%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP211_1 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:36:45 AM UTC 2026
% Result : Theorem 12.85s 4.49s
% Output : Refutation 13.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 223
% Syntax : Number of formulae : 448 ( 202 unt; 0 typ; 0 def)
% Number of atoms : 1049 ( 472 equ; 0 cnn)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 4891 ( 152 ~; 6 |; 119 &;4138 @)
% ( 58 <=>; 418 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Number of types : 521 ( 520 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 94 ( 92 usr; 29 con; 0-4 aty)
% Number of variables : 1046 ( 0 ^;1006 !; 40 ?;1046 :)
% Comments :
%------------------------------------------------------------------------------
thf(set_Pr6041871929502663225et_nat_type,type,
set_Pr6041871929502663225et_nat: $tType ).
thf(fun_Pr6803231168968006865t_bool_type,type,
fun_Pr6803231168968006865t_bool: $tType ).
thf(produc8012095931379219673et_nat_type,type,
produc8012095931379219673et_nat: $tType ).
thf(fun_Pr1766678018663252541t_bool_type,type,
fun_Pr1766678018663252541t_bool: $tType ).
thf(fun_Pr6535039171404285501et_nat_type,type,
fun_Pr6535039171404285501et_nat: $tType ).
thf(fun_Pr6859458860894228184et_nat_type,type,
fun_Pr6859458860894228184et_nat: $tType ).
thf(fun_Pr8176305432000512344et_nat_type,type,
fun_Pr8176305432000512344et_nat: $tType ).
thf(set_Pr4255865656320958847et_nat_type,type,
set_Pr4255865656320958847et_nat: $tType ).
thf(fun_Pr6052842969455678475t_bool_type,type,
fun_Pr6052842969455678475t_bool: $tType ).
thf(produc586578377766392095et_nat_type,type,
produc586578377766392095et_nat: $tType ).
thf(fun_Pr5123258793648662203et_nat_type,type,
fun_Pr5123258793648662203et_nat: $tType ).
thf(fun_Pr3712735747772465149t_bool_type,type,
fun_Pr3712735747772465149t_bool: $tType ).
thf(fun_Pr3659704428484505341et_nat_type,type,
fun_Pr3659704428484505341et_nat: $tType ).
thf(fun_Pr7301545579335958043nteger_type,type,
fun_Pr7301545579335958043nteger: $tType ).
thf(fun_Pr6127221218041104501nteger_type,type,
fun_Pr6127221218041104501nteger: $tType ).
thf(fun_Pr8555020547098233205nteger_type,type,
fun_Pr8555020547098233205nteger: $tType ).
thf(fun_Pr3001699213897242575nteger_type,type,
fun_Pr3001699213897242575nteger: $tType ).
thf(fun_se2730912884141707428t_bool_type,type,
fun_se2730912884141707428t_bool: $tType ).
thf(fun_Pr229822445725053876t_bool_type,type,
fun_Pr229822445725053876t_bool: $tType ).
thf(set_Pr9222568342844664434et_nat_type,type,
set_Pr9222568342844664434et_nat: $tType ).
thf(set_Pr222142748458615354t_bool_type,type,
set_Pr222142748458615354t_bool: $tType ).
thf(fun_fu5758690788630904038t_bool_type,type,
fun_fu5758690788630904038t_bool: $tType ).
thf(fun_Pr215885126604245128l_bool_type,type,
fun_Pr215885126604245128l_bool: $tType ).
thf(produc1542783094787327164et_nat_type,type,
produc1542783094787327164et_nat: $tType ).
thf(produc6968460846966063236t_bool_type,type,
produc6968460846966063236t_bool: $tType ).
thf(fun_fu7547279164713276502et_nat_type,type,
fun_fu7547279164713276502et_nat: $tType ).
thf(set_Pr8548855242995119074et_nat_type,type,
set_Pr8548855242995119074et_nat: $tType ).
thf(set_Pr8177988689565181538et_nat_type,type,
set_Pr8177988689565181538et_nat: $tType ).
thf(fun_Pr8311103421978789352t_bool_type,type,
fun_Pr8311103421978789352t_bool: $tType ).
thf(produc6036703516317769218et_nat_type,type,
produc6036703516317769218et_nat: $tType ).
thf(produc4587776716583620738et_nat_type,type,
produc4587776716583620738et_nat: $tType ).
thf(fun_Pr2210758139564844958et_nat_type,type,
fun_Pr2210758139564844958et_nat: $tType ).
thf(fun_Pr761831339830696478et_nat_type,type,
fun_Pr761831339830696478et_nat: $tType ).
thf(produc5081555286676025831nteger_type,type,
produc5081555286676025831nteger: $tType ).
thf(produc3632725533738474395et_nat_type,type,
produc3632725533738474395et_nat: $tType ).
thf(set_Pr6448005306607475463t_bool_type,type,
set_Pr6448005306607475463t_bool: $tType ).
thf(fun_Pr509543455618818233t_bool_type,type,
fun_Pr509543455618818233t_bool: $tType ).
thf(fun_Pr5350199696774050811at_nat_type,type,
fun_Pr5350199696774050811at_nat: $tType ).
thf(fun_Pr4213701301278458035et_nat_type,type,
fun_Pr4213701301278458035et_nat: $tType ).
thf(set_se2897448282425263847t_bool_type,type,
set_se2897448282425263847t_bool: $tType ).
thf(produc1329698249991434023t_bool_type,type,
produc1329698249991434023t_bool: $tType ).
thf(fun_fu5792599895934982715t_bool_type,type,
fun_fu5792599895934982715t_bool: $tType ).
thf(produc5182780385608778412et_nat_type,type,
produc5182780385608778412et_nat: $tType ).
thf(set_Pr2055239900342597383t_bool_type,type,
set_Pr2055239900342597383t_bool: $tType ).
thf(fun_se9066322626600930210et_nat_type,type,
fun_se9066322626600930210et_nat: $tType ).
thf(fun_se973636082235158211t_bool_type,type,
fun_se973636082235158211t_bool: $tType ).
thf(fun_fu7365307207611327597l_bool_type,type,
fun_fu7365307207611327597l_bool: $tType ).
thf(fun_Pr3073222722562426257t_bool_type,type,
fun_Pr3073222722562426257t_bool: $tType ).
thf(produc1469476007717053223t_bool_type,type,
produc1469476007717053223t_bool: $tType ).
thf(fun_in8942784645934064712et_nat_type,type,
fun_in8942784645934064712et_nat: $tType ).
thf(set_Pr1106803562331729365et_nat_type,type,
set_Pr1106803562331729365et_nat: $tType ).
thf(set_Pr8919652553310308119t_bool_type,type,
set_Pr8919652553310308119t_bool: $tType ).
thf(fun_fu7398481913972163267t_bool_type,type,
fun_fu7398481913972163267t_bool: $tType ).
thf(fun_Pr979140477516945259l_bool_type,type,
fun_Pr979140477516945259l_bool: $tType ).
thf(produc6108883039684432031et_nat_type,type,
produc6108883039684432031et_nat: $tType ).
thf(produc2123963014314306273t_bool_type,type,
produc2123963014314306273t_bool: $tType ).
thf(fun_fu1426818202555147193et_nat_type,type,
fun_fu1426818202555147193et_nat: $tType ).
thf(fun_Co1105491363547889651atural_type,type,
fun_Co1105491363547889651atural: $tType ).
thf(fun_fu4272674133525273539t_bool_type,type,
fun_fu4272674133525273539t_bool: $tType ).
thf(fun_fu2754956555950464963t_bool_type,type,
fun_fu2754956555950464963t_bool: $tType ).
thf(fun_Pr3757777938668859031t_bool_type,type,
fun_Pr3757777938668859031t_bool: $tType ).
thf(fun_Pr1014183174784581455t_bool_type,type,
fun_Pr1014183174784581455t_bool: $tType ).
thf(fun_Pr4983655124978328031t_bool_type,type,
fun_Pr4983655124978328031t_bool: $tType ).
thf(fun_Pr2240060361094050455t_bool_type,type,
fun_Pr2240060361094050455t_bool: $tType ).
thf(set_Pr719794911490849221et_nat_type,type,
set_Pr719794911490849221et_nat: $tType ).
thf(fun_Pr8933696392609397829t_bool_type,type,
fun_Pr8933696392609397829t_bool: $tType ).
thf(fun_fu4800041728187187127nteger_type,type,
fun_fu4800041728187187127nteger: $tType ).
thf(fun_Pr9027168029485879607nteger_type,type,
fun_Pr9027168029485879607nteger: $tType ).
thf(produc8111630337999740517et_nat_type,type,
produc8111630337999740517et_nat: $tType ).
thf(fun_Pr7769407664385210434atural_type,type,
fun_Pr7769407664385210434atural: $tType ).
thf(produc8903623710181579841nteger_type,type,
produc8903623710181579841nteger: $tType ).
thf(fun_Pr5504542249117545915et_nat_type,type,
fun_Pr5504542249117545915et_nat: $tType ).
thf(fun_Pr7214764501845804219t_unit_type,type,
fun_Pr7214764501845804219t_unit: $tType ).
thf(fun_Pr7091840695141096449et_nat_type,type,
fun_Pr7091840695141096449et_nat: $tType ).
thf(fun_fu3310558948973754387nteger_type,type,
fun_fu3310558948973754387nteger: $tType ).
thf(fun_fu8926436095885609094et_nat_type,type,
fun_fu8926436095885609094et_nat: $tType ).
thf(fun_fu9117715662874197469nteger_type,type,
fun_fu9117715662874197469nteger: $tType ).
thf(fun_Pr5458885100655985245nteger_type,type,
fun_Pr5458885100655985245nteger: $tType ).
thf(fun_Pr4857721227833164125nteger_type,type,
fun_Pr4857721227833164125nteger: $tType ).
thf(fun_Co6653309639117302568nteger_type,type,
fun_Co6653309639117302568nteger: $tType ).
thf(fun_Co1561183069634336733nteger_type,type,
fun_Co1561183069634336733nteger: $tType ).
thf(fun_fu4478038021464438563t_unit_type,type,
fun_fu4478038021464438563t_unit: $tType ).
thf(fun_Pr3800342156844704675nteger_type,type,
fun_Pr3800342156844704675nteger: $tType ).
thf(fun_fu5845048363982186797r_bool_type,type,
fun_fu5845048363982186797r_bool: $tType ).
thf(fun_bo1105078601566322605nteger_type,type,
fun_bo1105078601566322605nteger: $tType ).
thf(fun_fu7638885401485650896er_nat_type,type,
fun_fu7638885401485650896er_nat: $tType ).
thf(fun_na7028214812545403088nteger_type,type,
fun_na7028214812545403088nteger: $tType ).
thf(fun_in8262288108676414764nteger_type,type,
fun_in8262288108676414764nteger: $tType ).
thf(fun_he2597241314532250788t_bool_type,type,
fun_he2597241314532250788t_bool: $tType ).
thf(produc5697189838369619070et_nat_type,type,
produc5697189838369619070et_nat: $tType ).
thf(set_Pr1200603583047724451ol_nat_type,type,
set_Pr1200603583047724451ol_nat: $tType ).
thf(set_Pr6237782094582346185t_bool_type,type,
set_Pr6237782094582346185t_bool: $tType ).
thf(produc5766230810918527523et_nat_type,type,
produc5766230810918527523et_nat: $tType ).
thf(fun_fu5184991215612278548nteger_type,type,
fun_fu5184991215612278548nteger: $tType ).
thf(fun_fu4671764723984660721t_bool_type,type,
fun_fu4671764723984660721t_bool: $tType ).
thf(fun_fu2749353902725170073t_bool_type,type,
fun_fu2749353902725170073t_bool: $tType ).
thf(fun_Pr2477239776880934807at_nat_type,type,
fun_Pr2477239776880934807at_nat: $tType ).
thf(fun_Pr1308109350235310159nt_int_type,type,
fun_Pr1308109350235310159nt_int: $tType ).
thf(fun_Pr5876161306168176259nteger_type,type,
fun_Pr5876161306168176259nteger: $tType ).
thf(fun_Pr7672403737682949028t_unit_type,type,
fun_Pr7672403737682949028t_unit: $tType ).
thf(produc2721201938007151049ol_int_type,type,
produc2721201938007151049ol_int: $tType ).
thf(fun_Pr21663490405640598et_nat_type,type,
fun_Pr21663490405640598et_nat: $tType ).
thf(fun_Pr2304087830868576334et_nat_type,type,
fun_Pr2304087830868576334et_nat: $tType ).
thf(fun_Pr5444349417986836952at_nat_type,type,
fun_Pr5444349417986836952at_nat: $tType ).
thf(fun_Pr5141187847748131984nt_int_type,type,
fun_Pr5141187847748131984nt_int: $tType ).
thf(fun_se7275083947436752652l_bool_type,type,
fun_se7275083947436752652l_bool: $tType ).
thf(set_fu7884337747459999906l_bool_type,type,
set_fu7884337747459999906l_bool: $tType ).
thf(fun_fu8897467071111498631et_nat_type,type,
fun_fu8897467071111498631et_nat: $tType ).
thf(fun_na5616424005362821463t_bool_type,type,
fun_na5616424005362821463t_bool: $tType ).
thf(fun_fu4821026654811345315r_assn_type,type,
fun_fu4821026654811345315r_assn: $tType ).
thf(fun_Pr70611744221503047t_unit_type,type,
fun_Pr70611744221503047t_unit: $tType ).
thf(fun_fu6572814390356972386t_unit_type,type,
fun_fu6572814390356972386t_unit: $tType ).
thf(fun_fu3335091274710497827t_assn_type,type,
fun_fu3335091274710497827t_assn: $tType ).
thf(fun_fu1264473476461866025l_assn_type,type,
fun_fu1264473476461866025l_assn: $tType ).
thf(fun_as4100195077546555551t_bool_type,type,
fun_as4100195077546555551t_bool: $tType ).
thf(set_se2501078297044592302t_bool_type,type,
set_se2501078297044592302t_bool: $tType ).
thf(fun_fu3064074204415222357nt_int_type,type,
fun_fu3064074204415222357nt_int: $tType ).
thf(fun_fu1098312133097393581at_rat_type,type,
fun_fu1098312133097393581at_rat: $tType ).
thf(fun_Pr6172722220446688464nteger_type,type,
fun_Pr6172722220446688464nteger: $tType ).
thf(fun_na1668100129766719005at_nat_type,type,
fun_na1668100129766719005at_nat: $tType ).
thf(fun_Pr8052405283675813457r_bool_type,type,
fun_Pr8052405283675813457r_bool: $tType ).
thf(fun_Pr8543155049374816593t_unit_type,type,
fun_Pr8543155049374816593t_unit: $tType ).
thf(fun_Pr7273592372765610306er_nat_type,type,
fun_Pr7273592372765610306er_nat: $tType ).
thf(fun_Pr4783509227833883550er_int_type,type,
fun_Pr4783509227833883550er_int: $tType ).
thf(fun_Co2470855966376689427nteger_type,type,
fun_Co2470855966376689427nteger: $tType ).
thf(produc3974974285617410127nteger_type,type,
produc3974974285617410127nteger: $tType ).
thf(fun_fu9160419385450930796l_bool_type,type,
fun_fu9160419385450930796l_bool: $tType ).
thf(fun_fu7614330534255538897ol_nat_type,type,
fun_fu7614330534255538897ol_nat: $tType ).
thf(fun_na589949626680601079t_bool_type,type,
fun_na589949626680601079t_bool: $tType ).
thf(fun_in3344392145425689243t_bool_type,type,
fun_in3344392145425689243t_bool: $tType ).
thf(fun_fu7716566084524949747er_nat_type,type,
fun_fu7716566084524949747er_nat: $tType ).
thf(set_Pr1776176089890104647t_unit_type,type,
set_Pr1776176089890104647t_unit: $tType ).
thf(produc4428605777065428680et_nat_type,type,
produc4428605777065428680et_nat: $tType ).
thf(produc8065447618272157327et_nat_type,type,
produc8065447618272157327et_nat: $tType ).
thf(fun_fu5149662236961268259it_nat_type,type,
fun_fu5149662236961268259it_nat: $tType ).
thf(set_fu6080891106736489294t_bool_type,type,
set_fu6080891106736489294t_bool: $tType ).
thf(set_Pr8693737435421807431at_nat_type,type,
set_Pr8693737435421807431at_nat: $tType ).
thf(set_Pr5557702248415638087at_int_type,type,
set_Pr5557702248415638087at_int: $tType ).
thf(set_Pr5696620967126086215nt_nat_type,type,
set_Pr5696620967126086215nt_nat: $tType ).
thf(set_Pr2560585780119916871nt_int_type,type,
set_Pr2560585780119916871nt_int: $tType ).
thf(fun_se1339536933736954245et_nat_type,type,
fun_se1339536933736954245et_nat: $tType ).
thf(fun_Pr3337834798857116037et_nat_type,type,
fun_Pr3337834798857116037et_nat: $tType ).
thf(fun_Pr6272012943078625115r_bool_type,type,
fun_Pr6272012943078625115r_bool: $tType ).
thf(fun_Pr355790150511728056er_nat_type,type,
fun_Pr355790150511728056er_nat: $tType ).
thf(fun_Pr7089079042434777108er_int_type,type,
fun_Pr7089079042434777108er_int: $tType ).
thf(fun_he1004219788074801965t_bool_type,type,
fun_he1004219788074801965t_bool: $tType ).
thf(fun_fu4738270438141978787l_assn_type,type,
fun_fu4738270438141978787l_assn: $tType ).
thf(fun_fu5180488074244323977t_assn_type,type,
fun_fu5180488074244323977t_assn: $tType ).
thf(fun_fu7925354201654153025t_assn_type,type,
fun_fu7925354201654153025t_assn: $tType ).
thf(fun_fu727159081937814839r_assn_type,type,
fun_fu727159081937814839r_assn: $tType ).
thf(fun_se2593093895363294211t_unit_type,type,
fun_se2593093895363294211t_unit: $tType ).
thf(fun_Pr248683899324676269t_bool_type,type,
fun_Pr248683899324676269t_bool: $tType ).
thf(fun_Pr3099820731930151597t_bool_type,type,
fun_Pr3099820731930151597t_bool: $tType ).
thf(fun_na8713714802964096592at_nat_type,type,
fun_na8713714802964096592at_nat: $tType ).
thf(produc5835291356934675326atural_type,type,
produc5835291356934675326atural: $tType ).
thf(produc8126358835630522215t_unit_type,type,
produc8126358835630522215t_unit: $tType ).
thf(fun_fu3190366535859218979t_assn_type,type,
fun_fu3190366535859218979t_assn: $tType ).
thf(fun_fu3307002049327355231l_bool_type,type,
fun_fu3307002049327355231l_bool: $tType ).
thf(fun_fu6750301411456490045r_bool_type,type,
fun_fu6750301411456490045r_bool: $tType ).
thf(fun_Pr6001797050664311790t_bool_type,type,
fun_Pr6001797050664311790t_bool: $tType ).
thf(produc859450856879609959at_nat_type,type,
produc859450856879609959at_nat: $tType ).
thf(produc6495656768158660455at_int_type,type,
produc6495656768158660455at_int: $tType ).
thf(produc4806409095325742951nt_nat_type,type,
produc4806409095325742951nt_nat: $tType ).
thf(produc1219242969750017639nt_int_type,type,
produc1219242969750017639nt_int: $tType ).
thf(fun_Pr6529957239379720399at_nat_type,type,
fun_Pr6529957239379720399at_nat: $tType ).
thf(fun_Pr2352106219870523691at_int_type,type,
fun_Pr2352106219870523691at_int: $tType ).
thf(fun_na1841593615831545295et_nat_type,type,
fun_na1841593615831545295et_nat: $tType ).
thf(fun_in4666789911842550827et_nat_type,type,
fun_in4666789911842550827et_nat: $tType ).
thf(fun_Co1555053522382583933nteger_type,type,
fun_Co1555053522382583933nteger: $tType ).
thf(set_Pr7577011563204128103nteger_type,type,
set_Pr7577011563204128103nteger: $tType ).
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thf(fun_fu6225000568980017287er_nat_type,type,
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thf(fun_Co6597186368970283863nteger_type,type,
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thf(produc9072561841945455293at_nat_type,type,
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thf(produc1306064898605085721nt_int_type,type,
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thf(fun_fu3065856773340909731l_assn_type,type,
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thf(fun_na572088516609390416t_unit_type,type,
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thf(fun_he8038253169496836892et_nat_type,type,
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thf(set_se8994758365886191399t_unit_type,type,
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thf(fun_Co2652536811680367946nteger_type,type,
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thf(fun_Pr3763555631386913362t_unit_type,type,
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thf(fun_fi5759838706352575625t_bool_type,type,
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thf(fun_Pr3145601080792579042t_bool_type,type,
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thf(set_Pr4811707699266497531nteger_type,type,
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thf(fun_fu1358573228874515237nt_nat_type,type,
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thf(fun_se1992738044240919715nteger_type,type,
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thf(set_Pr4580871404036792859t_unit_type,type,
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thf(produc6653097349344004940it_nat_type,type,
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thf(fun_Pr3513738403344720850et_nat_type,type,
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thf(fun_Pr1791375292569619697at_nat_type,type,
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thf(set_se3685025362742366375l_bool_type,type,
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thf(produc6172120975061646567t_bool_type,type,
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thf(set_Pr9123050470547338789r_bool_type,type,
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thf(set_Pr2406931829603198446nteger_type,type,
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thf(set_Pr8986988648414616686er_nat_type,type,
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thf(set_Pr6496905503482889930er_int_type,type,
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thf(produc7819656566062154093et_nat_type,type,
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thf(produc2115011035271226405et_int_type,type,
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thf(set_Pr1261947904930325089at_nat_type,type,
set_Pr1261947904930325089at_nat: $tType ).
thf(set_Pr7995236796853374141at_int_type,type,
set_Pr7995236796853374141at_int: $tType ).
thf(set_Pr3448869479623346877nt_nat_type,type,
set_Pr3448869479623346877nt_nat: $tType ).
thf(set_Pr958786334691620121nt_int_type,type,
set_Pr958786334691620121nt_int: $tType ).
thf(produc2400336064389900727et_nat_type,type,
produc2400336064389900727et_nat: $tType ).
thf(produc2771989624626745363et_nat_type,type,
produc2771989624626745363et_nat: $tType ).
thf(fun_se1093428521897753731t_bool_type,type,
fun_se1093428521897753731t_bool: $tType ).
thf(fun_set_set_bool_nat_type,type,
fun_set_set_bool_nat: $tType ).
thf(fun_se2712834123562403997r_bool_type,type,
fun_se2712834123562403997r_bool: $tType ).
thf(fun_bo8700639080905871165nteger_type,type,
fun_bo8700639080905871165nteger: $tType ).
thf(fun_Co5127707541723817779t_bool_type,type,
fun_Co5127707541723817779t_bool: $tType ).
thf(produc2151345699928993137t_bool_type,type,
produc2151345699928993137t_bool: $tType ).
thf(produc2470230561889619165t_unit_type,type,
produc2470230561889619165t_unit: $tType ).
thf(fun_set_set_nat_nat_type,type,
fun_set_set_nat_nat: $tType ).
thf(fun_set_set_int_nat_type,type,
fun_set_set_int_nat: $tType ).
thf(fun_set_set_int_int_type,type,
fun_set_set_int_int: $tType ).
thf(fun_set_nat_set_nat_type,type,
fun_set_nat_set_nat: $tType ).
thf(fun_set_int_set_int_type,type,
fun_set_int_set_int: $tType ).
thf(fun_se5752938643995848800er_nat_type,type,
fun_se5752938643995848800er_nat: $tType ).
thf(fun_na9118744110877893344nteger_type,type,
fun_na9118744110877893344nteger: $tType ).
thf(fun_in6808926178784942396nteger_type,type,
fun_in6808926178784942396nteger: $tType ).
thf(fun_Co7398788559141407565atural_type,type,
fun_Co7398788559141407565atural: $tType ).
thf(fun_Co2940338738630218498nteger_type,type,
fun_Co2940338738630218498nteger: $tType ).
thf(fun_Co8307959106670069728et_nat_type,type,
fun_Co8307959106670069728et_nat: $tType ).
thf(fun_Co5817875961738342972et_int_type,type,
fun_Co5817875961738342972et_int: $tType ).
thf(fun_Co3734316457315071362atural_type,type,
fun_Co3734316457315071362atural: $tType ).
thf(fun_Co8499238673658658103nteger_type,type,
fun_Co8499238673658658103nteger: $tType ).
thf(produc600557818389255820it_nat_type,type,
produc600557818389255820it_nat: $tType ).
thf(produc5646078835734834920it_int_type,type,
produc5646078835734834920it_int: $tType ).
thf(produc526117512892780850t_unit_type,type,
produc526117512892780850t_unit: $tType ).
thf(produc6865911496949736918t_unit_type,type,
produc6865911496949736918t_unit: $tType ).
thf(fun_se407542756755239981t_bool_type,type,
fun_se407542756755239981t_bool: $tType ).
thf(fun_Pr6388117812002676717t_bool_type,type,
fun_Pr6388117812002676717t_bool: $tType ).
thf(fun_bo8182086032597355865t_unit_type,type,
fun_bo8182086032597355865t_unit: $tType ).
thf(set_fu6339532538019888579t_bool_type,type,
set_fu6339532538019888579t_bool: $tType ).
thf(fun_se6196082035949986000it_nat_type,type,
fun_se6196082035949986000it_nat: $tType ).
thf(fun_Pr1628945989756059814et_nat_type,type,
fun_Pr1628945989756059814et_nat: $tType ).
thf(fun_Pr8362234881679108866et_int_type,type,
fun_Pr8362234881679108866et_int: $tType ).
thf(fun_Pr6278675377255837256atural_type,type,
fun_Pr6278675377255837256atural: $tType ).
thf(fun_Pr1820225556744648189nteger_type,type,
fun_Pr1820225556744648189nteger: $tType ).
thf(fun_na896991816813928310t_unit_type,type,
fun_na896991816813928310t_unit: $tType ).
thf(fun_in4731230917697954842t_unit_type,type,
fun_in4731230917697954842t_unit: $tType ).
thf(fun_Co3228878137750316606t_unit_type,type,
fun_Co3228878137750316606t_unit: $tType ).
thf(fun_Co1365676809456677961t_unit_type,type,
fun_Co1365676809456677961t_unit: $tType ).
thf(fun_bo1841576699660343469l_bool_type,type,
fun_bo1841576699660343469l_bool: $tType ).
thf(fun_Pr2191293291710260995t_unit_type,type,
fun_Pr2191293291710260995t_unit: $tType ).
thf(fun_set_bool_assn_type,type,
fun_set_bool_assn: $tType ).
thf(fun_rat_fun_rat_bool_type,type,
fun_rat_fun_rat_bool: $tType ).
thf(fun_nat_fun_nat_bool_type,type,
fun_nat_fun_nat_bool: $tType ).
thf(fun_int_fun_int_bool_type,type,
fun_int_fun_int_bool: $tType ).
thf(fun_set_nat_assn_type,type,
fun_set_nat_assn: $tType ).
thf(fun_set_int_assn_type,type,
fun_set_int_assn: $tType ).
thf(fun_rat_fun_rat_rat_type,type,
fun_rat_fun_rat_rat: $tType ).
thf(fun_nat_fun_nat_nat_type,type,
fun_nat_fun_nat_nat: $tType ).
