_Time_effect_b: heap_Time_Heap_b > heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit > b > fun_nat_bool ).

thf(heap_T584514906347983379t_unit_type,type,
    heap_T584514906347983379t_unit: heap_T5738788834812785303t_unit > fun_he6201055237484778573t_bool ).

thf(heap_Time_success_a_type,type,
    heap_Time_success_a: heap_Time_Heap_a > fun_he6201055237484778573t_bool ).

thf(heap_Time_success_b_type,type,
    heap_Time_success_b: heap_Time_Heap_b > fun_he6201055237484778573t_bool ).

thf(hoare_8945653483474564448t_unit_type,type,
    hoare_8945653483474564448t_unit: assn > heap_T5738788834812785303t_unit > fun_Pr6626665806141890376t_assn > $o ).

thf(hoare_hoare_triple_a_type,type,
    hoare_hoare_triple_a: assn > heap_Time_Heap_a > fun_a_assn > $o ).

thf(hoare_hoare_triple_b_type,type,
    hoare_hoare_triple_b: assn > heap_Time_Heap_b > fun_b_assn > $o ).

thf(hoare_new_addrs_type,type,
    hoare_new_addrs: heap_e7401611519738050253t_unit > set_nat > heap_e7401611519738050253t_unit > set_nat ).

thf(bot_bot_assn_type,type,
    bot_bot_assn: assn ).

thf(bot_bot_set_nat_type,type,
    bot_bot_set_nat: set_nat ).

thf(ord_le2468614981408567801t_bool_type,type,
    ord_le2468614981408567801t_bool: fun_Pr7757163693017731481t_bool > fun_fu5641360819561228055l_bool ).

thf(ord_le2087689725136068685t_bool_type,type,
    ord_le2087689725136068685t_bool: fun_Pr248683899324676269t_bool > fun_Pr248683899324676269t_bool > $o ).

thf(ord_le998981803562422117m_bool_type,type,
    ord_le998981803562422117m_bool: fun_Pr6287530515171585797m_bool > fun_Pr6287530515171585797m_bool > $o ).

thf(ord_le7676714441581034317m_bool_type,type,
    ord_le7676714441581034317m_bool: fun_Pr5837708615769641901m_bool > fun_Pr5837708615769641901m_bool > $o ).

thf(top_top_assn_type,type,
    top_top_assn: assn ).

thf(produc7507926704131184380et_nat_type,type,
    produc7507926704131184380et_nat: heap_e7401611519738050253t_unit > set_nat > produc3658429121746597890et_nat ).

thf(produc8586169260539613262et_nat_type,type,
    produc8586169260539613262et_nat: produc3658429121746597890et_nat > set_nat ).

thf(collect_nat_type,type,
    collect_nat: fun_nat_bool > set_nat ).

thf(accp_P4275260045618599050at_nat_type,type,
    accp_P4275260045618599050at_nat: fun_Pr248683899324676269t_bool > fun_Pr7757163693017731481t_bool ).

thf(accp_P3113834385874906142um_num_type,type,
    accp_P3113834385874906142um_num: fun_Pr5837708615769641901m_bool > fun_Pr6287530515171585797m_bool ).

thf(aa_ass8975924923219239432t_bool_type,type,
    aa_ass8975924923219239432t_bool: fun_as4100195077546555551t_bool > assn > fun_Pr6001797050664311790t_bool ).

thf(aa_bool_assn_type,type,
    aa_bool_assn: fun_bool_assn > bool > assn ).

thf(aa_hea1793595068369496646t_bool_type,type,
    aa_hea1793595068369496646t_bool: fun_he6201055237484778573t_bool > heap_e7401611519738050253t_unit > bool ).

thf(aa_nat_bool_type,type,
    aa_nat_bool: fun_nat_bool > nat > bool ).

thf(aa_Pro2991721470636411351t_bool_type,type,
    aa_Pro2991721470636411351t_bool: fun_Pr6001797050664311790t_bool > produc3658429121746597890et_nat > bool ).

thf(aa_Pro2232559814647311250t_bool_type,type,
    aa_Pro2232559814647311250t_bool: fun_Pr7757163693017731481t_bool > product_prod_nat_nat > bool ).

thf(aa_Pro595088089689268830t_bool_type,type,
    aa_Pro595088089689268830t_bool: fun_Pr248683899324676269t_bool > product_prod_nat_nat > fun_Pr7757163693017731481t_bool ).

thf(aa_Pro762926636801165566m_bool_type,type,
    aa_Pro762926636801165566m_bool: fun_Pr6287530515171585797m_bool > product_prod_num_num > bool ).

thf(aa_Pro2164613399825298270m_bool_type,type,
    aa_Pro2164613399825298270m_bool: fun_Pr5837708615769641901m_bool > product_prod_num_num > fun_Pr6287530515171585797m_bool ).

thf(aa_Product_unit_assn_type,type,
    aa_Product_unit_assn: fun_Pr6626665806141890376t_assn > product_unit > assn ).

thf(aa_fun8663595511526100224l_bool_type,type,
    aa_fun8663595511526100224l_bool: fun_fu5641360819561228055l_bool > fun_Pr7757163693017731481t_bool > bool ).

thf(aa_a_assn_type,type,
    aa_a_assn: fun_a_assn > a > assn ).

thf(aa_a_H8829438778223708363Heap_b_type,type,
    aa_a_H8829438778223708363Heap_b: fun_a_6164325696594227994Heap_b > a > heap_Time_Heap_b ).

thf(aa_b_assn_type,type,
    aa_b_assn: fun_b_assn > b > assn ).

thf(fFalse_type,type,
    fFalse: bool ).

thf(fTrue_type,type,
    fTrue: bool ).

thf(pp_type,type,
    pp: bool > $o ).

thf(p_type,type,
    p: assn ).

thf(q_type,type,
    q: fun_b_assn ).

thf(r_type,type,
    r: fun_a_assn ).

thf(as_type,type,
    as: set_nat ).

thf(f_type,type,
    f: heap_Time_Heap_a ).

thf(g_type,type,
    g: fun_a_6164325696594227994Heap_b ).

thf(h_type,type,
    h: heap_e7401611519738050253t_unit ).

thf(h2_type,type,
    h2: heap_e7401611519738050253t_unit ).

thf(h3_type,type,
    h3: heap_e7401611519738050253t_unit ).

thf(rf_type,type,
    rf: a ).

thf(rg_type,type,
    rg: b ).

thf(13,axiom,
    ! [A: heap_T5738788834812785303t_unit,B: fun_Pr6626665806141890376t_assn] : ( hoare_8945653483474564448t_unit @ bot_bot_assn @ A @ B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1996_false__rule) ).

thf(153,plain,
    ! [A: heap_T5738788834812785303t_unit,B: fun_Pr6626665806141890376t_assn] : ( hoare_8945653483474564448t_unit @ bot_bot_assn @ A @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(91,axiom,
    ! [A: assn,B: produc3658429121746597890et_nat,C: assn] :
      ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ A ) @ B ) )
     => ( ( entails @ A @ C )
       => ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ C ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2498_ent__fwd) ).

thf(466,plain,
    ! [A: assn,B: produc3658429121746597890et_nat,C: assn] :
      ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ A ) @ B ) )
     => ( ( entails @ A @ C )
       => ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ C ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(39,axiom,
    ( ( aa_bool_assn @ pure_assn @ fTrue )
    = one_one_assn ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2118_pure__true) ).

thf(250,plain,
    ( ( aa_bool_assn @ pure_assn @ fTrue )
    = one_one_assn ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(94,axiom,
    ! [A: assn,B: assn] :
      ( ! [C: produc3658429121746597890et_nat] :
          ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ A ) @ C ) )
         => ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ B ) @ C ) ) )
     => ( entails @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2500_entailsI) ).

thf(481,plain,
    ! [A: assn,B: assn] :
      ( ! [C: produc3658429121746597890et_nat] :
          ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ A ) @ C ) )
         => ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ B ) @ C ) ) )
     => ( entails @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(64,axiom,
    ! [A: assn,B: assn,C: produc3658429121746597890et_nat] :
      ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( aa_ass8975924923219239432t_bool @ ( aTP_Lamm_gv @ A ) @ B ) @ C ) )
    <=> ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ A ) @ C ) )
        & ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10704_ATP_Olambda__498) ).

thf(352,plain,
    ! [A: assn,B: assn,C: produc3658429121746597890et_nat] :
      ( ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( aa_ass8975924923219239432t_bool @ ( aTP_Lamm_gv @ A ) @ B ) @ C ) )
       => ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ A ) @ C ) )
          & ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ B ) @ C ) ) ) )
      & ( ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ A ) @ C ) )
          & ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ B ) @ C ) ) )
       => ( pp @ ( aa_Pro2991721470636411351t_bool @ ( aa_ass8975924923219239432t_bool @ ( aTP_Lamm_gv @ A ) @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(18,axiom,
    ! [A: assn] : ( entails @ bot_bot_assn @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2533_ent__false) ).

thf(170,plain,
    ! [A: assn] : ( entails @ bot_bot_assn @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(104,axiom,
    ! [A: produc3658429121746597890et_nat] :
      ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ one_one_assn ) @ A ) )
    <=> ( ( produc8586169260539613262et_nat @ A )
        = bot_bot_set_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9815_mod__emp) ).

thf(523,plain,
    ! [A: produc3658429121746597890et_nat] :
      ( ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ one_one_assn ) @ A ) )
       => ( ( produc8586169260539613262et_nat @ A )
          = bot_bot_set_nat ) )
      & ( ( ( produc8586169260539613262et_nat @ A )
          = bot_bot_set_nat )
       => ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ one_one_assn ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(29,axiom,
    ! [A: assn,B: assn,C: heap_Time_Heap_a,D: fun_a_assn] :
      ( ( entails @ A @ B )
     => ( ( hoare_hoare_triple_a @ B @ C @ D )
       => ( hoare_hoare_triple_a @ A @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2566_cons__pre__rule) ).

thf(217,plain,
    ! [A: assn,B: assn,C: heap_Time_Heap_a,D: fun_a_assn] :
      ( ( entails @ A @ B )
     => ( ( hoare_hoare_triple_a @ B @ C @ D )
       => ( hoare_hoare_triple_a @ A @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(38,axiom,
    ! [A: assn,B: assn,C: assn] :
      ( ( entails @ A @ B )
     => ( ( entails @ B @ C )
       => ( entails @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2311_ent__trans) ).

thf(247,plain,
    ! [A: assn,B: assn,C: assn] :
      ( ( entails @ A @ B )
     => ( ( entails @ B @ C )
       => ( entails @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(70,axiom,
    ! [A: fun_Pr6001797050664311790t_bool,B: assn] :
      ( ! [C: produc3658429121746597890et_nat] :
          ( ( pp @ ( aa_Pro2991721470636411351t_bool @ A @ C ) )
        <=> ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ B ) @ C ) ) )
     => ( ( abs_assn @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3810_Abs__assn__eqI_I1_J) ).

