%------------------------------------------------------------------------------
% File     : Leo-III-SAT---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 : n023.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 22:28:24 EDT 2024

% Result   : Theorem 72.41s 12.56s
% Output   : Refutation 72.45s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      : 1025
% Syntax   : Number of formulae    : 1045 (  20 unt;1019 typ;   0 def)
%            Number of atoms       :   34 (  19 equ;   0 cnn)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :  184 (  10   ~;   6   |;   0   &; 168   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Number of types       : 1006 (1005 usr)
%            Number of type conns  :   11 (  11   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   17 (  14 usr;  10 con; 0-3 aty)
%            Number of variables   :    5 (   0   ^   5   !;   0   ?;   5   :)

% 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,
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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,
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thf(fun_fu3997796857297124035at_rat_type,type,
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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,
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thf(fun_fu1696078252837777177l_bool_type,type,
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thf(fun_fu4087525139388848025l_bool_type,type,
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thf(fun_fu8571960779141011225r_bool_type,type,
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thf(fun_fu2216953070675676215l_bool_type,type,
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thf(fun_na2419096353205528t_bool_type,type,
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thf(fun_li124330075790197867t_assn_type,type,
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thf(fun_in8031269491544239620t_bool_type,type,
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thf(fun_Co2470855966376689427nteger_type,type,
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thf(fun_fu9160419385450930796l_bool_type,type,
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thf(fun_fu1788334712973291331r_bool_type,type,
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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,
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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,
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thf(fun_Pr446604468264085555t_bool_type,type,
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thf(fun_Pr6553600481296542259t_bool_type,type,
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thf(fun_fu8715438531829836670t_bool_type,type,
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thf(fun_fu5963139849246984042t_bool_type,type,
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thf(fun_se3305628495172992525t_bool_type,type,
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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,
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thf(fun_Pr6180708418112149265at_num_type,type,
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thf(fun_Pr5472464481163311559at_nat_type,type,
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thf(fun_Pr5112106203349071120at_num_type,type,
    fun_Pr5112106203349071120at_num: $tType ).

thf(fun_Pr4403862266400233414at_nat_type,type,
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thf(fun_nu147038076112158225it_nat_type,type,
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thf(fun_nu8867722426328123536it_nat_type,type,
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thf(produc4428605777065428680et_nat_type,type,
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thf(fun_fu6605489587527791784l_assn_type,type,
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thf(list_f5857023252961307252t_bool_type,type,
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thf(fun_b_4190609728018899208t_bool_type,type,
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thf(fun_a_3884643061924904137t_bool_type,type,
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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,
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thf(fun_b_2332632271197754813et_int_type,type,
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thf(fun_a_8173838432492502368et_nat_type,type,
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thf(fun_fu1851216944655731660er_nat_type,type,
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thf(set_Pr8693737435421807431at_nat_type,type,
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thf(set_Pr2560585780119916871nt_int_type,type,
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thf(fun_fu3959123160307459545t_assn_type,type,
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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,
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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,
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thf(fun_Pr5837708615769641901m_bool_type,type,
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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,
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thf(produc5504626439533210094nt_int_type,type,
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thf(produc5835291356934675326atural_type,type,
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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,
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thf(fun_fu440692136686903449er_nat_type,type,
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thf(fun_fu7173981028609952501er_int_type,type,
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thf(fun_fu2200728800440014653er_nat_type,type,
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thf(fun_fu8934017692363063705er_int_type,type,
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thf(fun_Pr6001797050664311790t_bool_type,type,
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thf(fun_Pr554477149536188932t_bool_type,type,
    fun_Pr554477149536188932t_bool: $tType ).

thf(produc859450856879609959at_nat_type,type,
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thf(produc1219242969750017639nt_int_type,type,
    produc1219242969750017639nt_int: $tType ).

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

thf(fun_Pr1844946900262394667et_int_type,type,
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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,
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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,
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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,
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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_Pr292408699144966967t_unit_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_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_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_ar8560675821539856405t_assn_type,type,
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thf(fun_ar528246731820255437t_assn_type,type,
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thf(fun_li1703715468755832110t_assn_type,type,
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thf(fun_fu8422113094057456412t_bool_type,type,
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thf(fun_bo7720638723722887333nt_int_type,type,
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thf(fun_Pr5215307506330550056Heap_a_type,type,
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thf(set_set_Code_integer_type,type,
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thf(heap_T5738788834812785303t_unit_type,type,
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thf(fun_option_num_bool_type,type,
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thf(fun_option_num_int_type,type,
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thf(fun_int_option_num_type,type,
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thf(fun_int_option_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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thf(fun_nat_set_nat_type,type,
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thf(fun_nat_set_int_type,type,
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thf(fun_nat_Code_natural_type,type,
    fun_nat_Code_natural: $tType ).

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

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

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

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

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(q_type,type,
    q: fun_b_assn ).

thf(as_type,type,
    as: set_nat ).

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(rg_type,type,
    rg: b ).

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(111,plain,
    ~ ( pp @ fFalse ),
    inference(polarity_switch,[status(thm)],[110]) ).

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(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(398,plain,
    ( ( hoare_new_addrs @ h2 @ ( hoare_new_addrs @ h3 @ as @ h2 ) @ h )
    = ( hoare_new_addrs @ h3 @ as @ h ) ),
    inference(lifteq,[status(thm)],[397]) ).