thf(fun_int_fun_int_int_type,type,
fun_int_fun_int_int: $tType ).
thf(fun_Co4490034186337852034r_assn_type,type,
fun_Co4490034186337852034r_assn: $tType ).
thf(fun_as9138348466139350018nteger_type,type,
fun_as9138348466139350018nteger: $tType ).
thf(set_set_set_nat_type,type,
set_set_set_nat: $tType ).
thf(set_set_Code_integer_type,type,
set_set_Code_integer: $tType ).
thf(fun_bool_filter_nat_type,type,
fun_bool_filter_nat: $tType ).
thf(fun_filter_nat_bool_type,type,
fun_filter_nat_bool: $tType ).
thf(fun_rat_filter_nat_type,type,
fun_rat_filter_nat: $tType ).
thf(fun_nat_filter_nat_type,type,
fun_nat_filter_nat: $tType ).
thf(fun_int_filter_nat_type,type,
fun_int_filter_nat: $tType ).
thf(fun_filter_nat_rat_type,type,
fun_filter_nat_rat: $tType ).
thf(fun_Pr6626665806141890376t_assn_type,type,
fun_Pr6626665806141890376t_assn: $tType ).
thf(set_set_Product_unit_type,type,
set_set_Product_unit: $tType ).
thf(produc2804947525362035943l_bool_type,type,
produc2804947525362035943l_bool: $tType ).
thf(heap_e7401611519738050253t_unit_type,type,
heap_e7401611519738050253t_unit: $tType ).
thf(produc8000372497851584572t_bool_type,type,
produc8000372497851584572t_bool: $tType ).
thf(produc4876081531382960352t_bool_type,type,
produc4876081531382960352t_bool: $tType ).
thf(produc567104428201204118ol_nat_type,type,
produc567104428201204118ol_nat: $tType ).
thf(produc5612625445546783218ol_int_type,type,
produc5612625445546783218ol_int: $tType ).
thf(product_prod_nat_nat_type,type,
product_prod_nat_nat: $tType ).
thf(product_prod_nat_int_type,type,
product_prod_nat_int: $tType ).
thf(product_prod_int_nat_type,type,
product_prod_int_nat: $tType ).
thf(product_prod_int_int_type,type,
product_prod_int_int: $tType ).
thf(fun_set_bool_bool_type,type,
fun_set_bool_bool: $tType ).
thf(fun_bool_set_bool_type,type,
fun_bool_set_bool: $tType ).
thf(set_fun_bool_bool_type,type,
set_fun_bool_bool: $tType ).
thf(fun_set_rat_bool_type,type,
fun_set_rat_bool: $tType ).
thf(fun_set_nat_bool_type,type,
fun_set_nat_bool: $tType ).
thf(fun_set_int_bool_type,type,
fun_set_int_bool: $tType ).
thf(fun_set_bool_nat_type,type,
fun_set_bool_nat: $tType ).
thf(fun_nat_set_bool_type,type,
fun_nat_set_bool: $tType ).
thf(fun_int_set_bool_type,type,
fun_int_set_bool: $tType ).
thf(fun_bool_set_nat_type,type,
fun_bool_set_nat: $tType ).
thf(fun_bool_set_int_type,type,
fun_bool_set_int: $tType ).
thf(fun_bo2517147204845630802atural_type,type,
fun_bo2517147204845630802atural: $tType ).
thf(fun_bo7282069421189217543nteger_type,type,
fun_bo7282069421189217543nteger: $tType ).
thf(fun_Co7175331531449502024l_bool_type,type,
fun_Co7175331531449502024l_bool: $tType ).
thf(fun_Co8822979462182099027r_bool_type,type,
fun_Co8822979462182099027r_bool: $tType ).
thf(set_fun_nat_bool_type,type,
set_fun_nat_bool: $tType ).
thf(set_fun_int_bool_type,type,
set_fun_int_bool: $tType ).
thf(fun_set_nat_nat_type,type,
fun_set_nat_nat: $tType ).
thf(fun_set_nat_int_type,type,
fun_set_nat_int: $tType ).
thf(fun_set_int_nat_type,type,
fun_set_int_nat: $tType ).
thf(fun_set_int_int_type,type,
fun_set_int_int: $tType ).
thf(fun_rat_Code_integer_type,type,
fun_rat_Code_integer: $tType ).
thf(fun_nat_set_nat_type,type,
fun_nat_set_nat: $tType ).
thf(fun_nat_set_int_type,type,
fun_nat_set_int: $tType ).
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_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(fun_Pr1572506220757514509t_bool_type,type,
fun_Pr1572506220757514509t_bool: $tType ).
thf(fun_bo1891391082718140537t_unit_type,type,
fun_bo1891391082718140537t_unit: $tType ).
thf(sum_sum_nat_nat_type,type,
sum_sum_nat_nat: $tType ).
thf(set_filter_nat_type,type,
set_filter_nat: $tType ).
thf(filter_set_nat_type,type,
filter_set_nat: $tType ).
thf(fun_Product_unit_rat_type,type,
fun_Product_unit_rat: $tType ).
thf(fun_Product_unit_nat_type,type,
fun_Product_unit_nat: $tType ).
thf(fun_Product_unit_int_type,type,
fun_Product_unit_int: $tType ).
thf(fun_nat_Product_unit_type,type,
fun_nat_Product_unit: $tType ).
thf(fun_int_Product_unit_type,type,
fun_int_Product_unit: $tType ).
thf(fun_bool_assn_type,type,
fun_bool_assn: $tType ).
thf(fun_assn_bool_type,type,
fun_assn_bool: $tType ).
thf(set_set_bool_type,type,
set_set_bool: $tType ).
thf(fun_rat_assn_type,type,
fun_rat_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_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_natural_type,type,
set_Code_natural: $tType ).
thf(set_Code_integer_type,type,
set_Code_integer: $tType ).
thf(set_Product_unit_type,type,
set_Product_unit: $tType ).
thf(fun_bool_bool_type,type,
fun_bool_bool: $tType ).
thf(fun_rat_bool_type,type,
fun_rat_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_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_nat_type,type,
fun_rat_nat: $tType ).
thf(fun_rat_int_type,type,
fun_rat_int: $tType ).
thf(fun_nat_rat_type,type,
fun_nat_rat: $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_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(filter_nat_type,type,
filter_nat: $tType ).
thf(list_nat_type,type,
list_nat: $tType ).
thf(set_bool_type,type,
set_bool: $tType ).
thf(set_rat_type,type,
set_rat: $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(typerep_type,type,
typerep: $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(aTP_Lamm_a_decl,type,
aTP_Lamm_a: set_fu6080891106736489294t_bool > fun_fu9160419385450930796l_bool ).
thf(aTP_Lamm_ae_decl,type,
aTP_Lamm_ae: fun_Pr6001797050664311790t_bool > fun_fu7398481913972163267t_bool ).
thf(aTP_Lamm_af_decl,type,
aTP_Lamm_af: fun_Pr6001797050664311790t_bool > fun_fu7398481913972163267t_bool ).
thf(aTP_Lamm_ag_decl,type,
aTP_Lamm_ag: fun_Pr6001797050664311790t_bool ).
thf(aTP_Lamm_ah_decl,type,
aTP_Lamm_ah: fun_fu7398481913972163267t_bool ).
thf(aTP_Lamm_ai_decl,type,
aTP_Lamm_ai: assn > fun_as4100195077546555551t_bool ).
thf(aTP_Lamm_aj_decl,type,
aTP_Lamm_aj: assn > fun_as4100195077546555551t_bool ).
thf(aTP_Lamm_al_decl,type,
aTP_Lamm_al: fun_as4100195077546555551t_bool ).
thf(abs_assn_decl,type,
abs_assn: fun_fu1264473476461866025l_assn ).
thf(rep_assn_decl,type,
rep_assn: fun_as4100195077546555551t_bool ).
thf(in_range_decl,type,
in_range: fun_Pr6001797050664311790t_bool ).
thf(one_assn_raw_decl,type,
one_assn_raw: fun_Pr6001797050664311790t_bool ).
thf(one_assn_raw_rel_decl,type,
one_assn_raw_rel: fun_Pr8933696392609397829t_bool ).
thf(proper_decl,type,
proper: fun_fu9160419385450930796l_bool ).
thf(pure_a825153325127701367it_nat_decl,type,
pure_a825153325127701367it_nat: bool > fun_Pr6001797050664311790t_bool ).
thf(times_assn_raw_decl,type,
times_assn_raw: fun_Pr6001797050664311790t_bool > fun_fu7398481913972163267t_bool ).
thf(wand_assn_decl,type,
wand_assn: assn > fun_assn_assn ).
thf(wand_raw_decl,type,
wand_raw: fun_Pr6001797050664311790t_bool > fun_fu7398481913972163267t_bool ).
thf(bNF_fs3871268833404974121et_nat_decl,type,
bNF_fs3871268833404974121et_nat: fun_he7710493197641524256t_bool > fun_se707272970763642173t_bool > fun_Pr7091840695141096449et_nat ).
thf(bNF_pi3450177011487049898et_nat_decl,type,
bNF_pi3450177011487049898et_nat: fun_he1004219788074801965t_bool > fun_he7710493197641524256t_bool > heap_e7401611519738050253t_unit > set_nat > heap_e7401611519738050253t_unit ).
thf(bNF_pi4042512755101277815et_nat_decl,type,
bNF_pi4042512755101277815et_nat: fun_he7710493197641524256t_bool > fun_se707272970763642173t_bool > heap_e7401611519738050253t_unit > fun_set_nat_set_nat ).
thf(bNF_sn4039337771197282234et_nat_decl,type,
bNF_sn4039337771197282234et_nat: fun_he1004219788074801965t_bool > fun_he7710493197641524256t_bool > fun_Pr7091840695141096449et_nat ).
thf(basic_2698842327037663054et_nat_decl,type,
basic_2698842327037663054et_nat: produc3658429121746597890et_nat > set_set_nat ).
thf(comp_i6200299785623974754nt_int_decl,type,
comp_i6200299785623974754nt_int: fun_int_set_nat > fun_Pr982841511892225912nt_int > fun_Pr3513738403344720850et_nat ).
thf(comp_P2930521774885306735et_nat_decl,type,
comp_P2930521774885306735et_nat: fun_Pr3337834798857116037et_nat > fun_Pr7091840695141096449et_nat > fun_Pr3337834798857116037et_nat ).
thf(comp_P8606889026643445772nt_int_decl,type,
comp_P8606889026643445772nt_int: fun_Pr3337834798857116037et_nat > fun_Pr2304087830868576334et_nat > fun_Pr3513738403344720850et_nat ).
thf(comp_P8308861049717174982et_nat_decl,type,
comp_P8308861049717174982et_nat: fun_Pr982841511892225912nt_int > fun_Pr5141187847748131984nt_int > fun_Pr2352106219870523691at_int ).
thf(comp_s1601710177542341017et_nat_decl,type,
comp_s1601710177542341017et_nat: fun_set_nat_int > fun_Pr3337834798857116037et_nat > fun_Pr2352106219870523691at_int ).
thf(minus_minus_assn_decl,type,
minus_minus_assn: assn > fun_assn_assn ).
thf(one_one_assn_decl,type,
one_one_assn: assn ).
thf(times_times_assn_decl,type,
times_times_assn: assn > fun_assn_assn ).
thf(uminus_uminus_assn_decl,type,
uminus_uminus_assn: fun_assn_assn ).
thf(inf_inf_assn_decl,type,
inf_inf_assn: fun_as3983628580203722482n_assn ).
thf(inf_in1689267372175091004t_bool_decl,type,
inf_in1689267372175091004t_bool: set_fu6080891106736489294t_bool > set_fu6080891106736489294t_bool > set_fu6080891106736489294t_bool ).
thf(sup_sup_assn_decl,type,
sup_sup_assn: fun_as3983628580203722482n_assn ).
thf(rel_restrict_nat_decl,type,
rel_restrict_nat: set_Pr1261947904930325089at_nat > set_nat > set_Pr1261947904930325089at_nat ).
thf(bot_bot_assn_decl,type,
bot_bot_assn: assn ).
thf(bot_bot_set_nat_decl,type,
bot_bot_set_nat: set_nat ).
thf(bot_bo2714889297266208186t_bool_decl,type,
bot_bo2714889297266208186t_bool: set_fu6080891106736489294t_bool ).
thf(ord_le387542735852657390t_bool_decl,type,
ord_le387542735852657390t_bool: set_fu6080891106736489294t_bool > fun_se7275083947436752652l_bool ).
thf(top_top_assn_decl,type,
top_top_assn: assn ).
thf(top_to2524957550908328808et_nat_decl,type,
top_to2524957550908328808et_nat: set_Pr3948176798113811640et_nat ).
thf(top_top_set_set_nat_decl,type,
top_top_set_set_nat: set_set_nat ).
thf(top_to5841454426718376094t_bool_decl,type,
top_to5841454426718376094t_bool: set_fu6080891106736489294t_bool ).
thf(produc7507926704131184380et_nat_decl,type,
produc7507926704131184380et_nat: heap_e7401611519738050253t_unit > fun_se1339536933736954245et_nat ).
thf(produc2471974422597015918t_unit_decl,type,
produc2471974422597015918t_unit: set_nat > heap_e7401611519738050253t_unit > produc7348995623955488188t_unit ).
thf(produc4172003873565521026et_nat_decl,type,
produc4172003873565521026et_nat: fun_he2331061685413951235t_unit > fun_Pr7091840695141096449et_nat ).
thf(produc3286488329990770625t_unit_decl,type,
produc3286488329990770625t_unit: fun_set_nat_set_nat > fun_Pr7091840695141096449et_nat ).
thf(produc5973434381925408567at_int_decl,type,
produc5973434381925408567at_int: fun_he6078633327341457676it_int > fun_set_nat_int > fun_Pr5141187847748131984nt_int ).
thf(produc3152090231653401565et_nat_decl,type,
produc3152090231653401565et_nat: fun_in7572449478177386490t_unit > fun_int_set_nat > fun_Pr2304087830868576334et_nat ).
thf(produc1824681642469235216et_nat_decl,type,
produc1824681642469235216et_nat: fun_Pr7672403737682949028t_unit ).
thf(produc6012101397789842562t_unit_decl,type,
produc6012101397789842562t_unit: produc7348995623955488188t_unit > set_nat ).
thf(produc8586169260539613262et_nat_decl,type,
produc8586169260539613262et_nat: fun_Pr3337834798857116037et_nat ).
thf(product_snd_int_int_decl,type,
product_snd_int_int: fun_Pr982841511892225912nt_int ).
thf(produc3550216979005444800t_unit_decl,type,
produc3550216979005444800t_unit: produc7348995623955488188t_unit > heap_e7401611519738050253t_unit ).
thf(produc6300697153377358172et_nat_decl,type,
produc6300697153377358172et_nat: fun_Pr7214764501845804219t_unit ).
thf(produc1264744871843189710t_unit_decl,type,
produc1264744871843189710t_unit: fun_Pr5504542249117545915et_nat ).
thf(total_on_nat_decl,type,
total_on_nat: set_nat > set_Pr1261947904930325089at_nat > $o ).
thf(collec3007137136614167897t_bool_decl,type,
collec3007137136614167897t_bool: fun_fu5792599895934982715t_bool ).
thf(image_6088997261112373647et_nat_decl,type,
image_6088997261112373647et_nat: fun_Pr3337834798857116037et_nat > set_Pr3948176798113811640et_nat > set_set_nat ).
thf(is_empty_nat_decl,type,
is_empty_nat: fun_set_nat_bool ).
thf(remove7940366566026015955t_bool_decl,type,
remove7940366566026015955t_bool: fun_Pr6001797050664311790t_bool > set_fu6080891106736489294t_bool > set_fu6080891106736489294t_bool ).
thf(type_d18088346645320984t_bool_decl,type,
type_d18088346645320984t_bool: fun_as4100195077546555551t_bool > fun_fu1264473476461866025l_assn > fun_se7275083947436752652l_bool ).
thf(accp_P5801069581201407417et_nat_decl,type,
accp_P5801069581201407417et_nat: fun_Pr8933696392609397829t_bool > fun_Pr6001797050664311790t_bool ).
thf(pred_chain_nat_decl,type,
pred_chain_nat: set_nat > fun_nat_fun_nat_bool > fun_set_nat_bool ).
thf(aa_assn_assn_decl,type,
aa_assn_assn: fun_assn_assn > assn > assn ).
thf(aa_assn_bool_decl,type,
aa_assn_bool: fun_assn_bool > assn > bool ).
thf(aa_ass954072293579886259n_assn_decl,type,
aa_ass954072293579886259n_assn: fun_as3983628580203722482n_assn > assn > fun_assn_assn ).
thf(aa_ass8975924923219239432t_bool_decl,type,
aa_ass8975924923219239432t_bool: fun_as4100195077546555551t_bool > assn > fun_Pr6001797050664311790t_bool ).
thf(aa_hea1793595068369496646t_bool_decl,type,
aa_hea1793595068369496646t_bool: fun_he6201055237484778573t_bool > heap_e7401611519738050253t_unit > bool ).
thf(aa_hea2136485429539994620t_unit_decl,type,
aa_hea2136485429539994620t_unit: fun_he2331061685413951235t_unit > heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit ).
thf(aa_hea2782697410307197849t_bool_decl,type,
aa_hea2782697410307197849t_bool: fun_he7710493197641524256t_bool > heap_e7401611519738050253t_unit > fun_set_nat_bool ).
thf(aa_Pro2991721470636411351t_bool_decl,type,
aa_Pro2991721470636411351t_bool: fun_Pr6001797050664311790t_bool > produc3658429121746597890et_nat > bool ).
thf(aa_Pro1219312880135979149t_unit_decl,type,
aa_Pro1219312880135979149t_unit: fun_Pr7672403737682949028t_unit > produc3658429121746597890et_nat > heap_e7401611519738050253t_unit ).
thf(aa_Pro3679490825741336130et_nat_decl,type,
aa_Pro3679490825741336130et_nat: fun_Pr7091840695141096449et_nat > produc3658429121746597890et_nat > produc3658429121746597890et_nat ).
thf(aa_Pro7370057327950226428t_unit_decl,type,
aa_Pro7370057327950226428t_unit: fun_Pr7214764501845804219t_unit > produc3658429121746597890et_nat > produc7348995623955488188t_unit ).
thf(aa_Pro3416150927818442182et_nat_decl,type,
aa_Pro3416150927818442182et_nat: fun_Pr3337834798857116037et_nat > produc3658429121746597890et_nat > set_nat ).
thf(aa_Pro2092192379717785596et_nat_decl,type,
aa_Pro2092192379717785596et_nat: fun_Pr5504542249117545915et_nat > produc7348995623955488188t_unit > produc3658429121746597890et_nat ).
thf(aa_set_nat_bool_decl,type,
aa_set_nat_bool: fun_set_nat_bool > set_nat > bool ).
thf(aa_set3979848162462698438et_nat_decl,type,
aa_set3979848162462698438et_nat: fun_se1339536933736954245et_nat > set_nat > produc3658429121746597890et_nat ).
thf(aa_set_nat_set_nat_decl,type,
aa_set_nat_set_nat: fun_set_nat_set_nat > set_nat > set_nat ).
thf(aa_set6242977750710348305t_bool_decl,type,
aa_set6242977750710348305t_bool: fun_se9021057006710688848t_bool > set_nat > fun_he6201055237484778573t_bool ).
thf(aa_set3226752938961784069l_bool_decl,type,
aa_set3226752938961784069l_bool: fun_se7275083947436752652l_bool > set_fu6080891106736489294t_bool > bool ).
thf(aa_fun1993714536301460826l_assn_decl,type,
aa_fun1993714536301460826l_assn: fun_fu1264473476461866025l_assn > fun_Pr6001797050664311790t_bool > assn ).
thf(aa_fun5588795374382764133l_bool_decl,type,
aa_fun5588795374382764133l_bool: fun_fu9160419385450930796l_bool > fun_Pr6001797050664311790t_bool > bool ).
thf(aa_fun6808777976510360636t_bool_decl,type,
aa_fun6808777976510360636t_bool: fun_fu7398481913972163267t_bool > fun_Pr6001797050664311790t_bool > fun_Pr6001797050664311790t_bool ).
thf(aa_fun8162393684988594084t_bool_decl,type,
aa_fun8162393684988594084t_bool: fun_fu5792599895934982715t_bool > fun_fu9160419385450930796l_bool > set_fu6080891106736489294t_bool ).
thf(member6260224972018164377et_nat_decl,type,
member6260224972018164377et_nat: produc3658429121746597890et_nat > set_Pr3948176798113811640et_nat > $o ).
thf(member_set_nat_decl,type,
member_set_nat: set_nat > set_set_nat > $o ).
thf(member4125802036136091927t_bool_decl,type,
member4125802036136091927t_bool: fun_Pr6001797050664311790t_bool > fun_se7275083947436752652l_bool ).
thf(pp_decl,type,
pp: bool > $o ).
thf(h_decl,type,
h: produc3658429121746597890et_nat ).
thf(197,axiom,
! [A: produc3658429121746597890et_nat,B: produc3658429121746597890et_nat] :
( ( A = B )
<=> ( ( ( A @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) )
= ( B @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) ) )
& ( ( A @ ( produc1824681642469235216et_nat @ aa_Pro1219312880135979149t_unit ) )
= ( B @ ( produc1824681642469235216et_nat @ aa_Pro1219312880135979149t_unit ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4779_prod__eq__iff) ).
thf(1105,plain,
! [A: produc3658429121746597890et_nat,B: produc3658429121746597890et_nat] :
( ( ( ( ( A @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) )
= ( B @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) ) )
& ( ( A @ ( produc1824681642469235216et_nat @ aa_Pro1219312880135979149t_unit ) )
= ( B @ ( produc1824681642469235216et_nat @ aa_Pro1219312880135979149t_unit ) ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( ( A @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) )
= ( B @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) ) )
& ( ( A @ ( produc1824681642469235216et_nat @ aa_Pro1219312880135979149t_unit ) )
= ( B @ ( produc1824681642469235216et_nat @ aa_Pro1219312880135979149t_unit ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(3,axiom,
! [A: set_fu6080891106736489294t_bool,B: set_fu6080891106736489294t_bool] :
( ! [C: fun_Pr6001797050664311790t_bool] :
( ( A @ ( C @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ~ ( B @ ( C @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ) )
=> ( ( B @ ( A @ inf_in1689267372175091004t_bool ) )
= bot_bo2714889297266208186t_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1348_Int__emptyI) ).
thf(234,plain,
! [A: set_fu6080891106736489294t_bool,B: set_fu6080891106736489294t_bool] :
( ! [C: fun_Pr6001797050664311790t_bool] :
( ( A @ ( C @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ~ ( B @ ( C @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ) )
=> ( ( B @ ( A @ inf_in1689267372175091004t_bool ) )
= bot_bo2714889297266208186t_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(118,axiom,
! [A: assn] : ( proper @ ( collec3007137136614167897t_bool @ aa_fun8162393684988594084t_bool ) @ ( A @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_Rep__assn) ).
thf(762,plain,
! [A: assn] : ( proper @ ( collec3007137136614167897t_bool @ aa_fun8162393684988594084t_bool ) @ ( A @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(172,axiom,
! [A: assn,B: assn,C: assn] :
( ( C @ ( B @ ( A @ times_times_assn @ aa_assn_assn ) @ times_times_assn @ aa_assn_assn ) )
= ( C @ ( B @ times_times_assn @ aa_assn_assn ) @ ( A @ times_times_assn @ aa_assn_assn ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_465_mult_Oright__assoc) ).
thf(1005,plain,
! [A: assn,B: assn,C: assn] :
( ( C @ ( B @ ( A @ times_times_assn @ aa_assn_assn ) @ times_times_assn @ aa_assn_assn ) )
= ( C @ ( B @ times_times_assn @ aa_assn_assn ) @ ( A @ times_times_assn @ aa_assn_assn ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(100,axiom,
! [A: assn] :
( ( A @ ( uminus_uminus_assn @ aa_assn_assn ) @ ( A @ ( inf_inf_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) )
= bot_bot_assn ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6835_boolean__algebra_Oconj__cancel__right) ).
thf(683,plain,
! [A: assn] :
( ( A @ ( uminus_uminus_assn @ aa_assn_assn ) @ ( A @ ( inf_inf_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) )
= bot_bot_assn ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(187,axiom,
! [A: assn,B: assn,C: produc3658429121746597890et_nat] :
( ( C @ ( B @ ( A @ aTP_Lamm_aj @ aa_ass8975924923219239432t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp )
<=> ( ( C @ ( B @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp )
& ( C @ ( A @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7832_ATP_Olambda__37) ).
thf(1068,plain,
! [A: assn,B: assn,C: produc3658429121746597890et_nat] :
( ( ( ( C @ ( B @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp )
& ( C @ ( A @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp ) )
=> ( C @ ( B @ ( A @ aTP_Lamm_aj @ aa_ass8975924923219239432t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp ) )
& ( ( C @ ( B @ ( A @ aTP_Lamm_aj @ aa_ass8975924923219239432t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp )
=> ( ( C @ ( B @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp )
& ( C @ ( A @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(115,axiom,
! [A: assn,B: assn,C: assn] :
( ( C @ ( B @ ( A @ times_times_assn @ aa_assn_assn ) @ times_times_assn @ aa_assn_assn ) )
= ( C @ ( B @ times_times_assn @ aa_assn_assn ) @ ( A @ times_times_assn @ aa_assn_assn ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_382_assn__times__assoc) ).
thf(741,plain,
! [A: assn,B: assn,C: assn] :
( ( C @ ( B @ ( A @ times_times_assn @ aa_assn_assn ) @ times_times_assn @ aa_assn_assn ) )
= ( C @ ( B @ times_times_assn @ aa_assn_assn ) @ ( A @ times_times_assn @ aa_assn_assn ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(142,axiom,
! [A: fun_as4100195077546555551t_bool,B: fun_fu1264473476461866025l_assn,C: assn] :
( ( top_to5841454426718376094t_bool @ ( B @ ( A @ type_d18088346645320984t_bool ) @ aa_set3226752938961784069l_bool ) @ pp )
=> ~ ! [D: fun_Pr6001797050664311790t_bool] :
( C
!= ( D @ ( B @ aa_fun1993714536301460826l_assn ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4125_type__copy__obj__one__point__absE) ).
thf(873,plain,
! [A: fun_as4100195077546555551t_bool,B: fun_fu1264473476461866025l_assn,C: assn] :
( ( top_to5841454426718376094t_bool @ ( B @ ( A @ type_d18088346645320984t_bool ) @ aa_set3226752938961784069l_bool ) @ pp )
=> ~ ! [D: fun_Pr6001797050664311790t_bool] :
( C
!= ( D @ ( B @ aa_fun1993714536301460826l_assn ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(64,axiom,
! [A: fun_he7710493197641524256t_bool] :
( ! [B: heap_e7401611519738050253t_unit,C: set_nat] : ( C @ ( B @ ( A @ aa_hea2782697410307197849t_bool ) @ aa_set_nat_bool ) @ pp )
<=> ! [B: produc3658429121746597890et_nat] : ( B @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) @ ( B @ ( produc1824681642469235216et_nat @ aa_Pro1219312880135979149t_unit ) @ ( A @ aa_hea2782697410307197849t_bool ) @ aa_set_nat_bool ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4785_All__prod__contract) ).