thf(379,plain,
    ! [A: fun_Pr6001797050664311790t_bool,B: assn] :
      ( ! [C: produc3658429121746597890et_nat] :
          ( ( ( pp @ ( aa_Pro2991721470636411351t_bool @ A @ C ) )
           => ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ B ) @ C ) ) )
          & ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ B ) @ C ) )
           => ( pp @ ( aa_Pro2991721470636411351t_bool @ A @ C ) ) ) )
     => ( ( abs_assn @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(20,axiom,
    ! [A: set_nat,B: heap_e7401611519738050253t_unit,C: heap_e7401611519738050253t_unit,D: heap_e7401611519738050253t_unit] :
      ( ( pp @ ( aa_hea1793595068369496646t_bool @ ( relH @ A @ B ) @ C ) )
     => ( ( pp @ ( aa_hea1793595068369496646t_bool @ ( relH @ A @ C ) @ D ) )
       => ( pp @ ( aa_hea1793595068369496646t_bool @ ( relH @ A @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_331_relH__trans) ).

thf(174,plain,
    ! [A: set_nat,B: heap_e7401611519738050253t_unit,C: heap_e7401611519738050253t_unit,D: heap_e7401611519738050253t_unit] :
      ( ( pp @ ( aa_hea1793595068369496646t_bool @ ( relH @ A @ B ) @ C ) )
     => ( ( pp @ ( aa_hea1793595068369496646t_bool @ ( relH @ A @ C ) @ D ) )
       => ( pp @ ( aa_hea1793595068369496646t_bool @ ( relH @ A @ B ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(50,axiom,
    ! [A: bool,B: heap_Time_Heap_a,C: fun_a_assn] :
      ( ( hoare_hoare_triple_a @ ( aa_bool_assn @ pure_assn @ A ) @ B @ C )
    <=> ( ( pp @ A )
       => ( hoare_hoare_triple_a @ one_one_assn @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2121_norm__pre__pure__iff__sng) ).

thf(288,plain,
    ! [A: bool,B: heap_Time_Heap_a,C: fun_a_assn] :
      ( ( ( hoare_hoare_triple_a @ ( aa_bool_assn @ pure_assn @ A ) @ B @ C )
       => ( ( pp @ A )
         => ( hoare_hoare_triple_a @ one_one_assn @ B @ C ) ) )
      & ( ( ( pp @ A )
         => ( hoare_hoare_triple_a @ one_one_assn @ B @ C ) )
       => ( hoare_hoare_triple_a @ ( aa_bool_assn @ pure_assn @ A ) @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(71,axiom,
    ! [A: produc3658429121746597890et_nat] :
      ~ ! [B: heap_e7401611519738050253t_unit,C: set_nat] :
          ( A
         != ( produc7507926704131184380et_nat @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_one__assn__raw_Ocases) ).

thf(389,plain,
    ! [A: produc3658429121746597890et_nat] :
      ~ ! [B: heap_e7401611519738050253t_unit,C: set_nat] :
          ( A
         != ( produc7507926704131184380et_nat @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(68,axiom,
    ! [A: assn,B: heap_Time_Heap_b,C: fun_b_assn,D: heap_e7401611519738050253t_unit,E: set_nat] :
      ( ( hoare_hoare_triple_b @ A @ B @ C )
     => ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ A ) @ ( produc7507926704131184380et_nat @ D @ E ) ) )
       => ( pp @ ( aa_hea1793595068369496646t_bool @ ( heap_Time_success_b @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_hoare__triple__success) ).

thf(372,plain,
    ! [A: assn,B: heap_Time_Heap_b,C: fun_b_assn,D: heap_e7401611519738050253t_unit,E: set_nat] :
      ( ( hoare_hoare_triple_b @ A @ B @ C )
     => ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ A ) @ ( produc7507926704131184380et_nat @ D @ E ) ) )
       => ( pp @ ( aa_hea1793595068369496646t_bool @ ( heap_Time_success_b @ B ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(3,axiom,
    ~ ( pp @ fFalse ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).

thf(110,plain,
    ~ ( pp @ fFalse ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(24,axiom,
    ! [A: bool,B: bool] :
      ( ( ( aa_bool_assn @ pure_assn @ A )
        = ( aa_bool_assn @ pure_assn @ B ) )
    <=> ( ( pp @ A )
      <=> ( pp @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2115_pure__assn__eq__conv) ).

thf(189,plain,
    ! [A: bool,B: bool] :
      ( ( ( ( aa_bool_assn @ pure_assn @ A )
          = ( aa_bool_assn @ pure_assn @ B ) )
       => ( ( ( pp @ A )
           => ( pp @ B ) )
          & ( ( pp @ B )
           => ( pp @ A ) ) ) )
      & ( ( ( ( pp @ A )
           => ( pp @ B ) )
          & ( ( pp @ B )
           => ( pp @ A ) ) )
       => ( ( aa_bool_assn @ pure_assn @ A )
          = ( aa_bool_assn @ pure_assn @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(77,axiom,
    ! [A: bool,B: heap_e7401611519738050253t_unit,C: set_nat] :
      ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( pure_a825153325127701367it_nat @ A ) @ ( produc7507926704131184380et_nat @ B @ C ) ) )
    <=> ( ( C = bot_bot_set_nat )
        & ( pp @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2138_pure__assn__raw_Osimps) ).

thf(416,plain,
    ! [A: bool,B: heap_e7401611519738050253t_unit,C: set_nat] :
      ( ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( pure_a825153325127701367it_nat @ A ) @ ( produc7507926704131184380et_nat @ B @ C ) ) )
       => ( ( C = bot_bot_set_nat )
          & ( pp @ A ) ) )
      & ( ( ( C = bot_bot_set_nat )
          & ( pp @ A ) )
       => ( pp @ ( aa_Pro2991721470636411351t_bool @ ( pure_a825153325127701367it_nat @ A ) @ ( produc7507926704131184380et_nat @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(60,axiom,
    ! [A: fun_Pr5837708615769641901m_bool,B: fun_Pr5837708615769641901m_bool] :
      ( ( ord_le7676714441581034317m_bool @ A @ B )
     => ( ord_le998981803562422117m_bool @ ( accp_P3113834385874906142um_num @ B ) @ ( accp_P3113834385874906142um_num @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1728_accp__subset) ).

thf(325,plain,
    ! [A: fun_Pr5837708615769641901m_bool,B: fun_Pr5837708615769641901m_bool] :
      ( ( ord_le7676714441581034317m_bool @ A @ B )
     => ( ord_le998981803562422117m_bool @ ( accp_P3113834385874906142um_num @ B ) @ ( accp_P3113834385874906142um_num @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(85,axiom,
    ! [A: assn,B: produc3658429121746597890et_nat] :
      ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( aTP_Lamm_ho @ A ) @ B ) )
    <=> ( ( pp @ ( aa_Pro2991721470636411351t_bool @ in_range @ B ) )
        & ~ ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10335_ATP_Olambda__129) ).

thf(448,plain,
    ! [A: assn,B: produc3658429121746597890et_nat] :
      ( ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( aTP_Lamm_ho @ A ) @ B ) )
       => ( ( pp @ ( aa_Pro2991721470636411351t_bool @ in_range @ B ) )
          & ~ ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ A ) @ B ) ) ) )
      & ( ( ( pp @ ( aa_Pro2991721470636411351t_bool @ in_range @ B ) )
          & ~ ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ A ) @ B ) ) )
       => ( pp @ ( aa_Pro2991721470636411351t_bool @ ( aTP_Lamm_ho @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(57,axiom,
    ! [A: assn,B: assn] :
      ( ( entails @ A @ B )
     => ( ( entails @ B @ A )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2309_ent__iffI) ).

thf(316,plain,
    ! [A: assn,B: assn] :
      ( ( entails @ A @ B )
     => ( ( entails @ B @ A )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(97,axiom,
    ! [A: produc3658429121746597890et_nat] :
      ( ~ ( pp @ ( aa_Pro2991721470636411351t_bool @ one_assn_raw @ A ) )
     => ~ ! [B: heap_e7401611519738050253t_unit,C: set_nat] :
            ( ( A
              = ( produc7507926704131184380et_nat @ B @ C ) )
           => ( C = bot_bot_set_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10202_one__assn__raw_Oelims_I3_J) ).

thf(492,plain,
    ! [A: produc3658429121746597890et_nat] :
      ( ~ ( pp @ ( aa_Pro2991721470636411351t_bool @ one_assn_raw @ A ) )
     => ~ ! [B: heap_e7401611519738050253t_unit,C: set_nat] :
            ( ( A
              = ( produc7507926704131184380et_nat @ B @ C ) )
           => ( C = bot_bot_set_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(36,axiom,
    pp @ ( aa_hea1793595068369496646t_bool @ ( relH @ ( collect_nat @ aTP_Lamm_af ) @ h2 ) @ h ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_RH__G) ).

thf(238,plain,
    pp @ ( aa_hea1793595068369496646t_bool @ ( relH @ ( collect_nat @ aTP_Lamm_af ) @ h2 ) @ h ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(73,axiom,
    ( ( hoare_new_addrs @ h2 @ ( hoare_new_addrs @ h3 @ as @ h2 ) @ h )
    = ( hoare_new_addrs @ h3 @ as @ h ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__092_060open_062new__addrs_Ah_H_A_Inew__addrs_Ah_Aas_Ah_H_J_Ah_H_H_A_061_Anew__addrs_Ah_Aas_Ah_H_H_092_060close_062) ).

thf(397,plain,
    ( ( hoare_new_addrs @ h2 @ ( hoare_new_addrs @ h3 @ as @ h2 ) @ h )
    = ( hoare_new_addrs @ h3 @ as @ h ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(47,axiom,
    ! [A: a] : ( hoare_hoare_triple_b @ ( aa_a_assn @ r @ A ) @ ( aa_a_H8829438778223708363Heap_b @ g @ A ) @ q ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_T2) ).

thf(280,plain,
    ! [A: a] : ( hoare_hoare_triple_b @ ( aa_a_assn @ r @ A ) @ ( aa_a_H8829438778223708363Heap_b @ g @ A ) @ q ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(8,axiom,
    ! [A: fun_nat_bool] :
      ( ( bot_bot_set_nat
        = ( collect_nat @ A ) )
    <=> ! [B: nat] :
          ~ ( pp @ ( aa_nat_bool @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1759_empty__Collect__eq) ).