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(120,plain,
    ! [A: bool] :
      ( ( A = fTrue )
      | ( A = fFalse ) ),
    inference(cnf,[status(esa)],[119]) ).

thf(121,plain,
    ! [A: bool] :
      ( ( A = fTrue )
      | ( A = fFalse ) ),
    inference(lifteq,[status(thm)],[120]) ).

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(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(560,plain,
    ( ( pp @ ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ ( aa_b_assn @ q @ rg ) ) @ ( produc7507926704131184380et_nat @ h @ ( hoare_new_addrs @ h3 @ as @ h ) ) ) )
   != ( pp @ fTrue ) ),
    inference(paramod_ordered,[status(thm)],[122,109]) ).

thf(561,plain,
    ( ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ ( aa_b_assn @ q @ rg ) ) @ ( produc7507926704131184380et_nat @ h @ ( hoare_new_addrs @ h3 @ as @ h ) ) )
   != fTrue ),
    inference(simp,[status(thm)],[560]) ).

thf(635,plain,
    ! [A: bool] :
      ( ( A = fFalse )
      | ( A
       != ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ ( aa_b_assn @ q @ rg ) ) @ ( produc7507926704131184380et_nat @ h @ ( hoare_new_addrs @ h3 @ as @ h ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[121,561]) ).

thf(636,plain,
    ( ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ ( aa_b_assn @ q @ rg ) ) @ ( produc7507926704131184380et_nat @ h @ ( hoare_new_addrs @ h3 @ as @ h ) ) )
    = fFalse ),
    inference(pattern_uni,[status(thm)],[635:[bind(A,$thf( aa_Pro2991721470636411351t_bool @ ( rep_assn @ ( aa_b_assn @ q @ rg ) ) @ ( produc7507926704131184380et_nat @ h @ ( hoare_new_addrs @ h3 @ as @ h ) ) ))]]) ).

thf(1594,plain,
    ( ( ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ ( aa_b_assn @ q @ rg ) ) @ ( produc7507926704131184380et_nat @ h @ ( hoare_new_addrs @ h2 @ ( hoare_new_addrs @ h3 @ as @ h2 ) @ h ) ) )
      = fFalse )
    | ( ( hoare_new_addrs @ h3 @ as @ h )
     != ( hoare_new_addrs @ h3 @ as @ h ) ) ),
    inference(paramod_ordered,[status(thm)],[398,636]) ).

thf(1595,plain,
    ( ( aa_Pro2991721470636411351t_bool @ ( rep_assn @ ( aa_b_assn @ q @ rg ) ) @ ( produc7507926704131184380et_nat @ h @ ( hoare_new_addrs @ h2 @ ( hoare_new_addrs @ h3 @ as @ h2 ) @ h ) ) )
    = fFalse ),
    inference(pattern_uni,[status(thm)],[1594:[]]) ).

thf(10025,plain,
    pp @ fFalse,
    inference(rewrite,[status(thm)],[447,1595]) ).

thf(10026,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[111,10025]) ).

thf(10027,plain,
    $false,
    inference(simp,[status(thm)],[10026]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.09  % Problem  : ITP214_1 : TPTP v8.2.0. Released v8.0.0.
% 0.04/0.11  % Command  : run_Leo-III %s %d
% 0.10/0.31  % Computer : n023.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit : 300
% 0.10/0.31  % WCLimit  : 300
% 0.10/0.31  % DateTime : Sat May 18 16:56:39 EDT 2024
% 0.10/0.31  % CPUTime  : 
% 0.83/0.75  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 3.98/1.69  % [INFO] 	 Parsing done (937ms). 
% 3.98/1.71  % [INFO] 	 Running in sequential loop mode. 
% 4.49/1.93  % [INFO] 	 nitpick registered as external prover. 
% 4.49/1.93  % [INFO] 	 Scanning for conjecture ... 
% 7.49/2.68  % [INFO] 	 Found a conjecture (or negated_conjecture) and 11386 axioms. Running axiom selection ... 
% 9.18/3.27  % [INFO] 	 Axiom selection finished. Selected 106 axioms (removed 11280 axioms). 
% 9.57/3.37  % [INFO] 	 Problem is typed first-order (TPTP TFF). 
% 9.57/3.39  % [INFO] 	 Type checking passed. 
% 9.57/3.39  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 10.74/3.81  % [INFO] 	 [Domain constraints] Detected constraint on bool 
% 10.74/3.81  % [INFO] 	 [Domain constraints] dom(bool) ⊆ {fTrue,fFalse} 
% 72.41/12.56  % [INFO] 	 Killing All external provers ... 
% 72.41/12.56  % Time passed: 12122ms (effective reasoning time: 10846ms)
% 72.41/12.56  % 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)>
% 72.41/12.56  % Axioms used in derivation (5): help_fTrue_1_1_U, fact_3_POST__G, 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, help_fFalse_1_1_U, 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
% 72.41/12.56  % No. of inferences in proof: 26
% 72.41/12.56  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 12122 ms resp. 10846 ms w/o parsing
% 72.45/12.59  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 72.45/12.59  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------