thf(511,plain,
! [A: fun_he7710493197641524256t_bool] :
( ( ! [B: produc3658429121746597890et_nat] : ( B @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) @ ( B @ ( produc1824681642469235216et_nat @ aa_Pro1219312880135979149t_unit ) @ ( A @ aa_hea2782697410307197849t_bool ) @ aa_set_nat_bool ) @ pp )
=> ! [B: heap_e7401611519738050253t_unit,C: set_nat] : ( C @ ( B @ ( A @ aa_hea2782697410307197849t_bool ) @ aa_set_nat_bool ) @ pp ) )
& ( ! [B: heap_e7401611519738050253t_unit,C: set_nat] : ( C @ ( B @ ( A @ aa_hea2782697410307197849t_bool ) @ aa_set_nat_bool ) @ pp )
=> ! [B: produc3658429121746597890et_nat] : ( B @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) @ ( B @ ( produc1824681642469235216et_nat @ aa_Pro1219312880135979149t_unit ) @ ( A @ aa_hea2782697410307197849t_bool ) @ aa_set_nat_bool ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(180,axiom,
! [A: produc3658429121746597890et_nat] :
( ~ ( A @ ( one_assn_raw @ aa_Pro2991721470636411351t_bool ) @ pp )
=> ( ( A @ ( one_assn_raw_rel @ accp_P5801069581201407417et_nat @ aa_Pro2991721470636411351t_bool ) @ pp )
=> ~ ! [B: heap_e7401611519738050253t_unit,C: set_nat] :
( ( A
= ( C @ ( B @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) )
=> ( ( C @ ( B @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ ( one_assn_raw_rel @ accp_P5801069581201407417et_nat @ aa_Pro2991721470636411351t_bool ) @ pp )
=> ( C = bot_bot_set_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7763_one__assn__raw_Opelims_I3_J) ).
thf(1041,plain,
! [A: produc3658429121746597890et_nat] :
( ~ ( A @ ( one_assn_raw @ aa_Pro2991721470636411351t_bool ) @ pp )
=> ( ( A @ ( one_assn_raw_rel @ accp_P5801069581201407417et_nat @ aa_Pro2991721470636411351t_bool ) @ pp )
=> ~ ! [B: heap_e7401611519738050253t_unit,C: set_nat] :
( ( A
= ( C @ ( B @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) )
=> ( ( C @ ( B @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ ( one_assn_raw_rel @ accp_P5801069581201407417et_nat @ aa_Pro2991721470636411351t_bool ) @ pp )
=> ( C = bot_bot_set_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(189,axiom,
! [A: produc3658429121746597890et_nat] :
( ( A @ ( aTP_Lamm_ag @ aa_Pro2991721470636411351t_bool ) @ pp )
<=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7849_ATP_Olambda__54) ).
thf(1078,plain,
! [A: produc3658429121746597890et_nat] :
~ ( A @ ( aTP_Lamm_ag @ aa_Pro2991721470636411351t_bool ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(38,axiom,
! [A: fun_se9021057006710688848t_bool,B: produc3658429121746597890et_nat] :
( ( B @ ( produc1824681642469235216et_nat @ aa_Pro1219312880135979149t_unit ) @ ( B @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) @ ( A @ aa_set6242977750710348305t_bool ) @ aa_hea1793595068369496646t_bool ) @ pp )
=> ~ ! [C: heap_e7401611519738050253t_unit,D: set_nat] :
~ ( C @ ( D @ ( A @ aa_set6242977750710348305t_bool ) @ aa_hea1793595068369496646t_bool ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4988_exE__realizer_H) ).
thf(385,plain,
! [A: fun_se9021057006710688848t_bool,B: produc3658429121746597890et_nat] :
( ( B @ ( produc1824681642469235216et_nat @ aa_Pro1219312880135979149t_unit ) @ ( B @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) @ ( A @ aa_set6242977750710348305t_bool ) @ aa_hea1793595068369496646t_bool ) @ pp )
=> ~ ! [C: heap_e7401611519738050253t_unit,D: set_nat] :
~ ( C @ ( D @ ( A @ aa_set6242977750710348305t_bool ) @ aa_hea1793595068369496646t_bool ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(55,axiom,
! [A: assn,B: assn] :
( ( bot_bot_assn
= ( B @ ( A @ ( sup_sup_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) ) )
<=> ( ( B = bot_bot_assn )
& ( A = bot_bot_assn ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1551_bot__eq__sup__iff) ).
thf(472,plain,
! [A: assn,B: assn] :
( ( ( ( B = bot_bot_assn )
& ( A = bot_bot_assn ) )
=> ( bot_bot_assn
= ( B @ ( A @ ( sup_sup_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) ) ) )
& ( ( bot_bot_assn
= ( B @ ( A @ ( sup_sup_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) ) )
=> ( ( B = bot_bot_assn )
& ( A = bot_bot_assn ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(219,axiom,
! [A: produc3658429121746597890et_nat,B: bool] :
( ( ( A @ ( one_assn_raw @ aa_Pro2991721470636411351t_bool ) @ pp )
<=> ( B @ pp ) )
=> ( ( A @ ( one_assn_raw_rel @ accp_P5801069581201407417et_nat @ aa_Pro2991721470636411351t_bool ) @ pp )
=> ~ ! [C: heap_e7401611519738050253t_unit,D: set_nat] :
( ( A
= ( D @ ( C @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) )
=> ( ( ( B @ pp )
<=> ( D = bot_bot_set_nat ) )
=> ~ ( D @ ( C @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ ( one_assn_raw_rel @ accp_P5801069581201407417et_nat @ aa_Pro2991721470636411351t_bool ) @ pp ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7765_one__assn__raw_Opelims_I1_J) ).
thf(1233,plain,
! [A: produc3658429121746597890et_nat,B: bool] :
( ( ( ( B @ pp )
=> ( A @ ( one_assn_raw @ aa_Pro2991721470636411351t_bool ) @ pp ) )
& ( ( A @ ( one_assn_raw @ aa_Pro2991721470636411351t_bool ) @ pp )
=> ( B @ pp ) ) )
=> ( ( A @ ( one_assn_raw_rel @ accp_P5801069581201407417et_nat @ aa_Pro2991721470636411351t_bool ) @ pp )
=> ~ ! [C: heap_e7401611519738050253t_unit,D: set_nat] :
( ( A
= ( D @ ( C @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) )
=> ( ( ( ( D = bot_bot_set_nat )
=> ( B @ pp ) )
& ( ( B @ pp )
=> ( D = bot_bot_set_nat ) ) )
=> ~ ( D @ ( C @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ ( one_assn_raw_rel @ accp_P5801069581201407417et_nat @ aa_Pro2991721470636411351t_bool ) @ pp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(105,axiom,
! [A: assn,B: assn] :
( ( bot_bot_assn
= ( B @ ( A @ ( sup_sup_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) ) )
<=> ( ( B = bot_bot_assn )
& ( A = bot_bot_assn ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1523_sup__bot_Oneutr__eq__iff) ).
thf(698,plain,
! [A: assn,B: assn] :
( ( ( ( B = bot_bot_assn )
& ( A = bot_bot_assn ) )
=> ( bot_bot_assn
= ( B @ ( A @ ( sup_sup_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) ) ) )
& ( ( bot_bot_assn
= ( B @ ( A @ ( sup_sup_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) ) )
=> ( ( B = bot_bot_assn )
& ( A = bot_bot_assn ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(147,axiom,
! [A: produc3658429121746597890et_nat] :
( ( A @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) @ ( A @ ( produc1824681642469235216et_nat @ aa_Pro1219312880135979149t_unit ) @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4705_prod_Ocollapse) ).
thf(913,plain,
! [A: produc3658429121746597890et_nat] :
( ( A @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) @ ( A @ ( produc1824681642469235216et_nat @ aa_Pro1219312880135979149t_unit ) @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(218,axiom,
! [A: fun_Pr6001797050664311790t_bool,B: assn] :
( ! [C: produc3658429121746597890et_nat] :
( ( C @ ( A @ aa_Pro2991721470636411351t_bool ) @ pp )
<=> ( C @ ( B @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp ) )
=> ( B
= ( A @ ( abs_assn @ aa_fun1993714536301460826l_assn ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_Abs__assn__eqI_I2_J) ).
thf(1222,plain,
! [A: fun_Pr6001797050664311790t_bool,B: assn] :
( ! [C: produc3658429121746597890et_nat] :
( ( ( C @ ( B @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp )
=> ( C @ ( A @ aa_Pro2991721470636411351t_bool ) @ pp ) )
& ( ( C @ ( A @ aa_Pro2991721470636411351t_bool ) @ pp )
=> ( C @ ( B @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp ) ) )
=> ( B
= ( A @ ( abs_assn @ aa_fun1993714536301460826l_assn ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(42,axiom,
! [A: set_fu6080891106736489294t_bool] :
( ( bot_bo2714889297266208186t_bool @ ( A @ ord_le387542735852657390t_bool @ aa_set3226752938961784069l_bool ) @ pp )
<=> ( A = bot_bo2714889297266208186t_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_880_subset__empty) ).
thf(404,plain,
! [A: set_fu6080891106736489294t_bool] :
( ( ( A = bot_bo2714889297266208186t_bool )
=> ( bot_bo2714889297266208186t_bool @ ( A @ ord_le387542735852657390t_bool @ aa_set3226752938961784069l_bool ) @ pp ) )
& ( ( bot_bo2714889297266208186t_bool @ ( A @ ord_le387542735852657390t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( A = bot_bo2714889297266208186t_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(144,axiom,
! [A: bool,B: produc3658429121746597890et_nat,C: bool] :
( ( ( B @ ( A @ pure_a825153325127701367it_nat @ aa_Pro2991721470636411351t_bool ) @ pp )
<=> ( C @ pp ) )
=> ~ ! [D: heap_e7401611519738050253t_unit,E: set_nat] :
( ( B
= ( E @ ( D @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) )
=> ( ( C @ pp )
<=> ~ ( ( A @ pp )
& ( E = bot_bot_set_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_pure__assn__raw_Oelims_I1_J) ).
thf(885,plain,
! [A: bool,B: produc3658429121746597890et_nat,C: bool] :
( ( ( ( C @ pp )
=> ( B @ ( A @ pure_a825153325127701367it_nat @ aa_Pro2991721470636411351t_bool ) @ pp ) )
& ( ( B @ ( A @ pure_a825153325127701367it_nat @ aa_Pro2991721470636411351t_bool ) @ pp )
=> ( C @ pp ) ) )
=> ~ ! [D: heap_e7401611519738050253t_unit,E: set_nat] :
( ( B
= ( E @ ( D @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) )
=> ( ( ~ ( ( A @ pp )
& ( E = bot_bot_set_nat ) )
=> ( C @ pp ) )
& ( ( C @ pp )
=> ~ ( ( A @ pp )
& ( E = bot_bot_set_nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(21,axiom,
! [A: set_fu6080891106736489294t_bool] : ( A @ ( bot_bo2714889297266208186t_bool @ ord_le387542735852657390t_bool @ aa_set3226752938961784069l_bool ) @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_875_empty__subsetI) ).
thf(320,plain,
! [A: set_fu6080891106736489294t_bool] : ( A @ ( bot_bo2714889297266208186t_bool @ ord_le387542735852657390t_bool @ aa_set3226752938961784069l_bool ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(223,axiom,
! [A: produc7348995623955488188t_unit] :
( ( A @ ( produc1264744871843189710t_unit @ aa_Pro2092192379717785596et_nat ) @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) )
= ( A @ produc6012101397789842562t_unit ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4721_snd__swap) ).
thf(1265,plain,
! [A: produc7348995623955488188t_unit] :
( ( A @ ( produc1264744871843189710t_unit @ aa_Pro2092192379717785596et_nat ) @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) )
= ( A @ produc6012101397789842562t_unit ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(73,axiom,
! [A: assn,B: assn] :
( ( B @ ( A @ ( uminus_uminus_assn @ aa_assn_assn ) @ ( inf_inf_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) @ ( A @ ( inf_inf_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) )
= bot_bot_assn ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6856_inf__compl__bot__left2) ).
thf(570,plain,
! [A: assn,B: assn] :
( ( B @ ( A @ ( uminus_uminus_assn @ aa_assn_assn ) @ ( inf_inf_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) @ ( A @ ( inf_inf_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) )
= bot_bot_assn ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(184,axiom,
( top_top_assn
= ( in_range @ ( abs_assn @ aa_fun1993714536301460826l_assn ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4396_top__assn__def) ).
thf(1059,plain,
( top_top_assn
= ( in_range @ ( abs_assn @ aa_fun1993714536301460826l_assn ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(154,axiom,
! [A: fun_he7710493197641524256t_bool,B: heap_e7401611519738050253t_unit,C: set_nat,D: produc3658429121746597890et_nat] :
( ( C @ ( B @ ( A @ aa_hea2782697410307197849t_bool ) @ aa_set_nat_bool ) @ pp )
=> ( ( D
= ( C @ ( B @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) )
=> ( D @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) @ ( D @ ( produc1824681642469235216et_nat @ aa_Pro1219312880135979149t_unit ) @ ( A @ aa_hea2782697410307197849t_bool ) @ aa_set_nat_bool ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4832_BNF__Greatest__Fixpoint_Osubst__Pair) ).
thf(934,plain,
! [A: fun_he7710493197641524256t_bool,B: heap_e7401611519738050253t_unit,C: set_nat,D: produc3658429121746597890et_nat] :
( ( C @ ( B @ ( A @ aa_hea2782697410307197849t_bool ) @ aa_set_nat_bool ) @ pp )
=> ( ( D
= ( C @ ( B @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) )
=> ( D @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) @ ( D @ ( produc1824681642469235216et_nat @ aa_Pro1219312880135979149t_unit ) @ ( A @ aa_hea2782697410307197849t_bool ) @ aa_set_nat_bool ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(213,axiom,
! [A: assn,B: assn] :
( ( ( A @ ( rep_assn @ aa_ass8975924923219239432t_bool ) )
= ( B @ ( rep_assn @ aa_ass8975924923219239432t_bool ) ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_Rep__assn__inject) ).
thf(1191,plain,
! [A: assn,B: assn] :
( ( ( A = B )
=> ( ( A @ ( rep_assn @ aa_ass8975924923219239432t_bool ) )
= ( B @ ( rep_assn @ aa_ass8975924923219239432t_bool ) ) ) )
& ( ( ( A @ ( rep_assn @ aa_ass8975924923219239432t_bool ) )
= ( B @ ( rep_assn @ aa_ass8975924923219239432t_bool ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(141,axiom,
! [A: fun_he2331061685413951235t_unit,B: fun_set_nat_set_nat,C: produc3658429121746597890et_nat] :
( ( C @ ( B @ produc3286488329990770625t_unit @ aa_Pro3679490825741336130et_nat ) @ ( A @ produc4172003873565521026et_nat @ aa_Pro3679490825741336130et_nat ) )
= ( C @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) @ ( B @ aa_set_nat_set_nat ) @ ( C @ ( produc1824681642469235216et_nat @ aa_Pro1219312880135979149t_unit ) @ ( A @ aa_hea2136485429539994620t_unit ) @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4733_apfst__apsnd) ).
thf(870,plain,
! [A: fun_he2331061685413951235t_unit,B: fun_set_nat_set_nat,C: produc3658429121746597890et_nat] :
( ( C @ ( B @ produc3286488329990770625t_unit @ aa_Pro3679490825741336130et_nat ) @ ( A @ produc4172003873565521026et_nat @ aa_Pro3679490825741336130et_nat ) )
= ( C @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) @ ( B @ aa_set_nat_set_nat ) @ ( C @ ( produc1824681642469235216et_nat @ aa_Pro1219312880135979149t_unit ) @ ( A @ aa_hea2136485429539994620t_unit ) @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(161,axiom,
! [A: fun_he1004219788074801965t_bool,B: fun_he7710493197641524256t_bool,C: produc3658429121746597890et_nat] :
( ( C @ ( B @ ( A @ bNF_sn4039337771197282234et_nat ) @ aa_Pro3679490825741336130et_nat ) )
= ( C @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) @ ( C @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) @ ( C @ ( produc1824681642469235216et_nat @ aa_Pro1219312880135979149t_unit ) @ ( B @ ( A @ bNF_pi3450177011487049898et_nat ) ) ) @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5374_sndOp__def) ).
thf(969,plain,
! [A: fun_he1004219788074801965t_bool,B: fun_he7710493197641524256t_bool,C: produc3658429121746597890et_nat] :
( ( C @ ( B @ ( A @ bNF_sn4039337771197282234et_nat ) @ aa_Pro3679490825741336130et_nat ) )
= ( C @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) @ ( C @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) @ ( C @ ( produc1824681642469235216et_nat @ aa_Pro1219312880135979149t_unit ) @ ( B @ ( A @ bNF_pi3450177011487049898et_nat ) ) ) @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(120,axiom,
! [A: fun_he6201055237484778573t_bool,B: heap_e7401611519738050253t_unit,C: fun_set_nat_bool,D: set_nat] :
( ( B @ ( A @ aa_hea1793595068369496646t_bool ) @ pp )
=> ( ( D @ ( C @ aa_set_nat_bool ) @ pp )
=> ( ( D @ ( B @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) @ ( C @ aa_set_nat_bool ) @ pp )
& ( D @ ( B @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ ( produc1824681642469235216et_nat @ aa_Pro1219312880135979149t_unit ) @ ( A @ aa_hea1793595068369496646t_bool ) @ pp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4981_conjI__realizer) ).
thf(770,plain,
! [A: fun_he6201055237484778573t_bool,B: heap_e7401611519738050253t_unit,C: fun_set_nat_bool,D: set_nat] :
( ( B @ ( A @ aa_hea1793595068369496646t_bool ) @ pp )
=> ( ( D @ ( C @ aa_set_nat_bool ) @ pp )
=> ( ( D @ ( B @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) @ ( C @ aa_set_nat_bool ) @ pp )
& ( D @ ( B @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ ( produc1824681642469235216et_nat @ aa_Pro1219312880135979149t_unit ) @ ( A @ aa_hea1793595068369496646t_bool ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(23,axiom,
! [A: set_fu6080891106736489294t_bool,B: set_fu6080891106736489294t_bool,C: fun_fu9160419385450930796l_bool,D: fun_fu9160419385450930796l_bool] :
( ( B @ ( A @ ord_le387542735852657390t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( ! [E: fun_Pr6001797050664311790t_bool] :
( ( A @ ( E @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( ( E @ ( C @ aa_fun5588795374382764133l_bool ) @ pp )
=> ( E @ ( D @ aa_fun5588795374382764133l_bool ) @ pp ) ) )
=> ( D @ ( collec3007137136614167897t_bool @ aa_fun8162393684988594084t_bool ) @ ( B @ inf_in1689267372175091004t_bool ) @ ( C @ ( collec3007137136614167897t_bool @ aa_fun8162393684988594084t_bool ) @ ( A @ inf_in1689267372175091004t_bool ) @ ord_le387542735852657390t_bool @ aa_set3226752938961784069l_bool ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1063_Int__Collect__mono) ).
thf(325,plain,
! [A: set_fu6080891106736489294t_bool,B: set_fu6080891106736489294t_bool,C: fun_fu9160419385450930796l_bool,D: fun_fu9160419385450930796l_bool] :
( ( B @ ( A @ ord_le387542735852657390t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( ! [E: fun_Pr6001797050664311790t_bool] :
( ( A @ ( E @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( ( E @ ( C @ aa_fun5588795374382764133l_bool ) @ pp )
=> ( E @ ( D @ aa_fun5588795374382764133l_bool ) @ pp ) ) )
=> ( D @ ( collec3007137136614167897t_bool @ aa_fun8162393684988594084t_bool ) @ ( B @ inf_in1689267372175091004t_bool ) @ ( C @ ( collec3007137136614167897t_bool @ aa_fun8162393684988594084t_bool ) @ ( A @ inf_in1689267372175091004t_bool ) @ ord_le387542735852657390t_bool @ aa_set3226752938961784069l_bool ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(124,axiom,
! [A: fun_as4100195077546555551t_bool,B: fun_fu1264473476461866025l_assn,C: set_fu6080891106736489294t_bool] :
( ( C @ ( B @ ( A @ type_d18088346645320984t_bool ) @ aa_set3226752938961784069l_bool ) @ pp )
<=> ( ! [D: fun_Pr6001797050664311790t_bool] :
( ( C @ ( D @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( ( D @ ( B @ aa_fun1993714536301460826l_assn ) @ ( A @ aa_ass8975924923219239432t_bool ) )
= D ) )
& ! [D: assn] :
( ( D @ ( A @ aa_ass8975924923219239432t_bool ) @ ( B @ aa_fun1993714536301460826l_assn ) )
= D )
& ! [D: assn] : ( C @ ( D @ ( A @ aa_ass8975924923219239432t_bool ) @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_335_type__definition__def) ).
thf(789,plain,
! [A: fun_as4100195077546555551t_bool,B: fun_fu1264473476461866025l_assn,C: set_fu6080891106736489294t_bool] :
( ( ( ! [D: fun_Pr6001797050664311790t_bool] :
( ( C @ ( D @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( ( D @ ( B @ aa_fun1993714536301460826l_assn ) @ ( A @ aa_ass8975924923219239432t_bool ) )
= D ) )
& ! [D: assn] :
( ( D @ ( A @ aa_ass8975924923219239432t_bool ) @ ( B @ aa_fun1993714536301460826l_assn ) )
= D )
& ! [D: assn] : ( C @ ( D @ ( A @ aa_ass8975924923219239432t_bool ) @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ) )
=> ( C @ ( B @ ( A @ type_d18088346645320984t_bool ) @ aa_set3226752938961784069l_bool ) @ pp ) )
& ( ( C @ ( B @ ( A @ type_d18088346645320984t_bool ) @ aa_set3226752938961784069l_bool ) @ pp )
=> ( ! [D: fun_Pr6001797050664311790t_bool] :
( ( C @ ( D @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( ( D @ ( B @ aa_fun1993714536301460826l_assn ) @ ( A @ aa_ass8975924923219239432t_bool ) )
= D ) )
& ! [D: assn] :
( ( D @ ( A @ aa_ass8975924923219239432t_bool ) @ ( B @ aa_fun1993714536301460826l_assn ) )
= D )
& ! [D: assn] : ( C @ ( D @ ( A @ aa_ass8975924923219239432t_bool ) @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(77,axiom,
! [A: fun_as4100195077546555551t_bool,B: fun_fu1264473476461866025l_assn,C: set_fu6080891106736489294t_bool,D: fun_Pr6001797050664311790t_bool] :
( ( C @ ( B @ ( A @ type_d18088346645320984t_bool ) @ aa_set3226752938961784069l_bool ) @ pp )
=> ( ( C @ ( D @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( ( D @ ( B @ aa_fun1993714536301460826l_assn ) @ ( A @ aa_ass8975924923219239432t_bool ) )
= D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_343_type__definition_OAbs__inverse) ).
thf(591,plain,
! [A: fun_as4100195077546555551t_bool,B: fun_fu1264473476461866025l_assn,C: set_fu6080891106736489294t_bool,D: fun_Pr6001797050664311790t_bool] :
( ( C @ ( B @ ( A @ type_d18088346645320984t_bool ) @ aa_set3226752938961784069l_bool ) @ pp )
=> ( ( C @ ( D @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( ( D @ ( B @ aa_fun1993714536301460826l_assn ) @ ( A @ aa_ass8975924923219239432t_bool ) )
= D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(91,axiom,
! [A: heap_e7401611519738050253t_unit,B: set_nat,C: set_nat] :
( ( ( B @ ( A @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) )
= C )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_snd__eqD) ).
thf(646,plain,
! [A: heap_e7401611519738050253t_unit,B: set_nat,C: set_nat] :
( ( ( B @ ( A @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) )
= C )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(28,axiom,
! [A: fun_Pr6001797050664311790t_bool] :
~ ( bot_bo2714889297266208186t_bool @ ( A @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_empty__iff) ).
thf(348,plain,
! [A: fun_Pr6001797050664311790t_bool] :
~ ( bot_bo2714889297266208186t_bool @ ( A @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(160,axiom,
! [A: heap_e7401611519738050253t_unit,B: set_nat] :
( ( B @ ( A @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ ( produc1824681642469235216et_nat @ aa_Pro1219312880135979149t_unit ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4764_fst__conv) ).
thf(966,plain,
! [A: heap_e7401611519738050253t_unit,B: set_nat] :
( ( B @ ( A @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ ( produc1824681642469235216et_nat @ aa_Pro1219312880135979149t_unit ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(57,axiom,
! [A: bool,B: produc3658429121746597890et_nat] :
( ~ ( B @ ( A @ pure_a825153325127701367it_nat @ aa_Pro2991721470636411351t_bool ) @ pp )
=> ~ ! [C: heap_e7401611519738050253t_unit,D: set_nat] :
( ( B
= ( D @ ( C @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) )
=> ( ( A @ pp )
& ( D = bot_bot_set_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_pure__assn__raw_Oelims_I3_J) ).
thf(485,plain,
! [A: bool,B: produc3658429121746597890et_nat] :
( ~ ( B @ ( A @ pure_a825153325127701367it_nat @ aa_Pro2991721470636411351t_bool ) @ pp )
=> ~ ! [C: heap_e7401611519738050253t_unit,D: set_nat] :
( ( B
= ( D @ ( C @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) )
=> ( ( A @ pp )
& ( D = bot_bot_set_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(201,axiom,
! [A: assn,B: assn] :
( ( B @ ( A @ times_times_assn @ aa_assn_assn ) )
= ( B @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ ( A @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ times_assn_raw @ aa_fun6808777976510360636t_bool ) @ ( abs_assn @ aa_fun1993714536301460826l_assn ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_334_times__assn__def) ).
thf(1136,plain,
! [A: assn,B: assn] :
( ( B @ ( A @ times_times_assn @ aa_assn_assn ) )
= ( B @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ ( A @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ times_assn_raw @ aa_fun6808777976510360636t_bool ) @ ( abs_assn @ aa_fun1993714536301460826l_assn ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(131,axiom,
! [A: heap_e7401611519738050253t_unit,B: set_nat] :
( ( B @ ( A @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_snd__conv) ).
thf(834,plain,
! [A: heap_e7401611519738050253t_unit,B: set_nat] :
( ( B @ ( A @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(182,axiom,
! [A: assn,B: assn,C: produc3658429121746597890et_nat] :
( ( C @ ( B @ ( A @ times_times_assn @ aa_assn_assn ) @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp )
=> ~ ( ? [D: produc3658429121746597890et_nat] : ( D @ ( A @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp )
=> ! [D: produc3658429121746597890et_nat] :
~ ( D @ ( B @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_407_mod__starE) ).
thf(1051,plain,
! [A: assn,B: assn,C: produc3658429121746597890et_nat] :
( ( C @ ( B @ ( A @ times_times_assn @ aa_assn_assn ) @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp )
=> ~ ( ? [D: produc3658429121746597890et_nat] : ( D @ ( A @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp )
=> ! [D: produc3658429121746597890et_nat] :
~ ( D @ ( B @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(128,axiom,
! [A: fun_Pr6001797050664311790t_bool,B: fun_Pr6001797050664311790t_bool] :
( ( A @ ( proper @ aa_fun5588795374382764133l_bool ) @ pp )
=> ( ( B @ ( proper @ aa_fun5588795374382764133l_bool ) @ pp )
=> ( B @ ( A @ aTP_Lamm_ae @ aa_fun6808777976510360636t_bool ) @ ( proper @ aa_fun5588795374382764133l_bool ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7584_bool__assn__proper_I4_J) ).