thf(133,plain,
    ! [A: fun_nat_bool] :
      ( ( ( bot_bot_set_nat
          = ( collect_nat @ A ) )
       => ! [B: nat] :
            ~ ( pp @ ( aa_nat_bool @ A @ B ) ) )
      & ( ! [B: nat] :
            ~ ( pp @ ( aa_nat_bool @ A @ B ) )
       => ( bot_bot_set_nat
          = ( collect_nat @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(43,axiom,
    ! [A: bool,B: heap_T5738788834812785303t_unit,C: fun_Pr6626665806141890376t_assn] :
      ( ( hoare_8945653483474564448t_unit @ ( aa_bool_assn @ pure_assn @ A ) @ B @ C )
    <=> ( ( pp @ A )
       => ( hoare_8945653483474564448t_unit @ one_one_assn @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2123_norm__pre__pure__iff__sng) ).

thf(265,plain,
    ! [A: bool,B: heap_T5738788834812785303t_unit,C: fun_Pr6626665806141890376t_assn] :
      ( ( ( hoare_8945653483474564448t_unit @ ( aa_bool_assn @ pure_assn @ A ) @ B @ C )
       => ( ( pp @ A )
         => ( hoare_8945653483474564448t_unit @ one_one_assn @ B @ C ) ) )
      & ( ( ( pp @ A )
         => ( hoare_8945653483474564448t_unit @ one_one_assn @ B @ C ) )
       => ( hoare_8945653483474564448t_unit @ ( aa_bool_assn @ pure_assn @ A ) @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(101,axiom,
    ! [A: assn,B: heap_T5738788834812785303t_unit,C: fun_Pr6626665806141890376t_assn,D: heap_e7401611519738050253t_unit,E: set_nat] :
      ( ( hoare_8945653483474564448t_unit @ A @ B @ C )
     => ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ A ) @ ( produc7507926704131184380et_nat @ D @ E ) ) )
       => ? [F: heap_e7401611519738050253t_unit,G: product_unit,H: nat] :
            ( ( pp @ ( aa_nat_bool @ ( heap_T6553295506729943825t_unit @ B @ D @ F @ G ) @ H ) )
            & ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ ( aa_Product_unit_assn @ C @ G ) ) @ ( produc7507926704131184380et_nat @ F @ ( hoare_new_addrs @ D @ E @ F ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_hoare__triple__effect) ).

thf(512,plain,
    ! [A: assn,B: heap_T5738788834812785303t_unit,C: fun_Pr6626665806141890376t_assn,D: heap_e7401611519738050253t_unit,E: set_nat] :
      ( ( hoare_8945653483474564448t_unit @ A @ B @ C )
     => ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ A ) @ ( produc7507926704131184380et_nat @ D @ E ) ) )
       => ? [F: heap_e7401611519738050253t_unit,G: product_unit,H: nat] :
            ( ( pp @ ( aa_nat_bool @ ( heap_T6553295506729943825t_unit @ B @ D @ F @ G ) @ H ) )
            & ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ ( aa_Product_unit_assn @ C @ G ) ) @ ( produc7507926704131184380et_nat @ F @ ( hoare_new_addrs @ D @ E @ F ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(30,axiom,
    ! [A: heap_Time_Heap_b,B: fun_b_assn] : ( hoare_hoare_triple_b @ bot_bot_assn @ A @ B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1995_false__rule) ).

thf(220,plain,
    ! [A: heap_Time_Heap_b,B: fun_b_assn] : ( hoare_hoare_triple_b @ bot_bot_assn @ A @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(63,axiom,
    ! [A: produc3658429121746597890et_nat] :
      ( ( pp @ ( aa_Pro2991721470636411351t_bool @ aTP_Lamm_gt @ A ) )
    <=> $false ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11298_ATP_Olambda__1092) ).

thf(349,plain,
    ! [A: produc3658429121746597890et_nat] :
      ~ ( pp @ ( aa_Pro2991721470636411351t_bool @ aTP_Lamm_gt @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(16,axiom,
    top_top_assn != one_one_assn,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9956_assn__basic__inequalities_I1_J) ).

thf(160,plain,
    top_top_assn != one_one_assn,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(78,axiom,
    ! [A: assn] :
      ( ( entails @ A @ bot_bot_assn )
    <=> ! [B: produc3658429121746597890et_nat] :
          ~ ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2239_ent__false__iff) ).

thf(424,plain,
    ! [A: assn] :
      ( ( ( entails @ A @ bot_bot_assn )
       => ! [B: produc3658429121746597890et_nat] :
            ~ ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ A ) @ B ) ) )
      & ( ! [B: produc3658429121746597890et_nat] :
            ~ ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ A ) @ B ) )
       => ( entails @ A @ bot_bot_assn ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(79,axiom,
    ! [A: assn,B: produc3658429121746597890et_nat] :
      ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ A ) @ B ) )
     => ( pp @ ( aa_Pro2991721470636411351t_bool @ in_range @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3653_models__in__range) ).

thf(429,plain,
    ! [A: assn,B: produc3658429121746597890et_nat] :
      ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ A ) @ B ) )
     => ( pp @ ( aa_Pro2991721470636411351t_bool @ in_range @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(45,axiom,
    ! [A: set_nat,B: heap_e7401611519738050253t_unit,C: heap_e7401611519738050253t_unit] :
      ( ( pp @ ( aa_hea1793595068369496646t_bool @ ( relH @ A @ B ) @ C ) )
     => ( pp @ ( aa_hea1793595068369496646t_bool @ ( relH @ A @ C ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_relH__sym) ).

thf(275,plain,
    ! [A: set_nat,B: heap_e7401611519738050253t_unit,C: heap_e7401611519738050253t_unit] :
      ( ( pp @ ( aa_hea1793595068369496646t_bool @ ( relH @ A @ B ) @ C ) )
     => ( pp @ ( aa_hea1793595068369496646t_bool @ ( relH @ A @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(95,axiom,
    ! [A: bool,B: produc3658429121746597890et_nat] :
      ( ~ ( pp @ ( aa_Pro2991721470636411351t_bool @ ( pure_a825153325127701367it_nat @ A ) @ B ) )
     => ~ ! [C: heap_e7401611519738050253t_unit,D: set_nat] :
            ( ( B
              = ( produc7507926704131184380et_nat @ C @ D ) )
           => ( ( D = bot_bot_set_nat )
              & ( pp @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2691_pure__assn__raw_Oelims_I3_J) ).

thf(484,plain,
    ! [A: bool,B: produc3658429121746597890et_nat] :
      ( ~ ( pp @ ( aa_Pro2991721470636411351t_bool @ ( pure_a825153325127701367it_nat @ A ) @ B ) )
     => ~ ! [C: heap_e7401611519738050253t_unit,D: set_nat] :
            ( ( B
              = ( produc7507926704131184380et_nat @ C @ D ) )
           => ( ( D = bot_bot_set_nat )
              & ( pp @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(40,axiom,
    ( bot_bot_assn
    = ( abs_assn @ aTP_Lamm_gt ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3849_bot__assn__def) ).

thf(252,plain,
    ( bot_bot_assn
    = ( abs_assn @ aTP_Lamm_gt ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(90,axiom,
    ! [A: assn,B: heap_e7401611519738050253t_unit,C: heap_e7401611519738050253t_unit] :
      ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ A ) @ ( produc7507926704131184380et_nat @ B @ bot_bot_set_nat ) ) )
    <=> ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ A ) @ ( produc7507926704131184380et_nat @ C @ bot_bot_set_nat ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1965_mod__h__bot__indep) ).

thf(461,plain,
    ! [A: assn,B: heap_e7401611519738050253t_unit,C: heap_e7401611519738050253t_unit] :
      ( ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ A ) @ ( produc7507926704131184380et_nat @ B @ bot_bot_set_nat ) ) )
       => ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ A ) @ ( produc7507926704131184380et_nat @ C @ bot_bot_set_nat ) ) ) )
      & ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ A ) @ ( produc7507926704131184380et_nat @ C @ bot_bot_set_nat ) ) )
       => ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ A ) @ ( produc7507926704131184380et_nat @ B @ bot_bot_set_nat ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(107,axiom,
    ! [A: heap_e7401611519738050253t_unit] : ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ top_top_assn ) @ ( produc7507926704131184380et_nat @ A @ bot_bot_set_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9965_mod__h__bot__iff_I2_J) ).

thf(551,plain,
    ! [A: heap_e7401611519738050253t_unit] : ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ top_top_assn ) @ ( produc7507926704131184380et_nat @ A @ bot_bot_set_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(87,axiom,
    pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ p ) @ ( produc7507926704131184380et_nat @ h3 @ as ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__092_060open_062_Ih_M_Aas_J_A_092_060Turnstile_062_AP_092_060close_062) ).

thf(456,plain,
    pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ p ) @ ( produc7507926704131184380et_nat @ h3 @ as ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(49,axiom,
    ! [A: product_unit] :
      ( ( aa_Product_unit_assn @ aTP_Lamm_ey @ A )
      = one_one_assn ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11289_ATP_Olambda__1083) ).

thf(285,plain,
    ! [A: product_unit] :
      ( ( aa_Product_unit_assn @ aTP_Lamm_ey @ A )
      = one_one_assn ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(103,axiom,
    ! [A: assn,B: heap_T5738788834812785303t_unit,C: fun_Pr6626665806141890376t_assn] :
      ( ! [D: produc3658429121746597890et_nat] :
          ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ A ) @ D ) )
         => ( hoare_8945653483474564448t_unit @ A @ B @ C ) )
     => ( hoare_8945653483474564448t_unit @ A @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_hoare__triple__preI) ).

thf(519,plain,
    ! [A: assn,B: heap_T5738788834812785303t_unit,C: fun_Pr6626665806141890376t_assn] :
      ( ! [D: produc3658429121746597890et_nat] :
          ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ A ) @ D ) )
         => ( hoare_8945653483474564448t_unit @ A @ B @ C ) )
     => ( hoare_8945653483474564448t_unit @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(10,axiom,
    ( bot_bot_set_nat
    = ( collect_nat @ aTP_Lamm_eo ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1900_Set_Oempty__def) ).

thf(141,plain,
    ( bot_bot_set_nat
    = ( collect_nat @ aTP_Lamm_eo ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(1,conjecture,
    pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ ( aa_b_assn @ q @ rg ) ) @ ( produc7507926704131184380et_nat @ h @ ( hoare_new_addrs @ h3 @ as @ h ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

thf(2,negated_conjecture,
    ~ ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ ( aa_b_assn @ q @ rg ) ) @ ( produc7507926704131184380et_nat @ h @ ( hoare_new_addrs @ h3 @ as @ h ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(109,plain,
    ~ ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ ( aa_b_assn @ q @ rg ) ) @ ( produc7507926704131184380et_nat @ h @ ( hoare_new_addrs @ h3 @ as @ h ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(32,axiom,
    ( ( aa_bool_assn @ pure_assn @ fFalse )
    = bot_bot_assn ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2120_pure__false) ).

thf(225,plain,
    ( ( aa_bool_assn @ pure_assn @ fFalse )
    = bot_bot_assn ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(96,axiom,
    ! [A: assn] :
      ( ( abs_assn @ ( rep_assn @ A ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3701_Rep__assn__inverse) ).