thf(821,plain,
! [A: fun_Pr6001797050664311790t_bool,B: fun_Pr6001797050664311790t_bool] :
( ( A @ ( proper @ aa_fun5588795374382764133l_bool ) @ pp )
=> ( ( B @ ( proper @ aa_fun5588795374382764133l_bool ) @ pp )
=> ( B @ ( A @ aTP_Lamm_ae @ aa_fun6808777976510360636t_bool ) @ ( proper @ aa_fun5588795374382764133l_bool ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(209,axiom,
! [A: assn,B: heap_e7401611519738050253t_unit,C: heap_e7401611519738050253t_unit] :
( ( bot_bot_set_nat @ ( B @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ ( A @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp )
<=> ( bot_bot_set_nat @ ( C @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ ( A @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_mod__h__bot__indep) ).
thf(1169,plain,
! [A: assn,B: heap_e7401611519738050253t_unit,C: heap_e7401611519738050253t_unit] :
( ( ( bot_bot_set_nat @ ( C @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ ( A @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp )
=> ( bot_bot_set_nat @ ( B @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ ( A @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp ) )
& ( ( bot_bot_set_nat @ ( B @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ ( A @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp )
=> ( bot_bot_set_nat @ ( C @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ ( A @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(89,axiom,
! [A: assn] :
( ( one_one_assn = A )
<=> ( A = one_one_assn ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_one__reorient) ).
thf(634,plain,
! [A: assn] :
( ( ( A = one_one_assn )
=> ( one_one_assn = A ) )
& ( ( one_one_assn = A )
=> ( A = one_one_assn ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(143,axiom,
! [A: fun_Pr6001797050664311790t_bool,B: fun_Pr6001797050664311790t_bool] :
( ( proper @ ( collec3007137136614167897t_bool @ aa_fun8162393684988594084t_bool ) @ ( A @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( ( proper @ ( collec3007137136614167897t_bool @ aa_fun8162393684988594084t_bool ) @ ( B @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( ( ( A @ ( abs_assn @ aa_fun1993714536301460826l_assn ) )
= ( B @ ( abs_assn @ aa_fun1993714536301460826l_assn ) ) )
<=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_Abs__assn__inject) ).
thf(877,plain,
! [A: fun_Pr6001797050664311790t_bool,B: fun_Pr6001797050664311790t_bool] :
( ( proper @ ( collec3007137136614167897t_bool @ aa_fun8162393684988594084t_bool ) @ ( A @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( ( proper @ ( collec3007137136614167897t_bool @ aa_fun8162393684988594084t_bool ) @ ( B @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( ( ( A = B )
=> ( ( A @ ( abs_assn @ aa_fun1993714536301460826l_assn ) )
= ( B @ ( abs_assn @ aa_fun1993714536301460826l_assn ) ) ) )
& ( ( ( A @ ( abs_assn @ aa_fun1993714536301460826l_assn ) )
= ( B @ ( abs_assn @ aa_fun1993714536301460826l_assn ) ) )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(113,axiom,
! [A: set_nat,B: set_Pr3948176798113811640et_nat] :
( ( B @ ( produc8586169260539613262et_nat @ image_6088997261112373647et_nat ) @ ( A @ member_set_nat ) )
=> ~ ! [C: heap_e7401611519738050253t_unit] :
~ ( B @ ( A @ ( C @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ member6260224972018164377et_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2617_in__snd__imageE) ).
thf(734,plain,
! [A: set_nat,B: set_Pr3948176798113811640et_nat] :
( ( B @ ( produc8586169260539613262et_nat @ image_6088997261112373647et_nat ) @ ( A @ member_set_nat ) )
=> ~ ! [C: heap_e7401611519738050253t_unit] :
~ ( B @ ( A @ ( C @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ member6260224972018164377et_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(51,axiom,
! [A: heap_e7401611519738050253t_unit,B: set_nat,C: heap_e7401611519738050253t_unit,D: set_nat] :
( ( ( B @ ( A @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) )
= ( D @ ( C @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) )
<=> ( ( B = D )
& ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_prod_Oinject) ).
thf(453,plain,
! [A: heap_e7401611519738050253t_unit,B: set_nat,C: heap_e7401611519738050253t_unit,D: set_nat] :
( ( ( ( B = D )
& ( A = C ) )
=> ( ( B @ ( A @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) )
= ( D @ ( C @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) ) )
& ( ( ( B @ ( A @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) )
= ( D @ ( C @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(199,axiom,
( one_one_assn
= ( one_assn_raw @ ( abs_assn @ aa_fun1993714536301460826l_assn ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_one__assn__def) ).
thf(1119,plain,
( one_one_assn
= ( one_assn_raw @ ( abs_assn @ aa_fun1993714536301460826l_assn ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(166,axiom,
! [A: assn,B: assn,C: assn] :
( ( ( B @ ( A @ ( inf_inf_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) )
= bot_bot_assn )
=> ( ( ( B @ ( A @ ( sup_sup_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) )
= top_top_assn )
=> ( ( ( C @ ( A @ ( inf_inf_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) )
= bot_bot_assn )
=> ( ( ( C @ ( A @ ( sup_sup_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) )
= top_top_assn )
=> ( B = C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4211_boolean__algebra_Ocomplement__unique) ).
thf(988,plain,
! [A: assn,B: assn,C: assn] :
( ( ( B @ ( A @ ( inf_inf_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) )
= bot_bot_assn )
=> ( ( ( B @ ( A @ ( sup_sup_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) )
= top_top_assn )
=> ( ( ( C @ ( A @ ( inf_inf_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) )
= bot_bot_assn )
=> ( ( ( C @ ( A @ ( sup_sup_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) )
= top_top_assn )
=> ( B = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(67,axiom,
! [A: heap_e7401611519738050253t_unit,B: produc3658429121746597890et_nat] :
( ( A
= ( B @ ( produc1824681642469235216et_nat @ aa_Pro1219312880135979149t_unit ) ) )
<=> ? [C: set_nat] :
( B
= ( C @ ( A @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4769_eq__fst__iff) ).
thf(527,plain,
! [A: heap_e7401611519738050253t_unit,B: produc3658429121746597890et_nat] :
( ( ? [C: set_nat] :
( B
= ( C @ ( A @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) )
=> ( A
= ( B @ ( produc1824681642469235216et_nat @ aa_Pro1219312880135979149t_unit ) ) ) )
& ( ( A
= ( B @ ( produc1824681642469235216et_nat @ aa_Pro1219312880135979149t_unit ) ) )
=> ? [C: set_nat] :
( B
= ( C @ ( A @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(17,axiom,
! [A: fun_Pr6001797050664311790t_bool,B: set_fu6080891106736489294t_bool,C: set_fu6080891106736489294t_bool] :
( ( B @ ( A @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( ( C @ ( A @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( C @ ( B @ inf_in1689267372175091004t_bool ) @ ( A @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_857_IntI) ).
thf(307,plain,
! [A: fun_Pr6001797050664311790t_bool,B: set_fu6080891106736489294t_bool,C: set_fu6080891106736489294t_bool] :
( ( B @ ( A @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( ( C @ ( A @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( C @ ( B @ inf_in1689267372175091004t_bool ) @ ( A @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(149,axiom,
! [A: fun_Pr6001797050664311790t_bool,B: heap_e7401611519738050253t_unit,C: set_nat] :
( ( A @ ( proper @ aa_fun5588795374382764133l_bool ) @ pp )
=> ( ( C @ ( B @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ ( A @ aa_Pro2991721470636411351t_bool ) @ pp )
=> ( C @ ( B @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ ( in_range @ aa_Pro2991721470636411351t_bool ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_583_properD1) ).
thf(920,plain,
! [A: fun_Pr6001797050664311790t_bool,B: heap_e7401611519738050253t_unit,C: set_nat] :
( ( A @ ( proper @ aa_fun5588795374382764133l_bool ) @ pp )
=> ( ( C @ ( B @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ ( A @ aa_Pro2991721470636411351t_bool ) @ pp )
=> ( C @ ( B @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ ( in_range @ aa_Pro2991721470636411351t_bool ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(36,axiom,
! [A: set_fu6080891106736489294t_bool,B: set_fu6080891106736489294t_bool,C: fun_Pr6001797050664311790t_bool] :
( ( B @ ( A @ ord_le387542735852657390t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( ( A @ ( C @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( B @ ( C @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1132_in__mono) ).
thf(380,plain,
! [A: set_fu6080891106736489294t_bool,B: set_fu6080891106736489294t_bool,C: fun_Pr6001797050664311790t_bool] :
( ( B @ ( A @ ord_le387542735852657390t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( ( A @ ( C @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( B @ ( C @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(156,axiom,
! [A: fun_Pr6001797050664311790t_bool] :
( ( A @ ( proper @ aa_fun5588795374382764133l_bool ) @ pp )
=> ( A @ ( aTP_Lamm_ah @ aa_fun6808777976510360636t_bool ) @ ( proper @ aa_fun5588795374382764133l_bool ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7587_bool__assn__proper_I5_J) ).
thf(942,plain,
! [A: fun_Pr6001797050664311790t_bool] :
( ( A @ ( proper @ aa_fun5588795374382764133l_bool ) @ pp )
=> ( A @ ( aTP_Lamm_ah @ aa_fun6808777976510360636t_bool ) @ ( proper @ aa_fun5588795374382764133l_bool ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(7,axiom,
! [A: fun_Pr6001797050664311790t_bool,B: set_fu6080891106736489294t_bool,C: set_fu6080891106736489294t_bool] :
( ( C @ ( B @ inf_in1689267372175091004t_bool ) @ ( A @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( B @ ( A @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1145_IntD1) ).
thf(270,plain,
! [A: fun_Pr6001797050664311790t_bool,B: set_fu6080891106736489294t_bool,C: set_fu6080891106736489294t_bool] :
( ( C @ ( B @ inf_in1689267372175091004t_bool ) @ ( A @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( B @ ( A @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(96,axiom,
! [A: fun_as4100195077546555551t_bool,B: fun_fu1264473476461866025l_assn,C: fun_fu9160419385450930796l_bool] :
( ( top_to5841454426718376094t_bool @ ( B @ ( A @ type_d18088346645320984t_bool ) @ aa_set3226752938961784069l_bool ) @ pp )
=> ( ? [D: fun_Pr6001797050664311790t_bool] : ( D @ ( C @ aa_fun5588795374382764133l_bool ) @ pp )
<=> ? [D: assn] : ( D @ ( A @ aa_ass8975924923219239432t_bool ) @ ( C @ aa_fun5588795374382764133l_bool ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4121_type__copy__ex__RepI) ).
thf(661,plain,
! [A: fun_as4100195077546555551t_bool,B: fun_fu1264473476461866025l_assn,C: fun_fu9160419385450930796l_bool] :
( ( top_to5841454426718376094t_bool @ ( B @ ( A @ type_d18088346645320984t_bool ) @ aa_set3226752938961784069l_bool ) @ pp )
=> ( ( ? [D: assn] : ( D @ ( A @ aa_ass8975924923219239432t_bool ) @ ( C @ aa_fun5588795374382764133l_bool ) @ pp )
=> ? [D: fun_Pr6001797050664311790t_bool] : ( D @ ( C @ aa_fun5588795374382764133l_bool ) @ pp ) )
& ( ? [D: fun_Pr6001797050664311790t_bool] : ( D @ ( C @ aa_fun5588795374382764133l_bool ) @ pp )
=> ? [D: assn] : ( D @ ( A @ aa_ass8975924923219239432t_bool ) @ ( C @ aa_fun5588795374382764133l_bool ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(214,axiom,
! [A: fun_Pr6001797050664311790t_bool,B: assn] :
( ! [C: produc3658429121746597890et_nat] :
( ( C @ ( A @ aa_Pro2991721470636411351t_bool ) @ pp )
<=> ( C @ ( B @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp ) )
=> ( ( A @ ( abs_assn @ aa_fun1993714536301460826l_assn ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_Abs__assn__eqI_I1_J) ).
thf(1199,plain,
! [A: fun_Pr6001797050664311790t_bool,B: assn] :
( ! [C: produc3658429121746597890et_nat] :
( ( ( C @ ( B @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp )
=> ( C @ ( A @ aa_Pro2991721470636411351t_bool ) @ pp ) )
& ( ( C @ ( A @ aa_Pro2991721470636411351t_bool ) @ pp )
=> ( C @ ( B @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp ) ) )
=> ( ( A @ ( abs_assn @ aa_fun1993714536301460826l_assn ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(108,axiom,
! [A: fun_fu9160419385450930796l_bool] :
( ( ( A @ ( collec3007137136614167897t_bool @ aa_fun8162393684988594084t_bool ) )
= bot_bo2714889297266208186t_bool )
<=> ! [B: fun_Pr6001797050664311790t_bool] :
~ ( B @ ( A @ aa_fun5588795374382764133l_bool ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_Collect__empty__eq) ).
thf(714,plain,
! [A: fun_fu9160419385450930796l_bool] :
( ( ! [B: fun_Pr6001797050664311790t_bool] :
~ ( B @ ( A @ aa_fun5588795374382764133l_bool ) @ pp )
=> ( ( A @ ( collec3007137136614167897t_bool @ aa_fun8162393684988594084t_bool ) )
= bot_bo2714889297266208186t_bool ) )
& ( ( ( A @ ( collec3007137136614167897t_bool @ aa_fun8162393684988594084t_bool ) )
= bot_bo2714889297266208186t_bool )
=> ! [B: fun_Pr6001797050664311790t_bool] :
~ ( B @ ( A @ aa_fun5588795374382764133l_bool ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(25,axiom,
! [A: set_fu6080891106736489294t_bool,B: set_fu6080891106736489294t_bool,C: fun_Pr6001797050664311790t_bool] :
( ( B @ ( A @ ord_le387542735852657390t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( ( A @ ( C @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( B @ ( C @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1127_subsetD) ).
thf(334,plain,
! [A: set_fu6080891106736489294t_bool,B: set_fu6080891106736489294t_bool,C: fun_Pr6001797050664311790t_bool] :
( ( B @ ( A @ ord_le387542735852657390t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( ( A @ ( C @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( B @ ( C @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(122,axiom,
! [A: assn] :
( ( A @ ( one_one_assn @ times_times_assn @ aa_assn_assn ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_409_assn__one__left) ).
thf(778,plain,
! [A: assn] :
( ( A @ ( one_one_assn @ times_times_assn @ aa_assn_assn ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(216,axiom,
! [A: set_Pr1261947904930325089at_nat] :
( ( bot_bot_set_nat @ ( A @ rel_restrict_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1987_rel__restrict__empty) ).
thf(1217,plain,
! [A: set_Pr1261947904930325089at_nat] :
( ( bot_bot_set_nat @ ( A @ rel_restrict_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(14,axiom,
! [A: set_fu6080891106736489294t_bool] :
( ( bot_bo2714889297266208186t_bool @ ( A @ inf_in1689267372175091004t_bool ) )
= bot_bo2714889297266208186t_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1578_boolean__algebra_Oconj__zero__right) ).
thf(297,plain,
! [A: set_fu6080891106736489294t_bool] :
( ( bot_bo2714889297266208186t_bool @ ( A @ inf_in1689267372175091004t_bool ) )
= bot_bo2714889297266208186t_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(103,axiom,
( ( top_top_assn @ ( top_top_assn @ times_times_assn @ aa_assn_assn ) )
= top_top_assn ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4332_merge__true__star) ).
thf(693,plain,
( ( top_top_assn @ ( top_top_assn @ times_times_assn @ aa_assn_assn ) )
= top_top_assn ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(148,axiom,
! [A: produc3658429121746597890et_nat,B: heap_e7401611519738050253t_unit,C: set_nat] :
( ( A
= ( C @ ( B @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) )
=> ( ( A @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_sndI) ).
thf(916,plain,
! [A: produc3658429121746597890et_nat,B: heap_e7401611519738050253t_unit,C: set_nat] :
( ( A
= ( C @ ( B @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) )
=> ( ( A @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(135,axiom,
! [A: assn] :
( ( A @ ( bot_bot_assn @ ( sup_sup_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1565_sup__bot__left) ).
thf(847,plain,
! [A: assn] :
( ( A @ ( bot_bot_assn @ ( sup_sup_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(211,axiom,
! [A: produc3658429121746597890et_nat] :
( ( A @ ( one_assn_raw @ aa_Pro2991721470636411351t_bool ) @ pp )
=> ( ( A @ ( one_assn_raw_rel @ accp_P5801069581201407417et_nat @ aa_Pro2991721470636411351t_bool ) @ pp )
=> ~ ! [B: heap_e7401611519738050253t_unit,C: set_nat] :
( ( A
= ( C @ ( B @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) )
=> ( ( C @ ( B @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ ( one_assn_raw_rel @ accp_P5801069581201407417et_nat @ aa_Pro2991721470636411351t_bool ) @ pp )
=> ( C != bot_bot_set_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7764_one__assn__raw_Opelims_I2_J) ).
thf(1178,plain,
! [A: produc3658429121746597890et_nat] :
( ( A @ ( one_assn_raw @ aa_Pro2991721470636411351t_bool ) @ pp )
=> ( ( A @ ( one_assn_raw_rel @ accp_P5801069581201407417et_nat @ aa_Pro2991721470636411351t_bool ) @ pp )
=> ~ ! [B: heap_e7401611519738050253t_unit,C: set_nat] :
( ( A
= ( C @ ( B @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) )
=> ( ( C @ ( B @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ ( one_assn_raw_rel @ accp_P5801069581201407417et_nat @ aa_Pro2991721470636411351t_bool ) @ pp )
=> ( C != bot_bot_set_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(215,axiom,
! [A: assn,B: produc3658429121746597890et_nat] :
( ( B @ ( A @ ( aTP_Lamm_al @ aa_ass8975924923219239432t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp )
<=> ( ~ ( B @ ( A @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp )
& ( B @ ( in_range @ aa_Pro2991721470636411351t_bool ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7805_ATP_Olambda__10) ).
thf(1210,plain,
! [A: assn,B: produc3658429121746597890et_nat] :
( ( ( ~ ( B @ ( A @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp )
& ( B @ ( in_range @ aa_Pro2991721470636411351t_bool ) @ pp ) )
=> ( B @ ( A @ ( aTP_Lamm_al @ aa_ass8975924923219239432t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp ) )
& ( ( B @ ( A @ ( aTP_Lamm_al @ aa_ass8975924923219239432t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp )
=> ( ~ ( B @ ( A @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp )
& ( B @ ( in_range @ aa_Pro2991721470636411351t_bool ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(163,axiom,
! [A: assn] :
~ ! [B: fun_Pr6001797050664311790t_bool] :
( ( A
= ( B @ ( abs_assn @ aa_fun1993714536301460826l_assn ) ) )
=> ~ ( proper @ ( collec3007137136614167897t_bool @ aa_fun8162393684988594084t_bool ) @ ( B @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_Abs__assn__cases) ).
thf(974,plain,
! [A: assn] :
~ ! [B: fun_Pr6001797050664311790t_bool] :
( ( A
= ( B @ ( abs_assn @ aa_fun1993714536301460826l_assn ) ) )
=> ~ ( proper @ ( collec3007137136614167897t_bool @ aa_fun8162393684988594084t_bool ) @ ( B @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(11,axiom,
! [A: fun_Pr6001797050664311790t_bool,B: set_fu6080891106736489294t_bool,C: set_fu6080891106736489294t_bool] :
( ( C @ ( B @ inf_in1689267372175091004t_bool ) @ ( A @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( C @ ( A @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1140_IntD2) ).
thf(285,plain,
! [A: fun_Pr6001797050664311790t_bool,B: set_fu6080891106736489294t_bool,C: set_fu6080891106736489294t_bool] :
( ( C @ ( B @ inf_in1689267372175091004t_bool ) @ ( A @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( C @ ( A @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(75,axiom,
! [A: assn] :
( ( bot_bot_assn @ ( A @ ( inf_inf_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) )
= bot_bot_assn ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1586_inf__bot__right) ).
thf(578,plain,
! [A: assn] :
( ( bot_bot_assn @ ( A @ ( inf_inf_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) )
= bot_bot_assn ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(20,axiom,
! [A: set_fu6080891106736489294t_bool] :
( ( bot_bo2714889297266208186t_bool @ ( A @ ord_le387542735852657390t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( A = bot_bo2714889297266208186t_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1372_bot_Oextremum__uniqueI) ).
thf(317,plain,
! [A: set_fu6080891106736489294t_bool] :
( ( bot_bo2714889297266208186t_bool @ ( A @ ord_le387542735852657390t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( A = bot_bo2714889297266208186t_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(92,axiom,
! [A: set_fu6080891106736489294t_bool] :
( ( A @ aTP_Lamm_a @ ( collec3007137136614167897t_bool @ aa_fun8162393684988594084t_bool ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_Collect__mem__eq) ).
thf(650,plain,
! [A: set_fu6080891106736489294t_bool] :
( ( A @ aTP_Lamm_a @ ( collec3007137136614167897t_bool @ aa_fun8162393684988594084t_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(175,axiom,
! [A: heap_e7401611519738050253t_unit,B: set_nat] :
( ( B @ ( A @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ ( one_assn_raw @ aa_Pro2991721470636411351t_bool ) @ pp )
<=> ( B = bot_bot_set_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_one__assn__raw_Osimps) ).
thf(1017,plain,
! [A: heap_e7401611519738050253t_unit,B: set_nat] :
( ( ( B = bot_bot_set_nat )
=> ( B @ ( A @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ ( one_assn_raw @ aa_Pro2991721470636411351t_bool ) @ pp ) )
& ( ( B @ ( A @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ ( one_assn_raw @ aa_Pro2991721470636411351t_bool ) @ pp )
=> ( B = bot_bot_set_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(200,axiom,
! [A: produc3658429121746597890et_nat,B: bool] :
( ( ( A @ ( one_assn_raw @ aa_Pro2991721470636411351t_bool ) @ pp )
<=> ( B @ pp ) )
=> ~ ! [C: heap_e7401611519738050253t_unit,D: set_nat] :
( ( A
= ( D @ ( C @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) )
=> ( ( B @ pp )
<=> ( D != bot_bot_set_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_one__assn__raw_Oelims_I1_J) ).
thf(1121,plain,
! [A: produc3658429121746597890et_nat,B: bool] :
( ( ( ( B @ pp )
=> ( A @ ( one_assn_raw @ aa_Pro2991721470636411351t_bool ) @ pp ) )
& ( ( A @ ( one_assn_raw @ aa_Pro2991721470636411351t_bool ) @ pp )
=> ( B @ pp ) ) )
=> ~ ! [C: heap_e7401611519738050253t_unit,D: set_nat] :
( ( A
= ( D @ ( C @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) )
=> ( ( ( D != bot_bot_set_nat )
=> ( B @ pp ) )
& ( ( B @ pp )
=> ( D != bot_bot_set_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(186,axiom,
! [A: fun_as4100195077546555551t_bool,B: fun_fu1264473476461866025l_assn,C: set_fu6080891106736489294t_bool,D: assn] :
( ( C @ ( B @ ( A @ type_d18088346645320984t_bool ) @ aa_set3226752938961784069l_bool ) @ pp )
=> ( ( D @ ( A @ aa_ass8975924923219239432t_bool ) @ ( B @ aa_fun1993714536301460826l_assn ) )
= D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_339_type__definition_ORep__inverse) ).
thf(1064,plain,
! [A: fun_as4100195077546555551t_bool,B: fun_fu1264473476461866025l_assn,C: set_fu6080891106736489294t_bool,D: assn] :
( ( C @ ( B @ ( A @ type_d18088346645320984t_bool ) @ aa_set3226752938961784069l_bool ) @ pp )
=> ( ( D @ ( A @ aa_ass8975924923219239432t_bool ) @ ( B @ aa_fun1993714536301460826l_assn ) )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(110,axiom,
! [A: fun_Pr6001797050664311790t_bool,B: fun_Pr6001797050664311790t_bool] :
( ( A @ ( proper @ aa_fun5588795374382764133l_bool ) @ pp )
=> ( ( B @ ( proper @ aa_fun5588795374382764133l_bool ) @ pp )
=> ( B @ ( A @ aTP_Lamm_af @ aa_fun6808777976510360636t_bool ) @ ( proper @ aa_fun5588795374382764133l_bool ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7585_bool__assn__proper_I3_J) ).
thf(725,plain,
! [A: fun_Pr6001797050664311790t_bool,B: fun_Pr6001797050664311790t_bool] :
( ( A @ ( proper @ aa_fun5588795374382764133l_bool ) @ pp )
=> ( ( B @ ( proper @ aa_fun5588795374382764133l_bool ) @ pp )
=> ( B @ ( A @ aTP_Lamm_af @ aa_fun6808777976510360636t_bool ) @ ( proper @ aa_fun5588795374382764133l_bool ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(164,axiom,
! [A: fun_Pr6001797050664311790t_bool,B: fun_Pr6001797050664311790t_bool] :
( ( A @ ( proper @ aa_fun5588795374382764133l_bool ) @ pp )
=> ( ( B @ ( proper @ aa_fun5588795374382764133l_bool ) @ pp )
=> ( B @ ( A @ times_assn_raw @ aa_fun6808777976510360636t_bool ) @ ( proper @ aa_fun5588795374382764133l_bool ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_times__assn__proper) ).
thf(980,plain,
! [A: fun_Pr6001797050664311790t_bool,B: fun_Pr6001797050664311790t_bool] :
( ( A @ ( proper @ aa_fun5588795374382764133l_bool ) @ pp )
=> ( ( B @ ( proper @ aa_fun5588795374382764133l_bool ) @ pp )
=> ( B @ ( A @ times_assn_raw @ aa_fun6808777976510360636t_bool ) @ ( proper @ aa_fun5588795374382764133l_bool ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(195,axiom,
! [A: set_Pr1261947904930325089at_nat] : ( A @ ( bot_bot_set_nat @ total_on_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_554_total__on__empty) ).
thf(1096,plain,
! [A: set_Pr1261947904930325089at_nat] : ( A @ ( bot_bot_set_nat @ total_on_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(39,axiom,
! [A: set_fu6080891106736489294t_bool] :
( ! [B: fun_Pr6001797050664311790t_bool] : ( A @ ( B @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( top_to5841454426718376094t_bool = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3654_UNIV__eq__I) ).
thf(388,plain,
! [A: set_fu6080891106736489294t_bool] :
( ! [B: fun_Pr6001797050664311790t_bool] : ( A @ ( B @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( top_to5841454426718376094t_bool = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(82,axiom,
in_range @ ( proper @ aa_fun5588795374382764133l_bool ) @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_499_bool__assn__proper_I1_J) ).
thf(610,plain,
in_range @ ( proper @ aa_fun5588795374382764133l_bool ) @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(138,axiom,
! [A: produc3658429121746597890et_nat,B: fun_he2331061685413951235t_unit,C: produc3658429121746597890et_nat] :
( ( A
= ( C @ ( B @ produc4172003873565521026et_nat @ aa_Pro3679490825741336130et_nat ) ) )
=> ~ ! [D: heap_e7401611519738050253t_unit,E: set_nat] :
( ( C
= ( E @ ( D @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) )
=> ( A
!= ( E @ ( D @ ( B @ aa_hea2136485429539994620t_unit ) @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4983_apfst__convE) ).
thf(857,plain,
! [A: produc3658429121746597890et_nat,B: fun_he2331061685413951235t_unit,C: produc3658429121746597890et_nat] :
( ( A
= ( C @ ( B @ produc4172003873565521026et_nat @ aa_Pro3679490825741336130et_nat ) ) )
=> ~ ! [D: heap_e7401611519738050253t_unit,E: set_nat] :
( ( C
= ( E @ ( D @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) )
=> ( A
!= ( E @ ( D @ ( B @ aa_hea2136485429539994620t_unit ) @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(207,axiom,
! [A: produc3658429121746597890et_nat] :
( ( A @ ( one_assn_raw @ aa_Pro2991721470636411351t_bool ) @ pp )
=> ~ ! [B: heap_e7401611519738050253t_unit,C: set_nat] :
( ( A
= ( C @ ( B @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) )
=> ( C != bot_bot_set_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_one__assn__raw_Oelims_I2_J) ).
thf(1160,plain,
! [A: produc3658429121746597890et_nat] :
( ( A @ ( one_assn_raw @ aa_Pro2991721470636411351t_bool ) @ pp )
=> ~ ! [B: heap_e7401611519738050253t_unit,C: set_nat] :
( ( A
= ( C @ ( B @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) )
=> ( C != bot_bot_set_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(177,axiom,
! [A: assn,B: produc3658429121746597890et_nat] :
( ( B @ ( A @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp )
=> ( B @ ( in_range @ aa_Pro2991721470636411351t_bool ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_557_models__in__range) ).
thf(1028,plain,
! [A: assn,B: produc3658429121746597890et_nat] :
( ( B @ ( A @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp )
=> ( B @ ( in_range @ aa_Pro2991721470636411351t_bool ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(1,conjecture,
( ( h @ ( one_assn_raw @ ( abs_assn @ aa_fun1993714536301460826l_assn ) @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp )
<=> ( ( h @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) )
= bot_bot_set_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ( h @ ( one_assn_raw @ ( abs_assn @ aa_fun1993714536301460826l_assn ) @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp )
<=> ( ( h @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) )
= bot_bot_set_nat ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(225,plain,
~ ( ( ( ( h @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) )
= bot_bot_set_nat )
=> ( h @ ( one_assn_raw @ ( abs_assn @ aa_fun1993714536301460826l_assn ) @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp ) )
& ( ( h @ ( one_assn_raw @ ( abs_assn @ aa_fun1993714536301460826l_assn ) @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp )
=> ( ( h @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) )
= bot_bot_set_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(99,axiom,
! [A: fun_Pr6001797050664311790t_bool] :
( ( proper @ ( collec3007137136614167897t_bool @ aa_fun8162393684988594084t_bool ) @ ( A @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ~ ! [B: assn] :
( A
!= ( B @ ( rep_assn @ aa_ass8975924923219239432t_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_Rep__assn__cases) ).
thf(679,plain,
! [A: fun_Pr6001797050664311790t_bool] :
( ( proper @ ( collec3007137136614167897t_bool @ aa_fun8162393684988594084t_bool ) @ ( A @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ~ ! [B: assn] :
( A
!= ( B @ ( rep_assn @ aa_ass8975924923219239432t_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(101,axiom,
! [A: assn] :
( ( A @ ( one_one_assn @ times_times_assn @ aa_assn_assn ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_368_mult__1) ).
thf(686,plain,
! [A: assn] :
( ( A @ ( one_one_assn @ times_times_assn @ aa_assn_assn ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(188,axiom,
! [A: produc3658429121746597890et_nat,B: fun_he1004219788074801965t_bool,C: fun_he7710493197641524256t_bool] :
( ( A @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) )
= ( A @ ( C @ ( B @ bNF_sn4039337771197282234et_nat ) @ ( produc8586169260539613262et_nat @ comp_P2930521774885306735et_nat ) @ aa_Pro3416150927818442182et_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4990_snd__sndOp) ).
thf(1075,plain,
! [A: produc3658429121746597890et_nat,B: fun_he1004219788074801965t_bool,C: fun_he7710493197641524256t_bool] :
( ( A @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) )
= ( A @ ( C @ ( B @ bNF_sn4039337771197282234et_nat ) @ ( produc8586169260539613262et_nat @ comp_P2930521774885306735et_nat ) @ aa_Pro3416150927818442182et_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(132,axiom,
! [A: assn,B: assn,C: assn] :
( ( C @ ( B @ ( A @ times_times_assn @ aa_assn_assn ) @ times_times_assn @ aa_assn_assn ) )
= ( C @ ( B @ times_times_assn @ aa_assn_assn ) @ ( A @ times_times_assn @ aa_assn_assn ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_391_mult_Oassoc) ).
thf(837,plain,
! [A: assn,B: assn,C: assn] :
( ( C @ ( B @ ( A @ times_times_assn @ aa_assn_assn ) @ times_times_assn @ aa_assn_assn ) )
= ( C @ ( B @ times_times_assn @ aa_assn_assn ) @ ( A @ times_times_assn @ aa_assn_assn ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(221,axiom,
! [A: assn,B: assn,C: produc3658429121746597890et_nat] :
( ( C @ ( B @ ( A @ aTP_Lamm_ai @ aa_ass8975924923219239432t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp )
<=> ( ( C @ ( B @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp )
| ( C @ ( A @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7831_ATP_Olambda__36) ).
thf(1249,plain,
! [A: assn,B: assn,C: produc3658429121746597890et_nat] :
( ( ( ( C @ ( B @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp )
| ( C @ ( A @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp ) )
=> ( C @ ( B @ ( A @ aTP_Lamm_ai @ aa_ass8975924923219239432t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp ) )
& ( ( C @ ( B @ ( A @ aTP_Lamm_ai @ aa_ass8975924923219239432t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp )
=> ( ( C @ ( B @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp )
| ( C @ ( A @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(171,axiom,
! [A: assn] :
( ( bot_bot_assn @ ( A @ ( inf_inf_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) )
= bot_bot_assn ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1572_boolean__algebra_Oconj__zero__right) ).
thf(1002,plain,
! [A: assn] :
( ( bot_bot_assn @ ( A @ ( inf_inf_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) )
= bot_bot_assn ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(220,axiom,
! [A: fun_he6078633327341457676it_int,B: fun_set_nat_int] :
( ( B @ ( A @ produc5973434381925408567at_int ) @ ( product_snd_int_int @ comp_P8308861049717174982et_nat ) )
= ( produc8586169260539613262et_nat @ ( B @ comp_s1601710177542341017et_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4488_snd__comp__map__prod) ).
thf(1246,plain,
! [A: fun_he6078633327341457676it_int,B: fun_set_nat_int] :
( ( B @ ( A @ produc5973434381925408567at_int ) @ ( product_snd_int_int @ comp_P8308861049717174982et_nat ) )
= ( produc8586169260539613262et_nat @ ( B @ comp_s1601710177542341017et_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(5,axiom,
! [A: set_fu6080891106736489294t_bool,B: set_fu6080891106736489294t_bool] :
( ( ( B @ ( A @ inf_in1689267372175091004t_bool ) )
= bot_bo2714889297266208186t_bool )
<=> ! [C: fun_Pr6001797050664311790t_bool] :
( ( A @ ( C @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ! [D: fun_Pr6001797050664311790t_bool] :
( ( B @ ( D @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( C != D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1328_disjoint__iff__not__equal) ).
thf(244,plain,
! [A: set_fu6080891106736489294t_bool,B: set_fu6080891106736489294t_bool] :
( ( ! [C: fun_Pr6001797050664311790t_bool] :
( ( A @ ( C @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ! [D: fun_Pr6001797050664311790t_bool] :
( ( B @ ( D @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( C != D ) ) )
=> ( ( B @ ( A @ inf_in1689267372175091004t_bool ) )
= bot_bo2714889297266208186t_bool ) )
& ( ( ( B @ ( A @ inf_in1689267372175091004t_bool ) )
= bot_bo2714889297266208186t_bool )
=> ! [C: fun_Pr6001797050664311790t_bool] :
( ( A @ ( C @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ! [D: fun_Pr6001797050664311790t_bool] :
( ( B @ ( D @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( C != D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(191,axiom,
! [A: set_nat,B: fun_nat_fun_nat_bool] : ( bot_bot_set_nat @ ( B @ ( A @ pred_chain_nat ) @ aa_set_nat_bool ) @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4368_pred__on_Ochain__empty) ).
thf(1086,plain,
! [A: set_nat,B: fun_nat_fun_nat_bool] : ( bot_bot_set_nat @ ( B @ ( A @ pred_chain_nat ) @ aa_set_nat_bool ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(125,axiom,
! [A: fun_Pr6001797050664311790t_bool,B: produc3658429121746597890et_nat] :
( ! [C: heap_e7401611519738050253t_unit,D: set_nat] : ( D @ ( C @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ ( A @ aa_Pro2991721470636411351t_bool ) @ pp )
=> ( B @ ( A @ aa_Pro2991721470636411351t_bool ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_prod__cases) ).
thf(805,plain,
! [A: fun_Pr6001797050664311790t_bool,B: produc3658429121746597890et_nat] :
( ! [C: heap_e7401611519738050253t_unit,D: set_nat] : ( D @ ( C @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ ( A @ aa_Pro2991721470636411351t_bool ) @ pp )
=> ( B @ ( A @ aa_Pro2991721470636411351t_bool ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(63,axiom,
! [A: produc3658429121746597890et_nat] :
( ( A @ ( produc6300697153377358172et_nat @ aa_Pro7370057327950226428t_unit ) )
= ( A @ ( produc1824681642469235216et_nat @ aa_Pro1219312880135979149t_unit ) @ ( A @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) @ produc2471974422597015918t_unit ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4955_prod_Oswap__def) ).
thf(508,plain,
! [A: produc3658429121746597890et_nat] :
( ( A @ ( produc6300697153377358172et_nat @ aa_Pro7370057327950226428t_unit ) )
= ( A @ ( produc1824681642469235216et_nat @ aa_Pro1219312880135979149t_unit ) @ ( A @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) @ produc2471974422597015918t_unit ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(69,axiom,
! [A: fun_as4100195077546555551t_bool,B: set_fu6080891106736489294t_bool,C: fun_fu1264473476461866025l_assn] :
( ! [D: assn] : ( B @ ( D @ ( A @ aa_ass8975924923219239432t_bool ) @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( ! [D: assn] :
( ( D @ ( A @ aa_ass8975924923219239432t_bool ) @ ( C @ aa_fun1993714536301460826l_assn ) )
= D )
=> ( ! [D: fun_Pr6001797050664311790t_bool] :
( ( B @ ( D @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( ( D @ ( C @ aa_fun1993714536301460826l_assn ) @ ( A @ aa_ass8975924923219239432t_bool ) )
= D ) )
=> ( B @ ( C @ ( A @ type_d18088346645320984t_bool ) @ aa_set3226752938961784069l_bool ) @ pp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_416_type__definition_Ointro) ).
thf(541,plain,
! [A: fun_as4100195077546555551t_bool,B: set_fu6080891106736489294t_bool,C: fun_fu1264473476461866025l_assn] :
( ! [D: assn] : ( B @ ( D @ ( A @ aa_ass8975924923219239432t_bool ) @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( ! [D: assn] :
( ( D @ ( A @ aa_ass8975924923219239432t_bool ) @ ( C @ aa_fun1993714536301460826l_assn ) )
= D )
=> ( ! [D: fun_Pr6001797050664311790t_bool] :
( ( B @ ( D @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( ( D @ ( C @ aa_fun1993714536301460826l_assn ) @ ( A @ aa_ass8975924923219239432t_bool ) )
= D ) )
=> ( B @ ( C @ ( A @ type_d18088346645320984t_bool ) @ aa_set3226752938961784069l_bool ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(212,axiom,
! [A: produc3658429121746597890et_nat] :
( ~ ( A @ ( one_assn_raw @ aa_Pro2991721470636411351t_bool ) @ pp )
=> ~ ! [B: heap_e7401611519738050253t_unit,C: set_nat] :
( ( A
= ( C @ ( B @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) )
=> ( C = bot_bot_set_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_one__assn__raw_Oelims_I3_J) ).
thf(1185,plain,
! [A: produc3658429121746597890et_nat] :
( ~ ( A @ ( one_assn_raw @ aa_Pro2991721470636411351t_bool ) @ pp )
=> ~ ! [B: heap_e7401611519738050253t_unit,C: set_nat] :
( ( A
= ( C @ ( B @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) )
=> ( C = bot_bot_set_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(151,axiom,
! [A: assn] :
( ( A @ ( bot_bot_assn @ ( sup_sup_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1530_sup__bot_Oleft__neutral) ).
thf(926,plain,
! [A: assn] :
( ( A @ ( bot_bot_assn @ ( sup_sup_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(146,axiom,
! [A: bool,B: produc3658429121746597890et_nat] :
( ( B @ ( A @ pure_a825153325127701367it_nat @ aa_Pro2991721470636411351t_bool ) @ pp )
=> ~ ! [C: heap_e7401611519738050253t_unit,D: set_nat] :
( ( B
= ( D @ ( C @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) )
=> ~ ( ( A @ pp )
& ( D = bot_bot_set_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_pure__assn__raw_Oelims_I2_J) ).
thf(906,plain,
! [A: bool,B: produc3658429121746597890et_nat] :
( ( B @ ( A @ pure_a825153325127701367it_nat @ aa_Pro2991721470636411351t_bool ) @ pp )
=> ~ ! [C: heap_e7401611519738050253t_unit,D: set_nat] :
( ( B
= ( D @ ( C @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) )
=> ~ ( ( A @ pp )
& ( D = bot_bot_set_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(43,axiom,
! [A: heap_e7401611519738050253t_unit,B: set_nat,C: set_Pr3948176798113811640et_nat,D: fun_he7710493197641524256t_bool] :
( ( C @ ( B @ ( A @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ member6260224972018164377et_nat ) )
=> ( ( ( C @ ( B @ ( A @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ member6260224972018164377et_nat ) )
=> ( B @ ( A @ ( D @ aa_hea2782697410307197849t_bool ) @ aa_set_nat_bool ) @ pp ) )
=> ? [E: heap_e7401611519738050253t_unit,F: set_nat] :
( ( F @ ( E @ ( D @ aa_hea2782697410307197849t_bool ) @ aa_set_nat_bool ) @ pp )
& ( C @ ( F @ ( E @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ member6260224972018164377et_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_bex2I) ).
thf(412,plain,
! [A: heap_e7401611519738050253t_unit,B: set_nat,C: set_Pr3948176798113811640et_nat,D: fun_he7710493197641524256t_bool] :
( ( C @ ( B @ ( A @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ member6260224972018164377et_nat ) )
=> ( ( ( C @ ( B @ ( A @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ member6260224972018164377et_nat ) )
=> ( B @ ( A @ ( D @ aa_hea2782697410307197849t_bool ) @ aa_set_nat_bool ) @ pp ) )
=> ? [E: heap_e7401611519738050253t_unit,F: set_nat] :
( ( F @ ( E @ ( D @ aa_hea2782697410307197849t_bool ) @ aa_set_nat_bool ) @ pp )
& ( C @ ( F @ ( E @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ member6260224972018164377et_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(85,axiom,
! [A: heap_e7401611519738050253t_unit,B: set_nat,C: heap_e7401611519738050253t_unit,D: set_nat] :
( ( ( B @ ( A @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) )
= ( D @ ( C @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_Pair__inject) ).
thf(618,plain,
! [A: heap_e7401611519738050253t_unit,B: set_nat,C: heap_e7401611519738050253t_unit,D: set_nat] :
( ( ( B @ ( A @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) )
= ( D @ ( C @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(129,axiom,
! [A: fun_fu9160419385450930796l_bool] :
( ( bot_bo2714889297266208186t_bool
= ( A @ ( collec3007137136614167897t_bool @ aa_fun8162393684988594084t_bool ) ) )
<=> ! [B: fun_Pr6001797050664311790t_bool] :
~ ( B @ ( A @ aa_fun5588795374382764133l_bool ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_empty__Collect__eq) ).
thf(824,plain,
! [A: fun_fu9160419385450930796l_bool] :
( ( ! [B: fun_Pr6001797050664311790t_bool] :
~ ( B @ ( A @ aa_fun5588795374382764133l_bool ) @ pp )
=> ( bot_bo2714889297266208186t_bool
= ( A @ ( collec3007137136614167897t_bool @ aa_fun8162393684988594084t_bool ) ) ) )
& ( ( bot_bo2714889297266208186t_bool
= ( A @ ( collec3007137136614167897t_bool @ aa_fun8162393684988594084t_bool ) ) )
=> ! [B: fun_Pr6001797050664311790t_bool] :
~ ( B @ ( A @ aa_fun5588795374382764133l_bool ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(9,axiom,
! [A: set_fu6080891106736489294t_bool] :
( ( bot_bo2714889297266208186t_bool @ ( A @ inf_in1689267372175091004t_bool ) )
= bot_bo2714889297266208186t_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1592_inf__bot__right) ).
thf(279,plain,
! [A: set_fu6080891106736489294t_bool] :
( ( bot_bo2714889297266208186t_bool @ ( A @ inf_in1689267372175091004t_bool ) )
= bot_bo2714889297266208186t_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(74,axiom,
! [A: fun_assn_bool,B: assn] :
( ! [C: fun_Pr6001797050664311790t_bool] :
( ( proper @ ( collec3007137136614167897t_bool @ aa_fun8162393684988594084t_bool ) @ ( C @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( C @ ( abs_assn @ aa_fun1993714536301460826l_assn ) @ ( A @ aa_assn_bool ) @ pp ) )
=> ( B @ ( A @ aa_assn_bool ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_Abs__assn__induct) ).
thf(573,plain,
! [A: fun_assn_bool,B: assn] :
( ! [C: fun_Pr6001797050664311790t_bool] :
( ( proper @ ( collec3007137136614167897t_bool @ aa_fun8162393684988594084t_bool ) @ ( C @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( C @ ( abs_assn @ aa_fun1993714536301460826l_assn ) @ ( A @ aa_assn_bool ) @ pp ) )
=> ( B @ ( A @ aa_assn_bool ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(102,axiom,
! [A: fun_as4100195077546555551t_bool,B: fun_fu1264473476461866025l_assn,C: set_fu6080891106736489294t_bool,D: fun_Pr6001797050664311790t_bool] :
( ( C @ ( B @ ( A @ type_d18088346645320984t_bool ) @ aa_set3226752938961784069l_bool ) @ pp )
=> ( ( C @ ( D @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ~ ! [E: assn] :
( D
!= ( E @ ( A @ aa_ass8975924923219239432t_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_424_type__definition_ORep__cases) ).
thf(689,plain,
! [A: fun_as4100195077546555551t_bool,B: fun_fu1264473476461866025l_assn,C: set_fu6080891106736489294t_bool,D: fun_Pr6001797050664311790t_bool] :
( ( C @ ( B @ ( A @ type_d18088346645320984t_bool ) @ aa_set3226752938961784069l_bool ) @ pp )
=> ( ( C @ ( D @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ~ ! [E: assn] :
( D
!= ( E @ ( A @ aa_ass8975924923219239432t_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(79,axiom,
! [A: produc7348995623955488188t_unit] :
( ( A @ ( produc1264744871843189710t_unit @ aa_Pro2092192379717785596et_nat ) )
= ( A @ produc6012101397789842562t_unit @ ( A @ produc3550216979005444800t_unit @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4951_prod_Oswap__def) ).
thf(601,plain,
! [A: produc7348995623955488188t_unit] :
( ( A @ ( produc1264744871843189710t_unit @ aa_Pro2092192379717785596et_nat ) )
= ( A @ produc6012101397789842562t_unit @ ( A @ produc3550216979005444800t_unit @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(204,axiom,
! [A: fun_Pr6001797050664311790t_bool] :
( ( proper @ ( collec3007137136614167897t_bool @ aa_fun8162393684988594084t_bool ) @ ( A @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( ( A @ ( abs_assn @ aa_fun1993714536301460826l_assn ) @ ( rep_assn @ aa_ass8975924923219239432t_bool ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_Abs__assn__inverse) ).
thf(1146,plain,
! [A: fun_Pr6001797050664311790t_bool] :
( ( proper @ ( collec3007137136614167897t_bool @ aa_fun8162393684988594084t_bool ) @ ( A @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( ( A @ ( abs_assn @ aa_fun1993714536301460826l_assn ) @ ( rep_assn @ aa_ass8975924923219239432t_bool ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(46,axiom,
! [A: set_fu6080891106736489294t_bool,B: set_fu6080891106736489294t_bool] :
( ( B @ ( A @ ord_le387542735852657390t_bool @ aa_set3226752938961784069l_bool ) @ pp )
<=> ! [C: fun_Pr6001797050664311790t_bool] :
( ( A @ ( C @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( B @ ( C @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1100_subset__iff) ).
thf(430,plain,
! [A: set_fu6080891106736489294t_bool,B: set_fu6080891106736489294t_bool] :
( ( ! [C: fun_Pr6001797050664311790t_bool] :
( ( A @ ( C @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( B @ ( C @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ) )
=> ( B @ ( A @ ord_le387542735852657390t_bool @ aa_set3226752938961784069l_bool ) @ pp ) )
& ( ( B @ ( A @ ord_le387542735852657390t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ! [C: fun_Pr6001797050664311790t_bool] :
( ( A @ ( C @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( B @ ( C @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(134,axiom,
! [A: fun_fu9160419385450930796l_bool,B: fun_fu9160419385450930796l_bool] :
( ! [C: fun_Pr6001797050664311790t_bool] :
( ( C @ ( A @ aa_fun5588795374382764133l_bool ) @ pp )
=> ( C @ ( B @ aa_fun5588795374382764133l_bool ) @ pp ) )
=> ( B @ ( collec3007137136614167897t_bool @ aa_fun8162393684988594084t_bool ) @ ( A @ ( collec3007137136614167897t_bool @ aa_fun8162393684988594084t_bool ) @ ord_le387542735852657390t_bool @ aa_set3226752938961784069l_bool ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1091_Collect__mono) ).
thf(843,plain,
! [A: fun_fu9160419385450930796l_bool,B: fun_fu9160419385450930796l_bool] :
( ! [C: fun_Pr6001797050664311790t_bool] :
( ( C @ ( A @ aa_fun5588795374382764133l_bool ) @ pp )
=> ( C @ ( B @ aa_fun5588795374382764133l_bool ) @ pp ) )
=> ( B @ ( collec3007137136614167897t_bool @ aa_fun8162393684988594084t_bool ) @ ( A @ ( collec3007137136614167897t_bool @ aa_fun8162393684988594084t_bool ) @ ord_le387542735852657390t_bool @ aa_set3226752938961784069l_bool ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(107,axiom,
! [A: assn] :
( ( A @ ( bot_bot_assn @ ( inf_inf_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) )
= bot_bot_assn ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1579_boolean__algebra_Oconj__zero__left) ).
thf(711,plain,
! [A: assn] :
( ( A @ ( bot_bot_assn @ ( inf_inf_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) )
= bot_bot_assn ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(159,axiom,
! [A: fun_fu9160419385450930796l_bool,B: fun_fu9160419385450930796l_bool] :
( ( B @ ( collec3007137136614167897t_bool @ aa_fun8162393684988594084t_bool ) @ ( A @ ( collec3007137136614167897t_bool @ aa_fun8162393684988594084t_bool ) @ ord_le387542735852657390t_bool @ aa_set3226752938961784069l_bool ) @ pp )
<=> ! [C: fun_Pr6001797050664311790t_bool] :
( ( C @ ( A @ aa_fun5588795374382764133l_bool ) @ pp )
=> ( C @ ( B @ aa_fun5588795374382764133l_bool ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1068_Collect__mono__iff) ).
thf(958,plain,
! [A: fun_fu9160419385450930796l_bool,B: fun_fu9160419385450930796l_bool] :
( ( ! [C: fun_Pr6001797050664311790t_bool] :
( ( C @ ( A @ aa_fun5588795374382764133l_bool ) @ pp )
=> ( C @ ( B @ aa_fun5588795374382764133l_bool ) @ pp ) )
=> ( B @ ( collec3007137136614167897t_bool @ aa_fun8162393684988594084t_bool ) @ ( A @ ( collec3007137136614167897t_bool @ aa_fun8162393684988594084t_bool ) @ ord_le387542735852657390t_bool @ aa_set3226752938961784069l_bool ) @ pp ) )
& ( ( B @ ( collec3007137136614167897t_bool @ aa_fun8162393684988594084t_bool ) @ ( A @ ( collec3007137136614167897t_bool @ aa_fun8162393684988594084t_bool ) @ ord_le387542735852657390t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ! [C: fun_Pr6001797050664311790t_bool] :
( ( C @ ( A @ aa_fun5588795374382764133l_bool ) @ pp )
=> ( C @ ( B @ aa_fun5588795374382764133l_bool ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(6,axiom,
! [A: set_fu6080891106736489294t_bool,B: set_fu6080891106736489294t_bool] :
( ( ( B @ ( A @ inf_in1689267372175091004t_bool ) )
= bot_bo2714889297266208186t_bool )
<=> ! [C: fun_Pr6001797050664311790t_bool] :
( ( A @ ( C @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ~ ( B @ ( C @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1343_disjoint__iff) ).
thf(259,plain,
! [A: set_fu6080891106736489294t_bool,B: set_fu6080891106736489294t_bool] :
( ( ! [C: fun_Pr6001797050664311790t_bool] :
( ( A @ ( C @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ~ ( B @ ( C @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ) )
=> ( ( B @ ( A @ inf_in1689267372175091004t_bool ) )
= bot_bo2714889297266208186t_bool ) )
& ( ( ( B @ ( A @ inf_in1689267372175091004t_bool ) )
= bot_bo2714889297266208186t_bool )
=> ! [C: fun_Pr6001797050664311790t_bool] :
( ( A @ ( C @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ~ ( B @ ( C @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(49,axiom,
! [A: fun_as4100195077546555551t_bool,B: fun_fu1264473476461866025l_assn,C: set_fu6080891106736489294t_bool,D: fun_assn_bool,E: assn] :
( ( C @ ( B @ ( A @ type_d18088346645320984t_bool ) @ aa_set3226752938961784069l_bool ) @ pp )
=> ( ! [F: fun_Pr6001797050664311790t_bool] :
( ( C @ ( F @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( F @ ( B @ aa_fun1993714536301460826l_assn ) @ ( D @ aa_assn_bool ) @ pp ) )
=> ( E @ ( D @ aa_assn_bool ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_428_type__definition_OAbs__induct) ).
thf(445,plain,
! [A: fun_as4100195077546555551t_bool,B: fun_fu1264473476461866025l_assn,C: set_fu6080891106736489294t_bool,D: fun_assn_bool,E: assn] :
( ( C @ ( B @ ( A @ type_d18088346645320984t_bool ) @ aa_set3226752938961784069l_bool ) @ pp )
=> ( ! [F: fun_Pr6001797050664311790t_bool] :
( ( C @ ( F @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( F @ ( B @ aa_fun1993714536301460826l_assn ) @ ( D @ aa_assn_bool ) @ pp ) )
=> ( E @ ( D @ aa_assn_bool ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(19,axiom,
! [A: set_fu6080891106736489294t_bool] :
( ! [B: fun_Pr6001797050664311790t_bool] :
~ ( A @ ( B @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( A = bot_bo2714889297266208186t_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_equals0I) ).