thf(489,plain,
    ! [A: assn] :
      ( ( abs_assn @ ( rep_assn @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(27,axiom,
    ! [A: assn,B: assn,C: heap_Time_Heap_b,D: fun_b_assn] :
      ( ( entails @ A @ B )
     => ( ( hoare_hoare_triple_b @ B @ C @ D )
       => ( hoare_hoare_triple_b @ A @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2567_cons__pre__rule) ).

thf(212,plain,
    ! [A: assn,B: assn,C: heap_Time_Heap_b,D: fun_b_assn] :
      ( ( entails @ A @ B )
     => ( ( hoare_hoare_triple_b @ B @ C @ D )
       => ( hoare_hoare_triple_b @ A @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(72,axiom,
    ! [A: assn,B: heap_Time_Heap_b,C: fun_b_assn,D: heap_e7401611519738050253t_unit,E: set_nat] :
      ( ( hoare_hoare_triple_b @ A @ B @ C )
     => ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ A ) @ ( produc7507926704131184380et_nat @ D @ E ) ) )
       => ? [F: heap_e7401611519738050253t_unit,G: b,H: nat] :
            ( ( pp @ ( aa_nat_bool @ ( heap_Time_effect_b @ B @ D @ F @ G ) @ H ) )
            & ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ ( aa_b_assn @ C @ G ) ) @ ( produc7507926704131184380et_nat @ F @ ( hoare_new_addrs @ D @ E @ F ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_hoare__triple__effect) ).

thf(393,plain,
    ! [A: assn,B: heap_Time_Heap_b,C: fun_b_assn,D: heap_e7401611519738050253t_unit,E: set_nat] :
      ( ( hoare_hoare_triple_b @ A @ B @ C )
     => ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ A ) @ ( produc7507926704131184380et_nat @ D @ E ) ) )
       => ? [F: heap_e7401611519738050253t_unit,G: b,H: nat] :
            ( ( pp @ ( aa_nat_bool @ ( heap_Time_effect_b @ B @ D @ F @ G ) @ H ) )
            & ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ ( aa_b_assn @ C @ G ) ) @ ( produc7507926704131184380et_nat @ F @ ( hoare_new_addrs @ D @ E @ F ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(88,axiom,
    pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ ( aa_a_assn @ r @ rf ) ) @ ( produc7507926704131184380et_nat @ h2 @ ( hoare_new_addrs @ h3 @ as @ h2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_POST__F) ).

thf(457,plain,
    pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ ( aa_a_assn @ r @ rf ) ) @ ( produc7507926704131184380et_nat @ h2 @ ( hoare_new_addrs @ h3 @ as @ h2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(35,axiom,
    hoare_hoare_triple_a @ p @ f @ r,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_T1) ).

thf(237,plain,
    hoare_hoare_triple_a @ p @ f @ r,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(66,axiom,
    ! [A: assn,B: heap_Time_Heap_a,C: fun_a_assn] :
      ( ! [D: produc3658429121746597890et_nat] :
          ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ A ) @ D ) )
         => ( hoare_hoare_triple_a @ A @ B @ C ) )
     => ( hoare_hoare_triple_a @ A @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_hoare__triple__preI) ).

thf(360,plain,
    ! [A: assn,B: heap_Time_Heap_a,C: fun_a_assn] :
      ( ! [D: produc3658429121746597890et_nat] :
          ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ A ) @ D ) )
         => ( hoare_hoare_triple_a @ A @ B @ C ) )
     => ( hoare_hoare_triple_a @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(100,axiom,
    ! [A: assn,B: heap_Time_Heap_a,C: fun_a_assn,D: heap_e7401611519738050253t_unit,E: set_nat] :
      ( ( hoare_hoare_triple_a @ A @ B @ C )
     => ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ A ) @ ( produc7507926704131184380et_nat @ D @ E ) ) )
       => ? [F: heap_e7401611519738050253t_unit,G: a,H: nat] :
            ( ( pp @ ( aa_nat_bool @ ( heap_Time_effect_a @ B @ D @ F @ G ) @ H ) )
            & ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ ( aa_a_assn @ C @ G ) ) @ ( produc7507926704131184380et_nat @ F @ ( hoare_new_addrs @ D @ E @ F ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_hoare__triple__effect) ).

thf(508,plain,
    ! [A: assn,B: heap_Time_Heap_a,C: fun_a_assn,D: heap_e7401611519738050253t_unit,E: set_nat] :
      ( ( hoare_hoare_triple_a @ A @ B @ C )
     => ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ A ) @ ( produc7507926704131184380et_nat @ D @ E ) ) )
       => ? [F: heap_e7401611519738050253t_unit,G: a,H: nat] :
            ( ( pp @ ( aa_nat_bool @ ( heap_Time_effect_a @ B @ D @ F @ G ) @ H ) )
            & ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ ( aa_a_assn @ C @ G ) ) @ ( produc7507926704131184380et_nat @ F @ ( hoare_new_addrs @ D @ E @ F ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(55,axiom,
    ! [A: assn,B: assn,C: fun_Pr6626665806141890376t_assn,D: fun_Pr6626665806141890376t_assn,E: heap_T5738788834812785303t_unit] :
      ( ( entails @ A @ B )
     => ( ! [F: product_unit] : ( entails @ ( aa_Product_unit_assn @ C @ F ) @ ( aa_Product_unit_assn @ D @ F ) )
       => ( ( hoare_8945653483474564448t_unit @ B @ E @ C )
         => ( hoare_8945653483474564448t_unit @ A @ E @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2522_cons__rule) ).

thf(311,plain,
    ! [A: assn,B: assn,C: fun_Pr6626665806141890376t_assn,D: fun_Pr6626665806141890376t_assn,E: heap_T5738788834812785303t_unit] :
      ( ( entails @ A @ B )
     => ( ! [F: product_unit] : ( entails @ ( aa_Product_unit_assn @ C @ F ) @ ( aa_Product_unit_assn @ D @ F ) )
       => ( ( hoare_8945653483474564448t_unit @ B @ E @ C )
         => ( hoare_8945653483474564448t_unit @ A @ E @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(105,axiom,
    ! [A: bool,B: produc3658429121746597890et_nat,C: bool] :
      ( ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( pure_a825153325127701367it_nat @ A ) @ B ) )
      <=> ( pp @ C ) )
     => ~ ! [D: heap_e7401611519738050253t_unit,E: set_nat] :
            ( ( B
              = ( produc7507926704131184380et_nat @ D @ E ) )
           => ( ( pp @ C )
            <=> ~ ( ( E = bot_bot_set_nat )
                  & ( pp @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2139_pure__assn__raw_Oelims_I1_J) ).

thf(530,plain,
    ! [A: bool,B: produc3658429121746597890et_nat,C: bool] :
      ( ( ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( pure_a825153325127701367it_nat @ A ) @ B ) )
         => ( pp @ C ) )
        & ( ( pp @ C )
         => ( pp @ ( aa_Pro2991721470636411351t_bool @ ( pure_a825153325127701367it_nat @ A ) @ B ) ) ) )
     => ~ ! [D: heap_e7401611519738050253t_unit,E: set_nat] :
            ( ( B
              = ( produc7507926704131184380et_nat @ D @ E ) )
           => ( ( ( pp @ C )
               => ~ ( ( E = bot_bot_set_nat )
                    & ( pp @ A ) ) )
              & ( ~ ( ( E = bot_bot_set_nat )
                    & ( pp @ A ) )
               => ( pp @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(22,axiom,
    ! [A: heap_e7401611519738050253t_unit,B: set_nat] :
      ( ( pp @ ( aa_Pro2991721470636411351t_bool @ in_range @ ( produc7507926704131184380et_nat @ A @ B ) ) )
     => ( pp @ ( aa_hea1793595068369496646t_bool @ ( relH @ B @ A ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3656_relH__refl) ).

thf(180,plain,
    ! [A: heap_e7401611519738050253t_unit,B: set_nat] :
      ( ( pp @ ( aa_Pro2991721470636411351t_bool @ in_range @ ( produc7507926704131184380et_nat @ A @ B ) ) )
     => ( pp @ ( aa_hea1793595068369496646t_bool @ ( relH @ B @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(83,axiom,
    ! [A: assn,B: heap_T5738788834812785303t_unit,C: fun_Pr6626665806141890376t_assn,D: heap_e7401611519738050253t_unit,E: set_nat] :
      ( ( hoare_8945653483474564448t_unit @ A @ B @ C )
     => ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ A ) @ ( produc7507926704131184380et_nat @ D @ E ) ) )
       => ( pp @ ( aa_hea1793595068369496646t_bool @ ( heap_T584514906347983379t_unit @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_hoare__triple__success) ).

thf(444,plain,
    ! [A: assn,B: heap_T5738788834812785303t_unit,C: fun_Pr6626665806141890376t_assn,D: heap_e7401611519738050253t_unit,E: set_nat] :
      ( ( hoare_8945653483474564448t_unit @ A @ B @ C )
     => ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ A ) @ ( produc7507926704131184380et_nat @ D @ E ) ) )
       => ( pp @ ( aa_hea1793595068369496646t_bool @ ( heap_T584514906347983379t_unit @ B ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(69,axiom,
    ! [A: assn,B: heap_Time_Heap_b,C: fun_b_assn] :
      ( ! [D: produc3658429121746597890et_nat] :
          ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ A ) @ D ) )
         => ( hoare_hoare_triple_b @ A @ B @ C ) )
     => ( hoare_hoare_triple_b @ A @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_hoare__triple__preI) ).

thf(375,plain,
    ! [A: assn,B: heap_Time_Heap_b,C: fun_b_assn] :
      ( ! [D: produc3658429121746597890et_nat] :
          ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ A ) @ D ) )
         => ( hoare_hoare_triple_b @ A @ B @ C ) )
     => ( hoare_hoare_triple_b @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(19,axiom,
    ! [A: heap_Time_Heap_a,B: fun_a_assn] : ( hoare_hoare_triple_a @ bot_bot_assn @ A @ B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1994_false__rule) ).

thf(172,plain,
    ! [A: heap_Time_Heap_a,B: fun_a_assn] : ( hoare_hoare_triple_a @ bot_bot_assn @ A @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(34,axiom,
    ! [A: bool] :
      ( ( ( aa_bool_assn @ pure_assn @ A )
        = one_one_assn )
    <=> ( pp @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2117_pure__assn__eq__emp__iff) ).

thf(230,plain,
    ! [A: bool] :
      ( ( ( ( aa_bool_assn @ pure_assn @ A )
          = one_one_assn )
       => ( pp @ A ) )
      & ( ( pp @ A )
       => ( ( aa_bool_assn @ pure_assn @ A )
          = one_one_assn ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(81,axiom,
    ! [A: assn,B: assn,C: produc3658429121746597890et_nat] :
      ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( aa_ass8975924923219239432t_bool @ ( aTP_Lamm_gu @ A ) @ B ) @ C ) )
    <=> ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ A ) @ C ) )
        | ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10681_ATP_Olambda__475) ).