thf(313,plain,
! [A: set_fu6080891106736489294t_bool] :
( ! [B: fun_Pr6001797050664311790t_bool] :
~ ( A @ ( B @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( A = bot_bo2714889297266208186t_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(83,axiom,
! [A: fun_se9021057006710688848t_bool,B: set_nat,C: heap_e7401611519738050253t_unit] :
( ( C @ ( B @ ( A @ aa_set6242977750710348305t_bool ) @ aa_hea1793595068369496646t_bool ) @ pp )
=> ( B @ ( C @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ ( produc1824681642469235216et_nat @ aa_Pro1219312880135979149t_unit ) @ ( B @ ( C @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) @ ( A @ aa_set6242977750710348305t_bool ) @ aa_hea1793595068369496646t_bool ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4976_exI__realizer) ).
thf(611,plain,
! [A: fun_se9021057006710688848t_bool,B: set_nat,C: heap_e7401611519738050253t_unit] :
( ( C @ ( B @ ( A @ aa_set6242977750710348305t_bool ) @ aa_hea1793595068369496646t_bool ) @ pp )
=> ( B @ ( C @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ ( produc1824681642469235216et_nat @ aa_Pro1219312880135979149t_unit ) @ ( B @ ( C @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) @ ( A @ aa_set6242977750710348305t_bool ) @ aa_hea1793595068369496646t_bool ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(53,axiom,
! [A: fun_as4100195077546555551t_bool,B: fun_fu1264473476461866025l_assn,C: set_fu6080891106736489294t_bool,D: fun_Pr6001797050664311790t_bool,E: fun_fu9160419385450930796l_bool] :
( ( C @ ( B @ ( A @ type_d18088346645320984t_bool ) @ aa_set3226752938961784069l_bool ) @ pp )
=> ( ( C @ ( D @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( ! [F: assn] : ( F @ ( A @ aa_ass8975924923219239432t_bool ) @ ( E @ aa_fun5588795374382764133l_bool ) @ pp )
=> ( D @ ( E @ aa_fun5588795374382764133l_bool ) @ pp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_351_type__definition_ORep__induct) ).
thf(466,plain,
! [A: fun_as4100195077546555551t_bool,B: fun_fu1264473476461866025l_assn,C: set_fu6080891106736489294t_bool,D: fun_Pr6001797050664311790t_bool,E: fun_fu9160419385450930796l_bool] :
( ( C @ ( B @ ( A @ type_d18088346645320984t_bool ) @ aa_set3226752938961784069l_bool ) @ pp )
=> ( ( C @ ( D @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( ! [F: assn] : ( F @ ( A @ aa_ass8975924923219239432t_bool ) @ ( E @ aa_fun5588795374382764133l_bool ) @ pp )
=> ( D @ ( E @ aa_fun5588795374382764133l_bool ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(193,axiom,
! [A: fun_in7572449478177386490t_unit,B: fun_int_set_nat] :
( ( B @ ( A @ produc3152090231653401565et_nat ) @ ( produc8586169260539613262et_nat @ comp_P8606889026643445772nt_int ) )
= ( product_snd_int_int @ ( B @ comp_i6200299785623974754nt_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4487_snd__comp__map__prod) ).
thf(1090,plain,
! [A: fun_in7572449478177386490t_unit,B: fun_int_set_nat] :
( ( B @ ( A @ produc3152090231653401565et_nat ) @ ( produc8586169260539613262et_nat @ comp_P8606889026643445772nt_int ) )
= ( product_snd_int_int @ ( B @ comp_i6200299785623974754nt_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(158,axiom,
! [A: fun_fu9160419385450930796l_bool,B: fun_fu9160419385450930796l_bool] :
( ! [C: fun_Pr6001797050664311790t_bool] :
( ( C @ ( A @ aa_fun5588795374382764133l_bool ) @ pp )
<=> ( C @ ( B @ aa_fun5588795374382764133l_bool ) @ pp ) )
=> ( ( A @ ( collec3007137136614167897t_bool @ aa_fun8162393684988594084t_bool ) )
= ( B @ ( collec3007137136614167897t_bool @ aa_fun8162393684988594084t_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_Collect__cong) ).
thf(947,plain,
! [A: fun_fu9160419385450930796l_bool,B: fun_fu9160419385450930796l_bool] :
( ! [C: fun_Pr6001797050664311790t_bool] :
( ( ( C @ ( B @ aa_fun5588795374382764133l_bool ) @ pp )
=> ( C @ ( A @ aa_fun5588795374382764133l_bool ) @ pp ) )
& ( ( C @ ( A @ aa_fun5588795374382764133l_bool ) @ pp )
=> ( C @ ( B @ aa_fun5588795374382764133l_bool ) @ pp ) ) )
=> ( ( A @ ( collec3007137136614167897t_bool @ aa_fun8162393684988594084t_bool ) )
= ( B @ ( collec3007137136614167897t_bool @ aa_fun8162393684988594084t_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(40,axiom,
! [A: set_fu6080891106736489294t_bool,B: set_fu6080891106736489294t_bool] :
( ( B @ ( A @ ord_le387542735852657390t_bool @ aa_set3226752938961784069l_bool ) @ pp )
<=> ! [C: fun_Pr6001797050664311790t_bool] :
( ( A @ ( C @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( B @ ( C @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1114_subset__eq) ).
thf(391,plain,
! [A: set_fu6080891106736489294t_bool,B: set_fu6080891106736489294t_bool] :
( ( ! [C: fun_Pr6001797050664311790t_bool] :
( ( A @ ( C @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( B @ ( C @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ) )
=> ( B @ ( A @ ord_le387542735852657390t_bool @ aa_set3226752938961784069l_bool ) @ pp ) )
& ( ( B @ ( A @ ord_le387542735852657390t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ! [C: fun_Pr6001797050664311790t_bool] :
( ( A @ ( C @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( B @ ( C @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(202,axiom,
! [A: produc3658429121746597890et_nat] :
( ( A @ ( top_top_assn @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp )
<=> ( A @ ( in_range @ aa_Pro2991721470636411351t_bool ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4335_mod__true) ).
thf(1139,plain,
! [A: produc3658429121746597890et_nat] :
( ( ( A @ ( in_range @ aa_Pro2991721470636411351t_bool ) @ pp )
=> ( A @ ( top_top_assn @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp ) )
& ( ( A @ ( top_top_assn @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp )
=> ( A @ ( in_range @ aa_Pro2991721470636411351t_bool ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(145,axiom,
! [A: set_fu6080891106736489294t_bool,B: fun_Pr6001797050664311790t_bool] :
( ( B @ ( A @ aTP_Lamm_a @ aa_fun5588795374382764133l_bool ) @ pp )
<=> ( A @ ( B @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7816_ATP_Olambda__21) ).
thf(900,plain,
! [A: set_fu6080891106736489294t_bool,B: fun_Pr6001797050664311790t_bool] :
( ( ( A @ ( B @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( B @ ( A @ aTP_Lamm_a @ aa_fun5588795374382764133l_bool ) @ pp ) )
& ( ( B @ ( A @ aTP_Lamm_a @ aa_fun5588795374382764133l_bool ) @ pp )
=> ( A @ ( B @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(198,axiom,
! [A: produc3658429121746597890et_nat] : ( A @ basic_2698842327037663054et_nat @ ( A @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) @ member_set_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1615_snds_Ointros) ).
thf(1117,plain,
! [A: produc3658429121746597890et_nat] : ( A @ basic_2698842327037663054et_nat @ ( A @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) @ member_set_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(44,axiom,
! [A: set_fu6080891106736489294t_bool] :
( ( bot_bo2714889297266208186t_bool @ ( A @ ord_le387542735852657390t_bool @ aa_set3226752938961784069l_bool ) @ pp )
<=> ( A = bot_bo2714889297266208186t_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1379_bot_Oextremum__unique) ).
thf(419,plain,
! [A: set_fu6080891106736489294t_bool] :
( ( ( A = bot_bo2714889297266208186t_bool )
=> ( bot_bo2714889297266208186t_bool @ ( A @ ord_le387542735852657390t_bool @ aa_set3226752938961784069l_bool ) @ pp ) )
& ( ( bot_bo2714889297266208186t_bool @ ( A @ ord_le387542735852657390t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( A = bot_bo2714889297266208186t_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(181,axiom,
! [A: produc3658429121746597890et_nat,B: produc3658429121746597890et_nat] :
( ( ( ( A @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) )
= ( B @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) ) )
& ( ( A @ ( produc1824681642469235216et_nat @ aa_Pro1219312880135979149t_unit ) )
= ( B @ ( produc1824681642469235216et_nat @ aa_Pro1219312880135979149t_unit ) ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4783_prod_Oexpand) ).
thf(1048,plain,
! [A: produc3658429121746597890et_nat,B: produc3658429121746597890et_nat] :
( ( ( ( A @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) )
= ( B @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) ) )
& ( ( A @ ( produc1824681642469235216et_nat @ aa_Pro1219312880135979149t_unit ) )
= ( B @ ( produc1824681642469235216et_nat @ aa_Pro1219312880135979149t_unit ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(169,axiom,
! [A: assn] :
( ( A @ ( A @ ( uminus_uminus_assn @ aa_assn_assn ) @ ( inf_inf_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) )
= bot_bot_assn ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6842_boolean__algebra_Oconj__cancel__left) ).
thf(996,plain,
! [A: assn] :
( ( A @ ( A @ ( uminus_uminus_assn @ aa_assn_assn ) @ ( inf_inf_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) )
= bot_bot_assn ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(114,axiom,
! [A: produc3658429121746597890et_nat] :
~ ! [B: heap_e7401611519738050253t_unit,C: set_nat] :
( A
!= ( C @ ( B @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_old_Oprod_Oexhaust) ).
thf(737,plain,
! [A: produc3658429121746597890et_nat] :
~ ! [B: heap_e7401611519738050253t_unit,C: set_nat] :
( A
!= ( C @ ( B @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(16,axiom,
! [A: fun_Pr6001797050664311790t_bool,B: set_fu6080891106736489294t_bool,C: set_fu6080891106736489294t_bool] :
( ( C @ ( B @ inf_in1689267372175091004t_bool ) @ ( A @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ~ ( ( B @ ( A @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ~ ( C @ ( A @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1160_IntE) ).
thf(303,plain,
! [A: fun_Pr6001797050664311790t_bool,B: set_fu6080891106736489294t_bool,C: set_fu6080891106736489294t_bool] :
( ( C @ ( B @ inf_in1689267372175091004t_bool ) @ ( A @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ~ ( ( B @ ( A @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ~ ( C @ ( A @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(210,axiom,
! [A: assn,B: assn] :
( ( B @ ( A @ ( inf_inf_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) )
= ( B @ ( A @ aTP_Lamm_aj @ aa_ass8975924923219239432t_bool ) @ ( abs_assn @ aa_fun1993714536301460826l_assn ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7590_inf__assn__def) ).
thf(1175,plain,
! [A: assn,B: assn] :
( ( B @ ( A @ ( inf_inf_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) )
= ( B @ ( A @ aTP_Lamm_aj @ aa_ass8975924923219239432t_bool ) @ ( abs_assn @ aa_fun1993714536301460826l_assn ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(119,axiom,
! [A: fun_Pr6001797050664311790t_bool,B: fun_fu9160419385450930796l_bool] :
( ( B @ ( collec3007137136614167897t_bool @ aa_fun8162393684988594084t_bool ) @ ( A @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
<=> ( A @ ( B @ aa_fun5588795374382764133l_bool ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_mem__Collect__eq) ).
thf(764,plain,
! [A: fun_Pr6001797050664311790t_bool,B: fun_fu9160419385450930796l_bool] :
( ( ( A @ ( B @ aa_fun5588795374382764133l_bool ) @ pp )
=> ( B @ ( collec3007137136614167897t_bool @ aa_fun8162393684988594084t_bool ) @ ( A @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ) )
& ( ( B @ ( collec3007137136614167897t_bool @ aa_fun8162393684988594084t_bool ) @ ( A @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( A @ ( B @ aa_fun5588795374382764133l_bool ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(80,axiom,
! [A: fun_Pr6001797050664311790t_bool,B: fun_fu9160419385450930796l_bool] :
( ( proper @ ( collec3007137136614167897t_bool @ aa_fun8162393684988594084t_bool ) @ ( A @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( ! [C: assn] : ( C @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ ( B @ aa_fun5588795374382764133l_bool ) @ pp )
=> ( A @ ( B @ aa_fun5588795374382764133l_bool ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_Rep__assn__induct) ).
thf(604,plain,
! [A: fun_Pr6001797050664311790t_bool,B: fun_fu9160419385450930796l_bool] :
( ( proper @ ( collec3007137136614167897t_bool @ aa_fun8162393684988594084t_bool ) @ ( A @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( ! [C: assn] : ( C @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ ( B @ aa_fun5588795374382764133l_bool ) @ pp )
=> ( A @ ( B @ aa_fun5588795374382764133l_bool ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(32,axiom,
! [A: set_fu6080891106736489294t_bool] :
( ! [B: fun_Pr6001797050664311790t_bool] :
~ ( A @ ( B @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
<=> ( A = bot_bo2714889297266208186t_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_all__not__in__conv) ).
thf(362,plain,
! [A: set_fu6080891106736489294t_bool] :
( ( ( A = bot_bo2714889297266208186t_bool )
=> ! [B: fun_Pr6001797050664311790t_bool] :
~ ( A @ ( B @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ) )
& ( ! [B: fun_Pr6001797050664311790t_bool] :
~ ( A @ ( B @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( A = bot_bo2714889297266208186t_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(72,axiom,
! [A: assn,B: assn] :
( ( B @ ( A @ minus_minus_assn @ aa_assn_assn ) )
= ( B @ ( uminus_uminus_assn @ aa_assn_assn ) @ ( A @ ( inf_inf_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7003_minus__assn__def) ).
thf(567,plain,
! [A: assn,B: assn] :
( ( B @ ( A @ minus_minus_assn @ aa_assn_assn ) )
= ( B @ ( uminus_uminus_assn @ aa_assn_assn ) @ ( A @ ( inf_inf_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(127,axiom,
! [A: assn,B: assn] :
( ( ( B @ ( A @ ( sup_sup_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) )
= bot_bot_assn )
<=> ( ( B = bot_bot_assn )
& ( A = bot_bot_assn ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1537_sup__bot_Oeq__neutr__iff) ).
thf(811,plain,
! [A: assn,B: assn] :
( ( ( ( B = bot_bot_assn )
& ( A = bot_bot_assn ) )
=> ( ( B @ ( A @ ( sup_sup_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) )
= bot_bot_assn ) )
& ( ( ( B @ ( A @ ( sup_sup_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) )
= bot_bot_assn )
=> ( ( B = bot_bot_assn )
& ( A = bot_bot_assn ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(59,axiom,
! [A: fun_as4100195077546555551t_bool,B: fun_fu1264473476461866025l_assn,C: set_fu6080891106736489294t_bool,D: fun_Pr6001797050664311790t_bool,E: fun_Pr6001797050664311790t_bool] :
( ( C @ ( B @ ( A @ type_d18088346645320984t_bool ) @ aa_set3226752938961784069l_bool ) @ pp )
=> ( ( C @ ( D @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( ( C @ ( E @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( ( ( D @ ( B @ aa_fun1993714536301460826l_assn ) )
= ( E @ ( B @ aa_fun1993714536301460826l_assn ) ) )
<=> ( D = E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_355_type__definition_OAbs__inject) ).
thf(494,plain,
! [A: fun_as4100195077546555551t_bool,B: fun_fu1264473476461866025l_assn,C: set_fu6080891106736489294t_bool,D: fun_Pr6001797050664311790t_bool,E: fun_Pr6001797050664311790t_bool] :
( ( C @ ( B @ ( A @ type_d18088346645320984t_bool ) @ aa_set3226752938961784069l_bool ) @ pp )
=> ( ( C @ ( D @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( ( C @ ( E @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( ( ( D = E )
=> ( ( D @ ( B @ aa_fun1993714536301460826l_assn ) )
= ( E @ ( B @ aa_fun1993714536301460826l_assn ) ) ) )
& ( ( ( D @ ( B @ aa_fun1993714536301460826l_assn ) )
= ( E @ ( B @ aa_fun1993714536301460826l_assn ) ) )
=> ( D = E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(88,axiom,
! [A: assn,B: assn,C: assn] :
( ( C @ ( B @ times_times_assn @ aa_assn_assn ) @ ( A @ times_times_assn @ aa_assn_assn ) )
= ( C @ ( A @ times_times_assn @ aa_assn_assn ) @ ( B @ times_times_assn @ aa_assn_assn ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_383_ab__semigroup__mult__class_Omult_Oleft__commute) ).
thf(631,plain,
! [A: assn,B: assn,C: assn] :
( ( C @ ( B @ times_times_assn @ aa_assn_assn ) @ ( A @ times_times_assn @ aa_assn_assn ) )
= ( C @ ( A @ times_times_assn @ aa_assn_assn ) @ ( B @ times_times_assn @ aa_assn_assn ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(66,axiom,
! [A: fun_Pr6001797050664311790t_bool,B: produc3658429121746597890et_nat] :
( ( B @ ( A @ ( aTP_Lamm_ah @ aa_fun6808777976510360636t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp )
<=> ( ~ ( B @ ( A @ aa_Pro2991721470636411351t_bool ) @ pp )
& ( B @ ( in_range @ aa_Pro2991721470636411351t_bool ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7806_ATP_Olambda__11) ).
thf(520,plain,
! [A: fun_Pr6001797050664311790t_bool,B: produc3658429121746597890et_nat] :
( ( ( ~ ( B @ ( A @ aa_Pro2991721470636411351t_bool ) @ pp )
& ( B @ ( in_range @ aa_Pro2991721470636411351t_bool ) @ pp ) )
=> ( B @ ( A @ ( aTP_Lamm_ah @ aa_fun6808777976510360636t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp ) )
& ( ( B @ ( A @ ( aTP_Lamm_ah @ aa_fun6808777976510360636t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp )
=> ( ~ ( B @ ( A @ aa_Pro2991721470636411351t_bool ) @ pp )
& ( B @ ( in_range @ aa_Pro2991721470636411351t_bool ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(4,axiom,
! [A: set_fu6080891106736489294t_bool,B: set_fu6080891106736489294t_bool,C: set_fu6080891106736489294t_bool,D: set_fu6080891106736489294t_bool] :
( ( B @ ( A @ ord_le387542735852657390t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( ( D @ ( C @ ord_le387542735852657390t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( ( ( D @ ( B @ inf_in1689267372175091004t_bool ) )
= bot_bo2714889297266208186t_bool )
=> ( ( C @ ( A @ inf_in1689267372175091004t_bool ) )
= bot_bo2714889297266208186t_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1236_disjoint__mono) ).
thf(240,plain,
! [A: set_fu6080891106736489294t_bool,B: set_fu6080891106736489294t_bool,C: set_fu6080891106736489294t_bool,D: set_fu6080891106736489294t_bool] :
( ( B @ ( A @ ord_le387542735852657390t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( ( D @ ( C @ ord_le387542735852657390t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( ( ( D @ ( B @ inf_in1689267372175091004t_bool ) )
= bot_bo2714889297266208186t_bool )
=> ( ( C @ ( A @ inf_in1689267372175091004t_bool ) )
= bot_bo2714889297266208186t_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(205,axiom,
! [A: assn,B: assn] :
( ( B @ ( A @ wand_assn @ aa_assn_assn ) )
= ( B @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ ( A @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ wand_raw @ aa_fun6808777976510360636t_bool ) @ ( abs_assn @ aa_fun1993714536301460826l_assn ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_wand__assn__def) ).
thf(1149,plain,
! [A: assn,B: assn] :
( ( B @ ( A @ wand_assn @ aa_assn_assn ) )
= ( B @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ ( A @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ wand_raw @ aa_fun6808777976510360636t_bool ) @ ( abs_assn @ aa_fun1993714536301460826l_assn ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(185,axiom,
! [A: set_nat,B: produc3658429121746597890et_nat] :
( ( B @ basic_2698842327037663054et_nat @ ( A @ member_set_nat ) )
=> ( A
= ( B @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1611_snds_Ocases) ).
thf(1061,plain,
! [A: set_nat,B: produc3658429121746597890et_nat] :
( ( B @ basic_2698842327037663054et_nat @ ( A @ member_set_nat ) )
=> ( A
= ( B @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(165,axiom,
! [A: produc3658429121746597890et_nat,B: heap_e7401611519738050253t_unit,C: set_nat] :
( ( A
= ( C @ ( B @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) )
=> ( ( A @ ( produc1824681642469235216et_nat @ aa_Pro1219312880135979149t_unit ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4754_fstI) ).
thf(983,plain,
! [A: produc3658429121746597890et_nat,B: heap_e7401611519738050253t_unit,C: set_nat] :
( ( A
= ( C @ ( B @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) )
=> ( ( A @ ( produc1824681642469235216et_nat @ aa_Pro1219312880135979149t_unit ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(41,axiom,
! [A: heap_e7401611519738050253t_unit,B: set_nat,C: set_Pr3948176798113811640et_nat,D: set_nat] :
( ( C @ ( B @ ( A @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ member6260224972018164377et_nat ) )
=> ( ( D = B )
=> ( C @ ( D @ ( A @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ member6260224972018164377et_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_ssubst__Pair__rhs) ).
thf(399,plain,
! [A: heap_e7401611519738050253t_unit,B: set_nat,C: set_Pr3948176798113811640et_nat,D: set_nat] :
( ( C @ ( B @ ( A @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ member6260224972018164377et_nat ) )
=> ( ( D = B )
=> ( C @ ( D @ ( A @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ member6260224972018164377et_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(104,axiom,
! [A: assn,B: assn,C: assn] :
( ( C @ ( A @ ( inf_inf_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) @ ( B @ ( A @ ( uminus_uminus_assn @ aa_assn_assn ) @ ( inf_inf_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) @ ( inf_inf_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) )
= bot_bot_assn ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7070_inf__cancel__left2) ).
thf(695,plain,
! [A: assn,B: assn,C: assn] :
( ( C @ ( A @ ( inf_inf_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) @ ( B @ ( A @ ( uminus_uminus_assn @ aa_assn_assn ) @ ( inf_inf_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) @ ( inf_inf_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) )
= bot_bot_assn ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(140,axiom,
! [A: heap_e7401611519738050253t_unit] : ( bot_bot_set_nat @ ( A @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ ( in_range @ aa_Pro2991721470636411351t_bool ) @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_473_in__range__empty) ).
thf(868,plain,
! [A: heap_e7401611519738050253t_unit] : ( bot_bot_set_nat @ ( A @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ ( in_range @ aa_Pro2991721470636411351t_bool ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(93,axiom,
! [A: assn] :
( ( bot_bot_assn @ ( A @ ( sup_sup_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1558_sup__bot__right) ).
thf(653,plain,
! [A: assn] :
( ( bot_bot_assn @ ( A @ ( sup_sup_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(61,axiom,
aTP_Lamm_ag @ ( proper @ aa_fun5588795374382764133l_bool ) @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7586_bool__assn__proper_I2_J) ).
thf(505,plain,
aTP_Lamm_ag @ ( proper @ aa_fun5588795374382764133l_bool ) @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(47,axiom,
! [A: fun_Pr6001797050664311790t_bool,B: set_fu6080891106736489294t_bool] :
( ( B @ ( A @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( B != bot_bo2714889297266208186t_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_memb__imp__not__empty) ).
thf(438,plain,
! [A: fun_Pr6001797050664311790t_bool,B: set_fu6080891106736489294t_bool] :
( ( B @ ( A @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( B != bot_bo2714889297266208186t_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(109,axiom,
top_top_assn != one_one_assn,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4334_assn__basic__inequalities_I1_J) ).
thf(722,plain,
top_top_assn != one_one_assn,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(208,axiom,
! [A: produc3658429121746597890et_nat,B: produc3658429121746597890et_nat] :
( ( ( A @ ( produc1824681642469235216et_nat @ aa_Pro1219312880135979149t_unit ) )
= ( B @ ( produc1824681642469235216et_nat @ aa_Pro1219312880135979149t_unit ) ) )
=> ( ( ( A @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) )
= ( B @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4781_prod__eqI) ).
thf(1166,plain,
! [A: produc3658429121746597890et_nat,B: produc3658429121746597890et_nat] :
( ( ( A @ ( produc1824681642469235216et_nat @ aa_Pro1219312880135979149t_unit ) )
= ( B @ ( produc1824681642469235216et_nat @ aa_Pro1219312880135979149t_unit ) ) )
=> ( ( ( A @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) )
= ( B @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(157,axiom,
! [A: fun_he2331061685413951235t_unit] :
( ( A @ produc4172003873565521026et_nat @ ( produc8586169260539613262et_nat @ comp_P2930521774885306735et_nat ) )
= produc8586169260539613262et_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4723_snd__comp__apfst) ).
thf(944,plain,
! [A: fun_he2331061685413951235t_unit] :
( ( A @ produc4172003873565521026et_nat @ ( produc8586169260539613262et_nat @ comp_P2930521774885306735et_nat ) )
= produc8586169260539613262et_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(70,axiom,
! [A: set_nat,B: produc3658429121746597890et_nat] :
( ( A
= ( B @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) ) )
<=> ? [C: heap_e7401611519738050253t_unit] :
( B
= ( A @ ( C @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_eq__snd__iff) ).
thf(548,plain,
! [A: set_nat,B: produc3658429121746597890et_nat] :
( ( ? [C: heap_e7401611519738050253t_unit] :
( B
= ( A @ ( C @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) )
=> ( A
= ( B @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) ) ) )
& ( ( A
= ( B @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) ) )
=> ? [C: heap_e7401611519738050253t_unit] :
( B
= ( A @ ( C @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(34,axiom,
! [A: set_fu6080891106736489294t_bool,B: set_fu6080891106736489294t_bool] :
( ! [C: fun_Pr6001797050664311790t_bool] :
( ( A @ ( C @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( B @ ( C @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ) )
=> ( B @ ( A @ ord_le387542735852657390t_bool @ aa_set3226752938961784069l_bool ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_847_subsetI) ).
thf(374,plain,
! [A: set_fu6080891106736489294t_bool,B: set_fu6080891106736489294t_bool] :
( ! [C: fun_Pr6001797050664311790t_bool] :
( ( A @ ( C @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( B @ ( C @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ) )
=> ( B @ ( A @ ord_le387542735852657390t_bool @ aa_set3226752938961784069l_bool ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(190,axiom,
! [A: assn,B: assn,C: produc3658429121746597890et_nat] :
( ( C @ ( B @ ( A @ times_times_assn @ aa_assn_assn ) @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp )
=> ? [D: produc3658429121746597890et_nat,E: produc3658429121746597890et_nat] :
( ( E @ ( B @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp )
& ( D @ ( A @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_408_mod__starD) ).
thf(1081,plain,
! [A: assn,B: assn,C: produc3658429121746597890et_nat] :
( ( C @ ( B @ ( A @ times_times_assn @ aa_assn_assn ) @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp )
=> ? [D: produc3658429121746597890et_nat,E: produc3658429121746597890et_nat] :
( ( E @ ( B @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp )
& ( D @ ( A @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(155,axiom,
! [A: produc3658429121746597890et_nat] :
( A
= ( A @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) @ ( A @ ( produc1824681642469235216et_nat @ aa_Pro1219312880135979149t_unit ) @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4837_prod_Oexhaust__sel) ).
thf(939,plain,
! [A: produc3658429121746597890et_nat] :
( A
= ( A @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) @ ( A @ ( produc1824681642469235216et_nat @ aa_Pro1219312880135979149t_unit ) @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(203,axiom,
one_assn_raw @ ( proper @ aa_fun5588795374382764133l_bool ) @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_one__assn__proper) ).
thf(1145,plain,
one_assn_raw @ ( proper @ aa_fun5588795374382764133l_bool ) @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(71,axiom,
! [A: heap_e7401611519738050253t_unit,B: set_nat,C: heap_e7401611519738050253t_unit,D: set_nat] :
( ( ( B @ ( A @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) )
= ( D @ ( C @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) )
<=> ( ( B = D )
& ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_old_Oprod_Oinject) ).
thf(557,plain,
! [A: heap_e7401611519738050253t_unit,B: set_nat,C: heap_e7401611519738050253t_unit,D: set_nat] :
( ( ( ( B = D )
& ( A = C ) )
=> ( ( B @ ( A @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) )
= ( D @ ( C @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) ) )
& ( ( ( B @ ( A @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) )
= ( D @ ( C @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(176,axiom,
! [A: assn] :
( ( A @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ ( abs_assn @ aa_fun1993714536301460826l_assn ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_Rep__assn__inverse) ).
thf(1025,plain,
! [A: assn] :
( ( A @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ ( abs_assn @ aa_fun1993714536301460826l_assn ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(10,axiom,
! [A: set_fu6080891106736489294t_bool] :
( ( A @ ( bot_bo2714889297266208186t_bool @ inf_in1689267372175091004t_bool ) )
= bot_bo2714889297266208186t_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1585_boolean__algebra_Oconj__zero__left) ).
thf(282,plain,
! [A: set_fu6080891106736489294t_bool] :
( ( A @ ( bot_bo2714889297266208186t_bool @ inf_in1689267372175091004t_bool ) )
= bot_bo2714889297266208186t_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(168,axiom,
! [A: assn] :
( ( A @ ( bot_bot_assn @ times_times_assn @ aa_assn_assn ) )
= bot_bot_assn ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_374_star__false__left) ).
thf(993,plain,
! [A: assn] :
( ( A @ ( bot_bot_assn @ times_times_assn @ aa_assn_assn ) )
= bot_bot_assn ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(196,axiom,
! [A: fun_Pr6001797050664311790t_bool,B: fun_Pr6001797050664311790t_bool,C: produc3658429121746597890et_nat] :
( ( C @ ( B @ ( A @ aTP_Lamm_ae @ aa_fun6808777976510360636t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp )
<=> ( ( C @ ( B @ aa_Pro2991721470636411351t_bool ) @ pp )
& ( C @ ( A @ aa_Pro2991721470636411351t_bool ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7835_ATP_Olambda__40) ).
thf(1098,plain,
! [A: fun_Pr6001797050664311790t_bool,B: fun_Pr6001797050664311790t_bool,C: produc3658429121746597890et_nat] :
( ( ( ( C @ ( B @ aa_Pro2991721470636411351t_bool ) @ pp )
& ( C @ ( A @ aa_Pro2991721470636411351t_bool ) @ pp ) )
=> ( C @ ( B @ ( A @ aTP_Lamm_ae @ aa_fun6808777976510360636t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp ) )
& ( ( C @ ( B @ ( A @ aTP_Lamm_ae @ aa_fun6808777976510360636t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp )
=> ( ( C @ ( B @ aa_Pro2991721470636411351t_bool ) @ pp )
& ( C @ ( A @ aa_Pro2991721470636411351t_bool ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(18,axiom,
! [A: set_fu6080891106736489294t_bool] :
( ( bot_bo2714889297266208186t_bool @ ( A @ inf_in1689267372175091004t_bool ) )
= bot_bo2714889297266208186t_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1333_Int__empty__right) ).
thf(310,plain,
! [A: set_fu6080891106736489294t_bool] :
( ( bot_bo2714889297266208186t_bool @ ( A @ inf_in1689267372175091004t_bool ) )
= bot_bo2714889297266208186t_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(24,axiom,
! [A: set_fu6080891106736489294t_bool] :
( ! [B: fun_Pr6001797050664311790t_bool] :
~ ( A @ ( B @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( bot_bo2714889297266208186t_bool @ ( A @ ord_le387542735852657390t_bool @ aa_set3226752938961784069l_bool ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1393_subset__emptyI) ).
thf(331,plain,
! [A: set_fu6080891106736489294t_bool] :
( ! [B: fun_Pr6001797050664311790t_bool] :
~ ( A @ ( B @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( bot_bo2714889297266208186t_bool @ ( A @ ord_le387542735852657390t_bool @ aa_set3226752938961784069l_bool ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(33,axiom,
! [A: set_fu6080891106736489294t_bool] :
( ( A != bot_bo2714889297266208186t_bool )
=> ~ ! [B: fun_Pr6001797050664311790t_bool] :
~ ( A @ ( B @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_set__notEmptyE) ).
thf(370,plain,
! [A: set_fu6080891106736489294t_bool] :
( ( A != bot_bo2714889297266208186t_bool )
=> ~ ! [B: fun_Pr6001797050664311790t_bool] :
~ ( A @ ( B @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(60,axiom,
! [A: assn] :
( ( one_one_assn @ ( A @ times_times_assn @ aa_assn_assn ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_403_mult_Ocomm__neutral) ).
thf(502,plain,
! [A: assn] :
( ( one_one_assn @ ( A @ times_times_assn @ aa_assn_assn ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(133,axiom,
! [A: fun_set_nat_set_nat,B: fun_he2331061685413951235t_unit,C: produc3658429121746597890et_nat] :
( ( C @ ( B @ produc4172003873565521026et_nat @ aa_Pro3679490825741336130et_nat ) @ ( A @ produc3286488329990770625t_unit @ aa_Pro3679490825741336130et_nat ) )
= ( C @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) @ ( A @ aa_set_nat_set_nat ) @ ( C @ ( produc1824681642469235216et_nat @ aa_Pro1219312880135979149t_unit ) @ ( B @ aa_hea2136485429539994620t_unit ) @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4743_apsnd__apfst) ).
thf(840,plain,
! [A: fun_set_nat_set_nat,B: fun_he2331061685413951235t_unit,C: produc3658429121746597890et_nat] :
( ( C @ ( B @ produc4172003873565521026et_nat @ aa_Pro3679490825741336130et_nat ) @ ( A @ produc3286488329990770625t_unit @ aa_Pro3679490825741336130et_nat ) )
= ( C @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) @ ( A @ aa_set_nat_set_nat ) @ ( C @ ( produc1824681642469235216et_nat @ aa_Pro1219312880135979149t_unit ) @ ( B @ aa_hea2136485429539994620t_unit ) @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(52,axiom,
! [A: assn,B: assn,C: assn] :
( ( C @ ( B @ ( A @ times_times_assn @ aa_assn_assn ) @ times_times_assn @ aa_assn_assn ) )
= ( B @ ( C @ ( A @ times_times_assn @ aa_assn_assn ) @ times_times_assn @ aa_assn_assn ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_469_mult_Oright__commute) ).
thf(463,plain,
! [A: assn,B: assn,C: assn] :
( ( C @ ( B @ ( A @ times_times_assn @ aa_assn_assn ) @ times_times_assn @ aa_assn_assn ) )
= ( B @ ( C @ ( A @ times_times_assn @ aa_assn_assn ) @ times_times_assn @ aa_assn_assn ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(126,axiom,
! [A: assn] :
( ( A @ ( one_one_assn @ times_times_assn @ aa_assn_assn ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_397_comm__monoid__mult__class_Omult__1) ).
thf(808,plain,
! [A: assn] :
( ( A @ ( one_one_assn @ times_times_assn @ aa_assn_assn ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(31,axiom,
bot_bo2714889297266208186t_bool != top_to5841454426718376094t_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4087_empty__not__UNIV) ).
thf(359,plain,
bot_bo2714889297266208186t_bool != top_to5841454426718376094t_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(90,axiom,
! [A: assn,B: assn] :
( ( B @ ( A @ times_times_assn @ aa_assn_assn ) )
= ( A @ ( B @ times_times_assn @ aa_assn_assn ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_387_ab__semigroup__mult__class_Omult_Ocommute) ).
thf(643,plain,
! [A: assn,B: assn] :
( ( B @ ( A @ times_times_assn @ aa_assn_assn ) )
= ( A @ ( B @ times_times_assn @ aa_assn_assn ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(217,axiom,
( bot_bot_assn
= ( aTP_Lamm_ag @ ( abs_assn @ aa_fun1993714536301460826l_assn ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7588_bot__assn__def) ).
thf(1220,plain,
( bot_bot_assn
= ( aTP_Lamm_ag @ ( abs_assn @ aa_fun1993714536301460826l_assn ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(116,axiom,
! [A: fun_as4100195077546555551t_bool,B: fun_fu1264473476461866025l_assn,C: set_fu6080891106736489294t_bool,D: assn,E: assn] :
( ( C @ ( B @ ( A @ type_d18088346645320984t_bool ) @ aa_set3226752938961784069l_bool ) @ pp )
=> ( ( ( D @ ( A @ aa_ass8975924923219239432t_bool ) )
= ( E @ ( A @ aa_ass8975924923219239432t_bool ) ) )
<=> ( D = E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_347_type__definition_ORep__inject) ).
thf(744,plain,
! [A: fun_as4100195077546555551t_bool,B: fun_fu1264473476461866025l_assn,C: set_fu6080891106736489294t_bool,D: assn,E: assn] :
( ( C @ ( B @ ( A @ type_d18088346645320984t_bool ) @ aa_set3226752938961784069l_bool ) @ pp )
=> ( ( ( D = E )
=> ( ( D @ ( A @ aa_ass8975924923219239432t_bool ) )
= ( E @ ( A @ aa_ass8975924923219239432t_bool ) ) ) )
& ( ( ( D @ ( A @ aa_ass8975924923219239432t_bool ) )
= ( E @ ( A @ aa_ass8975924923219239432t_bool ) ) )
=> ( D = E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(222,axiom,
! [A: set_nat] :
( ( A @ ( is_empty_nat @ aa_set_nat_bool ) @ pp )
<=> ( A = bot_bot_set_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_Set_Ois__empty__def) ).
thf(1257,plain,
! [A: set_nat] :
( ( ( A = bot_bot_set_nat )
=> ( A @ ( is_empty_nat @ aa_set_nat_bool ) @ pp ) )
& ( ( A @ ( is_empty_nat @ aa_set_nat_bool ) @ pp )
=> ( A = bot_bot_set_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(94,axiom,
! [A: assn,B: assn] :
( ( ( B @ ( A @ ( inf_inf_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) )
= bot_bot_assn )
=> ( ( ( B @ ( A @ ( sup_sup_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) )
= top_top_assn )
=> ( ( A @ ( uminus_uminus_assn @ aa_assn_assn ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7341_boolean__algebra__class_Oboolean__algebra_Ocompl__unique) ).
thf(656,plain,
! [A: assn,B: assn] :
( ( ( B @ ( A @ ( inf_inf_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) )
= bot_bot_assn )
=> ( ( ( B @ ( A @ ( sup_sup_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) )
= top_top_assn )
=> ( ( A @ ( uminus_uminus_assn @ aa_assn_assn ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(84,axiom,
! [A: produc3658429121746597890et_nat,B: heap_e7401611519738050253t_unit,C: set_nat,D: fun_he6201055237484778573t_bool] :
( ( A
= ( C @ ( B @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) )
=> ( ( A @ ( produc1824681642469235216et_nat @ aa_Pro1219312880135979149t_unit ) @ ( D @ aa_hea1793595068369496646t_bool ) @ pp )
=> ( B @ ( D @ aa_hea1793595068369496646t_bool ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4774_fstE) ).
thf(613,plain,
! [A: produc3658429121746597890et_nat,B: heap_e7401611519738050253t_unit,C: set_nat,D: fun_he6201055237484778573t_bool] :
( ( A
= ( C @ ( B @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) )
=> ( ( A @ ( produc1824681642469235216et_nat @ aa_Pro1219312880135979149t_unit ) @ ( D @ aa_hea1793595068369496646t_bool ) @ pp )
=> ( B @ ( D @ aa_hea1793595068369496646t_bool ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(173,axiom,
! [A: fun_he7710493197641524256t_bool] :
( ? [B: heap_e7401611519738050253t_unit,C: set_nat] : ( C @ ( B @ ( A @ aa_hea2782697410307197849t_bool ) @ aa_set_nat_bool ) @ pp )
<=> ? [B: produc3658429121746597890et_nat] : ( B @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) @ ( B @ ( produc1824681642469235216et_nat @ aa_Pro1219312880135979149t_unit ) @ ( A @ aa_hea2782697410307197849t_bool ) @ aa_set_nat_bool ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4787_Ex__prod__contract) ).
thf(1008,plain,
! [A: fun_he7710493197641524256t_bool] :
( ( ? [B: produc3658429121746597890et_nat] : ( B @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) @ ( B @ ( produc1824681642469235216et_nat @ aa_Pro1219312880135979149t_unit ) @ ( A @ aa_hea2782697410307197849t_bool ) @ aa_set_nat_bool ) @ pp )
=> ? [B: heap_e7401611519738050253t_unit,C: set_nat] : ( C @ ( B @ ( A @ aa_hea2782697410307197849t_bool ) @ aa_set_nat_bool ) @ pp ) )
& ( ? [B: heap_e7401611519738050253t_unit,C: set_nat] : ( C @ ( B @ ( A @ aa_hea2782697410307197849t_bool ) @ aa_set_nat_bool ) @ pp )
=> ? [B: produc3658429121746597890et_nat] : ( B @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) @ ( B @ ( produc1824681642469235216et_nat @ aa_Pro1219312880135979149t_unit ) @ ( A @ aa_hea2782697410307197849t_bool ) @ aa_set_nat_bool ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(78,axiom,
! [A: fun_as4100195077546555551t_bool,B: fun_fu1264473476461866025l_assn,C: set_fu6080891106736489294t_bool,D: assn] :
( ( C @ ( B @ ( A @ type_d18088346645320984t_bool ) @ aa_set3226752938961784069l_bool ) @ pp )
=> ~ ! [E: fun_Pr6001797050664311790t_bool] :
( ( D
= ( E @ ( B @ aa_fun1993714536301460826l_assn ) ) )
=> ~ ( C @ ( E @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_420_type__definition_OAbs__cases) ).
thf(595,plain,
! [A: fun_as4100195077546555551t_bool,B: fun_fu1264473476461866025l_assn,C: set_fu6080891106736489294t_bool,D: assn] :
( ( C @ ( B @ ( A @ type_d18088346645320984t_bool ) @ aa_set3226752938961784069l_bool ) @ pp )
=> ~ ! [E: fun_Pr6001797050664311790t_bool] :
( ( D
= ( E @ ( B @ aa_fun1993714536301460826l_assn ) ) )
=> ~ ( C @ ( E @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(87,axiom,
! [A: heap_e7401611519738050253t_unit,B: set_nat,C: heap_e7401611519738050253t_unit] :
( ( ( B @ ( A @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ ( produc1824681642469235216et_nat @ aa_Pro1219312880135979149t_unit ) )
= C )
=> ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4759_fst__eqD) ).
thf(627,plain,
! [A: heap_e7401611519738050253t_unit,B: set_nat,C: heap_e7401611519738050253t_unit] :
( ( ( B @ ( A @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ ( produc1824681642469235216et_nat @ aa_Pro1219312880135979149t_unit ) )
= C )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(50,axiom,
! [A: set_nat,B: heap_e7401611519738050253t_unit] :
( ( B @ ( A @ produc2471974422597015918t_unit ) @ ( produc1264744871843189710t_unit @ aa_Pro2092192379717785596et_nat ) )
= ( A @ ( B @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3370_swap__simp) ).
thf(450,plain,
! [A: set_nat,B: heap_e7401611519738050253t_unit] :
( ( B @ ( A @ produc2471974422597015918t_unit ) @ ( produc1264744871843189710t_unit @ aa_Pro2092192379717785596et_nat ) )
= ( A @ ( B @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(153,axiom,
! [A: assn] :
( ( bot_bot_assn @ ( A @ ( sup_sup_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1602_boolean__algebra_Odisj__zero__right) ).
thf(931,plain,
! [A: assn] :
( ( bot_bot_assn @ ( A @ ( sup_sup_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(56,axiom,
! [A: produc3658429121746597890et_nat] :
? [B: heap_e7401611519738050253t_unit,C: set_nat] :
( A
= ( C @ ( B @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_surj__pair) ).
thf(482,plain,
! [A: produc3658429121746597890et_nat] :
? [B: heap_e7401611519738050253t_unit,C: set_nat] :
( A
= ( C @ ( B @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(76,axiom,
! [A: assn,B: assn] :
( ( ( B @ ( A @ ( sup_sup_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) )
= bot_bot_assn )
<=> ( ( B = bot_bot_assn )
& ( A = bot_bot_assn ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1544_sup__eq__bot__iff) ).
thf(581,plain,
! [A: assn,B: assn] :
( ( ( ( B = bot_bot_assn )
& ( A = bot_bot_assn ) )
=> ( ( B @ ( A @ ( sup_sup_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) )
= bot_bot_assn ) )
& ( ( ( B @ ( A @ ( sup_sup_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) )
= bot_bot_assn )
=> ( ( B = bot_bot_assn )
& ( A = bot_bot_assn ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(65,axiom,
top_top_assn != bot_bot_assn,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4333_assn__basic__inequalities_I5_J) ).
thf(517,plain,
top_top_assn != bot_bot_assn,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(29,axiom,
! [A: fun_set_nat_set_nat,B: produc3658429121746597890et_nat] :
( ( B @ ( A @ produc3286488329990770625t_unit @ aa_Pro3679490825741336130et_nat ) @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) )
= ( B @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) @ ( A @ aa_set_nat_set_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4676_snd__apsnd) ).
thf(351,plain,
! [A: fun_set_nat_set_nat,B: produc3658429121746597890et_nat] :
( ( B @ ( A @ produc3286488329990770625t_unit @ aa_Pro3679490825741336130et_nat ) @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) )
= ( B @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) @ ( A @ aa_set_nat_set_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(112,axiom,
! [A: assn,B: assn,C: assn] :
( ( C @ ( A @ ( uminus_uminus_assn @ aa_assn_assn ) @ ( inf_inf_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) @ ( B @ ( A @ ( inf_inf_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) @ ( inf_inf_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) )
= bot_bot_assn ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7077_inf__cancel__left1) ).
thf(731,plain,
! [A: assn,B: assn,C: assn] :
( ( C @ ( A @ ( uminus_uminus_assn @ aa_assn_assn ) @ ( inf_inf_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) @ ( B @ ( A @ ( inf_inf_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) @ ( inf_inf_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) )
= bot_bot_assn ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(123,axiom,
! [A: set_fu6080891106736489294t_bool,B: fun_fu9160419385450930796l_bool] :
( ( B @ ( collec3007137136614167897t_bool @ aa_fun8162393684988594084t_bool ) @ ( A @ ord_le387542735852657390t_bool @ aa_set3226752938961784069l_bool ) @ pp )
<=> ! [C: fun_Pr6001797050664311790t_bool] :
( ( A @ ( C @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( C @ ( B @ aa_fun5588795374382764133l_bool ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1021_subset__Collect__conv) ).
thf(781,plain,
! [A: set_fu6080891106736489294t_bool,B: fun_fu9160419385450930796l_bool] :
( ( ! [C: fun_Pr6001797050664311790t_bool] :
( ( A @ ( C @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( C @ ( B @ aa_fun5588795374382764133l_bool ) @ pp ) )
=> ( B @ ( collec3007137136614167897t_bool @ aa_fun8162393684988594084t_bool ) @ ( A @ ord_le387542735852657390t_bool @ aa_set3226752938961784069l_bool ) @ pp ) )
& ( ( B @ ( collec3007137136614167897t_bool @ aa_fun8162393684988594084t_bool ) @ ( A @ ord_le387542735852657390t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ! [C: fun_Pr6001797050664311790t_bool] :
( ( A @ ( C @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( C @ ( B @ aa_fun5588795374382764133l_bool ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(178,axiom,
! [A: produc3658429121746597890et_nat] :
( ( A @ ( produc6300697153377358172et_nat @ aa_Pro7370057327950226428t_unit ) @ produc6012101397789842562t_unit )
= ( A @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4719_fst__swap) ).
thf(1030,plain,
! [A: produc3658429121746597890et_nat] :
( ( A @ ( produc6300697153377358172et_nat @ aa_Pro7370057327950226428t_unit ) @ produc6012101397789842562t_unit )
= ( A @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(35,axiom,
! [A: set_fu6080891106736489294t_bool] : ( A @ ( bot_bo2714889297266208186t_bool @ ord_le387542735852657390t_bool @ aa_set3226752938961784069l_bool ) @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1386_bot_Oextremum) ).
thf(378,plain,
! [A: set_fu6080891106736489294t_bool] : ( A @ ( bot_bo2714889297266208186t_bool @ ord_le387542735852657390t_bool @ aa_set3226752938961784069l_bool ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(97,axiom,
! [A: bool,B: heap_e7401611519738050253t_unit,C: set_nat] :
( ( C @ ( B @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ ( A @ pure_a825153325127701367it_nat @ aa_Pro2991721470636411351t_bool ) @ pp )
<=> ( ( A @ pp )
& ( C = bot_bot_set_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_pure__assn__raw_Osimps) ).
thf(667,plain,
! [A: bool,B: heap_e7401611519738050253t_unit,C: set_nat] :
( ( ( ( A @ pp )
& ( C = bot_bot_set_nat ) )
=> ( C @ ( B @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ ( A @ pure_a825153325127701367it_nat @ aa_Pro2991721470636411351t_bool ) @ pp ) )
& ( ( C @ ( B @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ ( A @ pure_a825153325127701367it_nat @ aa_Pro2991721470636411351t_bool ) @ pp )
=> ( ( A @ pp )
& ( C = bot_bot_set_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(152,axiom,
! [A: fun_Pr6001797050664311790t_bool,B: fun_Pr6001797050664311790t_bool] : ( B @ ( A @ wand_raw @ aa_fun6808777976510360636t_bool ) @ ( proper @ aa_fun5588795374382764133l_bool ) @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_wand__proper) ).
thf(929,plain,
! [A: fun_Pr6001797050664311790t_bool,B: fun_Pr6001797050664311790t_bool] : ( B @ ( A @ wand_raw @ aa_fun6808777976510360636t_bool ) @ ( proper @ aa_fun5588795374382764133l_bool ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(37,axiom,
? [A: fun_Pr6001797050664311790t_bool] : ( top_to5841454426718376094t_bool @ ( A @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3659_UNIV__witness) ).
thf(383,plain,
? [A: fun_Pr6001797050664311790t_bool] : ( top_to5841454426718376094t_bool @ ( A @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(130,axiom,
( ( top_top_assn @ ( uminus_uminus_assn @ aa_assn_assn ) )
= bot_bot_assn ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6821_boolean__algebra_Ocompl__one) ).
thf(832,plain,
( ( top_top_assn @ ( uminus_uminus_assn @ aa_assn_assn ) )
= bot_bot_assn ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(27,axiom,
! [A: fun_Pr6001797050664311790t_bool] : ( top_to5841454426718376094t_bool @ ( A @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3510_UNIV__I) ).
thf(346,plain,
! [A: fun_Pr6001797050664311790t_bool] : ( top_to5841454426718376094t_bool @ ( A @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(68,axiom,
! [A: produc3658429121746597890et_nat,B: heap_e7401611519738050253t_unit,C: set_nat,D: fun_set_nat_bool] :
( ( A
= ( C @ ( B @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) )
=> ( ( A @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) @ ( D @ aa_set_nat_bool ) @ pp )
=> ( C @ ( D @ aa_set_nat_bool ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_sndE) ).
thf(536,plain,
! [A: produc3658429121746597890et_nat,B: heap_e7401611519738050253t_unit,C: set_nat,D: fun_set_nat_bool] :
( ( A
= ( C @ ( B @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) )
=> ( ( A @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) @ ( D @ aa_set_nat_bool ) @ pp )
=> ( C @ ( D @ aa_set_nat_bool ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(12,axiom,
! [A: fun_Pr6001797050664311790t_bool,B: set_fu6080891106736489294t_bool,C: set_fu6080891106736489294t_bool] :
( ( C @ ( B @ inf_in1689267372175091004t_bool ) @ ( A @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
<=> ( ( C @ ( A @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
& ( B @ ( A @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_852_Int__iff) ).
thf(287,plain,
! [A: fun_Pr6001797050664311790t_bool,B: set_fu6080891106736489294t_bool,C: set_fu6080891106736489294t_bool] :
( ( ( ( C @ ( A @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
& ( B @ ( A @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ) )
=> ( C @ ( B @ inf_in1689267372175091004t_bool ) @ ( A @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ) )
& ( ( C @ ( B @ inf_in1689267372175091004t_bool ) @ ( A @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( ( C @ ( A @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
& ( B @ ( A @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(15,axiom,
! [A: set_fu6080891106736489294t_bool] :
( ( A @ ( bot_bo2714889297266208186t_bool @ inf_in1689267372175091004t_bool ) )
= bot_bo2714889297266208186t_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1601_inf__bot__left) ).
thf(300,plain,
! [A: set_fu6080891106736489294t_bool] :
( ( A @ ( bot_bo2714889297266208186t_bool @ inf_in1689267372175091004t_bool ) )
= bot_bo2714889297266208186t_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(170,axiom,
! [A: produc3658429121746597890et_nat] :
( A
= ( A @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) @ ( A @ ( produc1824681642469235216et_nat @ aa_Pro1219312880135979149t_unit ) @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4842_surjective__pairing) ).
thf(999,plain,
! [A: produc3658429121746597890et_nat] :
( A
= ( A @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) @ ( A @ ( produc1824681642469235216et_nat @ aa_Pro1219312880135979149t_unit ) @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(117,axiom,
! [A: fun_Pr6001797050664311790t_bool,B: fun_Pr6001797050664311790t_bool,C: set_fu6080891106736489294t_bool] :
( ( C @ ( B @ remove7940366566026015955t_bool ) @ ( A @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
<=> ( ( A != B )
& ( C @ ( A @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2875_member__remove) ).
thf(752,plain,
! [A: fun_Pr6001797050664311790t_bool,B: fun_Pr6001797050664311790t_bool,C: set_fu6080891106736489294t_bool] :
( ( ( ( A != B )
& ( C @ ( A @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ) )
=> ( C @ ( B @ remove7940366566026015955t_bool ) @ ( A @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ) )
& ( ( C @ ( B @ remove7940366566026015955t_bool ) @ ( A @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( ( A != B )
& ( C @ ( A @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(137,axiom,
! [A: assn] :
( ( A @ ( bot_bot_assn @ ( inf_inf_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) )
= bot_bot_assn ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1595_inf__bot__left) ).
thf(854,plain,
! [A: assn] :
( ( A @ ( bot_bot_assn @ ( inf_inf_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) )
= bot_bot_assn ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(8,axiom,
! [A: set_fu6080891106736489294t_bool,B: set_fu6080891106736489294t_bool] :
( ! [C: fun_Pr6001797050664311790t_bool] :
( ( A @ ( C @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ~ ( B @ ( C @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ) )
=> ( ( B @ ( A @ inf_in1689267372175091004t_bool ) )
= bot_bo2714889297266208186t_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1353_disjointI) ).