thf(434,plain,
    ! [A: assn,B: assn,C: produc3658429121746597890et_nat] :
      ( ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( aa_ass8975924923219239432t_bool @ ( aTP_Lamm_gu @ A ) @ B ) @ C ) )
       => ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ A ) @ C ) )
          | ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ B ) @ C ) ) ) )
      & ( ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ A ) @ C ) )
          | ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ B ) @ C ) ) )
       => ( pp @ ( aa_Pro2991721470636411351t_bool @ ( aa_ass8975924923219239432t_bool @ ( aTP_Lamm_gu @ A ) @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(52,axiom,
    ! [A: set_nat,B: heap_e7401611519738050253t_unit,C: heap_e7401611519738050253t_unit] :
      ( ( pp @ ( aa_hea1793595068369496646t_bool @ ( relH @ A @ B ) @ C ) )
     => ( pp @ ( aa_Pro2991721470636411351t_bool @ in_range @ ( produc7507926704131184380et_nat @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3655_relH__in__rangeI_I1_J) ).

thf(303,plain,
    ! [A: set_nat,B: heap_e7401611519738050253t_unit,C: heap_e7401611519738050253t_unit] :
      ( ( pp @ ( aa_hea1793595068369496646t_bool @ ( relH @ A @ B ) @ C ) )
     => ( pp @ ( aa_Pro2991721470636411351t_bool @ in_range @ ( produc7507926704131184380et_nat @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(9,axiom,
    pp @ ( aa_hea1793595068369496646t_bool @ ( relH @ ( collect_nat @ aTP_Lamm_ag ) @ h3 ) @ h2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_RH__F) ).

thf(140,plain,
    pp @ ( aa_hea1793595068369496646t_bool @ ( relH @ ( collect_nat @ aTP_Lamm_ag ) @ h3 ) @ h2 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(14,axiom,
    ! [A: assn,B: assn,C: heap_T5738788834812785303t_unit,D: fun_Pr6626665806141890376t_assn] :
      ( ( entails @ A @ B )
     => ( ( hoare_8945653483474564448t_unit @ B @ C @ D )
       => ( hoare_8945653483474564448t_unit @ A @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2568_cons__pre__rule) ).

thf(155,plain,
    ! [A: assn,B: assn,C: heap_T5738788834812785303t_unit,D: fun_Pr6626665806141890376t_assn] :
      ( ( entails @ A @ B )
     => ( ( hoare_8945653483474564448t_unit @ B @ C @ D )
       => ( hoare_8945653483474564448t_unit @ A @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(74,axiom,
    ! [A: fun_Pr6001797050664311790t_bool,B: assn] :
      ( ! [C: produc3658429121746597890et_nat] :
          ( ( pp @ ( aa_Pro2991721470636411351t_bool @ A @ C ) )
        <=> ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ B ) @ C ) ) )
     => ( B
        = ( abs_assn @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3811_Abs__assn__eqI_I2_J) ).

thf(399,plain,
    ! [A: fun_Pr6001797050664311790t_bool,B: assn] :
      ( ! [C: produc3658429121746597890et_nat] :
          ( ( ( pp @ ( aa_Pro2991721470636411351t_bool @ A @ C ) )
           => ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ B ) @ C ) ) )
          & ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ B ) @ C ) )
           => ( pp @ ( aa_Pro2991721470636411351t_bool @ A @ C ) ) ) )
     => ( B
        = ( abs_assn @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(53,axiom,
    ! [A: bool,B: heap_Time_Heap_b,C: fun_b_assn] :
      ( ( ( pp @ A )
       => ( hoare_hoare_triple_b @ one_one_assn @ B @ C ) )
     => ( hoare_hoare_triple_b @ ( aa_bool_assn @ pure_assn @ A ) @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2125_norm__pre__pure__rule2) ).

thf(306,plain,
    ! [A: bool,B: heap_Time_Heap_b,C: fun_b_assn] :
      ( ( ( pp @ A )
       => ( hoare_hoare_triple_b @ one_one_assn @ B @ C ) )
     => ( hoare_hoare_triple_b @ ( aa_bool_assn @ pure_assn @ A ) @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(80,axiom,
    ! [A: assn,B: heap_Time_Heap_a,C: fun_a_assn,D: heap_e7401611519738050253t_unit,E: set_nat] :
      ( ( hoare_hoare_triple_a @ A @ B @ C )
     => ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ A ) @ ( produc7507926704131184380et_nat @ D @ E ) ) )
       => ( pp @ ( aa_hea1793595068369496646t_bool @ ( heap_Time_success_a @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_hoare__triple__success) ).

thf(431,plain,
    ! [A: assn,B: heap_Time_Heap_a,C: fun_a_assn,D: heap_e7401611519738050253t_unit,E: set_nat] :
      ( ( hoare_hoare_triple_a @ A @ B @ C )
     => ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ A ) @ ( produc7507926704131184380et_nat @ D @ E ) ) )
       => ( pp @ ( aa_hea1793595068369496646t_bool @ ( heap_Time_success_a @ B ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(26,axiom,
    top_top_assn != bot_bot_assn,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9957_assn__basic__inequalities_I5_J) ).

thf(209,plain,
    top_top_assn != bot_bot_assn,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(4,axiom,
    ! [A: fun_nat_bool] :
      ( ( ( collect_nat @ A )
        = bot_bot_set_nat )
    <=> ! [B: nat] :
          ~ ( pp @ ( aa_nat_bool @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1766_Collect__empty__eq) ).

thf(112,plain,
    ! [A: fun_nat_bool] :
      ( ( ( ( collect_nat @ A )
          = bot_bot_set_nat )
       => ! [B: nat] :
            ~ ( pp @ ( aa_nat_bool @ A @ B ) ) )
      & ( ! [B: nat] :
            ~ ( pp @ ( aa_nat_bool @ A @ B ) )
       => ( ( collect_nat @ A )
          = bot_bot_set_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(102,axiom,
    ! [A: produc3658429121746597890et_nat] :
      ~ ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ bot_bot_assn ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2018_mod__false) ).

thf(516,plain,
    ! [A: produc3658429121746597890et_nat] :
      ~ ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ bot_bot_assn ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(7,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ! [C: nat] :
          ( ( pp @ ( aa_nat_bool @ A @ C ) )
        <=> ( pp @ ( aa_nat_bool @ B @ C ) ) )
     => ( ( collect_nat @ A )
        = ( collect_nat @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_Collect__cong) ).

thf(123,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ! [C: nat] :
          ( ( ( pp @ ( aa_nat_bool @ A @ C ) )
           => ( pp @ ( aa_nat_bool @ B @ C ) ) )
          & ( ( pp @ ( aa_nat_bool @ B @ C ) )
           => ( pp @ ( aa_nat_bool @ A @ C ) ) ) )
     => ( ( collect_nat @ A )
        = ( collect_nat @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(108,axiom,
    ! [A: bool,B: heap_e7401611519738050253t_unit] :
      ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ ( aa_bool_assn @ pure_assn @ A ) ) @ ( produc7507926704131184380et_nat @ B @ bot_bot_set_nat ) ) )
    <=> ( pp @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2114_mod__h__bot__iff_I1_J) ).

thf(553,plain,
    ! [A: bool,B: heap_e7401611519738050253t_unit] :
      ( ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ ( aa_bool_assn @ pure_assn @ A ) ) @ ( produc7507926704131184380et_nat @ B @ bot_bot_set_nat ) ) )
       => ( pp @ A ) )
      & ( ( pp @ A )
       => ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ ( aa_bool_assn @ pure_assn @ A ) ) @ ( produc7507926704131184380et_nat @ B @ bot_bot_set_nat ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(89,axiom,
    ! [A: heap_e7401611519738050253t_unit,B: set_nat] :
      ( ( hoare_new_addrs @ A @ B @ A )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_new__addr__refl) ).

thf(458,plain,
    ! [A: heap_e7401611519738050253t_unit,B: set_nat] :
      ( ( hoare_new_addrs @ A @ B @ A )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(51,axiom,
    ! [A: fun_Pr7757163693017731481t_bool,B: fun_Pr248683899324676269t_bool,C: product_prod_nat_nat,D: fun_Pr7757163693017731481t_bool] :
      ( ( pp @ ( aa_fun8663595511526100224l_bool @ ( ord_le2468614981408567801t_bool @ A ) @ ( accp_P4275260045618599050at_nat @ B ) ) )
     => ( ! [E: product_prod_nat_nat,F: product_prod_nat_nat] :
            ( ( pp @ ( aa_Pro2232559814647311250t_bool @ A @ E ) )
           => ( ( pp @ ( aa_Pro2232559814647311250t_bool @ ( aa_Pro595088089689268830t_bool @ B @ F ) @ E ) )
             => ( pp @ ( aa_Pro2232559814647311250t_bool @ A @ F ) ) ) )
       => ( ( pp @ ( aa_Pro2232559814647311250t_bool @ A @ C ) )
         => ( ! [E: product_prod_nat_nat] :
                ( ( pp @ ( aa_Pro2232559814647311250t_bool @ A @ E ) )
               => ( ! [F: product_prod_nat_nat] :
                      ( ( pp @ ( aa_Pro2232559814647311250t_bool @ ( aa_Pro595088089689268830t_bool @ B @ F ) @ E ) )
                     => ( pp @ ( aa_Pro2232559814647311250t_bool @ D @ F ) ) )
                 => ( pp @ ( aa_Pro2232559814647311250t_bool @ D @ E ) ) ) )
           => ( pp @ ( aa_Pro2232559814647311250t_bool @ D @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1734_accp__subset__induct) ).

thf(295,plain,
    ! [A: fun_Pr7757163693017731481t_bool,B: fun_Pr248683899324676269t_bool,C: product_prod_nat_nat,D: fun_Pr7757163693017731481t_bool] :
      ( ( pp @ ( aa_fun8663595511526100224l_bool @ ( ord_le2468614981408567801t_bool @ A ) @ ( accp_P4275260045618599050at_nat @ B ) ) )
     => ( ! [E: product_prod_nat_nat,F: product_prod_nat_nat] :
            ( ( pp @ ( aa_Pro2232559814647311250t_bool @ A @ E ) )
           => ( ( pp @ ( aa_Pro2232559814647311250t_bool @ ( aa_Pro595088089689268830t_bool @ B @ F ) @ E ) )
             => ( pp @ ( aa_Pro2232559814647311250t_bool @ A @ F ) ) ) )
       => ( ( pp @ ( aa_Pro2232559814647311250t_bool @ A @ C ) )
         => ( ! [E: product_prod_nat_nat] :
                ( ( pp @ ( aa_Pro2232559814647311250t_bool @ A @ E ) )
               => ( ! [F: product_prod_nat_nat] :
                      ( ( pp @ ( aa_Pro2232559814647311250t_bool @ ( aa_Pro595088089689268830t_bool @ B @ F ) @ E ) )
                     => ( pp @ ( aa_Pro2232559814647311250t_bool @ D @ F ) ) )
                 => ( pp @ ( aa_Pro2232559814647311250t_bool @ D @ E ) ) ) )
           => ( pp @ ( aa_Pro2232559814647311250t_bool @ D @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(48,axiom,
    ! [A: assn,B: heap_Time_Heap_a,C: fun_a_assn,D: fun_a_assn] :
      ( ( hoare_hoare_triple_a @ A @ B @ C )
     => ( ! [E: a] : ( entails @ ( aa_a_assn @ C @ E ) @ ( aa_a_assn @ D @ E ) )
       => ( hoare_hoare_triple_a @ A @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2517_cons__post__rule) ).

thf(282,plain,
    ! [A: assn,B: heap_Time_Heap_a,C: fun_a_assn,D: fun_a_assn] :
      ( ( hoare_hoare_triple_a @ A @ B @ C )
     => ( ! [E: a] : ( entails @ ( aa_a_assn @ C @ E ) @ ( aa_a_assn @ D @ E ) )
       => ( hoare_hoare_triple_a @ A @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(12,axiom,
    ! [A: bool] :
      ( ( aa_bool_assn @ pure_assn @ A )
      = ( abs_assn @ ( pure_a825153325127701367it_nat @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3812_pure__assn__def) ).

thf(150,plain,
    ! [A: bool] :
      ( ( aa_bool_assn @ pure_assn @ A )
      = ( abs_assn @ ( pure_a825153325127701367it_nat @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(76,axiom,
    ! [A: heap_e7401611519738050253t_unit] : ( pp @ ( aa_Pro2991721470636411351t_bool @ in_range @ ( produc7507926704131184380et_nat @ A @ bot_bot_set_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3646_in__range__empty) ).

thf(414,plain,
    ! [A: heap_e7401611519738050253t_unit] : ( pp @ ( aa_Pro2991721470636411351t_bool @ in_range @ ( produc7507926704131184380et_nat @ A @ bot_bot_set_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(61,axiom,
    ! [A: produc3658429121746597890et_nat,B: bool] :
      ( ( ( pp @ ( aa_Pro2991721470636411351t_bool @ one_assn_raw @ A ) )
      <=> ( pp @ B ) )
     => ~ ! [C: heap_e7401611519738050253t_unit,D: set_nat] :
            ( ( A
              = ( produc7507926704131184380et_nat @ C @ D ) )
           => ( ( pp @ B )
            <=> ( D != bot_bot_set_nat ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10200_one__assn__raw_Oelims_I1_J) ).

thf(327,plain,
    ! [A: produc3658429121746597890et_nat,B: bool] :
      ( ( ( ( pp @ ( aa_Pro2991721470636411351t_bool @ one_assn_raw @ A ) )
         => ( pp @ B ) )
        & ( ( pp @ B )
         => ( pp @ ( aa_Pro2991721470636411351t_bool @ one_assn_raw @ A ) ) ) )
     => ~ ! [C: heap_e7401611519738050253t_unit,D: set_nat] :
            ( ( A
              = ( produc7507926704131184380et_nat @ C @ D ) )
           => ( ( ( pp @ B )
               => ( D != bot_bot_set_nat ) )
              & ( ( D != bot_bot_set_nat )
               => ( pp @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(75,axiom,
    ! [A: produc3658429121746597890et_nat] :
      ( ( pp @ ( aa_Pro2991721470636411351t_bool @ one_assn_raw @ A ) )
     => ~ ! [B: heap_e7401611519738050253t_unit,C: set_nat] :
            ( ( A
              = ( produc7507926704131184380et_nat @ B @ C ) )
           => ( C != bot_bot_set_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10201_one__assn__raw_Oelims_I2_J) ).

thf(409,plain,
    ! [A: produc3658429121746597890et_nat] :
      ( ( pp @ ( aa_Pro2991721470636411351t_bool @ one_assn_raw @ A ) )
     => ~ ! [B: heap_e7401611519738050253t_unit,C: set_nat] :
            ( ( A
              = ( produc7507926704131184380et_nat @ B @ C ) )
           => ( C != bot_bot_set_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(82,axiom,
    ! [A: assn,B: assn,C: produc3658429121746597890et_nat] :
      ( ( entails @ A @ B )
     => ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ A ) @ C ) )
       => ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2499_entailsD) ).

thf(441,plain,
    ! [A: assn,B: assn,C: produc3658429121746597890et_nat] :
      ( ( entails @ A @ B )
     => ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ A ) @ C ) )
       => ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(99,axiom,
    ! [A: bool,B: produc3658429121746597890et_nat] :
      ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( pure_a825153325127701367it_nat @ A ) @ B ) )
     => ~ ! [C: heap_e7401611519738050253t_unit,D: set_nat] :
            ( ( B
              = ( produc7507926704131184380et_nat @ C @ D ) )
           => ~ ( ( D = bot_bot_set_nat )
                & ( pp @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2140_pure__assn__raw_Oelims_I2_J) ).

thf(502,plain,
    ! [A: bool,B: produc3658429121746597890et_nat] :
      ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( pure_a825153325127701367it_nat @ A ) @ B ) )
     => ~ ! [C: heap_e7401611519738050253t_unit,D: set_nat] :
            ( ( B
              = ( produc7507926704131184380et_nat @ C @ D ) )
           => ~ ( ( D = bot_bot_set_nat )
                & ( pp @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(106,axiom,
    ! [A: heap_e7401611519738050253t_unit,B: set_nat] :
      ( ( pp @ ( aa_Pro2991721470636411351t_bool @ one_assn_raw @ ( produc7507926704131184380et_nat @ A @ B ) ) )
    <=> ( B = bot_bot_set_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10199_one__assn__raw_Osimps) ).

thf(544,plain,
    ! [A: heap_e7401611519738050253t_unit,B: set_nat] :
      ( ( ( pp @ ( aa_Pro2991721470636411351t_bool @ one_assn_raw @ ( produc7507926704131184380et_nat @ A @ B ) ) )
       => ( B = bot_bot_set_nat ) )
      & ( ( B = bot_bot_set_nat )
       => ( pp @ ( aa_Pro2991721470636411351t_bool @ one_assn_raw @ ( produc7507926704131184380et_nat @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(21,axiom,
    bot_bot_assn != one_one_assn,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2050_assn__basic__inequalities_I3_J) ).

thf(177,plain,
    bot_bot_assn != one_one_assn,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(23,axiom,
    ! [A: bool] :
      ( ( ( aa_bool_assn @ pure_assn @ A )
        = bot_bot_assn )
    <=> ~ ( pp @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2119_pure__assn__eq__false__iff) ).

thf(182,plain,
    ! [A: bool] :
      ( ( ( ( aa_bool_assn @ pure_assn @ A )
          = bot_bot_assn )
       => ~ ( pp @ A ) )
      & ( ~ ( pp @ A )
       => ( ( aa_bool_assn @ pure_assn @ A )
          = bot_bot_assn ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(56,axiom,
    ! [A: assn] : ( entails @ A @ top_top_assn ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9960_ent__true) ).

thf(314,plain,
    ! [A: assn] : ( entails @ A @ top_top_assn ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(11,axiom,
    ! [A: bool,B: assn] :
      ( ( entails @ ( aa_bool_assn @ pure_assn @ A ) @ B )
    <=> ( ( pp @ A )
       => ( entails @ one_one_assn @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2240_ent__pure__pre__iff__sng) ).

thf(143,plain,
    ! [A: bool,B: assn] :
      ( ( ( entails @ ( aa_bool_assn @ pure_assn @ A ) @ B )
       => ( ( pp @ A )
         => ( entails @ one_one_assn @ B ) ) )
      & ( ( ( pp @ A )
         => ( entails @ one_one_assn @ B ) )
       => ( entails @ ( aa_bool_assn @ pure_assn @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(98,axiom,
    ! [A: set_nat,B: heap_e7401611519738050253t_unit,C: heap_e7401611519738050253t_unit,D: assn] :
      ( ( pp @ ( aa_hea1793595068369496646t_bool @ ( relH @ A @ B ) @ C ) )
     => ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ D ) @ ( produc7507926704131184380et_nat @ B @ A ) ) )
      <=> ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ D ) @ ( produc7507926704131184380et_nat @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_548_mod__relH) ).

thf(497,plain,
    ! [A: set_nat,B: heap_e7401611519738050253t_unit,C: heap_e7401611519738050253t_unit,D: assn] :
      ( ( pp @ ( aa_hea1793595068369496646t_bool @ ( relH @ A @ B ) @ C ) )
     => ( ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ D ) @ ( produc7507926704131184380et_nat @ B @ A ) ) )
         => ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ D ) @ ( produc7507926704131184380et_nat @ C @ A ) ) ) )
        & ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ D ) @ ( produc7507926704131184380et_nat @ C @ A ) ) )
         => ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ D ) @ ( produc7507926704131184380et_nat @ B @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(58,axiom,
    ! [A: bool,B: heap_Time_Heap_a,C: fun_a_assn] :
      ( ( ( pp @ A )
       => ( hoare_hoare_triple_a @ one_one_assn @ B @ C ) )
     => ( hoare_hoare_triple_a @ ( aa_bool_assn @ pure_assn @ A ) @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2124_norm__pre__pure__rule2) ).

thf(319,plain,
    ! [A: bool,B: heap_Time_Heap_a,C: fun_a_assn] :
      ( ( ( pp @ A )
       => ( hoare_hoare_triple_a @ one_one_assn @ B @ C ) )
     => ( hoare_hoare_triple_a @ ( aa_bool_assn @ pure_assn @ A ) @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(15,axiom,
    ( top_top_assn
    = ( abs_assn @ in_range ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9964_top__assn__def) ).

thf(158,plain,
    ( top_top_assn
    = ( abs_assn @ in_range ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(5,axiom,
    ! [A: bool] :
      ( ( A = fTrue )
      | ( A = fFalse ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_If_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_T) ).

thf(119,plain,
    ! [A: bool] :
      ( ( A = fTrue )
      | ( A = fFalse ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(25,axiom,
    ! [A: set_nat,B: heap_e7401611519738050253t_unit,C: heap_e7401611519738050253t_unit] :
      ( ( pp @ ( aa_hea1793595068369496646t_bool @ ( relH @ A @ B ) @ C ) )
     => ( pp @ ( aa_Pro2991721470636411351t_bool @ in_range @ ( produc7507926704131184380et_nat @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3654_relH__in__rangeI_I2_J) ).