thf(273,plain,
! [A: set_fu6080891106736489294t_bool,B: set_fu6080891106736489294t_bool] :
( ! [C: fun_Pr6001797050664311790t_bool] :
( ( A @ ( C @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ~ ( B @ ( C @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ) )
=> ( ( B @ ( A @ inf_in1689267372175091004t_bool ) )
= bot_bo2714889297266208186t_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(139,axiom,
! [A: fun_he7710493197641524256t_bool,B: fun_se707272970763642173t_bool,C: produc3658429121746597890et_nat] :
( ( C @ ( B @ ( A @ bNF_fs3871268833404974121et_nat ) @ aa_Pro3679490825741336130et_nat ) )
= ( C @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) @ ( C @ ( produc1824681642469235216et_nat @ aa_Pro1219312880135979149t_unit ) @ ( B @ ( A @ bNF_pi4042512755101277815et_nat ) ) @ aa_set_nat_set_nat ) @ ( C @ ( produc1824681642469235216et_nat @ aa_Pro1219312880135979149t_unit ) @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5372_fstOp__def) ).
thf(865,plain,
! [A: fun_he7710493197641524256t_bool,B: fun_se707272970763642173t_bool,C: produc3658429121746597890et_nat] :
( ( C @ ( B @ ( A @ bNF_fs3871268833404974121et_nat ) @ aa_Pro3679490825741336130et_nat ) )
= ( C @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) @ ( C @ ( produc1824681642469235216et_nat @ aa_Pro1219312880135979149t_unit ) @ ( B @ ( A @ bNF_pi4042512755101277815et_nat ) ) @ aa_set_nat_set_nat ) @ ( C @ ( produc1824681642469235216et_nat @ aa_Pro1219312880135979149t_unit ) @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(13,axiom,
! [A: set_fu6080891106736489294t_bool] :
( ( A @ ( bot_bo2714889297266208186t_bool @ inf_in1689267372175091004t_bool ) )
= bot_bo2714889297266208186t_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1338_Int__empty__left) ).
thf(294,plain,
! [A: set_fu6080891106736489294t_bool] :
( ( A @ ( bot_bo2714889297266208186t_bool @ inf_in1689267372175091004t_bool ) )
= bot_bo2714889297266208186t_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(62,axiom,
! [A: heap_e7401611519738050253t_unit,B: set_nat,C: set_Pr3948176798113811640et_nat] :
( ( C @ ( B @ ( A @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ member6260224972018164377et_nat ) )
=> ( C @ ( produc8586169260539613262et_nat @ image_6088997261112373647et_nat ) @ ( B @ member_set_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2384_img__snd) ).
thf(506,plain,
! [A: heap_e7401611519738050253t_unit,B: set_nat,C: set_Pr3948176798113811640et_nat] :
( ( C @ ( B @ ( A @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ member6260224972018164377et_nat ) )
=> ( C @ ( produc8586169260539613262et_nat @ image_6088997261112373647et_nat ) @ ( B @ member_set_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(183,axiom,
! [A: assn,B: assn] :
( ( B @ ( A @ ( sup_sup_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) )
= ( B @ ( A @ aTP_Lamm_ai @ aa_ass8975924923219239432t_bool ) @ ( abs_assn @ aa_fun1993714536301460826l_assn ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7589_sup__assn__def) ).
thf(1056,plain,
! [A: assn,B: assn] :
( ( B @ ( A @ ( sup_sup_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) )
= ( B @ ( A @ aTP_Lamm_ai @ aa_ass8975924923219239432t_bool ) @ ( abs_assn @ aa_fun1993714536301460826l_assn ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(179,axiom,
! [A: set_nat,B: produc3658429121746597890et_nat] :
( ( B @ basic_2698842327037663054et_nat @ ( A @ member_set_nat ) )
<=> ( A
= ( B @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1613_snds_Osimps) ).
thf(1033,plain,
! [A: set_nat,B: produc3658429121746597890et_nat] :
( ( ( A
= ( B @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) ) )
=> ( B @ basic_2698842327037663054et_nat @ ( A @ member_set_nat ) ) )
& ( ( B @ basic_2698842327037663054et_nat @ ( A @ member_set_nat ) )
=> ( A
= ( B @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(111,axiom,
! [A: assn] :
( ( bot_bot_assn @ ( A @ ( sup_sup_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1516_sup__bot_Oright__neutral) ).
thf(728,plain,
! [A: assn] :
( ( bot_bot_assn @ ( A @ ( sup_sup_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(224,axiom,
! [A: fun_he2331061685413951235t_unit,B: produc3658429121746597890et_nat] :
( ( B @ ( A @ produc4172003873565521026et_nat @ aa_Pro3679490825741336130et_nat ) @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) )
= ( B @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4666_snd__apfst) ).
thf(1268,plain,
! [A: fun_he2331061685413951235t_unit,B: produc3658429121746597890et_nat] :
( ( B @ ( A @ produc4172003873565521026et_nat @ aa_Pro3679490825741336130et_nat ) @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) )
= ( B @ ( produc8586169260539613262et_nat @ aa_Pro3416150927818442182et_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(167,axiom,
proper @ ( collec3007137136614167897t_bool @ aa_fun8162393684988594084t_bool ) @ ( abs_assn @ ( rep_assn @ type_d18088346645320984t_bool ) @ aa_set3226752938961784069l_bool ) @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_type__definition__assn) ).
thf(992,plain,
proper @ ( collec3007137136614167897t_bool @ aa_fun8162393684988594084t_bool ) @ ( abs_assn @ ( rep_assn @ type_d18088346645320984t_bool ) @ aa_set3226752938961784069l_bool ) @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(136,axiom,
! [A: produc3658429121746597890et_nat] :
~ ! [B: heap_e7401611519738050253t_unit,C: set_nat] :
( A
!= ( C @ ( B @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_one__assn__raw_Ocases) ).
thf(850,plain,
! [A: produc3658429121746597890et_nat] :
~ ! [B: heap_e7401611519738050253t_unit,C: set_nat] :
( A
!= ( C @ ( B @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(48,axiom,
! [A: assn] :
( ( one_one_assn @ ( A @ times_times_assn @ aa_assn_assn ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_362_mult_Oright__neutral) ).
thf(442,plain,
! [A: assn] :
( ( one_one_assn @ ( A @ times_times_assn @ aa_assn_assn ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(81,axiom,
! [A: fun_as4100195077546555551t_bool,B: fun_fu1264473476461866025l_assn,C: set_fu6080891106736489294t_bool,D: assn] :
( ( C @ ( B @ ( A @ type_d18088346645320984t_bool ) @ aa_set3226752938961784069l_bool ) @ pp )
=> ( C @ ( D @ ( A @ aa_ass8975924923219239432t_bool ) @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_412_type__definition_ORep) ).
thf(607,plain,
! [A: fun_as4100195077546555551t_bool,B: fun_fu1264473476461866025l_assn,C: set_fu6080891106736489294t_bool,D: assn] :
( ( C @ ( B @ ( A @ type_d18088346645320984t_bool ) @ aa_set3226752938961784069l_bool ) @ pp )
=> ( C @ ( D @ ( A @ aa_ass8975924923219239432t_bool ) @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(194,axiom,
! [A: assn] :
( ( A @ ( uminus_uminus_assn @ aa_assn_assn ) )
= ( A @ ( aTP_Lamm_al @ aa_ass8975924923219239432t_bool ) @ ( abs_assn @ aa_fun1993714536301460826l_assn ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7593_uminus__assn__def) ).
thf(1093,plain,
! [A: assn] :
( ( A @ ( uminus_uminus_assn @ aa_assn_assn ) )
= ( A @ ( aTP_Lamm_al @ aa_ass8975924923219239432t_bool ) @ ( abs_assn @ aa_fun1993714536301460826l_assn ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(86,axiom,
! [A: assn,B: assn] :
( ( A @ ( uminus_uminus_assn @ aa_assn_assn ) @ ( B @ ( inf_inf_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) @ ( A @ ( inf_inf_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) )
= bot_bot_assn ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6849_inf__compl__bot__right) ).
thf(624,plain,
! [A: assn,B: assn] :
( ( A @ ( uminus_uminus_assn @ aa_assn_assn ) @ ( B @ ( inf_inf_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) @ ( A @ ( inf_inf_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) )
= bot_bot_assn ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(206,axiom,
! [A: fun_Pr6001797050664311790t_bool,B: fun_Pr6001797050664311790t_bool,C: produc3658429121746597890et_nat] :
( ( C @ ( B @ ( A @ aTP_Lamm_af @ aa_fun6808777976510360636t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp )
<=> ( ( C @ ( B @ aa_Pro2991721470636411351t_bool ) @ pp )
| ( C @ ( A @ aa_Pro2991721470636411351t_bool ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7834_ATP_Olambda__39) ).
thf(1152,plain,
! [A: fun_Pr6001797050664311790t_bool,B: fun_Pr6001797050664311790t_bool,C: produc3658429121746597890et_nat] :
( ( ( ( C @ ( B @ aa_Pro2991721470636411351t_bool ) @ pp )
| ( C @ ( A @ aa_Pro2991721470636411351t_bool ) @ pp ) )
=> ( C @ ( B @ ( A @ aTP_Lamm_af @ aa_fun6808777976510360636t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp ) )
& ( ( C @ ( B @ ( A @ aTP_Lamm_af @ aa_fun6808777976510360636t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp )
=> ( ( C @ ( B @ aa_Pro2991721470636411351t_bool ) @ pp )
| ( C @ ( A @ aa_Pro2991721470636411351t_bool ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(45,axiom,
! [A: fun_Pr6001797050664311790t_bool] :
~ ( bot_bo2714889297266208186t_bool @ ( A @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_emptyE) ).
thf(427,plain,
! [A: fun_Pr6001797050664311790t_bool] :
~ ( bot_bo2714889297266208186t_bool @ ( A @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(22,axiom,
! [A: fun_set_nat_set_nat,B: heap_e7401611519738050253t_unit,C: set_nat] :
( ( C @ ( B @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ ( A @ produc3286488329990770625t_unit @ aa_Pro3679490825741336130et_nat ) )
= ( C @ ( A @ aa_set_nat_set_nat ) @ ( B @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4657_apsnd__conv) ).
thf(322,plain,
! [A: fun_set_nat_set_nat,B: heap_e7401611519738050253t_unit,C: set_nat] :
( ( C @ ( B @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ ( A @ produc3286488329990770625t_unit @ aa_Pro3679490825741336130et_nat ) )
= ( C @ ( A @ aa_set_nat_set_nat ) @ ( B @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(26,axiom,
! [A: set_fu6080891106736489294t_bool] :
( ? [B: fun_Pr6001797050664311790t_bool] : ( A @ ( B @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
<=> ( A != bot_bo2714889297266208186t_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_ex__in__conv) ).
thf(337,plain,
! [A: set_fu6080891106736489294t_bool] :
( ( ( A != bot_bo2714889297266208186t_bool )
=> ? [B: fun_Pr6001797050664311790t_bool] : ( A @ ( B @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ) )
& ( ? [B: fun_Pr6001797050664311790t_bool] : ( A @ ( B @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp )
=> ( A != bot_bo2714889297266208186t_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(54,axiom,
bot_bot_assn != one_one_assn,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_assn__basic__inequalities_I3_J) ).
thf(469,plain,
bot_bot_assn != one_one_assn,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(30,axiom,
! [A: set_fu6080891106736489294t_bool,B: fun_Pr6001797050664311790t_bool] :
( ( A = bot_bo2714889297266208186t_bool )
=> ~ ( A @ ( B @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_equals0D) ).
thf(354,plain,
! [A: set_fu6080891106736489294t_bool,B: fun_Pr6001797050664311790t_bool] :
( ( A = bot_bo2714889297266208186t_bool )
=> ~ ( A @ ( B @ member4125802036136091927t_bool @ aa_set3226752938961784069l_bool ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(150,axiom,
! [A: assn] :
( ( bot_bot_assn @ ( A @ times_times_assn @ aa_assn_assn ) )
= bot_bot_assn ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_373_star__false__right) ).
thf(923,plain,
! [A: assn] :
( ( bot_bot_assn @ ( A @ times_times_assn @ aa_assn_assn ) )
= bot_bot_assn ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(95,axiom,
! [A: bool] : ( A @ pure_a825153325127701367it_nat @ ( proper @ aa_fun5588795374382764133l_bool ) @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_pure__assn__proper) ).
thf(659,plain,
! [A: bool] : ( A @ pure_a825153325127701367it_nat @ ( proper @ aa_fun5588795374382764133l_bool ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(121,axiom,
! [A: assn,B: assn] :
( ( B @ ( A @ ( inf_inf_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) @ ( A @ ( uminus_uminus_assn @ aa_assn_assn ) @ ( inf_inf_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) )
= bot_bot_assn ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6863_inf__compl__bot__left1) ).
thf(775,plain,
! [A: assn,B: assn] :
( ( B @ ( A @ ( inf_inf_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) @ ( A @ ( uminus_uminus_assn @ aa_assn_assn ) @ ( inf_inf_assn @ aa_ass954072293579886259n_assn ) @ aa_assn_assn ) )
= bot_bot_assn ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(98,axiom,
! [A: heap_e7401611519738050253t_unit,B: set_nat] :
( ( B @ ( A @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ ( produc6300697153377358172et_nat @ aa_Pro7370057327950226428t_unit ) )
= ( A @ ( B @ produc2471974422597015918t_unit ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3373_swap__simp) ).
thf(676,plain,
! [A: heap_e7401611519738050253t_unit,B: set_nat] :
( ( B @ ( A @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ ( produc6300697153377358172et_nat @ aa_Pro7370057327950226428t_unit ) )
= ( A @ ( B @ produc2471974422597015918t_unit ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(106,axiom,
! [A: assn,B: assn] :
( ( B @ ( A @ times_times_assn @ aa_assn_assn ) )
= ( A @ ( B @ times_times_assn @ aa_assn_assn ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_381_assn__times__comm) ).
thf(708,plain,
! [A: assn,B: assn] :
( ( B @ ( A @ times_times_assn @ aa_assn_assn ) )
= ( A @ ( B @ times_times_assn @ aa_assn_assn ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(58,axiom,
! [A: fun_he2331061685413951235t_unit,B: heap_e7401611519738050253t_unit,C: set_nat] :
( ( C @ ( B @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ ( A @ produc4172003873565521026et_nat @ aa_Pro3679490825741336130et_nat ) )
= ( C @ ( B @ ( A @ aa_hea2136485429539994620t_unit ) @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4652_apfst__conv) ).
thf(491,plain,
! [A: fun_he2331061685413951235t_unit,B: heap_e7401611519738050253t_unit,C: set_nat] :
( ( C @ ( B @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) @ ( A @ produc4172003873565521026et_nat @ aa_Pro3679490825741336130et_nat ) )
= ( C @ ( B @ ( A @ aa_hea2136485429539994620t_unit ) @ produc7507926704131184380et_nat @ aa_set3979848162462698438et_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(192,axiom,
( ( top_to2524957550908328808et_nat @ ( produc8586169260539613262et_nat @ image_6088997261112373647et_nat ) )
= top_top_set_set_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3543_range__snd) ).
thf(1088,plain,
( ( top_to2524957550908328808et_nat @ ( produc8586169260539613262et_nat @ image_6088997261112373647et_nat ) )
= top_top_set_set_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(174,axiom,
! [A: produc3658429121746597890et_nat] :
~ ( A @ ( bot_bot_assn @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_mod__false) ).
thf(1014,plain,
! [A: produc3658429121746597890et_nat] :
~ ( A @ ( bot_bot_assn @ ( rep_assn @ aa_ass8975924923219239432t_bool ) @ aa_Pro2991721470636411351t_bool ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(162,axiom,
( ( bot_bot_assn @ ( uminus_uminus_assn @ aa_assn_assn ) )
= top_top_assn ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6828_boolean__algebra_Ocompl__zero) ).
thf(972,plain,
( ( bot_bot_assn @ ( uminus_uminus_assn @ aa_assn_assn ) )
= top_top_assn ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(1317,plain,
$false,
inference(e,[status(thm)],[1105,234,762,1005,683,1068,741,873,511,1041,1078,385,472,1233,698,913,1222,404,885,320,1265,570,1059,934,1191,870,969,770,325,789,591,646,348,966,485,1136,834,1051,821,1169,634,877,734,453,1119,988,527,307,920,380,942,270,661,1199,714,334,778,1217,297,693,916,847,1178,1210,974,285,578,317,650,1017,1121,1064,725,980,1096,388,610,857,1160,1028,225,679,686,1075,837,1249,1002,1246,244,1086,805,508,541,1185,926,906,412,618,824,279,573,689,601,1146,430,843,711,958,259,445,313,611,466,1090,947,391,1139,900,1117,419,1048,996,737,303,1175,764,604,362,567,811,494,631,520,240,1149,1061,983,399,695,868,653,505,438,722,1166,944,548,374,1081,939,1145,557,1025,282,993,1098,310,331,370,502,840,463,808,359,643,1220,744,1257,656,613,1008,595,627,450,931,482,581,517,351,731,781,1030,378,667,929,383,832,346,536,287,300,999,752,854,273,865,294,506,1056,1033,728,1268,992,850,442,607,1093,624,1152,427,322,337,469,354,923,659,775,676,708,491,1088,1014,972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ITP211_1 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.04 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.06/0.35 % Computer : n012.cluster.edu
% 0.06/0.35 % Model : x86_64 x86_64
% 0.06/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.35 % Memory : 8046.5625MB
% 0.06/0.35 % OS : Linux 6.8.0-71-generic
% 0.06/0.35 % CPULimit : 300
% 0.06/0.35 % WCLimit : 300
% 0.06/0.35 % DateTime : Fri Sep 25 18:08:37 UTC 2026
% 0.06/0.35 % CPUTime :
% 0.06/0.35 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.47/0.67 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 3.63/1.50 % [INFO] Parsing done (832ms).
% 3.63/1.52 % [INFO] Running in sequential loop mode.
% 3.85/1.70 % [INFO] eprover registered as external prover.
% 4.02/1.70 % [INFO] Scanning for conjecture ...
% 6.02/2.29 % [INFO] Found a conjecture (or negated_conjecture) and 7892 axioms. Running axiom selection ...
% 7.69/2.82 % [INFO] Axiom selection finished. Selected 222 axioms (removed 7670 axioms).
% 8.05/2.94 % [INFO] Problem is typed first-order (TPTP TFF).
% 8.05/2.95 % [INFO] Type checking passed.
% 8.05/2.95 % [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 ...
% 12.85/4.49 % External prover 'e' found a proof!
% 12.85/4.49 % [INFO] Killing All external provers ...
% 12.85/4.49 % Time passed: 4056ms (effective reasoning time: 2969ms)
% 12.85/4.49 % 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)>
% 12.85/4.49 % Axioms used in derivation (222): fact_4990_snd__sndOp, fact_43_ex__in__conv, fact_192_times__assn__proper, fact_4666_snd__apfst, fact_128_prod_Oinject, fact_1595_inf__bot__left, fact_7834_ATP_Olambda__39, fact_1578_boolean__algebra_Oconj__zero__right, fact_7588_bot__assn__def, fact_165_surj__pair, fact_186_one__reorient, fact_2875_member__remove, fact_4211_boolean__algebra_Ocomplement__unique, fact_4779_prod__eq__iff, fact_4774_fstE, fact_4657_apsnd__conv, fact_403_mult_Ocomm__neutral, fact_7764_one__assn__raw_Opelims_I2_J, fact_1613_snds_Osimps, fact_80_one__assn__raw_Oelims_I2_J, fact_4743_apsnd__apfst, fact_374_star__false__left, fact_852_Int__iff, fact_6842_boolean__algebra_Oconj__cancel__left, fact_4983_apfst__convE, fact_77_Abs__assn__inverse, fact_1338_Int__empty__left, fact_141_snd__eqD, fact_1530_sup__bot_Oleft__neutral, fact_75_wand__assn__def, fact_156_pure__assn__raw_Osimps, fact_4488_snd__comp__map__prod, fact_7589_sup__assn__def, fact_101_Rep__assn, fact_175_Pair__inject, fact_3373_swap__simp, fact_1565_sup__bot__left, fact_391_mult_Oassoc, fact_1516_sup__bot_Oright__neutral, fact_4705_prod_Ocollapse, fact_48_set__notEmptyE, fact_102_mem__Collect__eq, fact_81_one__assn__raw_Oelims_I3_J, fact_7077_inf__cancel__left1, fact_4121_type__copy__ex__RepI, fact_1372_bot_Oextremum__uniqueI, fact_4335_mod__true, fact_7003_minus__assn__def, fact_7832_ATP_Olambda__37, fact_4334_assn__basic__inequalities_I1_J, fact_347_type__definition_ORep__inject, fact_4955_prod_Oswap__def, fact_4333_assn__basic__inequalities_I5_J, fact_3_Abs__assn__eqI_I1_J, fact_499_bool__assn__proper_I1_J, fact_4781_prod__eqI, fact_409_assn__one__left, fact_1021_subset__Collect__conv, fact_4652_apfst__conv, fact_355_type__definition_OAbs__inject, fact_136_sndI, fact_469_mult_Oright__commute, fact_362_mult_Oright__neutral, fact_1537_sup__bot_Oeq__neutr__iff, fact_6821_boolean__algebra_Ocompl__one, fact_424_type__definition_ORep__cases, fact_4396_top__assn__def, fact_151_eq__snd__iff, fact_7835_ATP_Olambda__40, fact_1592_inf__bot__right, fact_2384_img__snd, fact_1348_Int__emptyI, fact_1140_IntD2, fact_88_one__assn__proper, fact_428_type__definition_OAbs__induct, fact_33_equals0D, fact_1114_subset__eq, fact_420_type__definition_OAbs__cases, fact_373_star__false__right, fact_4_empty__iff, fact_7765_one__assn__raw_Opelims_I1_J, fact_4764_fst__conv, fact_59_mod__false, fact_4837_prod_Oexhaust__sel, fact_153_pure__assn__raw_Oelims_I3_J, fact_2617_in__snd__imageE, fact_1572_boolean__algebra_Oconj__zero__right, fact_557_models__in__range, fact_7806_ATP_Olambda__11, fact_78_one__assn__raw_Osimps, fact_4676_snd__apsnd, fact_7816_ATP_Olambda__21, fact_383_ab__semigroup__mult__class_Omult_Oleft__commute, fact_7590_inf__assn__def, fact_170_prod__cases, fact_473_in__range__empty, fact_146_snd__conv, fact_4125_type__copy__obj__one__point__absE, fact_4981_conjI__realizer, fact_122_mod__h__bot__indep, fact_1_Rep__assn__inverse, fact_117_Rep__assn__cases, fact_7587_bool__assn__proper_I5_J, fact_583_properD1, fact_351_type__definition_ORep__induct, fact_1343_disjoint__iff, fact_7593_uminus__assn__def, fact_62_Set_Ois__empty__def, fact_112_Collect__cong, fact_3659_UNIV__witness, fact_90_bex2I, fact_1558_sup__bot__right, fact_4754_fstI, fact_4988_exE__realizer_H, fact_4832_BNF__Greatest__Fixpoint_Osubst__Pair, fact_7805_ATP_Olambda__10, fact_4759_fst__eqD, fact_7584_bool__assn__proper_I4_J, fact_335_type__definition__def, fact_1353_disjointI, fact_4951_prod_Oswap__def, fact_0_Rep__assn__inject, fact_1393_subset__emptyI, fact_4787_Ex__prod__contract, fact_1236_disjoint__mono, fact_368_mult__1, fact_334_times__assn__def, fact_1586_inf__bot__right, fact_1063_Int__Collect__mono, fact_1551_bot__eq__sup__iff, fact_1068_Collect__mono__iff, fact_4783_prod_Oexpand, fact_2_Abs__assn__eqI_I2_J, fact_1987_rel__restrict__empty, fact_397_comm__monoid__mult__class_Omult__1, fact_5374_sndOp__def, fact_847_subsetI, fact_9_all__not__in__conv, fact_79_one__assn__raw_Oelims_I1_J, fact_1386_bot_Oextremum, fact_160_old_Oprod_Oexhaust, fact_155_pure__assn__raw_Oelims_I1_J, fact_5372_fstOp__def, fact_4721_snd__swap, fact_4723_snd__comp__apfst, fact_4733_apfst__apsnd, fact_1544_sup__eq__bot__iff, fact_387_ab__semigroup__mult__class_Omult_Ocommute, fact_4976_exI__realizer, fact_416_type__definition_Ointro, fact_4332_merge__true__star, fact_465_mult_Oright__assoc, fact_382_assn__times__assoc, fact_4087_empty__not__UNIV, fact_19_empty__Collect__eq, fact_24_emptyE, fact_123_old_Oprod_Oinject, fact_6863_inf__compl__bot__left1, fact_1328_disjoint__iff__not__equal, fact_1602_boolean__algebra_Odisj__zero__right, fact_3370_swap__simp, fact_7849_ATP_Olambda__54, fact_1145_IntD1, fact_14_Collect__empty__eq, fact_118_Rep__assn__induct, fact_191_type__definition__assn, fact_99_sndE, fact_199_ssubst__Pair__rhs, fact_4785_All__prod__contract, fact_4487_snd__comp__map__prod, fact_6828_boolean__algebra_Ocompl__zero, fact_3543_range__snd, fact_407_mod__starE, fact_76_one__assn__def, fact_95_one__assn__raw_Ocases, fact_1379_bot_Oextremum__unique, fact_4842_surjective__pairing, fact_4719_fst__swap, fact_1579_boolean__algebra_Oconj__zero__left, fact_1127_subsetD, fact_1132_in__mono, fact_6849_inf__compl__bot__right, fact_343_type__definition_OAbs__inverse, fact_1160_IntE, fact_554_total__on__empty, fact_121_Abs__assn__inject, fact_157_pure__assn__proper, fact_1615_snds_Ointros, fact_1585_boolean__algebra_Oconj__zero__left, fact_7585_bool__assn__proper_I3_J, fact_1601_inf__bot__left, fact_7831_ATP_Olambda__36, fact_880_subset__empty, fact_119_Abs__assn__cases, fact_4368_pred__on_Ochain__empty, fact_154_pure__assn__raw_Oelims_I2_J, fact_3654_UNIV__eq__I, fact_107_Collect__mem__eq, fact_1333_Int__empty__right, fact_3510_UNIV__I, fact_875_empty__subsetI, fact_87_wand__proper, fact_6835_boolean__algebra_Oconj__cancel__right, fact_408_mod__starD, fact_1611_snds_Ocases, fact_7763_one__assn__raw_Opelims_I3_J, fact_38_equals0I, fact_1100_subset__iff, fact_4769_eq__fst__iff, fact_339_type__definition_ORep__inverse, fact_89_assn__basic__inequalities_I3_J, fact_120_Abs__assn__induct, fact_6856_inf__compl__bot__left2, fact_857_IntI, fact_7586_bool__assn__proper_I2_J, fact_381_assn__times__comm, fact_1091_Collect__mono, fact_7341_boolean__algebra__class_Oboolean__algebra_Ocompl__unique, fact_412_type__definition_ORep, fact_1523_sup__bot_Oneutr__eq__iff, fact_7070_inf__cancel__left2, fact_53_memb__imp__not__empty
% 12.85/4.49 % No. of inferences in proof: 448
% 12.85/4.49 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4056 ms resp. 2969 ms w/o parsing
% 13.76/4.65 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 13.76/4.65 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------