thf(207,plain,
    ! [A: set_nat,B: heap_e7401611519738050253t_unit,C: heap_e7401611519738050253t_unit] :
      ( ( pp @ ( aa_hea1793595068369496646t_bool @ ( relH @ A @ B ) @ C ) )
     => ( pp @ ( aa_Pro2991721470636411351t_bool @ in_range @ ( produc7507926704131184380et_nat @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(44,axiom,
    ! [A: assn,B: assn,C: fun_a_assn,D: fun_a_assn,E: heap_Time_Heap_a] :
      ( ( entails @ A @ B )
     => ( ! [F: a] : ( entails @ ( aa_a_assn @ C @ F ) @ ( aa_a_assn @ D @ F ) )
       => ( ( hoare_hoare_triple_a @ B @ E @ C )
         => ( hoare_hoare_triple_a @ A @ E @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2520_cons__rule) ).

thf(272,plain,
    ! [A: assn,B: assn,C: fun_a_assn,D: fun_a_assn,E: heap_Time_Heap_a] :
      ( ( entails @ A @ B )
     => ( ! [F: a] : ( entails @ ( aa_a_assn @ C @ F ) @ ( aa_a_assn @ D @ F ) )
       => ( ( hoare_hoare_triple_a @ B @ E @ C )
         => ( hoare_hoare_triple_a @ A @ E @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(84,axiom,
    pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ ( aa_b_assn @ q @ rg ) ) @ ( produc7507926704131184380et_nat @ h @ ( hoare_new_addrs @ h2 @ ( hoare_new_addrs @ h3 @ as @ h2 ) @ h ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_POST__G) ).

thf(447,plain,
    pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ ( aa_b_assn @ q @ rg ) ) @ ( produc7507926704131184380et_nat @ h @ ( hoare_new_addrs @ h2 @ ( hoare_new_addrs @ h3 @ as @ h2 ) @ h ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(42,axiom,
    ! [A: assn,B: heap_Time_Heap_b,C: fun_b_assn,D: fun_b_assn] :
      ( ( hoare_hoare_triple_b @ A @ B @ C )
     => ( ! [E: b] : ( entails @ ( aa_b_assn @ C @ E ) @ ( aa_b_assn @ D @ E ) )
       => ( hoare_hoare_triple_b @ A @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2518_cons__post__rule) ).

thf(262,plain,
    ! [A: assn,B: heap_Time_Heap_b,C: fun_b_assn,D: fun_b_assn] :
      ( ( hoare_hoare_triple_b @ A @ B @ C )
     => ( ! [E: b] : ( entails @ ( aa_b_assn @ C @ E ) @ ( aa_b_assn @ D @ E ) )
       => ( hoare_hoare_triple_b @ A @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(37,axiom,
    ! [A: assn,B: bool] :
      ( ( entails @ A @ ( aa_bool_assn @ pure_assn @ B ) )
    <=> ( ! [C: produc3658429121746597890et_nat] :
            ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ A ) @ C ) )
           => ( pp @ B ) )
        & ( entails @ A @ one_one_assn ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2137_ent__pure__post__iff__sng) ).

thf(239,plain,
    ! [A: assn,B: bool] :
      ( ( ( entails @ A @ ( aa_bool_assn @ pure_assn @ B ) )
       => ( ! [C: produc3658429121746597890et_nat] :
              ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ A ) @ C ) )
             => ( pp @ B ) )
          & ( entails @ A @ one_one_assn ) ) )
      & ( ( ! [C: produc3658429121746597890et_nat] :
              ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ A ) @ C ) )
             => ( pp @ B ) )
          & ( entails @ A @ one_one_assn ) )
       => ( entails @ A @ ( aa_bool_assn @ pure_assn @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(62,axiom,
    ! [A: assn,B: assn] :
      ( ( ( rep_assn @ A )
        = ( rep_assn @ B ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_Rep__assn__inject) ).

thf(341,plain,
    ! [A: assn,B: assn] :
      ( ( ( ( rep_assn @ A )
          = ( rep_assn @ B ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( ( rep_assn @ A )
          = ( rep_assn @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(65,axiom,
    ! [A: fun_Pr248683899324676269t_bool,B: fun_Pr248683899324676269t_bool] :
      ( ( ord_le2087689725136068685t_bool @ A @ B )
     => ( pp @ ( aa_fun8663595511526100224l_bool @ ( ord_le2468614981408567801t_bool @ ( accp_P4275260045618599050at_nat @ B ) ) @ ( accp_P4275260045618599050at_nat @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1729_accp__subset) ).

thf(358,plain,
    ! [A: fun_Pr248683899324676269t_bool,B: fun_Pr248683899324676269t_bool] :
      ( ( ord_le2087689725136068685t_bool @ A @ B )
     => ( pp @ ( aa_fun8663595511526100224l_bool @ ( ord_le2468614981408567801t_bool @ ( accp_P4275260045618599050at_nat @ B ) ) @ ( accp_P4275260045618599050at_nat @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(93,axiom,
    ! [A: assn,B: assn] :
      ( ( entails @ A @ B )
    <=> ! [C: produc3658429121746597890et_nat] :
          ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ A ) @ C ) )
         => ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2501_entails__def) ).

thf(474,plain,
    ! [A: assn,B: assn] :
      ( ( ( entails @ A @ B )
       => ! [C: produc3658429121746597890et_nat] :
            ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ A ) @ C ) )
           => ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ B ) @ C ) ) ) )
      & ( ! [C: produc3658429121746597890et_nat] :
            ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ A ) @ C ) )
           => ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ B ) @ C ) ) )
       => ( entails @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(17,axiom,
    ! [A: bool,B: heap_Time_Heap_b,C: fun_b_assn] :
      ( ( hoare_hoare_triple_b @ ( aa_bool_assn @ pure_assn @ A ) @ B @ C )
    <=> ( ( pp @ A )
       => ( hoare_hoare_triple_b @ one_one_assn @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2122_norm__pre__pure__iff__sng) ).

thf(163,plain,
    ! [A: bool,B: heap_Time_Heap_b,C: fun_b_assn] :
      ( ( ( hoare_hoare_triple_b @ ( aa_bool_assn @ pure_assn @ A ) @ B @ C )
       => ( ( pp @ A )
         => ( hoare_hoare_triple_b @ one_one_assn @ B @ C ) ) )
      & ( ( ( pp @ A )
         => ( hoare_hoare_triple_b @ one_one_assn @ B @ C ) )
       => ( hoare_hoare_triple_b @ ( aa_bool_assn @ pure_assn @ A ) @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(46,axiom,
    ! [A: assn,B: heap_T5738788834812785303t_unit,C: fun_Pr6626665806141890376t_assn,D: fun_Pr6626665806141890376t_assn] :
      ( ( hoare_8945653483474564448t_unit @ A @ B @ C )
     => ( ! [E: product_unit] : ( entails @ ( aa_Product_unit_assn @ C @ E ) @ ( aa_Product_unit_assn @ D @ E ) )
       => ( hoare_8945653483474564448t_unit @ A @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2519_cons__post__rule) ).

thf(277,plain,
    ! [A: assn,B: heap_T5738788834812785303t_unit,C: fun_Pr6626665806141890376t_assn,D: fun_Pr6626665806141890376t_assn] :
      ( ( hoare_8945653483474564448t_unit @ A @ B @ C )
     => ( ! [E: product_unit] : ( entails @ ( aa_Product_unit_assn @ C @ E ) @ ( aa_Product_unit_assn @ D @ E ) )
       => ( hoare_8945653483474564448t_unit @ A @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(59,axiom,
    ! [A: bool,B: heap_T5738788834812785303t_unit,C: fun_Pr6626665806141890376t_assn] :
      ( ( ( pp @ A )
       => ( hoare_8945653483474564448t_unit @ one_one_assn @ B @ C ) )
     => ( hoare_8945653483474564448t_unit @ ( aa_bool_assn @ pure_assn @ A ) @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2126_norm__pre__pure__rule2) ).

thf(322,plain,
    ! [A: bool,B: heap_T5738788834812785303t_unit,C: fun_Pr6626665806141890376t_assn] :
      ( ( ( pp @ A )
       => ( hoare_8945653483474564448t_unit @ one_one_assn @ B @ C ) )
     => ( hoare_8945653483474564448t_unit @ ( aa_bool_assn @ pure_assn @ A ) @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(6,axiom,
    pp @ fTrue,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fTrue_1_1_U) ).

thf(122,plain,
    pp @ fTrue,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(92,axiom,
    ! [A: produc3658429121746597890et_nat] :
      ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ top_top_assn ) @ A ) )
    <=> ( pp @ ( aa_Pro2991721470636411351t_bool @ in_range @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9958_mod__true) ).

thf(469,plain,
    ! [A: produc3658429121746597890et_nat] :
      ( ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ top_top_assn ) @ A ) )
       => ( pp @ ( aa_Pro2991721470636411351t_bool @ in_range @ A ) ) )
      & ( ( pp @ ( aa_Pro2991721470636411351t_bool @ in_range @ A ) )
       => ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ top_top_assn ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(54,axiom,
    ( one_one_assn
    = ( abs_assn @ one_assn_raw ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10197_one__assn__def) ).

thf(309,plain,
    ( one_one_assn
    = ( abs_assn @ one_assn_raw ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(28,axiom,
    ! [A: assn] : ( entails @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2310_ent__refl) ).

thf(215,plain,
    ! [A: assn] : ( entails @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(31,axiom,
    ! [A: assn,B: assn,C: fun_b_assn,D: fun_b_assn,E: heap_Time_Heap_b] :
      ( ( entails @ A @ B )
     => ( ! [F: b] : ( entails @ ( aa_b_assn @ C @ F ) @ ( aa_b_assn @ D @ F ) )
       => ( ( hoare_hoare_triple_b @ B @ E @ C )
         => ( hoare_hoare_triple_b @ A @ E @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2521_cons__rule) ).

thf(222,plain,
    ! [A: assn,B: assn,C: fun_b_assn,D: fun_b_assn,E: heap_Time_Heap_b] :
      ( ( entails @ A @ B )
     => ( ! [F: b] : ( entails @ ( aa_b_assn @ C @ F ) @ ( aa_b_assn @ D @ F ) )
       => ( ( hoare_hoare_triple_b @ B @ E @ C )
         => ( hoare_hoare_triple_b @ A @ E @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(86,axiom,
    ! [A: heap_e7401611519738050253t_unit] : ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ one_one_assn ) @ ( produc7507926704131184380et_nat @ A @ bot_bot_set_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2058_mod__emp__simp) ).

thf(454,plain,
    ! [A: heap_e7401611519738050253t_unit] : ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ one_one_assn ) @ ( produc7507926704131184380et_nat @ A @ bot_bot_set_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(67,axiom,
    ! [A: fun_Pr6287530515171585797m_bool,B: fun_Pr5837708615769641901m_bool,C: product_prod_num_num,D: fun_Pr6287530515171585797m_bool] :
      ( ( ord_le998981803562422117m_bool @ A @ ( accp_P3113834385874906142um_num @ B ) )
     => ( ! [E: product_prod_num_num,F: product_prod_num_num] :
            ( ( pp @ ( aa_Pro762926636801165566m_bool @ A @ E ) )
           => ( ( pp @ ( aa_Pro762926636801165566m_bool @ ( aa_Pro2164613399825298270m_bool @ B @ F ) @ E ) )
             => ( pp @ ( aa_Pro762926636801165566m_bool @ A @ F ) ) ) )
       => ( ( pp @ ( aa_Pro762926636801165566m_bool @ A @ C ) )
         => ( ! [E: product_prod_num_num] :
                ( ( pp @ ( aa_Pro762926636801165566m_bool @ A @ E ) )
               => ( ! [F: product_prod_num_num] :
                      ( ( pp @ ( aa_Pro762926636801165566m_bool @ ( aa_Pro2164613399825298270m_bool @ B @ F ) @ E ) )
                     => ( pp @ ( aa_Pro762926636801165566m_bool @ D @ F ) ) )
                 => ( pp @ ( aa_Pro762926636801165566m_bool @ D @ E ) ) ) )
           => ( pp @ ( aa_Pro762926636801165566m_bool @ D @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1733_accp__subset__induct) ).

thf(364,plain,
    ! [A: fun_Pr6287530515171585797m_bool,B: fun_Pr5837708615769641901m_bool,C: product_prod_num_num,D: fun_Pr6287530515171585797m_bool] :
      ( ( ord_le998981803562422117m_bool @ A @ ( accp_P3113834385874906142um_num @ B ) )
     => ( ! [E: product_prod_num_num,F: product_prod_num_num] :
            ( ( pp @ ( aa_Pro762926636801165566m_bool @ A @ E ) )
           => ( ( pp @ ( aa_Pro762926636801165566m_bool @ ( aa_Pro2164613399825298270m_bool @ B @ F ) @ E ) )
             => ( pp @ ( aa_Pro762926636801165566m_bool @ A @ F ) ) ) )
       => ( ( pp @ ( aa_Pro762926636801165566m_bool @ A @ C ) )
         => ( ! [E: product_prod_num_num] :
                ( ( pp @ ( aa_Pro762926636801165566m_bool @ A @ E ) )
               => ( ! [F: product_prod_num_num] :
                      ( ( pp @ ( aa_Pro762926636801165566m_bool @ ( aa_Pro2164613399825298270m_bool @ B @ F ) @ E ) )
                     => ( pp @ ( aa_Pro762926636801165566m_bool @ D @ F ) ) )
                 => ( pp @ ( aa_Pro762926636801165566m_bool @ D @ E ) ) ) )
           => ( pp @ ( aa_Pro762926636801165566m_bool @ D @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(41,axiom,
    ! [A: bool,B: produc3658429121746597890et_nat] :
      ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ ( aa_bool_assn @ pure_assn @ A ) ) @ B ) )
    <=> ( ( ( produc8586169260539613262et_nat @ B )
          = bot_bot_set_nat )
        & ( pp @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9814_mod__pure) ).

thf(254,plain,
    ! [A: bool,B: produc3658429121746597890et_nat] :
      ( ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ ( aa_bool_assn @ pure_assn @ A ) ) @ B ) )
       => ( ( ( produc8586169260539613262et_nat @ B )
            = bot_bot_set_nat )
          & ( pp @ A ) ) )
      & ( ( ( ( produc8586169260539613262et_nat @ B )
            = bot_bot_set_nat )
          & ( pp @ A ) )
       => ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ ( aa_bool_assn @ pure_assn @ A ) ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(33,axiom,
    ! [A: nat] :
      ( ( pp @ ( aa_nat_bool @ aTP_Lamm_eo @ A ) )
    <=> $false ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11305_ATP_Olambda__1099) ).

thf(227,plain,
    ! [A: nat] :
      ~ ( pp @ ( aa_nat_bool @ aTP_Lamm_eo @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(558,plain,
    $false,
    inference(e,[status(thm)],[153,466,250,481,352,170,523,217,247,379,174,288,389,372,110,189,416,325,448,316,492,238,397,280,133,265,512,220,349,160,424,429,275,484,252,461,551,456,285,519,141,109,225,489,212,393,457,237,360,508,311,530,180,444,375,172,230,434,303,140,155,399,306,431,209,112,516,123,553,458,295,282,150,414,327,409,441,502,544,177,182,314,143,497,319,158,119,207,272,447,262,239,341,358,474,163,277,322,122,469,309,215,222,454,364,254,227]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : ITP214_1 : TPTP v8.2.0. Released v8.0.0.
% 0.13/0.17  % Command  : run_Leo-III %s %d
% 0.15/0.38  % Computer : n022.cluster.edu
% 0.15/0.38  % Model    : x86_64 x86_64
% 0.15/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.38  % Memory   : 8042.1875MB
% 0.15/0.38  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.38  % CPULimit : 300
% 0.15/0.38  % WCLimit  : 300
% 0.15/0.38  % DateTime : Sat May 18 16:56:39 EDT 2024
% 0.15/0.38  % CPUTime  : 
% 1.01/0.94  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 5.00/2.04  % [INFO] 	 Parsing done (1103ms). 
% 5.00/2.06  % [INFO] 	 Running in sequential loop mode. 
% 5.55/2.30  % [INFO] 	 eprover registered as external prover. 
% 5.55/2.30  % [INFO] 	 cvc4 registered as external prover. 
% 5.71/2.30  % [INFO] 	 Scanning for conjecture ... 
% 9.70/3.34  % [INFO] 	 Found a conjecture (or negated_conjecture) and 11386 axioms. Running axiom selection ... 
% 12.11/4.01  % [INFO] 	 Axiom selection finished. Selected 106 axioms (removed 11280 axioms). 
% 12.70/4.16  % [INFO] 	 Problem is typed first-order (TPTP TFF). 
% 12.89/4.19  % [INFO] 	 Type checking passed. 
% 12.89/4.19  % [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 ... 
% 14.50/4.83  % [INFO] 	 [Domain constraints] Detected constraint on bool 
% 14.50/4.83  % [INFO] 	 [Domain constraints] dom(bool) ⊆ {fTrue,fFalse} 
% 19.38/5.95  % External prover 'e' found a proof!
% 19.38/5.95  % [INFO] 	 Killing All external provers ... 
% 19.38/5.96  % Time passed: 5416ms (effective reasoning time: 3894ms)
% 19.38/5.96  % 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)>
% 19.38/5.96  % Axioms used in derivation (106): fact_9957_assn__basic__inequalities_I5_J, fact_2517_cons__post__rule, fact_2519_cons__post__rule, fact_2520_cons__rule, fact_2_new__addr__refl, fact_1996_false__rule, fact_2050_assn__basic__inequalities_I3_J, fact_16_one__assn__raw_Ocases, fact_3654_relH__in__rangeI_I2_J, fact_10200_one__assn__raw_Oelims_I1_J, fact_2137_ent__pure__post__iff__sng, fact_2498_ent__fwd, fact_141_hoare__triple__effect, fact_139_hoare__triple__effect, fact_9965_mod__h__bot__iff_I2_J, fact_3849_bot__assn__def, fact_2499_entailsD, fact_101_hoare__triple__preI, fact_11305_ATP_Olambda__1099, fact_2123_norm__pre__pure__iff__sng, fact_2518_cons__post__rule, fact_10201_one__assn__raw_Oelims_I2_J, fact_102_hoare__triple__preI, fact_9814_mod__pure, fact_11289_ATP_Olambda__1083, fact_9956_assn__basic__inequalities_I1_J, fact_2125_norm__pre__pure__rule2, fact_1729_accp__subset, fact_74_Collect__cong, fact_2115_pure__assn__eq__conv, fact_3812_pure__assn__def, help_fTrue_1_1_U, fact_3646_in__range__empty, fact_2239_ent__false__iff, fact_2568_cons__pre__rule, fact_332_relH__sym, fact_9815_mod__emp, fact_2114_mod__h__bot__iff_I1_J, fact_54_T2, fact_2522_cons__rule, fact_1728_accp__subset, fact_2058_mod__emp__simp, fact_3_POST__G, fact_2310_ent__refl, fact_1995_false__rule, fact_10335_ATP_Olambda__129, fact_1766_Collect__empty__eq, fact_2124_norm__pre__pure__rule2, fact_548_mod__relH, fact_2119_pure__assn__eq__false__iff, fact_9964_top__assn__def, fact_10199_one__assn__raw_Osimps, fact_3810_Abs__assn__eqI_I1_J, fact_2140_pure__assn__raw_Oelims_I2_J, fact_10197_one__assn__def, fact_144_hoare__triple__success, fact_3655_relH__in__rangeI_I1_J, fact_9958_mod__true, fact_1900_Set_Oempty__def, fact_2126_norm__pre__pure__rule2, fact_2122_norm__pre__pure__iff__sng, fact_1__092_060open_062_Ih_M_Aas_J_A_092_060Turnstile_062_AP_092_060close_062, fact_331_relH__trans, fact_53_T1, fact_3811_Abs__assn__eqI_I2_J, fact_2566_cons__pre__rule, fact_2501_entails__def, fact_2139_pure__assn__raw_Oelims_I1_J, fact_1994_false__rule, fact_4_POST__F, help_If_3_1_If_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_T, fact_1759_empty__Collect__eq, fact_153_RH__F, fact_2567_cons__pre__rule, fact_2521_cons__rule, fact_9960_ent__true, fact_10202_one__assn__raw_Oelims_I3_J, fact_2120_pure__false, fact_3701_Rep__assn__inverse, fact_2309_ent__iffI, fact_2121_norm__pre__pure__iff__sng, fact_2311_ent__trans, fact_5_Rep__assn__inject, fact_11298_ATP_Olambda__1092, fact_103_hoare__triple__preI, fact_142_hoare__triple__success, fact_2118_pure__true, help_fFalse_1_1_U, fact_1965_mod__h__bot__indep, fact_2691_pure__assn__raw_Oelims_I3_J, fact_2240_ent__pure__pre__iff__sng, fact_2500_entailsI, fact_2117_pure__assn__eq__emp__iff, fact_140_hoare__triple__effect, fact_152_RH__G, fact_10704_ATP_Olambda__498, fact_2018_mod__false, fact_1733_accp__subset__induct, fact_3653_models__in__range, fact_3656_relH__refl, fact_0__092_060open_062new__addrs_Ah_H_A_Inew__addrs_Ah_Aas_Ah_H_J_Ah_H_H_A_061_Anew__addrs_Ah_Aas_Ah_H_H_092_060close_062, fact_1734_accp__subset__induct, fact_2138_pure__assn__raw_Osimps, fact_10681_ATP_Olambda__475, fact_143_hoare__triple__success, fact_2533_ent__false
% 19.38/5.96  % No. of inferences in proof: 216
% 19.38/5.96  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5416 ms resp. 3894 ms w/o parsing
% 20.00/6.08  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 20.00/6.08  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------